1 The two postulates in Special Relativity

>	We NOW know this is NOT what relativity says. In relativity, all clocks tick at their usual rates, regardless of how they might move or where they might be located (e.g. in a gravitational field).

In the book "Subtle is the Lord..." by Abraham Pais at page 140 and 141 we read:
The two postulates:
1. The laws of physics take the same form in all inertial frames.
2. In any given inertial system the velocity of light c is the same whether the light be emitted by a body at rest or by a body in uniform motion.

At page 138 we read: "By definition, any two of these (inertial frames) are in uniform motion with respect to each other"

Consider the following three situations: 1. a light at rest which emits a flash at position p1 at t1. 2. an uniform moving light which also emits a flash at p1 at t1. 3. an accelerating moving light which does the same. Question: for any observer at a certain distance are this one or three distinquished physical events? IMO: It is one physical event. From a frequency point of view this is a different story.

[[Mod. note -- Assuming that when you say "at rest" or "uniformly moving" or "accelerating" you really mean "... with respect to some specified inertial frame", then you're correct: neglecting any doppler shift of the light, a distant observer can't distinguish between situation 1, situation 2, and situation 3. (This remains true regardless of the distant observer's state of motion with respect to the inertial frame.) -- jt]]

When I study postulate 1 immediate certain some thoughts pop up: Which type of physical processes are we discussing here? Are this all physical processes or only some (i.e. subset)? Laws are descriptions of physical processes. That means (if my interpretation is correct) that all physical processes are indepent of uniform movement until the speed of light. This sounds "too optimistic" specific if you consider these clocks which inner working uses light signals to operate (i.e. counts)

2 The two postulates in Special Relativity

this doesn't seem to be widely accepted (not sure why), but i've always felt that postulate #2 comes directly from postulate #1. if the laws of physics are the same for all inertial frames of reference, every observer has the same epsilon_0 and mu_0 in their laws of physics. so c=(epsilon_0*mu_0)^(-1/2) is the same for every inertial observer hanging around in a vacuum.

and all postulate #1 says is that if a vacuum is physically nothing, you can't tell if a vacuum is whizzing past you at a speed of c/2 or not. the relative speed of a physical nothing is meaningless. so you could be whizzing past me at a constant relative speed of c/2, but there is no aether wind blowing in your face nor in mine. we both have equal claim to being "at rest". when we look at the **same** flash or beam of light, since we both have the same physics (because we're *both* "at rest"), then we both measure the speed of that flash of light to be the same speed. the only way for that to happen is if we both observe the other's clock as ticking more slowly than our own.

so, in my opinion, there is only one necessary postulate to special relativity and it is the first postulate.

>

At page 138 we read: "By definition, any two of these (inertial frames) are in uniform motion with respect to each other" Consider the following three situations: 1. a light at rest which emits a flash at position p1 at t1. 2. an uniform moving light which also emits a flash at p1 at t1. 3. an accelerating moving light which does the same. Question: for any observer at a certain distance are this one or three distinquished physical events? IMO: It is one physical event. From a frequency point of view this is a different story.

once the EM wave departs the mechanism that created it (the emitter), all we have is a changing electric field which causes a changing magnetic field which, in turn, causes a changing electric field which causes another changing magnetic field, etc.

the light is a propagating EM field and, once emitted, has no idea about the emitter including what the velocity or motion the emitter had.

--

r b-j r...@audioimagination.com

"Imagination is more important than knowledge."

3 The two postulates in Special Relativity

4 The two postulates in Special Relativity

All types.

>

Laws are descriptions of physical processes. That means (if my interpretation is correct) that all physical processes are indepent of uniform movement until the speed of light. This sounds "too optimistic" specific if you consider these clocks which inner working uses light signals to operate (i.e. counts)

Instead of inertial frames, consider this proposition: all physical phenomena are independent of coordinates. This must be true if physics is possible, because coordinates are arbitrary human constructs; they are part of the model, not the world. Once you accept this, then it's easy to see that inertial frames are just a subset of possible coordinates.

So this is not "too optimistic".

>	Also here the question arises to which extend these oscillations are independent of the speed of the clock and does not influence the ticking rate.

Assuming Einstein's first postulate is valid, then the physics that governs the clock's ticking is the same regardless of which inertial frame it finds itself at rest in. So the "speed of the clock" (relative to any coordinates one might choose) does not affect its ticking rate.

>	A whole different thought is: why are accelarations not discussed?

In 1905 Einstein did not get that far. Modern textbooks on SR certainly do discuss acceleration. Many experiments have shown that acceleration does not affect a clock's ticking rate, as long as the clock is not damaged. Commercial clocks come with a specification of how large an acceleration they can sustain without damage.

Tom Roberts

5 The two postulates in Special Relativity

> >	Laws are descriptions of physical processes. That means that all physical processes are indepent of uniform movement until the speed of light. This sounds "too optimistic" specific if you consider these clocks which inner working uses light signals to operate (i.e. counts)

>	Instead of inertial frames, consider this proposition: all physical phenomena are independent of coordinates.

That is correct, but it does not say anything about (the inner working) of the processes them self

>	Once you accept this, then it's easy to see that inertial frames are just a subset of possible coordinates.

Again that is correct, but etc (see above)

6 The two postulates in Special Relativity

*only* dimensionless constants are fundamental.

all c needs to be is real, positive, and finite. no matter how "God" (or whatever hypothetical immortal being not governed by the laws of nature) perceives the speed of instantaneous interactions (EM, gravity, strong force) meditated by massless particles, we mortals would continue to perceive it as moving 299792456 of our meters in the time elapsed by one of our seconds. (we would also measure the same epsilon_0 and define the same mu_0.)

cut c in half (from the POV of the god-like being) and the rest of us get our length and time scaled in such a manner that c remains the same.

c will always be 1 Planck Length per Planck Time. and if none of the dimensionless fundamental constants change, then the number of Planck Lengths per meter will remain the same and the number of Planck Times per second will remain the same. - show quoted text -

7 The two postulates in Special Relativity

Why? An hourglass is NOT a clock. Only hourglass+earth is a (modestly accurate) clock, and you cannot possibly put that into a spacecraft.

Ditto for pendulum clocks and sundials (etc.).

>	The question is: what is the influence on the accuracy of a pendulum clock when you move such a clock (fast?) from A to B.

That question is useless, because you cannot move the earth with it.

>

The issue is the ticking rate (tr) of two clocks (as measured by the final clock count = fcc) relative to each other. Consider two identical clocks. A) IMO if both clocks are not "moved" the fcc will be the same B) IMO if both clocks are moved from A to B following the same path the fcc will be the same. C) IMO if both clocks are moved from A to B following a different path there are two options: C1) The fcc is the same. IMO this has a low chance. C2) The fcc is different. IMO this has a high chance. C2 IMO implies that the ticking rate is different.

No to this last -- you DID NOT MEASURE the tick rate of either clock, and therefore cannot make any conclusion about it.

In relativity this difference is modeled as being the difference in the "length of the paths", where "length" for such timelike paths is really the elapsed proper time.

When cars' odometers indicate different distances for different paths between A and B, do you really think the odometers' tick rates are different? OF COURSE NOT! The odometers increment 1 mile for every mile traveled -- that is their (intrinsic) tick rate. The clocks increment 1 second for every second of elapsed proper time -- that is their (intrinsic) tick rate.

Note your implicit assumption hidden in your conclusion: you are assuming your personal appreciation of "time" is important. That is, you have added a HIDDEN third clock, your mind, and you are really assessing "tick rate" relative to it, WITHOUT MENTIONING IT. Yes, if you measured the tick rates of those clocks RELATIVE TO A CLOCK CO-LOCATED and CO_MOVING WITH YOURSELF, then you could conclude their tick rates RELATIVE TO THAT CLOCK are different.

But as I have said before, when you just discuss the "tick rate of a clock", that phrase inherently refers to the INTRINSIC tick rate of the clock, because that is how words behave. The intrinsic rate of the clock never changes; only tick rates RELATIVE TO OTHER CLOCKS can change (really relative to other coordinate systems).

Bottom line: your "common sense" is insufficient to understand what is happening in relativity. The world is more complicated than your common sense can capture. Relativity models it well, "common sense" does not.

>>>	A whole different thought is: why are accelarations not discussed?

>>	In 1905 Einstein did not get that far.

>	IMO all experiments with moving clocks imply acceleration

>>	Modern textbooks on SR certainly do discuss acceleration. Many experiments have shown that acceleration does not affect a clock's ticking rate, as long as the clock is not damaged.

>	What is the definition of damaged?

A clock is not damaged if it continues ticking at its intrinsic tick rate.

>	When you first perform test C and than test A and the fcc is different than at least one clock is damaged.

No. Had you measured each clock's (intrinsic) tick rate, you would have found them to be correct.

There is more going on here than you understand, and you keep making assumptions based on your personal experience, which is woefully inadequate because you have no personal experience with speeds approaching c. You need to study relativity, and its underlying geometry.

Tom Roberts

8 The two postulates in Special Relativity

9 The two postulates in Special Relativity

>	So why write down ANY laws or postulates that are known to be true?

Postulates are not any laws.

These are the supplementary assumptions only, and of a special type; for example, in the model of the collisions there are used two assumption usually: ideal elastic collision, or ideal inelastic.

And we know very well these both are false in any practical case. But this not a problem - the models works well... in some limited conditions, which are known commonly.

And the same rule applies to every postulate - to these of SR too.

Especially: the 'light speed is invariant' is not any discovery, but a modeled-assumption only, on which the SR is based (or on the assumption of the relativity principle, which is equivalent, or maybe a superior, to the invariance of a light speed).

>	In any case, it's not obvious from first principles that c is the limiting speed, even if we haven't found anything that goes faster. Sure, you can deduce that based on observations too. But ultimately, you must state enough postulates to describe the physics that you want to describe.

No. The postulates are suplementary always, therefore these are present in the models only, never in a theory itself.

There is none of postulates in a real theory, but just axioms only! And an axiom is not a postulate.

So, what is a difference between an axiom and postulate? It should be rather obvious...

10 The two postulates in Special Relativity

it's not to me. seems to me that, operationally, postulates and axioms are the same. they are initial statements that are taken as true without proof and other substantive conclusions are made from those postulates or axioms. - show quoted text -

11 The two postulates in Special Relativity

There are no axioms in physics exept the axiom of "use logic and numbers, make an experiment and adapt the mathematical model to its outcomes".

Axioms can be formulated in an axiomatic theory as a mathematical framework to serve as a specific model describing the measurable observables of a given system.

Postulates are more general: They fomulate model independent features which all mathematical models of a physical reality have to incorporate, like use of a space-time universe, Poincare invariance, probabilistic interpretation, gauge invariance, locality, causality, determinism aof system states by a given set of starting conditions at the time of preparation of experiments.

These postulates drive the development in quite different models like relativistic mechanics, cosmology, quantum theory, field theory or classical and quantum statistical mechanics.

--

Roland Franzius

12 The two postulates in Special Relativity

Indeed, because the whole physics is not a theoretical domain in fact.

The physics is just about the models.

>	Axioms can be formulated in an axiomatic theory as a mathematical framework to serve as a specific model describing the measurable observables of a given system.

No, axioms are just of a theory basis... a model is besed on a theory, of course, because there is nothig more to start!

>

Postulates are more general: They fomulate model independent features which all mathematical models of a physical reality have to incorporate, like use of a space-time universe, Poincare invariance, probabilistic interpretation, gauge invariance, locality, causality, determinism aof system states by a given set of starting conditions at the time of preparation of experiments.

Yes. Maybe a postulate can be a something more than an axiom.

But it's only because we have more freedom in this case... any axiom are independent of any our decision - it's just a fact, an obvious truth.

Finally: there are unlimited postulates possible, but an axioms set is very limited.

>	These postulates drive the development in quite different models like relativistic mechanics, cosmology, quantum theory, field theory or classical and quantum statistical mechanics.

These all 'theories' are just the models only, in fact, because: the relativity, quantum, ect. are based on the general theory - the math itself, what is evident... and sametime on a specfic theory, like in the case of relativity: the Lorentz - Poincare's Theory.

13 The two postulates in Special Relativity

There isn't much support for giving them different meanings:

14 The two postulates in Special Relativity

You will find two unique truly axiomatic theories in physics and both have no working model, that proves its existence in the mathematical sense for a faily general rich set of observables and their time development:

1) Analytical Lagrangian mechanics: Plainly wrong physical, mathematical not existent because of lack of predictability for many point-particle systems with interaction.

2) Axiomatic Quantum field theory: While starting with beautiful results in the 1950 after the work of Wigner, Wightman, Haag, Kastler there was little physical progress later on. Now it is a branch of pure mathematics applied to an physical motivated axiomatic setting.

Again there exists no mathematical realisation beyond free fields could be established in a physical acceptable number of space-time dimensions.

Of course this is symptomatic for theoretical physics:

Physics is about time development of 3d-geometric systems with an indefinite bilinear form invariant under the local families of representations of the Poincare group.

The general lack of a unique canonical euclidean norm for systems in space-time makes convergency theorems in relativistic mechanics and field theories extremely hard to prove.

In most cases one has to introduce smoothness conditions on series solutions in some much too rich taylored solution spaces that are by no means capable to select a unique mathematical model.

So finally the best thing one gets as an aximotic setting in physics is the selection of some interesting categories like continuous representations of Lie-groups over tensor products.

In axiomatic field theories like General Relativity and QED and Quantum Field Theory it is not known until today if the choosen set of axioms is consistent and free of contradictions except perhaps for the toy theories of free test systems in external backgrounds.

--

Roland Franzius

15 The two postulates in Special Relativity

Op woensdag 13 mei 2015 10:21:35 UTC+2 schreef Tom Roberts:

>	On 5/5/15 5/5/15 - 8:24 PM, Nicolaas Vroom wrote:

> >	Which type of physical processes are we discussing here?

>	All types.

Okay. That implies all physical changes.

> >	Laws are descriptions of physical processes. That means that all physical processes are indepent of uniform movement until the speed of light. This sounds "too optimistic" specific if you consider these clocks which inner working uses light signals to operate (i.e. counts)

>	Instead of inertial frames, consider this proposition: all physical phenomena are independent of coordinates.

That is correct, but it does not say anything about (the inner working) of the processes them self

>	Once you accept this, then it's easy to see that inertial frames are just a subset of possible coordinates.

Again that is correct, but etc (see above)

>	So this is not "too optimistic".

16 The two postulates in Special Relativity

W dniu sroda, 27 maja 2015 13:19:32 UTC+2 uzytkownik Jos Bergervoet napisal:

>	On 5/25/2015 3:45 PM, Roland Franzius wrote:

>>	Am 25.05.2015 um 10:02 schrieb robert bristow-johnson:

>>>	On 5/23/15 10:30 PM, al...@interia.pl wrote: ...

>>>>	There is none of postulates in a real theory, but just axioms only! And an axiom is not a postulate. So, what is a difference between an axiom and postulate? It should be rather obvious...

>>>	it's not to me. seems to me that, operationally, postulates and axioms are the same. they are initial statements that are taken as true without proof and other substantive conclusions are made from those postulates or axioms.

>>	There are no axioms in physics exept the

>

... ...

>>	Postulates are more general: They fomulate model independent features

>	There isn't much support for giving them different meanings: http://math.stackexchange.com/questions/258346/what-is-the-difference-between-an-axiom-and-a-postulate (Although stackexchange is of course less authoritative than sci.physics.research, let's postulate that first!) -- Jos

Any postulate is some trick math trick in fact, which leads to more simplicity... of the equations... so, any model is based just on such trick.

The great example is the c = inv in the SR model: it's evident that: c' = c - v, due to the strict math: a gemetry principles, logics, ect.

But it's to poor fact, because a speed can't be measured directly, but omly indirect: by a time and a distance measure.

Therefore if there is in fact: c' = c-v, then we still can assume it's: c = inv, but then we must transform a time or a distance adecuatelly, to cancel the obvious change of the speed of light.

A distance is rather hard to transform, because if we have some rod with a fixed length, say L = 1m, then we assume it's preserved unconditionaly (in any local system).

Thus we must transform a time - it's the one real possibility!

Therefore the relativity model, which is based on the postulate: c = inv, postulates in fact just that: a transformation of a light speed = tr. of a time.

And it's all obout this model, because such convention lands directly on the well known transformation:

x' = k(x - vt) and t' = k(t - xv)

17 The two postulates in Special Relativity

>>	No, axioms are just of a theory basis... a model is besed on a theory, of course, because there is nothig more to start!

>

You will find two unique truly axiomatic theories in physics and both have no working model, that proves its existence in the mathematical sense for a faily general rich set of observables and their time development: 1) Analytical Lagrangian mechanics: Plainly wrong physical, mathematical not existent because of lack of predictability for many point-particle systems with interaction.

This is just a model, which is based explicityly on some postulates; and the model gives very good predictions... for example: a simulation of the Solar System, basing on this model, is possible, and rather easy, and the final results are quite good.

>	Again there exists no mathematical realisation beyond free fields could be established in a physical acceptable number of space-time dimensions.

The whole space-time concempt is just a model-specific postulate... and it depends totaly on an abstract mathematical space theory.

>	In axiomatic field theories like General Relativity and QED and Quantum Field Theory it is not known until today if the choosen set of axioms is consistent and free of contradictions except perhaps for the toy theories of free test systems in external backgrounds.

There is no axioms in the GR, nor QM... similarily the hiperbolic geometry is not of SR domain at all, nor the complex algebra is a part of the waves theory.

18 The two postulates in Special Relativity

That is the question. What is a clock and what is not a clock. If SR describes all processes and all clocks and if that is the case than it should also describe a hourglass and a pendulum.

>	That question is useless, because you cannot move the earth with it.

Than you cannot perform any experiment with any clock ? (because of the earth)

> >	The issue is the ticking rate (tr) of two clocks (as measured by the final clock count = fcc) relative to each other. Consider two identical clocks. C2) The fcc is different. IMO this has a high chance. C2 IMO implies that the ticking rate is different.

>	No to this last -- you DID NOT MEASURE the tick rate of either clock, and therefore cannot make any conclusion about it.

I agree, but I did not write that. I specific use the word "implies". The issue is that the final clock counts are different. If you agree that that is possible, than the Q is: how do you explain that.

>	Note your implicit assumption hidden in your conclusion: you are assuming your personal appreciation of "time" is important. That is, you have added a HIDDEN third clock, your mind, and you are really assessing "tick rate" relative to it, WITHOUT MENTIONING IT.

I'm comparing the result (counts) of an experiment with two clocks. My mind has nothing to do with this. You can add a third clock, (and call each count of that clock 1 second) but that does not really makes a difference.

>	But as I have said before, when you just discuss the "tick rate of a clock", that phrase inherently refers to the INTRINSIC tick rate of the clock, because that is how words behave.

Exactly what is your definition of the INTRINSIC (tick rate)

>	The intrinsic rate of the clock never changes.

Even in the case when you perform experiment C/C2 and the fcc is different?

>	Bottom line: your "common sense" is insufficient to understand what is happening in relativity.

I would never use the words "common sense". Generally you should perform experiments without any (directly) people involved.

>	A clock is not damaged if it continues ticking at its intrinsic tick rate.

I will come back to this remark when the meaning of the word intrinsic is clear.

> >	When you first perform test C and than test A and the fcc is different than at least one clock is damaged.

>	No. Had you measured each clock's (intrinsic) tick rate, you would have found them to be correct.

The issue is the definition of damaged. When you supposedly have two identical clocks and when you perform experiment A (both clocks are not "moved") and the fcc is different than at least one clock is damaged.

Nicolaas Vroom

19 The two postulates in Special Relativity

Nick, Tom has explained to you that pendulum clocks by themselves are not clocks because they operate only in an acceleration field. Hourglasses are the same. Ideal clocks keep perfect time within their range of operation. Pendulum clocks and hourglasses are far from perfect even in their range of operation and don't work at all in free fall. The best clocks we have are atomic clocks.

> >	That question is useless, because you cannot move the earth with it.

>	Than you cannot perform any experiment with any clock ? (because of the earth)

The earth, or rather its acceleration field, is PART of hourglasses and pendulum clocks. The earth is NOT part of an atomic clock. That's why they keep excellent time even in orbit.

Gary

20 The two postulates in Special Relativity

The above two postulates are not the total picture. In the same book at page 142 is written: Einstein spells out three additional assumptions which are made in this reasoning (See volume 7 doc 50) 3) Homogeneity: the properties of rods and clocks depend neither on position nor on the time at which they move, but only on the way in which they move. 4) Isotropy: the properties of rods and clocks are independent of direction. 5) these properties are also independent of their history. (in the text the 3 assumptions are idicated as 1. 2. and 3.)

Accordingly to Websters a postulate is a statement that is assumed and as such requires no proof of its validity. As such IMO relativity is based on 5 assumptions. The next step is to make testable (observable) predictions using a a common set of "logical" reasoning.

One important issue is that the assumptions should be clear. IMO all the words or concepts: inertial system, at rest, in (uniform) motion and properties require a clear definition. As such assumption 3 should be divided in two assumptions:
3a) the properties of rods depend on the way in which they move. 3b) the properties of clocks depend on the way in which they move. What does the word property in each instant mean? Does "on the way in which clocks move" imply that clock count if two identical clocks move from A to B (at a different path) could be different?

Assumption 2 can be used to make the following prediction (?):
The speed of light in any inertial sytem is the same in (any) two opposite directions. Can this prediction being tested?

Nicolaas Vroom

21 The two postulates in Special Relativity

Gary. I (almost) 100% agree with you. However the real question is what are ideal clocks. How do you know that they keep perfect time? That is why I raised the 3 question/experiments using two identical clocks. The assumption is that both clocks keep the same time when 1) not moved or 2) both moved together from A to B. The third possibility is that both are moved from A to B accordingly to a different path. The Q is: Do they both keep perfect time? IMO even when you use atomic clocks that is not always the case. IMO when both clocks meet and the time (count) is different than at least one clock does not indicate the perfect time.

If you agree than the next question is: How come? When your answer depents about "range of operation" then you have to explain what you mean. IMO when both clocks meet and the time (count) is different than always different accelerations are involved. (Those different accelerations are the cause that the clocks behave differently)

Nicolaas Vroom

22 The two postulates in Special Relativity

Hi Nick,

Well, there's no such thing as a perfect clock. USNO provides the time standard and NIST has a bank of atomic clocks. A large number is needed because atomic clocks have a tendency to randomly jump a nanosecond from time to time, and real clocks do have failure modes so you can't count on one particular clock.

>	That is why I raised the 3 question/experiments using two identical clocks. The assumption is that both clocks keep the same time when 1) not moved or 2) both moved together from A to B.

The standard clocks are indeed "moving together" since the earth is moving. That should take care of that question.

>

The third possibility is that both are moved from A to B accordingly to a different path. The Q is: Do they both keep perfect time? IMO even when you use atomic clocks that is not always the case. IMO when both clocks meet and the time (count) is different than at least one clock does not indicate the perfect time.

If two clocks travel different paths and then meet, they certainly will not indicate the same elapsed time. You seem to believe that there is some "universal time" a la Newton, but there is only proper time. If you took one bank of clocks (say, 100 of them) down one path and another bank down another path, all the clocks in one bank would agree among themselves but they would disagree with all the clocks in the other bank.

"Perfect" time is nonexistent, unless you want to define that as far from the influence of any gravitational field and "motionless" (whatever that means), but there is no such place.

>	If you agree than the next question is: How come?

Relativity explains that.

>	When your answer depents about "range of operation" then you have to explain what you mean.

That has been explained. Atomic clocks work as long as they aren't accelerated beyond 2g. This is a technological problem involving the atomic beam hitting the wall of the clock body instead of remaining in free fall.

>	IMO when both clocks meet and the time (count) is different than always different accelerations are involved.

That is correct (unless, of course, they never parted from each other).

>	(Those different accelerations are the cause that the clocks behave differently) Nicolaas Vroom

But that's part of the cause but not the whole story. Half correct is not correct. In SR, distance between clocks when the acceleration occurs affects the outcome. If the distance is zero, there is no time dilation regardless of the acceleration.

Concerning your post to Gerry Quinn, you are correct about assumptions 3, 4 and 5. You might, in fact, add another: v = delta_x/delta_t, but that's more of a definition.

However, I must disagree with Websters. That may be true in mathematics but in physics everything is subject to experimental verification.

Gary

23 The two postulates in Special Relativity

Sure he does: F = MA. A massless particle subject to a finite force will undergo infinite acceleration. If you integrate the motion of a particle over a finite distance you will find that the terminal velocity rises proportional to the square root of the acceleration, so in the limiting case of infinite acceleration, the velocity would be infinite.

>	Also IMO newton's physics is independent about the speed of light. IMO his assumption is that gravity acts instantaneous.

Yes. Newton actually knew well that there were problems with instantaneous gravity, but he could not see a way to avoid it.

>

The above two postulates are not the total picture. In the same book at page 142 is written: Einstein spells out three additional assumptions which are made in this reasoning (See volume 7 doc 50) 3) Homogeneity: the properties of rods and clocks depend neither on position nor on the time at which they move, but only on the way in which they move. 4) Isotropy: the properties of rods and clocks are independent of direction. 5) these properties are also independent of their history. (in the text the 3 assumptions are idicated as 1. 2. and 3.) Accordingly to Websters a postulate is a statement that is assumed and as such requires no proof of its validity. As such IMO relativity is based on 5 assumptions. The next step is to make testable (observable) predictions using a a common set of "logical" reasoning. One important issue is that the assumptions should be clear. IMO all the words or concepts: inertial system, at rest, in (uniform) motion and properties require a clear definition. As such assumption 3 should be divided in two assumptions: 3a) the properties of rods depend on the way in which they move. 3b) the properties of clocks depend on the way in which they move. What does the word property in each instant mean?

What it always means in relativity theory: the result of a measurement that could be made.

>	Does "on the way in which clocks move" imply that clock count if two identical clocks move from A to B (at a different path) could be different?

Clearly it is intended to allow for that, since Einstein would have noticed if the consequences of his theory were in complete contradiction to one of his postulates!

>	Assumption 2 can be used to make the following prediction (?): The speed of light in any inertial sytem is the same in (any) two opposite directions. Can this prediction being tested?

Seems reasonably testable. You can set up a coordinated system of clocks at two separate positions, and then fire light beams to and fro, comparing the clock readings for sent and received signals at your leisure. You will find that you measure the same speed whichever way the beam is going.

- Gerry Quinn

24 The two postulates in Special Relativity

Gary, I agree with you. Science should not use the wording perfect. In that sense "everything" is relatif because you are comparing either different working clocks under the same conditions or "identical" clocks under different conditions.

> >

The third possibility is that both are moved from A to B accordingly to a different path. The Q is: Do they both keep perfect time? IMO even when you use atomic clocks that is not always the case. IMO when both clocks meet and the time (count) is different than at least one clock does not indicate the perfect time.

In stead of 'perfect' I should have written: 'the same'

>

If two clocks travel different paths and then meet, they certainly will not indicate the same elapsed time. You seem to believe that there is some "universal time" a la Newton, but there is only proper time. If you took one bank of clocks (say, 100 of them) down one path and another bank down another path, all the clocks in one bank would agree among themselves but they would disagree with all the clocks in the other bank.

I 100% agree with you. The next question is which bank is correct? Suppose one bank shows on average 1000 counts and the other bank 900 counts

which one is correct? Next I perform a test with three banks all going from A to B, accordingly to a different path and I get 1100, 1000 and 900 counts. Which one is "correct"? (or the best) Of course you can answer they are all correct because each behaves as it should behave. IMO the bank (of clocks) which the highest count is the best. All the other clocks are running behind.

> >	If you agree than the next question is: How come?

>	Relativity explains that.

Which do you mean SR or GR? IMO inorder to understand the behaviour of clocks (pendulums) you can use

Newton's Law. IMO to fully understand the behaviour of clocks you should use GR. IMO when you can only use SR to do the same under a rather strict set of limitations i.e. lineair motion.

> >	(Those different accelerations are the cause that the clocks behave differently)

>	But that's part of the cause but not the whole story.

That means you agree with me that acceleration in order to explain the behaviour of clocks is an issue. Okay.

>	In SR, distance between clocks when the acceleration occurs affects the outcome.

In all (?) cases when the accelerations are different the behaviour of the two clocks is different.

>	If the distance is zero, there is no time dilation regardless of the acceleration.

I agree 100%. That is the case when the two clocks follow the same path together.

>

Concerning your post to Gerry Quinn, you are correct about assumptions 3, 4 and 5. You might, in fact, add another: v = delta_x/delta_t, but that's more of a definition. However, I must disagree with Websters. That may be true in mathematics but in physics everything is subject to experimental verification.

In the book Newton's law by 's Chandrasekbar Chapter 2 Basic Concepts explains 8 definitions and 3 Laws. Law 3 can be stated as: Action is reaction. The text is: This Law is central to proving the important Corollaries IV and V etc. IMO it is not directly necessary to prove the assumptions but it is important that these assumptions lead to predictions which can be verified by means of observations.

Nicolaas Vroom

25 The two postulates in Special Relativity

> > >

Newtonian physics, in which the velocity of a massless particle is infinite, would be compatible with it.

> >	I do not expect that Newton makes any statement about the speed of a massless particle.

>	Sure he does: F = MA. A massless particle subject to a finite force will undergo infinite acceleration. etc

Studying the book Newton's Principia by s'Chandrasekhar I can not find any mentioning of this. The issue is why should Newton study massless particles ?

> >	Also IMO newton's physics is independent about the speed of light. IMO his assumption is that gravity acts instantaneous.

>	Yes. Newton actually knew well that there were problems with instantaneous gravity, but he could not see a way to avoid it.

Again same remark as above.

> >

One important issue is that the assumptions should be clear. IMO all the words or concepts: inertial system, at rest, in (uniform) motion and properties require a clear definition. As such assumption 3 should be divided in two assumptions: 3a) the properties of rods depend on the way in which they move. 3b) the properties of clocks depend on the way in which they move. What does the word property in each instant mean?

>	What it always means in relativity theory: the result of a measurement that could be made.

For example the length of a rod? But why mention this as an assumption?

> >	Does "on the way in which clocks move" imply that clock count if two identical clocks move from A to B (at a different path) could be different?

>	Clearly it is intended to allow for that, since Einstein would have noticed if the consequences of his theory were in complete contradiction to one of his postulates!

Again also here: Why mention clocks? Newton studies pendulums as a mechanical object, subject of gravity.

> >	Assumption 2 can be used to make the following prediction (?): The speed of light in any inertial sytem is the same in (any) two opposite directions. Can this prediction being tested?

>

Seems reasonably testable. You "C" can set up a coordinated system of clocks at two separate positions "A" and "B", and then fire light beams to and fro, comparing the clock readings for sent and received signals at your leisure. You "C" will find that you measure the same speed whichever way the beam is going.

Assuming the observer C is half way between the two clocks at A and B, that means the distance AC and BC is the same and stays the same during the whole experiment. The speed in both (opposite) directions is the same when the arrival times of the two beams is the same at A and B. That means the counts of the clocks at A and B should be the same. In order to do that you first have to synchronise the clocks at A and B. How do you that? by using light signals. That means you use the same strategy to synchronise as to measure the speed, which ofcourse gives the same value in both directions.

The problem this test depents about the position and speed of "C". IMO you should perform a test indepent of "C"

Nicolaas Vroom.

26 The two postulates in Special Relativity

Does he say anywhere that M should be greater than zero?

> > >

One important issue is that the assumptions should be clear. IMO all the words or concepts: inertial system, at rest, in (uniform) motion and properties require a clear definition. As such assumption 3 should be divided in two assumptions: 3a) the properties of rods depend on the way in which they move. 3b) the properties of clocks depend on the way in which they move. What does the word property in each instant mean?

> >	What it always means in relativity theory: the result of a measurement that could be made.

>	For example the length of a rod? But why mention this as an assumption?

Because in other theories properties could be defined differently. For example, in ether-based theories, the actual length of a rod is reduced when it is in motion with respect to the ether. But this actual length, although it is a property of the object, cannot be measured by any known method.

> > >

Does "on the way in which clocks move" imply that clock count if two identical clocks move from A to B (at a different path) could be different?

> >	Clearly it is intended to allow for that, since Einstein would have noticed if the consequences of his theory were in complete contradiction to one of his postulates!

>	Again also here: Why mention clocks? Newton studies pendulums as a mechanical object, subject of gravity.

You were the one to mention clocks!

> > >

Assumption 2 can be used to make the following prediction (?): The speed of light in any inertial sytem is the same in (any) two opposite directions. Can this prediction being tested?

> >

Seems reasonably testable. You "C" can set up a coordinated system of clocks at two separate positions "A" and "B", and then fire light beams to and fro, comparing the clock readings for sent and received signals at your leisure. You "C" will find that you measure the same speed whichever way the beam is going.

There were no A, B and C in what I wrote. Please note when posting edited versions of what I say. I did not place A, B and C in equivalent statuses. A and B can be considered measuring devices. C is a scientist, not a measuring device. C studies the results of measurements made at A and B.

>

Assuming the observer C is half way between the two clocks at A and B, that means the distance AC and BC is the same and stays the same during the whole experiment. The speed in both (opposite) directions is the same when the arrival times of the two beams is the same at A and B. That means the counts of the clocks at A and B should be the same. In order to do that you first have to synchronise the clocks at A and B. How do you that? by using light signals. That means you use the same strategy to synchronise as to measure the speed, which ofcourse gives the same value in both directions. The problem this test depents about the position and speed of "C". IMO you should perform a test indepent of "C"

Unless you can find a way to synchronise them with does not ultimately depend on such signals, or other signals which also obey the Lorentz symmetries, then according to relativity theory, your point is irrelevant, because things that can't be measured are not physical properties.

- Gerry Quinn

27 The two postulates in Special Relativity

W dniu pitek, 5 czerwca 2015 14:59:20 UTC+2 uytkownik Nicolaas Vroom napisa:

>

In the same book at page 142 is written: Einstein spells out three additional assumptions which are made in this reasoning (See volume 7 doc 50) 3) Homogeneity: the properties of rods and clocks depend neither on position nor on the time at which they move, but only on the way in which they move. 4) Isotropy: the properties of rods and clocks are independent of direction. 5) these properties are also independent of their history. (in the text the 3 assumptions are idicated as 1. 2. and 3.)

These are not any postulates, but a trivial facts, deduced from math directly, ie. from a theory.

>	Does "on the way in which clocks move" imply that clock count if two identical clocks move from A to B (at a different path) could be different?

Yes. It is independent on the path. The experimantal data show this explicitly, a logics - theory also.

In the SR model it depends on path... because thes model is based on: c = inv, and on some other simplifications/idealisations.

>	Assumption 2 can be used to make the following prediction (?): The speed of light in any inertial sytem is the same in (any) two opposite directions.> Can this prediction being tested?

Yes, it can be tested, but still superflous because Lorentz theory predicts this: c'(f) = k(c - vcosf) = c/k(1-v/c cosf');

therefore the measured two-way speed of light, in the vacuum, is constant: c = inv.

And it's due to the first Lorentz's equation only: x' = k(x - vt); So, we catch at once the whole experimental data, from the 20 century without any superfluous postulates... the strict ans strong math is good enought.

28 The two postulates in Special Relativity

Newton at page 18 defines the notion of mass as a quantity of matter. Newton defines: quantity of motion = mass * velocity. (IMO) When mass = 0 the body or object does not exist.

> > >

What it always means in relativity theory: the result of a measurement that could be made.

> >	For example the length of a rod? But why mention this as an assumption?

>	Because in other theories properties could be defined differently. For example, in ether-based theories, the actual length of a rod is reduced when it is in motion with respect to the ether. But this actual length, although it is a property of the object, cannot be measured by any known method.

You make it even more complex. IMO assumption 3 is not very clear. Why not rewrite assumption 3 that the length? and mass? depend on the way in which they move. Of course the last part of this sentence is also not clear.

>	You were the one to mention clocks!

Assumption 3 is described in the book by A Pais which discusses what Einstein write. The proporties of a clock are: Length, mass and "frequency".

> > >

You "C" will find that you measure the same speed whichever way the beam is going.

>	There were no A, B and C in what I wrote.

That is correct. The problem is how you measure the same speed whichever way the beam is going.

>	Please note when posting edited versions of what I say. I did not place A, B and C in equivalent statuses. A and B can be considered measuring devices. C is a scientist, not a measuring device. C studies the results of measurements made at A and B.

That is 100% correct.

> >

Assuming the observer C is half way between the two clocks at A and B, that means the distance AC and BC is the same and stays the same during the whole experiment. The speed in both (opposite) directions is the same when the arrival times of the two beams is the same at A and B. That means the counts of the clocks at A and B should be the same. In order to do that you first have to synchronise the clocks at A and B. How do you that? by using light signals. That means you use the same strategy to synchronise as to measure the speed, which ofcourse gives the same value in both directions. The problem this test depents about the position and speed of "C". IMO you should perform a test indepent of "C"

>	Unless you can find a way to synchronise them with does not ultimately depend on such signals, or other signals which also obey the Lorentz symmetries, then according to relativity theory, your point is irrelevant, because things that can't be measured are not physical properties.

The problem is my question: how can you test or measure the speed of light in any inertial system in both directions and come to the conclusion that this speed is always the same. Of course if this can not be measured than this becomes a whole different story. You could also claim that this is true by definition i.e. that the speed of light is (physical) the same in both directions. But if that is the case why mention: "in any inertial system".

Nicolaas Vroom

29 The two postulates in Special Relativity

Am 20.06.2015 um 05:41 schrieb Nicolaas Vroom:

>	Op donderdag 11 juni 2015 09:00:42 UTC+2 schreef Gerry Quinn:

>>	Does he say anywhere that M should be greater than zero?

>	Newton at page 18 defines the notion of mass as a quantity of matter. Newton defines: quantity of motion = mass * velocity. (IMO) When mass = 0 the body or object does not exist.

Thats the question.

It originated with detection of the duality of the two mathematical concepts of waves and point particles as the possible nature of light.

Fermat Huyghens, Newton, Kirchhoff and even people like Goethe and Schopenhauer engaged in that widely philosophically shaped academic discussion.

The two generic Newtonian equations of motion of point particles m x'' = K = m g for acceleration in static gravity and m x'' = e E for charged particles clearly have simple limits m->0. The first equation is stating universality of gravitation independent of mass, the second aimes to conclude that classes of charged point particles in the limit m->0 should have constant specific charge per mass density.

That idea was the starting point of quantum theory and the redetection of Demokritos' and Leibniz' fundamental concept of the atomism of matter, where the atoms represent the smallest unit having the same physical and chemical identity as a pure macroscopic body composed of them.

In the times of the glorius physical revolution between Maxwell and Heisenberg/Schroedinger the idea of a point particle disappeared together with its velocity and acceleration.

The first doubt was raised by H.A. Lorentz who showed the impossibility to make the relativistic limit for charged point particles to diameter -> 0 at fixed e/m.

Today we are left now with a widely algebraically equivalent Hamiltonian canonical picture of position and momentum variables in a quantised wave theory where the mass m is a fixed parameter in the relativistic Einstein wave dispersion relation

(E/c)^2 - p^2 == (m c)^2

to be fulfilled at every space time point where E/c and p are the local frequency and wave number in units of hbar.

In this Q-theory mass m (and charge e and spin s) are fixed parameters of a group representation and the limit m->0 cannot be taken on representation spaces.

But representations with m=0, e=0 exist (scalar bosons, neutrinos, photons, gravitons). The limits to be taken are mathematically involved and notoriously difficult to understand.

--

Roland Franzius

30 The two postulates in Special Relativity

>

The problem is my question: how can you test or measure the speed of light in any inertial system in both directions and come to the conclusion that this speed is always the same. Of course if this can not be measured than this becomes a whole different story. You could also claim that this is true by definition i.e. that the speed of light is (physical) the same in both directions. But if that is the case why mention: "in any inertial system". Nicolaas Vroom

There is no problem with a lightspeed, because it's: c' = c - v due to the fact: x' = x - vt;

But in a moving frame we measure a different quantity, due to the physical contraction, in a moving system, which rescale the unit of distance, like this: d' = kd, where k = gamma;

hence the Lorentz transform: x' = k(x-vt); thus the light =velocity= must be rescaled in the same way: c'_vec = k(c - v)

thus a speed is: c'(f) = k(c - vcosf)

where the angle f is measured in a stationary frame; but we should use f' - the angle in the moving frame, which is: cosf' = ...

and finally the light speed (measured in a moving frame) is eq.: c'(f') = c/k(1-v/c cosf'); ... so, we can measure just that quatnity only.

The two-way speed of light, ie. a harmonic mean of the: c'(f') and c'(f'+180) is constant, of course... therefore the SR model - as a very simplified version of the Lorentz's theory.

31 The two postulates in Special Relativity

The measurements leading up to the redefinition of the meter in 1983 did precisely that, for all inertial frames occupied by laboratories on earth. As they are rotating and orbiting with the earth, a large number of different inertial frames were sampled, and the accuracy of the measurements was ~ 60,000 times better than the variations in velocities of the frames relative to the solar system rest frame.

Today (post 1983) standards organizations are not interested in measuring the speed of light, as it is a constant used to define the meter.

You may argue that those were all round-trip measurements. True, but unimportant, because one-way measurements are conventional in that they require one to select an ARBITRARY convention for synchronizing clocks, and the result depends on your ARBITRARY choice.

Using pre-1983 standards and modern equipment, direct measurements of the one-way speed of light suffer from large systematic errors, but there are many measurements of the isotropy of the one-way speed of light that are far more accurate; they use slow clock transport for synchronization. The combination of isotropy of one-way propagation and accurate measurements of the round-trip speed is sufficient to test the various fundamental theories of physics, and the only theories that survive are SR and the other theories that are experimentally indistinguishable from it (none of which are useful or interesting other than historically).

Tom Roberts

32 The two postulates in Special Relativity

33 The two postulates in Special Relativity

>

We certainly consider that entities with zero mas exist nowadays. I don't know what Newton thought about the issue, though perhaps we could get some clue from considering his various thoughts regarding infinitesimals etc. But in any case, it is clearly implicit in his equations that an object of zero mass would gain infinite velocity if impelled by a force. And even if zero mass objects cannot exist, there is no obvious limit on the velocities attainable by objects of very low mass subjected to large forces.

Reading the previous mentioned book objects of zero mass are no issue for Newton. At page 236 we read: "If the masses m1,m2,m3 etc are sufficiently tiny (compared to M) then the center of gravity will not be sensibly different from the location of M, which may, then, be considered to be at rest or moving uniformly forward in a right line; and about which the lesser bodies will revolve."

One of the most amazing chapters is #10 "On revolving orbits" In this chapter he discusses different "Laws of force". In example 1 (page 194) the situation close to the movement of the planet Mercury is discussed. Truly amazing.

> >	The problem is my question: how can you test or measure the speed of light in any inertial system in both directions and come to the conclusion that this speed is always the same. Of course if this can not be measured than this becomes a whole different story.

>	If you adopt the philosophy that what cannot be measured is not real, then there is no difference.

If you cannot measure what the proposition describes than you cannot validate the proposition.

>	My view is that the philosophy is justified by what we know of quantum theory.

Certain aspects of the quantum theory are also different to measure i.e. to validate, but that is not the subject here.

Nicolaas Vroom

34 The two postulates in Special Relativity

How did they measure the speed in one direction ? I think it is rather difficult to measure the speed of light in a laboratory accurately, with the emphasis on accurate.

>	Today (post 1983) standards organizations are not interested in measuring the speed of light, as it is a constant used to define the meter.

35 The two postulates in Special Relativity

They didn't. They measured the speed over a round-trip laboratory path (in vacuum), and verified isotropy in many different OTHER experiments. The many different round-trip measurements were accurate to better than 1 m/s, and did not vary significantly over the location, year, month, or day.

>	I think it is rather difficult to measure the speed of light in a laboratory accurately, with the emphasis on accurate.

Not at all. The accuracy back then was a few parts per billion; could do better today, but:

>>	Today (post 1983) standards organizations are not interested in measuring the speed of light, as it is a constant used to define the meter.

>	I can understand that you define the speed of light as a constant. However that is only a part of the problem.

WHAT "problem"??? The definitions as of 1983 have proven to be robust and useful.

OK, YOU seem to have a problem understanding this. The only cure is to STUDY. Your "20 questions" approach here is USELESS. Get a good textbook; I recommend: Misner, Thorne, and Wheeler, _Gravitation_.

>	The first question is: is the speed of individual photons everywhere the same?

If you actually knew what photons are, you would know that this question is meaningless. We measure the speed of LIGHT PULSES, not "individual photons".

In our best theory of all this, GR, the LOCAL speed of LIGHT PULSES (in vacuum) is indeed everywhere the same. And in all places we have managed to measure it, the measurements are consistent with this prediction.

>	Is the speed the same at "my" position as near a blackhole?

Nobody has ventured near a black hole to measure. But in our only theory that describes black holes, GR, the LOCAL speed of light is equal to c EVERYWHERE, including near and even inside a black hole.

>	The second question is when you draw a space time diagram, Is the space diagram the same at "my" position as on a moving train from the position of an observer on the moving train.

The diagrams themselves are of course the same, but the objects depicted in them can be displayed in different places, with different orientations. This is no different from "left" to you being "right" to me as we face different directions -- remember that in relativity, relative motion is a change in orientation (in spaceTIME) as well as a (time-dependent) change in (relative) position.

>	Is it always correct to draw the light lines at the same angle in both directions.

Yes, as long as the diagram is drawn from the perspective of an inertial frame, and as long as the diagram is no larger than the domain of validity of that frame's coordinates.

>	[... more questions too complicated to parse]

Tom Roberts

36 The two postulates in Special Relativity

> >	If you adopt the philosophy that what cannot be measured is not real, then there is no difference.

>	If you cannot measure what the proposition describes than you cannot validate the proposition.

Not relevant if from your philosophical perspective the proposition (a 'true' each-way velocity that cannot be measured by any means) is meaningless! Meaningless propositions are neither susceptible to validation, nor needful of it.

It is perfectly legitimate to adopt another perspective in which the proposition is meaningful - this leads us to ether-like interpretations along the lines proposed by Lorentz and Poincare. If our physical intuitions invoke a pre-quantum world, in which every phenomenon must be explicable in terms of the workings of constituent local mechanisms, and counterfactual definiteness is a given, this approach is very attractive. For example, in this approach there is no such thing as the 'twin paradox' - regardless of the twins' motions, the aging of each twin is controlled at all times simply by his velocity with respect to the ether, and no other factor need be considered at all.

Unfortunately it's rather clear that we do not in fact live in such a world. In the world we live in, it has been demonstrated that quantities we choose not to measure are not meaningful, even if we could have measured them had we wanted to. For example, when we set up a two slit experiment, "the slit the particle goes through" is something we can measure if we choose, by monitoring one or both slits. But if we don't choose to monitor that, and we send a large number of particles through, the resulting distribution will be consistent only with the idea that each particle in some sense goes through both slits. Because we did not measure which slit, the question of 'which slit' has become meaningless.

In such a world, the existential status of something that we not only do not measure, but do not know how to measure, is precarious!

> >	My view is that the philosophy is justified by what we know of quantum theory.

>	Certain aspects of the quantum theory are also different to measure i.e. to validate, but that is not the subject here.

What parts of the quantum theory are asserted to be measureable, but cannot be measured? - show quoted text -

37 The two postulates in Special Relativity

On Monday, July 6, 2015 at 1:56:45 AM UTC-4, Gerry Quinn wrote:

> > >

My view is that the philosophy is justified by what we know of quantum theory.

>

> >	Certain aspects of the quantum theory are also different to measure i.e. to validate, but that is not the subject here.

>	What parts of the quantum theory are asserted to be measureable, but cannot be measured?

Hi Gerry

"Meaningless propositions are neither susceptible to validation, nor needful of it."

Well said.

Would like to touch on developmental psychology with respect to the 2 postulates.

There are two general types in science. A Faraday and an Oppenheimer.

A Faraday will compare the postulate with the math to verify the math. The postulates are of greater importance. I will venture a guess at 12 he required cloves tied to coat sleeves to keep them from being lost. Forgetful is the key leading to an intuitive thinker later in life.

An Oppenheimer will compare the math with the postulates to verify the postulates. The math is of greater importance. Oppy has no need for cloves tied to sleeves as they are in a draw organize chronologically. A well organized mind that is not forgetful is the key.

I would put myself in the Faraday camp. The postulates are heart of special relativity. If it turned out the math in SR is wrong then one simply corrects the math somewhat like a spelling mistake. It is the postulates that may not be violated.

This placers a greater burden on us. Dr Einstein could not violate Newtonian physics in 1905 as he would no longer have a floor to stand on. When the last dot was put on SR Newtonian physics was not violated with regards to energy and arrival times for a given frame of reference. Both theories render the same answer. This makes SR foundational to Newtonian physics. From a physics foundational position we today can not violate the two postulates as we will no longer have a floor to stand on in the same way Dr Einstein could not violate Newtonian physics.

38 The two postulates in Special Relativity

It's much worse than merely "tricky", it is AMBIGUOUS and therefore not well defined.

Consider a simple one-way measurement of the speed of light from a mountaintop to the adjacent valley, using two (ideal) clocks, neglecting air. The clocks must be synchronized, so imagine you do that using a light ray. Obviously if you make the measurement immediately thereafter, you will obtain c. Wait a while, and you will obtain a value smaller than c (due to the relative drift of the clocks due to "gravitational redshift"). Wait long enough, and you will obtain a NEGATIVE result! Use the same endpoints but measure in the other direction, and you can obtain an arbitrarily large answer!

That is why when physicists measure a speed, they always intend the measurement to be made in a locally inertial frame. The size of that frame, of course, depends on both the local curvature of spacetime and the measurement accuracy. For marathons and auto races this doesn't matter; for measuring the speed of light it can.

Note, however, if the two endpoints are on earth's geoid, then the measurement will be independent of time, even though the path is the same length as before. It would be disingenuous to claim this uses SR -- one must apply GR, and for this case it predicts the constant value c.

But if one measures in a lab over a horizontal path of a few meters, then one CAN apply SR -- a locally inertial (free- falling) frame that is at rest with the apparatus when the measurement begins will fall much less than the measurement accuracy during the few nanoseconds of the measurement.

>	Of course the simplest solution is to declare the speed of light constant.

HUH??? That is no "solution" at all.

Of course physicists don't do that -- the constancy of the speed of light applies to SR, not GR, and SR is only APPROXIMATELY valid, and only in a locally inertial frame; the maximum size of that frame, of course, depends on both the local curvature of spacetime and the measurement accuracy.

>	If you cannot use GR what than?

Then YOU must find another hobby.... Those of us who do this sort of thing for a living can and will use GR. Most likely in an appropriate approximation, of course.

Tom Roberts

39 The two postulates in Special Relativity

Just some thoughts. IMO this synchronisation process is already rather complex. IMO the mountaintop should issue a light signal at regular intervals. You get than a string like 6, 8, 10, 12 and 14. The next step is to record the arrival times of these signals at the valley clock. You could get than a string like 11, 13, 15, 17 and 19. (A) But also You could get than a string like 11, 12.9, 14.8, 16.7 and 18.6 (B) In case B the valley clock runs faster, which have to adjusted to take care that both clocks run at the same rate. After this adjustment the time to go from top to valley is always the same, which it physical should be. The next step consists of two parts: You must first reflect the received valley signals back to the top. You get a string like 10, 12, 14, 16 and 18 Secondly you must adjust the valley clocks such that their readings are a string like: (6+10)/2 = 8, 10, 12, 14 and 16 Now the clocks are synchronised?

However you do not know if the speed is constant during the whole trip. To test that you have to repeat the same process half way between top and valley.

>	That is why when physicists measure a speed, they always intend the measurement to be made in a locally inertial frame.

But if you perform such a test at a locally inertial frame at the top and a second time at a locally inertial frame at the valley and the speeds are different what is the point of declaring the speed of light constant?

See also you posting at 20 June 2015: "Today (post 1983) standards organizations are not interested in measuring the speed of light, as it is a constant used to define the meter."

> >	Of course the simplest solution is to declare the speed of light constant.

>	HUH??? That is no "solution" at all.

I agree

>	Of course physicists don't do that -- the constancy of the speed of light applies to SR, not GR, and SR is only APPROXIMATELY valid, and only in a locally inertial frame; the maximum size of that frame, of course, depends on both the local curvature of spacetime and the measurement accuracy.

The problem is what I want to do is to simulate the movements of the planets around the sun, specific the planet Mercury. Also I want to calculate a Galaxy Rotation Curve. In both cases I want to see what is involved when I use GR. Apperently SR is out of the question, including the two (five) postulates on which it is based. The question than remains: what is the purpose of SR?

> >	If you cannot use GR what than?

>	Then YOU must find another hobby....

I'm too old to learn fishing.

>	Those of us who do this sort of thing for a living can and will use GR. Most likely in an appropriate approximation, of course.

Of course if you remove too much, is it than still GR or does it become Newton+

If you start from one mutual agreed reference frame and if you do not use moving clocks (after synchronisation) things are becoming simpler.

IMO one important question to answer is what is the function of the speed of light (ie photons) in relation to the laws of nature i.e. GR. This question is specific important in relation to dark matter.

Nicolaas Vroom

40 The two postulates in Special Relativity

Nicolaas Vroom wrote:

>

Just some thoughts. IMO this synchronisation process is already rather complex. IMO the mountaintop should issue a light signal at regular intervals. You get than a string like 6, 8, 10, 12 and 14. The next step is to record the arrival times of these signals at the valley clock. You could get than a string like 11, 13, 15, 17 and 19. (A) But also You could get than a string like 11, 12.9, 14.8, 16.7 and 18.6 (B) In case B the valley clock runs faster, which have to adjusted to take care that both clocks run at the same rate. After this adjustment the time to go from top to valley is always the same, which it physical should be.

What do you mean with "time to go from top to valley"? The time a signal takes to run from top to valley? In GR, this time can mean the proper time of the signal (what is zero in the case of a light signal) or the coordinate time interval in some coordinate system. The coordinate time interval is, assumed the coordinate system is time translation invariant like Schwarzschild coordinates are, always the same, fully independent from adjustments of the valley clock.

>

The next step consists of two parts: You must first reflect the received valley signals back to the top. You get a string like 10, 12, 14, 16 and 18 Secondly you must adjust the valley clocks such that their readings are a string like: (6+10)/2 = 8, 10, 12, 14 and 16 Now the clocks are synchronised?

The clocks are synchronized in Schwarzschild coordinates if both run with the same running speed with respect to Schwarzschild coordinate time and show the same clock time at the same Schwarzschild coordinate time. I.e. on any spacelike hypersurface defined by t = const, where t is Schwarzschild coordinate time, they must show the same clock time.

The division by 2 in your procedure sounds as if you want to apply SR clock synchronization that assumes a constant speed of light. Since the speed of light with respect to Schwarzschild coordinates is not constant, your procedure will probably fail.

>	However you do not know if the speed is constant during the whole trip.

Applying the Schwazschild solution, you know that the speed of light is not constant with respect to Schwarzschild coordinates.

>>	That is why when physicists measure a speed, they always intend the measurement to be made in a locally inertial frame.

>	But if you perform such a test at a locally inertial frame at the top and a second time at a locally inertial frame at the valley and the speeds are different

No, they are not. The speeds measured in the particular local inertial frame are the same, namely c. Only the speeds indicated in a coordinate like Schwarzschild coordinates are different.

More mathematically: take two clocks A and B that are radially free falling. For each clock, you take a small spacetime region, so small that you can approximate each clock as resting in Schwarzschild coordinates, i.e. dr/dt = 0, where r ist Schwarzschild radial coordinate. So, in the particular spacetime region, you can imagine clock A as resting at radial coordinate rA, clock B at rB.

Now take a light ray passing clock A radially. In Schwarzschild coordinates, the speed of the light ray is

dr/dt = (1 - rs/rA) c (1)

Now let's calculate the speed of that light ray in the local inertial frame of clock A. To do so, we at first have to calculate the proper time interval d(tauA) elapsing for clock A during the Schwarzschild coordinate time interval dt. We get

d(tauA) = sqrt(g_tt(rA)) = sqrt(1 - rs/rA) dt

with g_tt(rA) = 1 - rs/rA being the tt-component of the metric tensor in Schwarzschild coordinates at r = rA. Next, we need to calculate the spatial distance d(lA) in clock A's local inertial frame between the points rA and rA + dr between which the light ray is travelling during the Schwarzschild coordinate time interval dt. We get

d(lA) = sqrt(-g_rr(rA)) = dr / sqrt(1 - rs/rA)

with g_rr(rA) = -1/(1 - rs/rA) being the rr-component of the metric tensor in Schwarzschild coordinates at r = rA. For dr, we insert (1):

dr = (1 - rs/rA) c dt

=> d(lA) = (1 - rs/rA) c dt / sqrt(1 - rs/rA)

= sqrt(1 - rs/rA) c dt

To get now the speed of light in the local inertial frame of clock A, we need to calculate

d(lA) / d(tauA) = sqrt(1 - rs/rA) c dt / sqrt(1 - rs/rA) dt

= c

So, in the local inertial frame of clock A, the speed of that light ray is c.

The procedure we apply to clock B: the speed of a light ray passing clock B radially is in Schwarzschild coordinates:

dr/dt = (1 - rs/rB) c (2)

The elapsing proper time on clock B is

d(tauB) = sqrt(g_tt(rB)) = sqrt(1 - rs/rB) dt

and the spatial distance in clock B's local inertial frame

d(lB) = sqrt(-g_rr(rB)) = dr / sqrt(1 - rs/rB)

We again insert (2):

d(lB) = sqrt(-g_rr(rB)) = (1 - rs/rB) c dt / sqrt(1 - rs/rB)

= sqrt(1 - rs/rB) c dt

and calculate the speed of the light ray in clock B's local inertial frame:

d(lB) / d(tauB) = sqrt(1 - rs/rB) c dt / sqrt(1 - rs/rB) dt

= c

We again get c as speed.

In other words: the speed of light slows down in Schwarzschild coordinates when r is decreasing, but clocks of local inertial frames are slowing down, too, with respect to Schwarzschild coordinate time, and in combination with the effects of spatial curvature, expressed by g_rr, this provides that the speed of light remains the same, namely c, in all local inertial frames.

In fact, the causality of GR is the other way round: the constancy of the speed of light in all local inertial frames is the fundamental principle, and the slowing down of the speed of light with respect to Schwarzschild coordinates in Schwarzschild solution is derived from that.

And it is important to note, that the speed of light in local inertial frames is, compared to the speed of light in Schwarzschild coordinates, the more fundamental one. Schwarzschild coordinates are just an arbitrarily chosen coordinate system, one could as well chose various different coordinate systems, like one does in the case of black holes, e.g. Eddingtin-Finkelstein coordinates, free-falling coordinates, or Kruskal coordinates, that yield totally different speeds of light.

>>	Of course physicists don't do that -- the constancy of the speed of light applies to SR, not GR, and SR is only APPROXIMATELY valid, and only in a locally inertial frame; the maximum size of that frame, of course, depends on both the local curvature of spacetime and the measurement accuracy.

>

The problem is what I want to do is to simulate the movements of the planets around the sun, specific the planet Mercury. Also I want to calculate a Galaxy Rotation Curve. In both cases I want to see what is involved when I use GR. Apperently SR is out of the question, including the two (five) postulates on which it is based.

In GR, the postulate of the constancy of the speed of light remains valid in that way that the speed of light measured in local inertial frames is constant.

>	The question than remains: what is the purpose of SR?

Describing situation where gravity can be neglected.

>>>	If you cannot use GR what than?

>>	Then YOU must find another hobby....

>	I'm too old to learn fishing.

>>	Those of us who do this sort of thing for a living can and will use GR. Most likely in an appropriate approximation, of course.

>	Of course if you remove too much, is it than still GR or does it become Newton+

That depends on how much too much is.

>	If you start from one mutual agreed reference frame and if you do not use moving clocks (after synchronisation) things are becoming simpler.

If you want to use reference frames in a regime ruled by gravity, then you cannot use GR. But why don't you simply use GR and accept that you have to use coordinate systems instead of inertial frames?

And: your desire to use reference frames but not to use moving clocks, seems a little strange. Usually, using reference frames is combined with using moving clocks.

>	IMO one important question to answer is what is the function of the speed of light (ie photons) in relation to the laws of nature i.e. GR.

I'm not sure whether I can make any sense in this question. In coordinate systems in which the speed of light is not constant, e.g. Schwarzschild coordinates in Schwarzschild solution, you can write the speed of light as function of some parameters, like r in the case of Schwarzschild coordinates:

v(r) = (1 - rs/r) c

Or did you rather want to ask in what way the postulate of the constancy of the speed of light from SR remains valid in GR?

41 The two postulates in Special Relativity

If the speeds were measurably different then you would have refuted GR in a rather big way. To date that has not happened, and most physicists would give rather long odds that this sort of refutation won't ever happen.

>	The problem is what I want to do is to simulate the movements of the planets around the sun, specific the planet Mercury.

Using Newtonian gravitation (NG) this is simple if you ignore the other planets, but quite complicated if you include them (and you must include them if you want accuracy [#]).

[#] e.g. sufficient accuracy to see the difference between NG and GR.

>	Also I want to calculate a Galaxy Rotation Curve.

Let's not discuss this now, there's too much else on the table. (But this is VERY different from the solar system calculations.)

>	In both cases I want to see what is involved when I use GR.

Using NG for the solar system is already quite complicated; AFAIK nobody has used GR for this, as that is far too complicated. What people actually do is use the post-Newtonian (or post-post-Netonian) approximation to GR. This is more complicated than using NG alone, but is tractable. Note, however, that programs to calculate the solar system at this level have been developed over many staff-years by experts; you have a long and arduous road ahead.... And a lot to learn....

>	what is the purpose of SR?

It was a VERY important step on the road to GR. And since GR is so complicated to apply, SR remains quite useful in situations in which gravitation can be neglected.

Consider the LHC experiments. Each is in a cavern less than 100 meters large, and all the particles of interest travel with speed > 0.99 c relative to the cavern. So let's apply SR in the locally inertial frame that is at rest relative to the cavern at the instant of the crossing (the interaction that produces the particles of interest). Within 300 ns all the particles have left the cavern and can no longer be observed by the detector. During 300 ns that locally inertial frame falls 0.5 g t^2 = 4.4E-12 meters. The detectors have resolutions on the order of a micron or more, so the error in assuming the detector is at rest in an inertial frame is FAR below the experimental resolution -- SR can be used without problem. (A calculation for the rotation of the earth yields an error that's even smaller than this.)

>	IMO one important question to answer is what is the function of the speed of light (ie photons) in relation to the laws of nature...

I suspect it has essentially no role at all in fundamental physical phenomena. That's because all such phenomena appear to be LOCAL (<< 1E-6 meters), so the propagation of light is just irrelevant.

>	... i.e. GR.

Most physicists doubt very much that GR is a "law of nature". It seems MUCH more likely that it is merely an approximation to something more fundamental. But the jury is still out....

Tom Roberts

42 The two postulates in Special Relativity

Skip

>	What do you mean with "time to go from top to valley"? The time a signal takes to run from top to valley? In GR, this time can mean the proper time of the signal (what is zero in the case of a light signal) or the

Skip

It is important to remember that my posting is a reply on the following posting by Tom Roberts:

>	Op woensdag 5 augustus 2015 21:38:22 UTC+2 schreef Tom Roberts:

>>	On 8/4/15 8/4/15 7:48 AM, Nicolaas Vroom wrote:

>> >	IMO to calculate the speed of light under such conditions is tricky.

>>

It's much worse than merely "tricky", it is AMBIGUOUS and therefore not well defined. Consider a simple one-way measurement of the speed of light from a mountaintop to the adjacent valley, using two (ideal) clocks, neglecting air. The clocks must be synchronized, so imagine you do that using a light ray.

What I try to do is answer the question is the speed of light constant. To do that let me first define a simple experiment. The experiment consists of dropping a ball from the Tower of Pisa, which bounches back. The objective is to measure the time when the ball reaches its highest point. In order to measure this time I use a small ball which bounces between two horizontal plates. The total number of counts (bounces) is 10. Next I perform the same experiment but I use half the distance. The total number of counts is 7. That means for the first part the number of counts is 7 and for the second part 3. My reasoning the speed of the ball is not constant. Is this correct?

The second experiment is physical identical as above but instead of a ball I use a light ray which is reflected. To measure the time I also use a light ray between two mirrors. The results are totally different but suppose I get for the total count 2000 and for the first part 1001. That means for the second part 999. Is this feasible? My conclusion is the same: The speed of light is not constant. Is this correct?

> >	The question than remains: what is the purpose of SR?

>	Describing situation where gravity can be neglected.

Interesting. My impression is that in all (?) experiments in the realm of SR gravity is involved. (moving clocks in airplane) That means (My impresion) you can describe each of these experiments also without SR and only solely with GR. or is this wrong reasoning?

Nicolaas Vroom

43 The two postulates in Special Relativity

[[Mod. note -- Note that as well as "all" the planets, you probably want lots of moons and asteroids, too. -- jt]]

The problem is the perihelion shift of Mercury of 43 arc sec. You can also use NG as a bassis to solve that, but than you have to modify NG and take into account that gravity does act instantaneous.

> >	Also I want to calculate a Galaxy Rotation Curve.

>	Let's not discuss this now, there's too much else on the table. (But this is VERY different from the solar system calculations.)

44 The two postulates in Special Relativity

>	What I try to do is answer the question is the speed of light constant.

This question is not precise enough. When talking about a speed in GR, you have to distinguish between the speed measured in a local inertial frame and the speed measured in a coordinate system. The description you provide below indicates that you refer to the speed measured in a coordinate system (for more details see below). For the speed of light, this indeed implies that it is not constant, unlike the speed of light measured in a local inertial frame that remains constant in GR.

>

To do that let me first define a simple experiment. The experiment consists of dropping a ball from the Tower of Pisa, which bounches back. The objective is to measure the time when the ball reaches its highest point. In order to measure this time I use a small ball which bounces between two horizontal plates. The total number of counts (bounces) is 10. Next I perform the same experiment but I use half the distance. The total number of counts is 7. That means for the first part the number of counts is 7 and for the second part 3. My reasoning the speed of the ball is not constant.

Your descrption implies that you define a coordinate system, with the following properties:

(1) The top and the ground of the Tower have fixed spatial coordinates

(2) The elapsing coordinate time is proportional to the number of bounces of the bouncing ball between the plates.

(3) Time translation invariance applies: the coordinate time interval that the ball takes for the trip from top to ground is the same as the coordinate time interval the ball takes for the back-trip from ground to top.

The speed of the ball measured in that coordinate system is not constant, that is correct.

>

The second experiment is physical identical as above but instead of a ball I use a light ray which is reflected. To measure the time I also use a light ray between two mirrors. The results are totally different but suppose I get for the total count 2000 and for the first part 1001. That means for the second part 999. Is this feasible? My conclusion is the same: The speed of light is not constant.

Measured with respect to the coordinate system that you apply here, which is the same coordinate system as in the ball version of the experiment, the speed of light is not constant, that is correct.

However, that speed of light is not "the speed of light". It is just the speed of light *in the coordinate system you have chosen*. In GR, the choice of the coordinate system is arbitrary, instead of the coordinate system that you applied above you could as well choose any other coordinate system, e.g. one in which the speed of light turns out to be constant for your experiment. Due to this, the speed of light in the currently chosen coordinate system is an arbitrary quantity in GR and therefore not very meaningful.

A rather meaningful indication of the speed of light is the indication with respect to a local inertial frame. That speed of light is always constant in GR. In your experiment, you can apply a local inertial frame at the top of the Towever, and you will find the speed of light constant. You can apply a different local inertial frame at the middle of the tower, and you will find the speed of light constant again. Finally, you can apply another local inertial frame at the bottom of the tower, and you will find the speed of light constant another time.

What is not possible, though, is to apply the same local inertial frame for the whole trip from top to bottom, since the corresponding spacetime region is not sufficiently limited.

>>>	The question than remains: what is the purpose of SR?

>>	Describing situation where gravity can be neglected.

>	Interesting. My impression is that in all (?) experiments in the realm of SR gravity is involved. (moving clocks in airplane)

The Hafele-Keating experiment to which you seem to be referring indeed did not test the effects of SR on their own, but rather the combined effects of SR and GR.

However, there have been different experiments where GR effects were not relevant. Take e.g. experiments in particle accelerators. Since all parts of an accelerator are at the same height with respect to the ground, differences in gravitational field are out of relevance. Or take muon experiments. The muons are changing in height, though, but the gravitational time dilation effects are neglectible compared to the SR time dilation due to the high speed of the muons.

45 The two postulates in Special Relativity

I think that my question is rather simple ? Is the speed of light (the speed of the photons) in the universe everywhere the same and if not what is the physical cause.

>	When talking about a speed in GR, you have to distinguish between the speed measured in a local inertial frame and the speed measured in a coordinate system.

Ofcourse if you want to measure the speed of light you have to quantify the distance and time you use which implies a coordinate system. That is not what I have done. The speed is in counts of one counter.

>	The description you provide below indicates that you refer to the speed measured in a coordinate system (for more details see below). For the speed of light, this indeed implies that it is not constant, unlike the speed of light measured in a local inertial frame that remains constant in GR.

My suggestion is to define your experiment which demonstrates that the speed of light is constant. By preference you should not include any moving clock.

> >	My reasoning the speed of the ball is not constant.

>

skip

>	The speed of the ball measured in that coordinate system is not constant, that is correct.

In fact you can also make the coordinate system much larger. You can easily include the earth in total.

> >	The second experiment is physical identical as above etc My conclusion is the same: The speed of light is not constant.

>	Measured with respect to the coordinate system that you apply here, which is the same coordinate system as in the ball version of the experiment, the speed of light is not constant, that is correct.

It is something more: the speed of light increases when it travels towards the earth. However also in reverse sense: The speed of light decreases when the distance from the earth increases. (Within limits of the solar system)

>	instead etc. you could as well choose any other coordinate system, e.g. one in which the speed of light turns out to be constant for your experiment.

My same suggestion: Supply me the details.

>	In your experiment, you can apply a local inertial frame at the top of the Towever, and you will find the speed of light constant.

The same as above

>	You can apply a different local inertial frame at the middle of the tower, and you will find the speed of light constant again.

IMO why should I do that it makes a simulation of the solar system of a galaxy terrible complicated (I think)

>	What is not possible, though, is to apply the same local inertial frame for the whole trip from top to bottom, since the corresponding spacetime region is not sufficiently limited.

What is wrong in using one coordinate system for our whole galaxy?

[[Mod. note -- The issue is that you can't use a single (global) *inertial* coordinate system for the whole trip -- the whole message of GR is that no such coordinate system can exist, i.e., that no coordinate system can have the property of being global-inertial (i.e., flat) *and* cover a large region of a spacetime with significant gravitational effects. -- jt]]

>	The Hafele-Keating experiment to which you seem to be referring indeed did not test the effects of SR on their own, but rather the combined effects of SR and GR.

But why not solely using GR for the whole experiment?

[[Mod. note -- Since GR is a superset of SR, you *could* analyse the whole experiment in the framework of GR. However, some (though not all) of the effects in this experiment (= flying atomic clocks around the world) are already present in an SR model, and it's useful to analyses these effects from the perspective of SR. -- jt]]

Nicolaas Vroom

46 The two postulates in Special Relativity

>>>	What I try to do is answer the question is the speed of light constant.

>>	This question is not precise enough.

>	I think that my question is rather simple ? Is the speed of light (the speed of the photons) in the universe everywhere the same

Within the framework of a theory in which the term "speed of light" has a clear, unique meaning (e.g. SR), your question might be simple. But in GR, the term "speed of light" does not have such a clear meaning. "Speed of light" can either mean the speed of light measured in a local inertial frame, or the speed of light measured in a coordinate system.

>	and if not what is the physical cause.

What is in general not constant in GR is the speed of light in a coordinate system. However, this does not have a physical cause, since it is just a property of the chosen coordinate system. At best, one can ask for the physical cause why one cannot apply inertial frames like in SR, but is obliged to come along with more general coordinate systems. The physical cause for that is the curvature of spacetime: in a curved spacetime, inertial frames can only be constructed locally, not globally for the complete spacetime.

Take for illustration the surface of sphere. That is a curved two-dimensional space. It's easy to seen that it's impossible to construct a Cartesian (x,y) coordinate system that covers the complete surface. A Cartesian coordinate system can only be constructed locally around a chosen point on the surface, in an environment that is small compared to the sphere's radius. The same applies for inertial frames in a curved spacetime.

>>	When talking about a speed in GR, you have to distinguish between the speed measured in a local inertial frame and the speed measured in a coordinate system.

>	Ofcourse if you want to measure the speed of light you have to quantify the distance and time you use which implies a coordinate system. That is not what I have done. The speed is in counts of one counter.

If we follow your description, the counts of the counter are nothing but a number that is proportional to the coordinate time of a coordinate system you apply. That means that you are using a coordinate system and measure speeds with respect to it.

>>	The description you provide below indicates that you refer to the speed measured in a coordinate system (for more details see below). For the speed of light, this indeed implies that it is not constant, unlike the speed of light measured in a local inertial frame that remains constant in GR.

>	My suggestion is to define your experiment which demonstrates that the speed of light is constant.

Since the term "the speed of light" does not have a clear meaning in GR, this requirement is not well-formulated. Let's assume that your requirement was instead to define an experiment that demonstrates that the speed of light *in a local inertial frame* is constant.

This can e.g. be done by performing three experiments, one at the top of the tower, one at the middle, and one at the bottom. In each experiment, you measure the speed of light in the following way:

Put two clocks that are synchronized to two positions that are close to each other, where close means that the distance between both positions is much smaller than the height of the tower. Let a light ray run from the first clock to the second one. Not the clock time the first clock shows when the light ray starts, and the clock time the second clock shows when the light ray arrives. Divide the distance between the two clocks by the difference between the noted clock times.

The resulting quantity is the speed of light measured in a local inertial frame that is momentarily resting relative to the particular stage of the tower (top, middle, bottom). According to GR, that quantity is the same in all three experiments.

>>	The speed of the ball measured in that coordinate system is not constant, that is correct.

>	In fact you can also make the coordinate system much larger. You can easily include the earth in total.

Different coordinate systems are not constructed by making a given coordinate system larger, but rather by attaching different coordinates to the same spacetime points.

Take the coordinate system that you defined in the description of your experiment. In that coordinate system, top and bottom of the tower have fixed spatial coordinates, i.e. the spatial coordinates are always the same for all values of the coordinate time. In a different coordinate system, the spatial coordinates of these two positions may be changing by time. Or they may be fixed, too, but time translation invariance does not apply, i.e. the time coordinate is different in that way that the trip from top to bottom takes a different coordinate time interval than the back-trip from bottom to top.

More in detail: the coordinate system that you are using can be easily identified with Schwarzschild coordinates. These coordinates are very useful to describe situations in the gravitational field of an ordinary celestial body, like a star or planet. However, they become impractical if you want to describe a black hole, since they have a coordinate singularity at the event horizon. Therefore, one has to apply alternative coordinate systems. Two examples are Eddington-Finkelstein coordinates and free-falling coordinates. In both, top and bottom of your tower have fixed spatial coordinates like in Schwarzschild coordinates, but time coordinates of events are different.

As you can read e.g. here:

47 The two postulates in Special Relativity

Can you give me an idea what is the difference between measuring something in a local inertial frame versus in a coordinate system? I my opinion in practice when you perform an experiment there exists not such a difference.

> >	and if not what is the physical cause.

>

What is in general not constant in GR is the speed of light in a coordinate system. However, this does not have a physical cause, since it is just a property of the chosen coordinate system. At best, one can ask for the physical cause why one cannot apply inertial frames like in SR, but is obliged to come along with more general coordinate systems. The physical cause for that is the curvature of spacetime: in a curved spacetime, inertial frames can only be constructed locally, not globally for the complete spacetime.

48 The two postulates in Special Relativity

Nicolaas Vroom wrote:

>>>>>

What I try to do is answer the question is the speed of light constant.

>>>>	This question is not precise enough.

>>>	I think that my question is rather simple ? Is the speed of light (the speed of the photons) in the universe everywhere the same

>>

Within the framework of a theory in which the term "speed of light" has a clear, unique meaning (e.g. SR), your question might be simple. But in GR, the term "speed of light" does not have such a clear meaning. "Speed of light" can either mean the speed of light measured in a local inertial frame, or the speed of light measured in a coordinate system.

>	Can you give me an idea what is the difference between measuring something in a local inertial frame versus in a coordinate system? I my opinion in practice when you perform an experiment there exists not such a difference.

As far as the procedure is concerned, there is no difference. In both, local inertial frames and general coordinate systems, a speed measurement for some body can be performed by the following procedure:

- Take two points P and Q on the worldline of the body - Determine the coordinates xP^mu = (tP, xP^i), mu=0,1,2,3, i=1,2,3, of point P - Determine the coordinates xQ^mu = (tQ, xQ^i) of point Q - Divide the difference in spatial coordinates by the difference in time coordinate: v^i = (xQ^i - xP^i) / (tQ - tP)

What makes the difference is that the general coordinate system is a general coordinate system whereas the local inertial frame is a local inertial frame. The result in the general coordinate system is arbitrary, since the coordinate system itself is arbitrary. The result in the local inertial frame, however, is meaningful, because the local inertial frame is very special.

For a better understanding of this fact, consider a two-dimensional space. Let's first assume the this space is flat, i.e. not curved, and has a Euklidian metric. In this space, you can construct various coordinate systems. However, there is a very special class of coordinate systems, the Cartesian coordinate systems. In such a Cartesian coordinate system, you have two coordinates (x,y), and the coordinate system has two crucial properties:

- x and y coordinate lines are perpendicular to each other everywhere
- x and y coordinate lines are straight everywhere

You can construct non-Cartesian coordinate systems, that violate at least one of these properties. For example, you can construct an oblique-angled coordinate system. The coordinate lines are still straight then, but not perpendicular to each other. Or you can construct polar coordinates (r,phi). The coordinate lines are perpendicular to each other then, but the phi coordinate lines are not straight.

No let's assume that the two-dimensional space is no longer flat, but is curved. One the first things you will found out is that it is no longer possible to construct a Cartesian coordinate system globally. You can try to construct a coordinate system with straight coordinate lines, but you will soon find out that the coordinate lines are not perpendicular to each other everywhere. Or you can try to construct a coordinate system with coordinate lines that are perpendicular everywhere, but the coordinate lines are not straight everywhere. Only locally, in a region small compared to the curvature radius of the space, a coordinate system can be construct that matches the properties of a Cartesian coordinate system in good approximation.

Now let's return to the four-dimensional spacetime of Relativity. In SR, where the spacetime is flat, things are similar to the flat two-dimensional space discussed above. As you can construct global Cartesian coordinate systems (x,y) in flat two-dimensional space, you can construct inertial frames (t,x,y,z) in flat spacetime. You can imagine inertial frames as generalization of Cartesian coordinate systems: all four coordinate lines, the three spatial ones and the time coordinate line, are straight, and all four coordinate lines are orthogonal to each other ("orthogonal" means something like "perpendicular", but is more general, in mathematics, one uses the term "perpendicular" only for special spaces).

As you can construct non-Cartesian coordinate systems in flat two-dimensional space, you can as well construct general coordinate systems in flat SR spacetime that are no inertial frames, e.g. coordinate systems in which the time coordinate line is not orthogonal to the three spatial coordinate lines. In such a coordinate system, the SR postulate of constant speed of light does NOT apply. Only in inertial frames, that postulate applies generally. Analogously, in flat two-dimensional space, there are rules that apply in Cartesian coordinate systems only, not in general coordinate systems.

Finally, let's come to the curved spacetime of GR. As we cannot construct global Cartesian coordinate systems in curved two-dimensional space, we cannot construct global inertial frames here. Trying to construct a global inertial frame would either result in non-orthogonal coordinate lines or in coordinate lines not being straight.

Take e.g. Schwarzschild coordinates (t,r,phi,theta) that are similar to the coordinates you used in your Pisa Tower thought experiment: the coordinate lines are orthogonal, but not straight. As far as the angle coordinates (phi,theta) are concerned, this is trivial, however, the same is true for time coordinate t and radial coordinate r: a body resting at fixed spatial coordinates, i.e. travelling on a time coordinat line, is not free-falling, implying that the body's wordline is not a geodesic. In turn, this means that the time coordinate line is no geodesic, too, and thefore not straight.

And as in SR, the postulate of constant speed of light applies in inertial frames only, but not in general coordinate systems, the analog is true in GR: the postulate of constant speed of light applies in local inertial frames only, not in general coordinate systems. So, it is even wrong to say the postulate of constant speed of light is less valid in GR than in SR. It is valid in GR as much as in SR: in SR, it applies in inertial frames only, and analogously, in GR, the postulate applies in local inertial frames only.

>>>	and if not what is the physical cause.

>>

What is in general not constant in GR is the speed of light in a coordinate system. However, this does not have a physical cause, since it is just a property of the chosen coordinate system. At best, one can ask for the physical cause why one cannot apply inertial frames like in SR, but is obliged to come along with more general coordinate systems. The physical cause for that is the curvature of spacetime: in a curved spacetime, inertial frames can only be constructed locally, not globally for the complete spacetime.

>	This gives me the impression that you can not use GR to simulate a complete galaxy.

Why this? Do you maybe presume that one needs to use an inertial frame to simulate a galaxy? There is no reason why this should be true - one can use a general coordinate system as well.

>	Using Newton's Law this is difficult in practice because you have to know the initial positions of all objects at the same instance.

The same is true in GR. It's even worse in GR: since the gravitational field has own dynamical degrees of freedom, you need to know the initial configuration of the gravitational field.

>>>>	When talking about a speed in GR, you have to distinguish between the speed measured in a local inertial frame and the speed measured in a coordinate system.

>>>	Ofcourse if you want to measure the speed of light you have to quantify the distance and time you use which implies a coordinate system. That is not what I have done. The speed is in counts of one counter.

>>	If we follow your description, the counts of the counter are nothing but a number that is proportional to the coordinate time of a coordinate system you apply. That means that you are using a coordinate system and measure speeds with respect to it.

>

I performed two experiments: One with a ball and one with light. Both are reflected. In both cases each experiment consists of two parts: full distance and half distance. In each case starting point is the same. In order to "measure" I use a counter, one using a ball and the other one using light. The result in both cases (my prediction) that the speed is not constant.

No, this is not the result. Primarily, the result is that there is a quantity with the dimension of a speed ([length]/[time]) that is not constant. To interpret this result as "the speed" not being constant, you at first would have to apply a theory that allows you for interpreting the measured quantity as "the speed".

Newtonian Gravity as well as a special-relativistic theory of gravity (if there were any) would allow you for interpreting the quantity as the speed in an inertial frame, which can be imagined meaningfully as "the speed". GR, however, does not allow you for that. In GR, the quantity you measured can only be interpreted as the speed in a general coordinate system, which is an arbitrary and therfore not very meaningful quantity, since the choice of the coordinate system is arbitrary.

>>	Since the term "the speed of light" does not have a clear meaning in GR, this requirement is not well-formulated. Let's assume that your requirement was instead to define an experiment that demonstrates that the speed of light *in a local inertial frame* is constant.

>	What I am discussing is the result of experiments. First "we" have to agree about the outcome of the experiment. The second step is to agree which theories predict or describe these experiments.

In your "first step", i.e. without referring to a theory like GR or Newtonian Gravity, all you know about the outcome of the experiment you described is that it is a quantity with the dimension of a speed ([length]/[time]) and that it is not constant. To find out whether and how far you can identify this quantity with a meaningful speed, you need to refer to a theory, i.a. proceed to your "second step".

>>

This can e.g. be done by performing three experiments, one at the top of the tower, one at the middle, and one at the bottom. In each experiment, you measure the speed of light in the following way: Put two clocks that are synchronized to two positions that are close to each other, where close means that the distance between both positions is much smaller than the height of the tower. Let a light ray run from the first clock to the second one. Not the clock time the first clock shows when the light ray starts, and the clock time the second clock shows when the light ray arrives. Divide the distance between the two clocks by the difference between the noted clock times.

>	No this is not the way I propose.

You asked me for an experiment that demonstrates that the speed of light in a local inertial frame is constant. My description answers your question, no matter if it matches what you propose.

>>	Different coordinate systems are not constructed by making a given coordinate system larger, but rather by attaching different coordinates to the same spacetime points.

>	IMO this makes everything very complex.

Maybe. But in GR, you are obliged to take into account that the particular coordinate system you are actually using is not the only one that can be used, what makes the results that you gain in this coordinate system arbitrary if they turn out to be coordinate-dependent.

>>>	It is something more: the speed of light increases when it travels towards the earth.

>>	No. The sentence is not well-formulated, seen from the viewpoint of GR. The speed of light *in Schwarzschild coordinates* increases.

>	The result of the experiment show in both cases that the number of counts in each half distance is different. To be more specific the number of counts in the second part is smaller than the first part. This means that the speed is different. This means that the speed in the second part is larger.

No, is does not mean that. It does not mean anything concerning any speed as long as you do not apply a special coordinate system with the three properties I alreay mentioned:

(1) The top and the ground of the Tower have fixed spatial coordinates

(2) The elapsing coordinate time is proportional to the number of bounces of the bouncing ball between the plates.

(3) Time translation invariance applies: the coordinate time interval that the ball takes for the trip from top to ground is the same as the coordinate time interval the ball takes for the back-trip from ground to top.

The speed *in this special coordinate system* is larger in the second part. But since this coordinate system is arbitrary, this result is arbitrary, too.

>>

See above: Kruskal-Szekeres coordinates. Also see: https://en.wikipedia.org/wiki/Kruskal%E2%80%93Szekeres_coordinates Take the diagram to the right, we the numbers I, II, III and IV in different colors. Imagine the top of the Tower having the hyperbola r=1.6 as wordline, the middle r=1.4 and the bottom r=1.2. Radial light ray follow diagonal lines in the diagram, i.e. their speed (in that coordinate system) is constant.

>	In that article they discuss physical singularity. IMO singualrities only "exist" in mathematical sense.

That does not change in any way the fact that Kruskal-Szekeres coordinates are an example for what you asked me, namely an example for a coordinate system in which the speed of light turns out to be constant for your experiment.

Or did you intend to reject the concept of black holes because of their central singularities and therefore the usage of Kruskal coordinates that can be used to describe the interior of a black hole? Then you would reject GR at all, and then it wouldn't make sense for you to ask whether the speed of light is constant in GR.

>	The important thing is that in order to discuss or perform experiments related to the speed of light you should not use clocks which are affected by your experiment. As such I'am not measuring the speed of light quantitative, but only demonstrate that the speed is not constant.

No, you do not demonstrate that. You demonstrate that the speed of light *in the special coordinate system you are using* is not constant. Seen from GR, this result is arbitrary, though, since your choice of coordinate system is arbitrary.

>	See also paragraph 7.3 in the book Gravitation which discusses an experiment I try to perform a simpler experiment.

You mean figure 7.1B? In this figure, however, a special coordinate system was used, namely Schwarzschild coordinates, or at least a coordinate system in which the two observers have fixed spatial coordinates and time translation invariance applies. The variable speed of light to see in figure 7.1B is valid in that special coordinate system only.

>

Albert Einstein's used thought experiments to "demonstrate" SR and GR (my impression) He used thought experiments to demonstrate or explain that the path of lightrays are bended around mass. IMO that is very tricky. Page 13 in the book Gravitation states: "In each case one is following a natural track through spacetime". That maybe true, but what does it mean?

That means that the worldline of a free-falling body is a geodesic in spacetime. Let a stone fall from your hand. The stone falls towards the ground and touches the ground after some seconds. The segment of the stone's wordline between your hand and the ground is a geodesic. Unlike your own worldline that is no geodesic since you are not free falling.

49 The two postulates in Special Relativity

Thanks.

>	Nicolaas Vroom wrote:

> >	Can you give me an idea what is the difference between measuring something in a local inertial frame versus in a coordinate system? I my opinion in practice when you perform an experiment there exists not such a difference.

>	As far as the procedure is concerned, there is no difference. In both, local inertial frames and general coordinate systems, a speed measurement for some body can be performed by the following procedure: - Take two points P and Q on the worldline of the body

And how do you do that in practice? The same for next sentences.

>	The result in the general coordinate system is arbitrary, since the coordinate system itself is arbitrary.

That means should not be used ?

>	The result in the local inertial frame, however, is meaningful, because the local inertial frame is very special.

An coordinate system should be unambigeous. The same for people overhere as overthere. In a different galaxy.

>	For a better understanding of this fact, consider a two-dimensional space.

Two dimensional SPACE does not exist. Sorry I'm lost.

Skip.

>	As you can construct non-Cartesian coordinate systems in flat two-dimensional space

Sorry I'm lost.

>	Take e.g. Schwarzschild coordinates (t,r,phi,theta) that are similar to the coordinates you used in your Pisa Tower thought experiment: the coordinate lines are orthogonal, but not straight.

The Tower of Pisa experiment is not a thought experiment. It is a description of an actual experiment. It is something like: You put a camera at a large distance from the tower. You drop an apple from the tower. You take a picture with the camera each second. When you compare the pictures you will see that the speed of the apple is not constant but increases.

The problem with this experiment is that you need a clock.

In the experiment I propose there is no clock. In the experiment I use a bouncing ball and the clock becomes a counter which is also a bouncing ball. Using that scenenario and performing the experiment from two different hights, the result is that the speed of the ball is not constant.

In stead of a ball in principle I can also use a light signal. Of course to perform this experiment from the Tower of Pisa is not realistic. However what I expect that the result of the experiment is the same: that the speed of light is not constant. The question of course is if this conclusion is correct.

>

As far as the angle coordinates (phi,theta) are concerned, this is trivial, however, the same is true for time coordinate t and radial coordinate r: a body resting at fixed spatial coordinates, i.e. travelling on a time coordinat line, is not free-falling, implying that the body's wordline is not a geodesic. In turn, this means that the time coordinate line is no geodesic, too, and thefore not straight. And as in SR, the postulate of constant speed of light applies in inertial frames only, but not in general coordinate systems, the analog is true in GR: the postulate of constant speed of light applies in local inertial frames only, not in general coordinate systems. So, it is even wrong to say the postulate of constant speed of light is less valid in GR than in SR. It is valid in GR as much as in SR: in SR, it applies in inertial frames only, and analogously, in GR, the postulate applies in local inertial frames only.

Do I really need of all this to answer my question?

> >	This gives me the impression that you can not use GR to simulate a complete galaxy.

>	Why this? Do you maybe presume that one needs to use an inertial frame to simulate a galaxy? There is no reason why this should be true - one can use a general coordinate system as well.

See next.

> >	Using Newton's Law this is difficult in practice because you have to know the initial positions of all objects at the same instance.

>	The same is true in GR. It's even worse in GR: since the gravitational field has own dynamical degrees of freedom, you need to know the initial configuration of the gravitational field.

That means you agree with my previous remark: GR is "tricky"

> >

I performed two experiments: One with a ball and one with light. Both are reflected. In both cases each experiment consists of two parts: full distance and half distance. In each case starting point is the same. In order to "measure" I use a counter, one using a ball and the other one using light. The result in both cases (my prediction) that the speed is not constant.

>

No, this is not the result. Primarily, the result is that there is a quantity with the dimension of a speed ([length]/[time]) that is not constant. To interpret this result as "the speed" not being constant, you at first would have to apply a theory that allows you for interpreting the measured quantity as "the speed".

The first conclusion is that the number of counts to travel (fall) over the two identical distances (first part and second part) is not identical. This is "translated" that the speed is not constant and that there is acceleration involved.

>

Newtonian Gravity as well as a special-relativistic theory of gravity (if there were any) would allow you for interpreting the quantity as the speed in an inertial frame, which can be imagined meaningfully as "the speed". GR, however, does not allow you for that. In GR, the quantity you measured can only be interpreted as the speed in a general coordinate system, which is an arbitrary and therfore not very meaningful quantity, since the choice of the coordinate system is arbitrary.

The first question to answer if you agree with the outcome of the two experiments. The next question is if the outcome is in agreement with Newton's Law. The same for GR.

> >	The result of the experiment show in both cases that the number of counts in each half distance is different. To be more specific the number of counts in the second part is smaller than the first part. This means that the speed is different. This means that the speed in the second part is larger.

>

No, is does not mean that. It does not mean anything concerning any speed as long as you do not apply a special coordinate system with the three properties I alreay mentioned: (1) The top and the ground of the Tower have fixed spatial coordinates (2) The elapsing coordinate time is proportional to the number of bounces of the bouncing ball between the plates. (3) Time translation invariance applies: the coordinate time interval that the ball takes for the trip from top to ground is the same as the coordinate time interval the ball takes for the back-trip from ground to top. The speed *in this special coordinate system* is larger in the second part. But since this coordinate system is arbitrary, this result is arbitrary, too.

I would agree with you if you call this a local experiment, in the sense that the speed of the ball in this local experiment is not constant. The same should than also be true for the speed of light.

But if you agree that the speed of light is not constant in this local experiment why should than this also not to be true in a much broader sense?

Why should the speed of light be physical constant if you transmit a light signal from the earth to the moon?

> >	Page 13 in the book Gravitation states: "In each case one is following a natural track through spacetime". That maybe true, but what does it mean?

>	That means that the worldline of a free-falling body is a geodesic in spacetime.

Is that a natural track through spacetime?

GR is "tricky"

Nicolaas Vroom

50 The two postulates in Special Relativity

>>>	Can you give me an idea what is the difference between measuring something in a local inertial frame versus in a coordinate system? I my opinion in practice when you perform an experiment there exists not such a difference.

>>	As far as the procedure is concerned, there is no difference. In both, local inertial frames and general coordinate systems, a speed measurement for some body can be performed by the following procedure: - Take two points P and Q on the worldline of the body

>	And how do you do that in practice?

Attach two clocks to two different spatial positions with known spatial coordinates. Ensure that the two clocks are synchronous with the coordinate time. Note the displayed clock times at which the body passes each of the two clocks.

>>	The result in the general coordinate system is arbitrary, since the coordinate system itself is arbitrary.

>	That means should not be used ?

You can use it if you want, but you have to be aware that it is arbitrary.

>>	The result in the local inertial frame, however, is meaningful, because the local inertial frame is very special.

>	An coordinate system should be unambigeous.

A coordinate system is unambigeous, or unique, in that sense that every spacetime point is assigned to a unique set of coordinates. A general coordinate system is not unambigeous, though, in that sense that the choice of the coordinate system is arbitrary, i.e. that one could choose a different coordinate system as well. An inertial frame (in Newtonian Mechanics or SR) is more unambigeous in this sense: if you choose an observer, e.g. yourself, then you already fix the inertial frame to be used.

>>	For a better understanding of this fact, consider a two-dimensional space.

>	Two dimensional SPACE does not exist. Sorry I'm lost.

The two-dimensional space was just to make the understanding easier. We can of course do all consideration in four-dimensional spacetime if you prefer that. It's just a little more complicated.

>>	Take e.g. Schwarzschild coordinates (t,r,phi,theta) that are similar to the coordinates you used in your Pisa Tower thought experiment: the coordinate lines are orthogonal, but not straight.

>

The Tower of Pisa experiment is not a thought experiment. It is a description of an actual experiment. It is something like: You put a camera at a large distance from the tower. You drop an apple from the tower. You take a picture with the camera each second. When you compare the pictures you will see that the speed of the apple is not constant but increases.

No, I don't see that. And you don't see that, too. You may conclude that from what you see, but to draw this conclusion, you have to make some assumptions. Those assumptions contain the usage of a coordinate system, and that quantities measured with respect to this coordinate systems are in some way meaningful.

More in detail:
- Primarily, you have a collection of pictures. You then emumerate the pictures (1,2,3,...).
- Then you assume that you can apply a coordinate system to a spacetime region that contains the wordline of the apple, the worldlines of the light signals that travel from the apple to the camera, and the wordline of the camera itself.
- Then you assume that the coordinate time interval for a light signal to travel from the apple to the camera is the same for all light signals, so that you can identify the coordinate time interval between two light signals reaching the camera with the interval between two light signals emitted by the apple.
- Then you identify the number of each picture with the coordinate time at which the particular light signal reached the camera.
- Then you identify the apple's position on the particular picture with the spatial coordinates of the apple at the particular coordinate time minus the coordinate time the light signal took from the apple to the camera.

After doing this, you can draw the conclusion that the speed of the apple in the coordinate system you have chosen increases. Then you assume that this coordinate system is very special, so that you can interpret the speed of the apple in this coordinate system as "the" speed of the apple.

>	The problem with this experiment is that you need a clock. In the experiment I propose there is no clock. In the experiment I use a bouncing ball and the clock becomes a counter which is also a bouncing ball.

In the one experiment, the role of the clock is undertaken by the bouncing ball, in the other experiment, the role of the clock is undertaken by the enumeration of the picture photographed by the camera. I don't see a great difference. In both cases, you use a number (count of ball bounces, index of picture) as a replacement for the coordinate time.

>	Using that scenenario and performing the experiment from two different hights, the result is that the speed of the ball is not constant.

No, the result is not that the speed of the ball is not constant. The result is that in the one case, the round trip of the ball takes more bounces than in the other case.

To draw any conclusions from this result that concern the speed of the ball, you again have to construct a coordinate system. Then you have the speed of the ball in the particular coordinate system. To interpret this speed as "the" speed of the ball, you again have to assume that this coordinate system is specially meaningful.

>

In stead of a ball in principle I can also use a light signal. Of course to perform this experiment from the Tower of Pisa is not realistic. However what I expect that the result of the experiment is the same: that the speed of light is not constant. The question of course is if this conclusion is correct.

The answer is: no. The conclusion would be correct if the assumptions you make would be correct. In Newtonian Gravity, they would: the coordinate system you are using could be considered as an inertial frame (of an observer resting with respect to the Tower, or of the Tower itself). In GR, however, they do not: the coordinate system you are using for your conclusion is arbitrary there.

>>

As far as the angle coordinates (phi,theta) are concerned, this is trivial, however, the same is true for time coordinate t and radial coordinate r: a body resting at fixed spatial coordinates, i.e. travelling on a time coordinat line, is not free-falling, implying that the body's wordline is not a geodesic. In turn, this means that the time coordinate line is no geodesic, too, and thefore not straight. And as in SR, the postulate of constant speed of light applies in inertial frames only, but not in general coordinate systems, the analog is true in GR: the postulate of constant speed of light applies in local inertial frames only, not in general coordinate systems. So, it is even wrong to say the postulate of constant speed of light is less valid in GR than in SR. It is valid in GR as much as in SR: in SR, it applies in inertial frames only, and analogously, in GR, the postulate applies in local inertial frames only.

>	Do I really need of all this to answer my question?

To answer your question whether the SR postulate of constant light speed applies in GR, yes.

>>>	This gives me the impression that you can not use GR to simulate a complete galaxy.

>>	Why this? Do you maybe presume that one needs to use an inertial frame to simulate a galaxy? There is no reason why this should be true - one can use a general coordinate system as well.

>

See next.

>>>	Using Newton's Law this is difficult in practice because you have to know the initial positions of all objects at the same instance.

>>	The same is true in GR. It's even worse in GR: since the gravitational field has own dynamical degrees of freedom, you need to know the initial configuration of the gravitational field.

>	That means you agree with my previous remark: GR is "tricky"

Your previous remark was: "See next". And now, when I see next, you suggest me your previous remark again?

Or do you want to say that you cannot GR to simulate a galaxy because a simulation based on GR would be more complicated than one base on Newtonian Gravity? This, however, has little to do with inertial frames not being applicable in GR.

>>>

I performed two experiments: One with a ball and one with light. Both are reflected. In both cases each experiment consists of two parts: full distance and half distance. In each case starting point is the same. In order to "measure" I use a counter, one using a ball and the other one using light. The result in both cases (my prediction) that the speed is not constant.

>>

No, this is not the result. Primarily, the result is that there is a quantity with the dimension of a speed ([length]/[time]) that is not constant. To interpret this result as "the speed" not being constant, you at first would have to apply a theory that allows you for interpreting the measured quantity as "the speed".

>	The first conclusion is that the number of counts to travel (fall) over the two identical distances (first part and second part) is not identical.

For this conclusion, you already need to apply a coordinate system that tells you that the spatial distances of the two parts are identical. This property of the two distances is coordinate-dependent.

>	This is "translated" that the speed is not constant and that there is acceleration involved.

For this translation, you need to apply a theory that tells you whether the coordinate system you are using is specially meaningful (e.g. an inertial frame) and therefore the speed in this coordinate system considerable as "the" speed.

>>

Newtonian Gravity as well as a special-relativistic theory of gravity (if there were any) would allow you for interpreting the quantity as the speed in an inertial frame, which can be imagined meaningfully as "the speed". GR, however, does not allow you for that. In GR, the quantity you measured can only be interpreted as the speed in a general coordinate system, which is an arbitrary and therfore not very meaningful quantity, since the choice of the coordinate system is arbitrary.

>	The first question to answer if you agree with the outcome of the two experiments.

No, I don't. What you call the outcome of the experiments is not the outcome of the experiments, but a conclusion from the outcome that is based on wrong assumptions.

>	The next question is if the outcome is in agreement with Newton's Law. The same for GR.

To gain what you call the outcome of the experiments, but which is rather a conclusion from the outcome and not the outcome itself, you apply assumptions that are in contradiction to GR (namely that the coordinate system you are using would be specially meaningful). So, you already presume that GR is wrong. To ask whether results are in agreement with GR does not make sense any more then. - show quoted text - No, I do not call your experiment a local experiment, in that sense that this experiment would be local whereas an experiment that involves a broader spatial region that include Earth and Moon would not be local. Your experiment as well as a comparable experiment that involve Earth and Moon are not local, in that sense that they both involve spacetime regions that are not sufficiently limited to apply the concept of an inertial frame. A local experiment would be one that involves a spacetime region that is sufficiently limited, e.g. one that involves a small region around the top (or the bottom) of the Towor.

In other words: the postulate of constant speed of light does not apply in a spatially *broader* sense in GR, but in a spatially *narrower" sense, namely in that sense that the speed of light is constant in a local inertial frame. The region where a local inertial frame can be applied is not broader, it is narrower.

One could explain this quite easy using a two-dimensional space, but since you reject such a consideration, you'll have to come along with the more complicated consideration of four-dimensional spacetime.

>>>	Page 13 in the book Gravitation states: "In each case one is following a natural track through spacetime". That maybe true, but what does it mean?

>>	That means that the worldline of a free-falling body is a geodesic in spacetime.

>	Is that a natural track through spacetime?

Yes. Like moving in a straight line with constant speed is the natural track in a flat, uncurved spacetime.

Remember Newton's first law: a body remains in the state of rest or uniform motion unless it is enforced to change its state by acting forces. In a flat spacetime, this means that a force-free body moves along a straight worldline. In a curved spacetime, it means that a force-free body moves along a geodesic worldline.

Again: this could be very easiely illustrated in a two-dimensional space, but you reject that.

51 The two postulates in Special Relativity

>

The Tower of Pisa experiment is not a thought experiment. It is a description of an actual experiment. It is something like: You put a camera at a large distance from the tower. You drop an apple from the tower. You take a picture with the camera each second. When you compare the pictures you will see that the speed of the apple is not constant but increases. The problem with this experiment is that you need a clock. In the experiment I propose there is no clock. In the experiment I use a bouncing ball and the clock becomes a counter which is also a bouncing ball.

A remark to this experiment: the bouncing ball that is used as clock bounces do to gravitational effects. So, by definition, this experiment necessarily involves a spacetime region that is not sufficiently limited to apply SR. Therefore, an experiment of this kind cannot be performed within a local inertial frame. In other words: to perform measurements with respect to a local inertial frame (for which you asked me), this type of experiment is impractical.

52 The two postulates in Special Relativity

53 The two postulates in Special Relativity

I think it is something more. See below.

> >	In the experiment I propose there is no clock. In the experiment I use a bouncing ball and the clock becomes a counter which is also a bouncing ball.

>

A 'clock' in the sense of a time-measuring device is any device that allows to count well-defined time intervals. It is for convenience that usually these time intervalls are of identical length, i.e. the device counts the cycles of a periodic system like the oscillations between two electronic states of an atom or the swinging of a pendulum. So your bouncing ball *is* a clock. A lousy one, but a clock nevertheless.

What I do is to compare the outcome of two identical physical experiments. In the first experiment I use two balls. Ball #1 bounces between two plates and services as an oscillator. Ball #2 bounces only once in two different cases. In case 1 the ball starts at the top, bounces at the bottom. The experiment finishes when the ball is back at its highest position. In case 2 the ball bounces back halfway between top and bottom. The object of the experiment is to count the number of bounces/counts of the oscillator. The results of the experiment show (as an example) that the number of counts when you drop ball #2 in case 1 is 17 and 10 in case 2 (first half) The strategy of the experiment is that the oscillator does not move! The first question is if you agree that the number of counts from in-between to the bottom is 7? (second half) The second question is if you agree that the speed is increasing when the ball drops from top to in-between to the bottom? Speed defined as distance divided by counts.

The whole purpose of this experiment to perform the same experiments but now not with balls but with two light signals. The oscillator in this case becomes light signal #1. Again also in this case the first question is if you agree that there is a difference in counts in the first half compared with the second half. The second question is if you agree that when the counts are different that the speed of light is not constant but has increased,

The whole idea behind each experiment is to use in each case only one physical concept. In the first experiment this is a falling ball #2 which is influenced by the gravitational field of the earth. In the second experiment this is a lightsignal #2 which is also supposed to be influenced by the gravitational field of the earth.

IMO this is identical from a physical point of view if you shoot a bullet horizontal or if you shine a lightsignal horizontal. Both the path of the bullet and of the lightsignal are bended.

To call each of the two oscillators ie ball #1 and light signal #1, a clock is only in the name. The issue is that both oscillators are physical processes and are influenced by the same physical phenomena as their counter parts.

To perform experiment #1 with the bouncing balls is rather simple The biggest problem that the bouncing should be perfect. This means the two distances (down and up) should be the same.

Experiment #2 is extremely difficult and IMO is much more like a thought experiment, but requires an honnest investigation. The experiment becomes more tricky when the movement of the earth around the Sun, and more global in our Galaxy is included. Still the two lightsignals behave the same. Experiment #2 is different from the Pound and Rebka experiment and from the concept of Gravitational redshift.

Nicolaas Vroom

54 The two postulates in Special Relativity

>>

And as in SR, the postulate of constant speed of light applies in inertial frames only, but not in general coordinate systems, the analog is true in GR: the postulate of constant speed of light applies in local inertial frames only, not in general coordinate systems. So, it is even wrong to say the postulate of constant speed of light is less valid in GR than in SR. It is valid in GR as much as in SR: in SR, it applies in inertial frames only, and analogously, in GR, the postulate applies in local inertial frames only.

>	Do I really need of all this to answer my question?

A remark: maybe you are not really interested in the question whether the SR postulate of constant speed of light applies in GR, but rather in the question whether you can consider the speed of light as being variable in the coordinate system you are using for a galaxy simulation? That is question is very much simpler, and very easy to answer: yes, you can do that.

55 The two postulates in Special Relativity

I would add that Einstein himself gave serious consideration to the consistency of the speed of light being relative not absolute. That is to say the speed of light is constant for a given frame of reference. The speed of light being constant to all frames of reference is not the same as saying the speed of light is constant in a absolute sense. If someone very close to a black hole and time dilated to the point that their voice is notably 1 octave lower do you trust their judgement when they tell they measure the speed of light to be c ? With a clock running at half speed I would not trust that voice in the dark. More likely the speed is 1/2 c but they measure it to be c with a clock that is ticking at 1/2 its normal rate.

[[Mod. note -- Many of the questions you pose are (in their present form) insufficiently precise to be answered.

For example, "If someone very close to a black hole and time dilated to the point that their voice is notably 1 octave lower" doesn't specify (the spacetime worldline of) the observer who measures that time dialation. And simply saying "1 octave lower" leaves unanswered the question of "1 octave lower than what?". (The standard answer to this latter question is, "with respect to a recording of the now-close-to-the-BH speaker, made when she was far from the BH, and coincident with and at rest with respect to the recorder". In other words, adiabatic clock transport, treating the speaker's vocal cords as a clock. Is this what you mean?)

And when that observer "measure[s] the speed of light", we need to know just how that measurement is made. For example, it might be a local measurement made in a free-falling local Lorenz frame... [n.b. "local" here means "small enough that we can approximate spacetime as flat within this region"] ... but then within that frame special relativity applies, and the answer of that measurement MUST be 299792458 m/s. So I guess you mean some other sort of measurement... which needs to be specified. -- jt]]

56 The two postulates in Special Relativity

>

I would add that Einstein himself gave serious consideration to the consistency of the speed of light being relative not absolute. That is to say the speed of light is constant for a given frame of reference. The speed of light being constant to all frames of reference is not the same as saying the speed of light is constant in a absolute sense. If someone very close to a black hole and time dilated to the point that their voice is notably 1 octave lower do you trust their judgement when they tell they measure the speed of light to be c ? With a clock running at half speed I would not trust that voice in the dark. More likely the speed is 1/2 c

In GR, you have to distinguish between local inertial frames and general coordinate systems, like e.g. Schwarzschild coordinates in Schwarzschild solution. Considered in Schwarzschild coordinates, the clock of the observer near the black hole is running at half speed (compared to Schwarzschild coordinate time), and the speed of light is 1/2 c. However, choosing Schwarzschild coordinates is an arbitrary choice, one could as well choose Eddington-Finkelstein coordinates, free-falling coordinates or Kruskal coordinates. In each of those coordinate systems, you'll gather different results for the clock running speed and for the speed of light. Therefore, the speed of light measured with respect to a general coordinate system is arbitrary, and due to that, little meaningful.

The only meaningful speed measurements in GR are those that are performed with respect to a local inertial frame. According to GR, the observer near the black hole will measure c for the speed of light, and since he performed his measurement with respect to a local inertial frame, one can trust his result.

57 The two postulates in Special Relativity

Good point. I made the measurement leaving earth with a calibrated 1 meter stick and an atomic clock. I reported to you from near a black hole that the speed of light is c as I measure it with my 1 meter stick and atomic clock. The gravitational time dilation from this location near a black hole caused my atomic clock to run at 1/2 its normal speed compared with earth. When talking to you on my intergalactic cell phone you noted my voice was one octave lower than normal suggesting my clock has been compromised running at only 1/2 its normal rate caused by gravitational time dilation. With these conditions I put the question to you on earth. Is the speed of light in my location near a black hole , c or 1/2 c ? Keep in mind I should have said 2 c not c if the speed of light is absolute with a time dilated clock but I do not want to bias your thoughts. In your mind in the broader sense is the consistency of the speed of light absolute or relative in the big picture. It is all relative so you may use the earth as the as an arbitrary reference point to make this judgement and assume idea conditions of the earth not changing.

58 The two postulates in Special Relativity

>

Good point. I made the measurement leaving earth with a calibrated 1 meter stick and an atomic clock. I reported to you from near a black hole that the speed of light is c as I measure it with my 1 meter stick and atomic clock. The gravitational time dilation from this location near a black hole caused my atomic clock to run at 1/2 its normal speed compared with earth. When talking to you on my intergalactic cell phone you noted my voice was one octave lower than normal suggesting my clock has been compromised running at only 1/2 its normal rate caused by gravitational time dilation.

That I noted your voice one octave lower is primarily due to the gravitational redshift which the electromagnetic waves emitted by your cell phone undergo on their towards me.

To conclude that this gravitational redshift is caused by gravitational time dilation, you need to apply Schwarzschild coordinates, in which we both have fixes spatial positions (wordlines with r = const, where r is the Schwarzschild radial coordinate) and time translation invariance applies, so that the waves emitted by your cell phone propagate on wordlines that are equivalent, except a coordinate time shift.

However, instead of Schwarzschild coordinates, we can as well apply a coordinate system with a time coordinate tau that relates to Schwazschild coordinates by

tau = (1 - rs/r) t

so that

d(tau) = (1 - rs/r) dt - rs t dr / r^2

On our worldlines, r = const applies so that dr = 0, resulting in

d(tau) = (1 - rs/r) dt

In this coordinate system, there is no gravitational time dilation. Of course, we again observe the gravitational redhift, since it is coordinate-independent, but in this coordinate system, we do not conclude that is is caused by gravitational time dilation, but rather by differences in propagation of subsequently emitted waves: the later a wave is emitted from your cell phone, the longer is the coordinate time interval the wave takes to reach me (there is no time-translation invariance like in Schwarzschild coordinates).

Or let use apply Kruskal coordinates. Then our is result is that we both are moving (our worldlines are hyperbolas in a Kruskal spacetime diagram), and that the gravitational redshift is mainly due to our different movements.

So, we see: the gravitational redshift is coordinate-independent, but its relation to a gravitational time dilation depends on the applied coordinate system.

Due to the general covariance of GR, all three mentioned coordinate systems are in the same way valid, there is none of them more valid than the other ones. Therefore, the result you gather in Schwarzschild coordinates, namely that the gravitational redshift is caused by a gravitational time dilation only, is arbitrary and therefore little meaningful.

The only coordinate systems in GR that are valid in a greater measure are the local inertial frames, and in those, there is neither a gravitational time dilation nor a gravitational redshift, since they are limited to spacetime regions that too small to recognize gravitational effects.

To get a better impression of different coordinate systems for Scharzschild geometry, have a look on the spacetime diagrams on this page:

59 The two postulates in Special Relativity

Really now! If the experiment were actually performed, there would be only ONE result. This "arbitrariness" makes no sense and sounds like obfuscation to me.

Gary

60 The two postulates in Special Relativity

Nice link , I bookmarked it. And thanks for taking the time for a long response. I can see I have failed to set the conditions of the test in a clear way. Perhaps I should state the condition instead of creating the condition . I will state the conditions.

A] Alice is on earth with a 1 meter stick and a atomic clock to measure the speed of light.

B] Bob is gravity time dilated 50 percent. His clock is ticking at 1/2 its rate relative to Alice's clock.

C] There is no Doppler effect or SR effects. Assume ideal conditions of no movement between Alice and Bob.

If Bob measures the speed of light to be 2c then we can assume that the speed of light is absolute at c and it is his slow clock that is causing him to think it is 2c. If Bob measures the speed of light to be c then we can assume the speed of light will always measure c and is not absolute but relative to the observer. This would require the speed of light to be variable in the larger picture to guarantee that all observers measure the speed of light to be c. It should be noted that Alice on earth is the observer. If Bob is the observer then Alice should say the measured speed of light is 1/2 c caused by her fast clock relative to Bob if light speed is absolute. If light speed is relative then Alice will measure it to be c and therefore speed of light is variable in the larger picture , god's view.

The Schwarzschild model requires a more complicated setup of a copper wire link between Alice and Bob to demonstrate causality concerns with multiple time lines. For this reason I have set it aside for now in the interest of clarity of thought. I would enjoy going there but for now it will confuse the issue at hand with too many variables on the table.

To return to the burning question. In your mind is the speed of light absolute or variable. It is a given light will always measure c but is it constant in the larger picture of god looking down at Alice and Bob from a great distance?

[[Mod. note -- Once again, many of these questions are insufficiently precise to have well-defined answers.

For example, you write "If Bob measures the speed of light to be 2c". But any (correct) *local* measurement [i.e., a measurement made entirely within a (freely-falling) local inertial reference frame] of the speed of light gives c (independendent of the details of how the measurement is made). So your description must refer to some sort of *non-local* measurement. You need to specificy precisely how that measurement is made.

-- jt]]

61 The two postulates in Special Relativity

Gary Harnagel replied:

>	Really now! If the experiment were actually performed, there would be only ONE result. This "arbitrariness" makes no sense and sounds like obfuscation to me.

The problem is that you (Gary harnagel) haven't specified the experiment in sufficient detail. There are many possible experiments which would be consistent with your description, and (in general) these experiments will give different answers.

For example, here are four possible experiments consisten with your description: (a) The far-away observer is a rest with respect to the black hole (BH). She drops a clock into the BH; that clock sends out a sequence of radio-wave "ticks" at uniform time intervals as measured by the falling clock; each "tick" also encodes the falling clock's current position (areal radial coordinate) with respect to the BH. The far-away observer measures the arrival frequency of the radio-wave "ticks" as a function of the encoded position. (b) Same thing as (a), but change "areal radial coordinate" to "isotropic radial coordinate". (c) The far-away observer is a rest with respect to the BH. She releases a clock which is just like the clock in (a), but is also equipped with a rocket engine. The rocket-engine-clock is programmed to fly down to a specific position (areal radial coordinate) with respect to the BH, hold itself at that position for a while, then fly to a new position (areal radial coordinate) with respect to the BH, hold itself at that position for a while, then fly to another position, etc etc. The far-away observer measures the arrival frequency of the radio-wave "ticks" at each rocket-engine-clock position, as a function of the encoded radius. (d) Same thing as (c), but change "areal radial coordinate" to "tortise radial coordinate". [there are many other possibilities as well]

As I suggested above, experiments (a), (b), (c), and (d) will (in general) give four different answers to the question "at what rate do the clock-near-the-BH ticks arrive at the far-from-the-BH clock when the clock-near-the-BH is at the position r=3M?". You haven't specified which of these is the experiment which you're asking about, and nature doesn't single out any of these as "the natural or obvious way to do this experiment".

The fact that there are these multiple possibilities, all of them equally physically meaningful and all of them plausible operational definitions of "the gravitational redshift at a distance r=3M from the BH", is a consequence of the arbitrariness which Gregor Scholten was referring to.

-- -- "Jonathan Thornburg [remove -animal to reply]" Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA "There was of course no way of knowing whether you were being watched at any given moment. How often, or on what system, the Thought Police plugged in on any individual wire was guesswork. It was even conceivable that they watched everybody all the time." -- George Orwell, "1984"

62 The two postulates in Special Relativity

>

Nice link , I bookmarked it. And thanks for taking the time for a long response. I can see I have failed to set the conditions of the test in a clear way. Perhaps I should state the condition instead of creating the condition . I will state the conditions. A] Alice is on earth with a 1 meter stick and a atomic clock to measure the speed of light. B] Bob is gravity time dilated 50 percent. His clock is ticking at 1/2 its rate relative to Alice's clock.

According to GR, this statement is ambigous. You missed indicating what coordinate system you applied to compare Bob's clock to Alice's clock.

In SR, you would be finished by just stating "relative to Alice's clock" because that would define a frame of reference. In GR, however, you are not finished, you in addition need to indicate what coordinate system you are applying.

Let's assume you are applying Schwarzschild coordinates.

>

C] There is no Doppler effect or SR effects. Assume ideal conditions of no movement between Alice and Bob. If Bob measures the speed of light to be 2c then we can assume that the speed of light is absolute at c and it is his slow clock that is causing him to think it is 2c. If Bob measures the speed of light to be c then we can assume the speed of light will always measure c and is not absolute but relative to the observer.

According to GR, this is another ambigous statement. When talking about Bob measuring a speed, you have to indicate with respect to what coordinate systems he is performing his measurement.

Let's assume he measures the speed of light to a local inertial frame. If he then measures the speed of light to be 2c, he has falsified GR and we can immediately skip this discussion about statements of GR. If he, instead, measures to speed of light to be c, we can assume that GR remains applicable, and that with respect to Schwarzschild coordinates, the speed of light at Bob's position is c/2.

What we cannot assume then, though, is that the speed of light would be relative to the observer. Because being relative to an observer is a concept from SR that implies that choosing an observer defines a frame of reference. In GR, there is no concept of frames of reference - except in SR limit - and therefore no concept of being relative to an observer.

>	This would require the speed of light to be variable in the larger picture to guarantee that all observers measure the speed of light to be c.

Assumed, you mean Schwarzschild coordinates when saying "in the larger picture", you are right. This "larger picture", however, is arbitrary, since one could as well apply different coordinates that yield a different running speed ratio between Bob's clock and Alice's clock than 1/2.

>	It should be noted that Alice on earth is the observer. If Bob is the observer then Alice should say the measured speed of light is 1/2 c caused by her fast clock relative to Bob if light speed is absolute.

In GR, it does not make sense to say that Bob is "the" observer or that Alice is "the" observer. Defining someone as "the" observer makes sense in SR only, where one can apply the concept of a frame of reference. In SR, one could assign a frame of reference to Alice and one to Bob, and by choosing one of both frames, one would choose either Alice or Bob as "the" observer. In GR, however, there's no frame of reference. One can consider each of both, Alice and Bob, as "an" observer, but none of them as "the" observer.

>	If light speed is relative

When talking about "relative" or "absolute", you seem to SR's concept of relative and absolute: relative means "depending on the frame of reference" and absolute means "not depending on the frame of reference". In GR, this concept is obsolete, since there's no frame of reference.

>	To return to the burning question. In your mind is the speed of light absolute or variable. It is a given light will always measure c but is it constant in the larger picture of god looking down at Alice and Bob from a great distance?

In my mind, your question is based on assumptions that aren't valid in GR. When asking for being absolute or relative/variable, you seem to refer to SR concepts that are obsolete in GR. Therefore, your question cannot be answered meaningfully.

63 The two postulates in Special Relativity

>>	So, by choosing the far away observer as "reference point", you do not fix the clock near the black hole to run with half speed. You need to choose to apply Schwarzschild coordinates in addition. And that choice is arbitrary.

>	Really now! If the experiment were actually performed, there would be only ONE result.

This one result, however, would be a result for gravitational redshift, not for gravitational time dilation. You CAN, if you want, apply Schwarzschild coordinates, and based on that, interpret the result as caused by gravitational time dilation. This interpretation, however, is arbitrary, since applying Schwarzschild coordinates is arbitrary.

Or you can modifiy the experiment's prescription by explicitly specifying that Schwarzschild coordinates are to be applied and that observed redshift is to be interpreted as time dilation with respect to Schwarzschild coordinates. This, however, would make the experiment's prescription arbitrary, since one could as well define a prescription specifying the application of a different coordinate system.

64 The two postulates in Special Relativity

>>	Really now! If the experiment were actually performed, there would be only ONE result. This "arbitrariness" makes no sense and sounds like obfuscation to me.

>

The problem is that you (Gary harnagel) haven't specified the experiment in sufficient detail. There are many possible experiments which would be consistent with your description, and (in general) these experiments will give different answers. For example, here are four possible experiments consisten with your description: (a) The far-away observer is a rest with respect to the black hole (BH).

This specification, however, isn't sufficiently detailed, too. "At rest with respect to the blach hole" does not have a disctinct meaning in GR, since there is no such thing like a frame of reference of the black hole. To specify the observer as being resting, you need to specify a coordinate system with respect to which the observer is resting. If you want, you can take Schwarzschild coordinates, like John and Gary obviously do.

>

She drops a clock into the BH; that clock sends out a sequence of radio-wave "ticks" at uniform time intervals as measured by the falling clock; each "tick" also encodes the falling clock's current position (areal radial coordinate) with respect to the BH. The far-away observer measures the arrival frequency of the radio-wave "ticks" as a function of the encoded position. (b) Same thing as (a), but change "areal radial coordinate" to "isotropic radial coordinate". (c) The far-away observer is a rest with respect to the BH. She releases a clock which is just like the clock in (a), but is also equipped with a rocket engine. The rocket-engine-clock is programmed to fly down to a specific position (areal radial coordinate) with respect to the BH, hold itself at that position for a while

As far as John specified the experiment, thise case (c) is presumed, with "holding itself at that position" meaning holding at a fixed Schwarzschild radial coordinate r = const.

What makes the experiment's outcome for gravitational time dilation arbitrary is NOT that there also the cases (a), (b) and (d), but rather that choosing Schwarzschild coordinates for conclusions about the apperaring time dilation is arbitrary.

>	As I suggested above, experiments (a), (b), (c), and (d) will (in general) give four different answers to the question "at what rate do the clock-near-the-BH ticks arrive at the far-from-the-BH clock when the clock-near-the-BH is at the position r=3M?".

No, they will give many more different answers, since for each of them, one can apply different coordinate systems. Only for the gravitational redshift, they yield only four different results.

>	You haven't specified which of these is the experiment which you're asking about

But John had done this before.

[[Mod. note -- I agree with all of Gregor Scholten's points. Mea culpa for trying to post about GR when tired and in a rush. :) -- jt]]

65 The two postulates in Special Relativity

[--]

>	To return to the burning question. In your mind is the speed of light absolute or variable. It is a given light will always measure c but is it constant in the larger picture of god looking down at Alice and Bob from a great distance?

I would argue that there are two reasonably consistent ways of describing 'what's actually going on'. One is the GR model, in which spacetime is curved, and light (and other energy) travels along those curves at c everywhere. The other is a model in which gravity is a kind of force that causes light (and other energy) to bend and slow. In this way of describing things, light slows down in gravitational fields, and the background spacetime is considered flat just as in your 'god's eye' view.

When I say 'what's actually going on' I mean descriptions that connect or could possibly connect with deeper or separated areas of physics. Descriptions that are not necessarily great for solving specific problems, but better for understanding fundamentals. Each of these descriptions naturally suggests a particular type of coordinate system, but neither is really 'about' coordinate systems.

So, does light *really* slow down or not? Pick one of the above, and you have chosen the answer you prefer. No further measurement required, as we already understand the implications quite well. These two descriptions are the ones we can reasonably offer at present when the question of "what really happens" is asked. (Maybe there are 'deeper' options, but in the current context there are only these two.)

However, much of physics involves discussions of particular physical situations which in the context of gravity tend to involve various carefully selected curved coordinate systems. Because even if the 'gravity as force' model is the best fundamental description, its effects are often most easily described in terms of geometry. Anyway, all these ad hoc coordinate systems are essentially arbitrary as Gregor was saying - or more precisely, they are chosen to fit a particular problem. For example, Schwarzschild coordinates are useful in describing the gravitational field surrounding a star or a black hole.

Hope that is some help.

- Gerry Quinn

66 The two postulates in Special Relativity

I understand that choosing an experiment where r is constant for Bob leaves out how that condition can be maintained. Specifying that phi and theta are also constant, all wrt a distant observer, means that either Bob is standing on a surface or he is in a rocket. Specifying that the derivative of phi or theta is constant means that he maintains r = constant by orbital motion. Different experimental conditions. But it appears to me that either case can be addressed using Schwarzschild coordinates. One may get different results for the two cases, but the results must agree regardless of the coordinate system used.

Also, there seems to be some conflation about gravitational red shift versus time dilation. Just use an atomic clock to measure the difference in time. Then the change in the wavelength of the carrier is irrelevant.

Gary

67 The two postulates in Special Relativity

>	I like Jonathon's explanation that choosing different coordinate types means choosing a different experiment

Jonathan did not bring up such an explanation. Jonathan described different experiment, though, but those experiments are not defined by different choices of coordinates. As I pointed out in my reply to Jonathan, the experiments were are talking about here are of (c) type. And as I pointed out, one can choose different coordinate types for experiment (c).

>	to which you allude in your last paragraph. The problem is that by calling out different coordinate systems, the shift to a different experiment isn't made explicit, and this is VERY confusing to neophytes like me.

This depends on the experiment's prescription. If the prescrition defines that the experiment just measures the gravitational redshift, then the result is just a gravitational redshift, not a gravitational time dilation. Conclusions that the resulting redshift may be caused by gravitational time dilation are not part of the experiment then, and an eventually concluded time dilation is not part of the result then. Choosing different coordinates does not change the experiment then.

If, on the other hand, the experiment's prescription explicitly specifies that Schwarzschild coordinates are to be used, and that gravitational redshift is to be interpreted as gravitational time dilation, then choosing different coordinates changes the experiment, since it changes its prescription.

>

I understand that choosing an experiment where r is constant for Bob leaves out how that condition can be maintained. Specifying that phi and theta are also constant, all wrt a distant observer, means that either Bob is standing on a surface or he is in a rocket. Specifying that the derivative of phi or theta is constant means that he maintains r = constant by orbital motion. Different experimental conditions.

These are out of interest, though, since John's experiment definition specified that both, the far distant observer and the observer near the black hole, are resting with respect to Schwarzschild coordinates, i.e. for both apply r = const, theta = const and phi = const.

>	But it appears to me that either case can be addressed using Schwarzschild coordinates.

Of course. But as well, each case can be addressed different coordinates. And due to that, using Schwarzschild coordinates is arbitrary.

>	One may get different results for the two cases, but the results must agree regardless of the coordinate system used.

That depends on the experiment's prescription, as explained above. A prescription that defines the experiment as measuring a coordinate-independent quantity, like the gravitational redshift, then the result is coordinate-independent. If, however, the prescription defines the experiment as measuring a coordinate-dependent quantity, like gravitational time dilation, and specifies a coordinate system to measure that quantity, like Schwarzschild coordinates, the result may be different for different coordinate systems.

>	Also, there seems to be some conflation about gravitational red shift versus time dilation. Just use an atomic clock to measure the difference in time. Then the change in the wavelength of the carrier is irrelevant.

However, one single atomic clock cannot be used to measure a gravitational time dilation. You need at least two of them, and they must the spatially separated. To measure the gravitational time dilation in Schwarzschild coordinates, one could e.h. the following experiment:

Attach two clocks to two different spatial positions, the first at r = r1, the second at r = r2 > r1. For both clocks apply theta = const and phi = const. Now let the first clock emit a light signal to the second one. Note the proper time tau2_1 displayed by the second clock when the light signals arrives it. After some proper time interval Delta tau1 on the first clock, e.g. 1 second, let this clock emit another light signal to the second clock. Note again ther proper time tau2_2 the second clocks displays when this second signals arrives.

You will find out that the proper time interval on the second clock,

Delta tau_2 = tau2_2 - tau2_1

is different from the proper interval Delta tau1 on the first clock, namely that Delta tau2 is longer: Delta tau_2 > Delta tau1. Since the propagation of both light signals is equivalent in Schwarzschild coordinate due to time translation invariance, you will conclude that this difference in the proper time interval is caused by gravitational time dilation.

This result, however, is coordinate-dependent. Instead of Schwarzschild coordinates (t, r, theta, phi), you could instead use a coordinate system (T, R, Theta, Phi), that transforms from Schwarzschild coordinates by

T = (1 - rs/r) t R = r Theta = theta Phi = phi

Applying these coordinates, wou will NOT conclude that the difference in proper time interval is due to gravitational time dilation, but rather by different propagation of the two light signals (there is no time translation invariance in these coordinates): the second signal took a longer coordinate time interval to reach the second clock.

You can define different experiments than this one to measure the gravitational time dilation, but as long as the two uses clocks always remain in their fixed different spatial positions, you will be obliged to use some kind of signals travelling between them to perform the experiment, and this makes necessary to take the propagation of these signals into account.

Alternatively, you can use clocks that are initially close together and encounter again finally. Then you do not need signals. You can assume, the both clocks start at r = r2, and that the first clocks moves from r2 to r1 then, stays at r1 for a long proper time interval, and then return to r2 finally. When the first clocks returns to r2, you can compare the different elapsed proper time intervals of the to clocks.

However, also in this experiment, conclusions from the result that concern gravitational time dilation are coordinate-dependent again: in Schwarzschild coordinates, you will conclude that during the most elapsed coordinate time, the first clocks stayed at r = r1, and that the time intervals the clock took to transit from r2 to r1 and from r1 to r2 again were neglectably short, so that the difference in elapsed proper time obviously came from the time when the fist clock stayed at r1.

Applying the coordinate (T, R, Theta, Phi) I described above, on the other hand, your conclusions are completely different: the difference in elapsed proper time comes from the phases where the clock was travelling from r2 to r1, and back from r1 to r2, not from the phase where it stayed at r1.

Now, one could be temptated to claim that Schwarzschild coordinates are more valid than the coordinates (T, R, Theta, Phi) since in Schwarzschild coordinates, time translation invariance applies, making these coordinates specially meaningful. As far as the Schwarzschild solution is considered on its own, one could indeed think that this argumentation would be valid.

However, in any solutions of the field equations of GR, one always has to keep in mind the full symmetries of GR, and these include general covariance which implies that coordinate systems without time translation invariance are as good as coordinate systems with time translation invariance. Keep in mind that there are solutions of field equations where you cannot construct coordinate systems with translation invariance at all, e.g. cosmological solutions that describe an expanding universe. Therefore, GR cannot ascribe a special validity to time translation invariant coordinate systems, and this remains valid even for solution where such coordinate systems can be concstructed.

The only special coordinate systems in GR are the local inertial frames, since they can be constructed in any arbitrary solution of the field equations.

68 The two postulates in Special Relativity

69 The two postulates in Special Relativity

I wish to convey the simultaneity of time to a class using the classic train and lightening strikes. A hand goes up in the back of the class wanting to know if it is a steam powered train or a diesel powered train. How do I respond? Jumping out the window to just end it all is one option.

70 The two postulates in Special Relativity

But when does "at rest" have a meaning, then? Being at rest w.r.t. empty space has no meaning, so at least we need one particle in it and how is a black hole different from a particle? (OK, it's mass might be of a different scale, but what is essentially different?)

-- Jos

[[Mod. note -- In the context of general relativity: For an asymptotically-flat spacetime (this includes Schwarzschild and Kerr black holes) we can define a notion of the total 4-momentum of the spacetime, as measured far from the BH (either at spatial infinity or at future null infinity). This then lets us define "at rest" (choose a far-from-the-BH observer, then Lorentz-boost her until she measures no spatial component to the total 4-momentum). -- jt]]

71 The two postulates in Special Relativity

[[Mod. note -- Please limit your text to fit within 80 columns, preferably around 70, so that readers don't have to scroll horizontally to read each line. I have manually reformatted this article, making an educated guess at paragraph breaks. -- jt]]

Well said. If memory serves your last post was the same in that you understood the point being made the first time. If I were smart I would leave at that on a high note but it is not in my nature:<). I would like to demonstrate from a philosophical position that gravitational red shift could be in violation of causality provided ideal conditions of Doppler and SR effects are set aside. The way to do this is to state ahead of time that there is no movement between A and B therefore there can not be a Doppler or SR effect. Now that the clutter of too many variables on the table has cleared we have only gravitation time dilation and gravitational red shift of B atomic clock observed by A that is not time dilated. The exact amount of time dilation is not relevant other than being consistent so I leave it to the read to assume then set ideal condition for it to be so. If Schwarzschild coordinates are useful then a toss of dice could set the exact time dilation and then reverse construct the Schwarzschild coordinates. I am kidding of course :<). Clock B may have missing ticks without violating causality as it is time dilated therefore justified to have missing ticks as observed by A. However if gravitational red shift were in any way effect the B clock rate as observed by A then there is a violation to causality. Where are the missing ticks? There is no longer a Doppler effect to continuously hide them in space. Where did they go? From this I conclude that gravitational red shift is simply the observation of gravity time dilation.

There in is the rub. From energy conservation laws the frequency of a photon must go down caused by G red shift. From a causality position the frequency can not go down as it violates causality. Where are you going to hide the missing tick . Only gravity time dilation is allowed to have missing ticks not gravitational red shift as it is only a carrier of information. I do not have an answer for this.

72 The two postulates in Special Relativity

On 12/11/15 12/11/15 - 6:00 AM, Gary Harnagel wrote:

>	Really now! If the experiment were actually performed, there would be only ONE result. This "arbitrariness" makes no sense and sounds like obfuscation to me.

If one specifies the experiment sufficiently well, then GR predicts a single result. For a basic redshift measurement of an electromagnetic signal, a sufficient specification consists of: 1) the metric of spacetime at all events of interest 2) the position and 4-velocity of the emitter when the signal is emitted 3) the position and 4-velocity of the detector when the signal is detected 4) the path of the EM signal between emission and detection 5) the proper period of the emitted EM signal; it must be very much smaller than any other timescale in the problem

Without all that, one cannot calculate the redshift. But with all that one can calculate the redshift in a coordinate-independent way:

A) Form the displacement 4-vector between two successive wavecrests of the emitted wave. This is necessarily parallel to the emitter's 4-velocity, with norm (5). B) Parallel propagate that displacement 4-vector along the signal path to the detector. C) Compute the dot product of the result of (B) with the detector's 4-velocity. This is the measured period of the detected wave.

Note this algorithm is quite general and works in any manifold of GR (including Minkowski spacetime of SR, and non-static/non-stationary manifolds). It depends on the metric at the emission event, everywhere along the signal path, and at the detection event.

Note also it does not distinguish among "gravitational time dilation", "gravitational redshift", "redshift due to relative velocity", and "Doppler shift" -- all it does is give you the predicted numerical result; what label one chooses to apply does not really matter.

Tom Roberts

73 The two postulates in Special Relativity

>	However if gravitational red shift were in any way effect the B clock rate as observed by A then there is a violation to causality. Where are the missing ticks?

Instead of Schwarzschild coordinates, you can e.g. choose coordinates in which time translation invariance does not apply. In such coordinates, the light signals propagating from clock B to clock A may propagate differently: the later a signal is emitted by clock B, the more coordinate time takes it to reach clock A. Due to the symmetry of GR, such a coordinate is as valid as Schwarzschild coordinates are.

I made two spacetime diagrams that illustrate this:

74 The two postulates in Special Relativity

>>>	(a) The far-away observer is a rest with respect to the black hole (BH).

>>	This specification, however, isn't sufficiently detailed, too. "At rest with respect to the blach hole" does not have a disctinct meaning in GR,

>	But when does "at rest" have a meaning, then? Being at rest w.r.t. empty space has no meaning, so at least we need one particle in it and how is a black hole different from a particle?

In GR, a particle is even not sufficient to define being at rest, since unlike in SR, the particle does not define a frame of reference. So, in addition to a particle, you need a coordinate system.

In SR, a particle would be sufficient, but not in GR.

More in detail: an inertial frame, like it is constructable in SR, is like a four-dimensional Cartesian coordinate systems: the coordinate lines of it four coordinates (t,x,y,z) are straight lines and orthogonal to each other. In the flat spacetime of SR, such an inertial frame can be defined in a distinct way by choosing a uniformly moving particle: the wordline of that particle is a straight line, and all the t coordinate lines of the inertial frame are parallel to the particle's worldline, while the spatial coordinate lines are orthogonal to the so defined t coordinate lines. In the curved spacetime of GR, however, there is no such procedure to define an inertial frame or any other type of coordinate system from just choosing a particle. You won't be able to construct a coordinate system where all coordinate lines are straight (i.e. geodesic) everywhere and at the same time orthogonal to each other everywhere.

Take e.g. Schwarzschild coordinates, those are orthogonal, but their coordinate lines are not straight (proof: a particle with a worldline on which r = const, theta = const, phi = const applies, i.e. with a wordline that matches a t coordinate line, is not free-falling, so the wordline is not goedesic, and by this, the t coordinate line is not geodesic, too). Therefore, choosing Schwarzschild coordinates is arbitrary. Instead, one could as well choose coordinates where the coordinate lines are geodesic, but not orthogonal to each other. In those coordinates, being at rest will probably have a different meaning than in Schwarzschild coordinates (e.g. a free falling particle might have a wordline that matches a t coordinate line, implying it is at rest in these coordinates, whereas it is surely not at rest in Schwarzschild coordinates.).

>	(OK, it's mass might be of a different scale, but what is essentially different?)

Different to a particle in the flat spacetime of SR? The spacetime curvature generated by the black hole that destroys to applicability of frames of reference.

75 The two postulates in Special Relativity

I appreciate the effort you are making to get your point across and I would add Tom as well for taking the time to make the counter argument as clear as possible. I know from experience that it takes a good hour if not more to word it just right , for myself anyways , so I appreciate the time taken to conveying these thoughts. l hear you.

Founding principles of physics are not to be played with. Energy conservation , momentum conservation , causality. This is our candle of light to navigate this wonderful subject of physics. These principles can not be set aside if it is inconvenient. On another note one can have 1 variable on the table and be okay. You can have 2 variables on the table and still be okay provided one is willing to pace the floor a few nights to sort out all the possible alternatives. If there are 3 variables on the table it is unlikely anything productive can come out as there are just too many roads to explore. If there are 4 variables on the table forget it as it not going to happen. Maybe a computer but not the human mind with a clock rate of 25 Hz at best.

I have made what I consider a valid argument from a philosophical position that gravitational red shift can not change rate of ticks , amount of time dilation , without being in conflict with causality within the limitations of no SR effects and no Doppler effects. The only two variables are gravitational time dilation and gravitational red shift. If new variables are introduce such as this coordinate system vs that then we have 3 or 4 variables on the table to consider. This is beyond human capacity and will lead to nothing more than dogs barking at the moon into the wee hours. Surely we are better than dogs barking at the moon into the wee hours. Please restrict your self to gravitational time dilation and gravitational red shift only to proceed in a productive way.

For clarification a photon leaving earth must be reduced in frequency to satisfy energy concentration laws. If the frequency of the photon is reduced within a medium , medium between earth and space , there will be a violation to causality.

To understand why think of a rigid hollow rod between A and B with information of atomic clock ticks being conveyed by a laser in the middle of the rigid rod. With the rigid rod there can not be Doppler effects. With this in place make sure the rod is not rotating relative to the stars so that there can not be a SR effects within that local area. This leavers us with only 2 variables of G time dilation and G red shift between A and B. I do not think it is possible for G red shift to change time dilation without being in violation of causality. However if photon energy therefore frequency is not adjusted for G red shift then energy conservation will be violated. Either way it is dead end road. Where is the compromise for both causality and energy conservation to be satisfied under these conditions?

Always good to describe a problems two ways to best communicate a thought. B sends a sample of 1000 pules to A from his atomic clock to test for time dilation caused by G time dilation. There is not a violation to causality here. However for G red shift to change measurements of time dilation it must change 1000 pulses to 999 or 1001 pulses which is a clear violation to causality. Keep in mind G red shift is information on a laser beam of light that can not go back in time to change the atomic clock as it is just a wave of information of 1000 pulses. There is no Doppler effect to hide pulses. Only G time dilation can change atomic tick rates. G red shift does not have the means to effect clock rate other than delayed in time but it will still be 1000 pulses only at a rate consistent with the rate pulses are leaving B. If not there will be too many or not enough pulses in the information channel which will be unmanageable over a period of time if 1000 pulses is changed to 1 10^10 pulses. Where can one hide these pulses in a G red shift as it is just a medium that conveys information from A to B.

[[Mod. note -- Energy and momentum conservation are nice principles, but they're very tricky in a curved spacetime. Notably, it's very hard to even *define* the total energy/momentum in some finite volume: You can (fairly) easily define the energy/momentum in an infinitesimal volume, but in a generic curved spacetime there's no unique way to add up (volume-integrate) the contributions from all the different infinitesimal regions. -- jt]]

76 The two postulates in Special Relativity

[--] - show quoted text - I'm not precisely clear as to your exact thought experiment, but it seems to me that you can start by looking at things through 'god's eye' coordinates, a.k.a. coordinates natural to an observer in a low gravitational far from the system of interest. In these flat spacetime coordinates, light slows and bends in gravitational fields. But so long as you consider only regions outside event horizons, you can describe any physical system in a way that is consistent with any system of GR curved coordinates.

There is no causality violation in either description. If B moves in close to a black hole for a while and comes back again, he will have aged less than A, according to either formulation. But there are no 'missing ticks'. In the flat spacetime formulation, that's because light and time slowed down where he was. In the curved spacetime formulation, light and time go at the same speed everywhere, but spacetime is distorted. So when he meets up again with A, he finds less time passed on the route he took. And when they meet, the number of ticks observed by both parties will be identical.

Remember, in relativity it's very important to talk only about local measurements - so you can't safely add the ticks until A and B meet, nor can you claim that there is no relative movement. In the flat spacetime formulation, that's still technically the case if we are talking about relative movement and invoking special relativity, but where there is no relative movement [and no acceleration - this doesn't apply in a rotating system!] we can assert the fact without tripping ourselves up. In the discussion of the general relativistic formulation of this thought experiment, we can't really do that. You can't claim a paradox in a theory based on non-measureable entities that aren't considered meaningful in that theory.

Also, note that energy conservation applies in asymptotically flat spacetimes in GR, but is not necessarily applicable when only part of such a spacetime is considered.

- Gerry Quinn

77 The two postulates in Special Relativity

>

For clarification a photon leaving earth must be reduced in frequency to satisfy energy concentration laws. If the frequency of the photon is reduced within a medium , medium between earth and space , there will be a violation to causality. To understand why think of a rigid hollow rod between A and B with information of atomic clock ticks being conveyed by a laser in the middle of the rigid rod. With the rigid rod there can not be Doppler effects.

You have to keep in mind, though, that according to Relativity, there is no such thing like an ideal rigid rod. Any real rod is deformable. Imagine a rod consisting of atoms. The atoms are bound together by interatomic forces. With the rod exposed to a gravitational field, the position of each atom is determined by an equilibrium of the gravitational forces (the rod and its atoms are not free-falling, so each atom experiences a gravitational force) and the interatomic forces from the other atoms.

Now consider things in Schwarzschild coordinates. The gravitational field is static there (in the sense that the derivatives to coordinate time vanish), so the equilibrium positions of the atoms of the rod are static, too, making the rod not stretching or shrinking.

But now consider things in e.g. Kruskal coordinates. With passing Kruskal coordinate time v, a rod with two ends for which r = const applies each is shrinking more and more. This is in full compliance with the rod atoms' positions being determined by equilibrium between gravitational force and interatomic forces: the gravitational field is not static in Kruskal coordinates, but rather changing by coordinate time v. So, the equilibrium positions of the rod atoms are changing, too, making the rod being shrinking.

Therefore, your argument that there cannot be a Doppler effect - or let's say: a redshift due to movement - is wrong.

In principle, this rod examples shows what I said in a parallel post in this thread, namely that in a curved spacetime, there is no distinct procedure to construct a frame of reference. With the assumption of a rigid rod, one could be temptated to claim that such a rod should provide such a procedure: namely that the wordlines of the rod atoms might define the t coordinate lines of a frame of reference. But this is wrong: there is no reason why a rod had to be rigid, and therefore no reasong to prefer coordinate systems in which both ends of the rod are resting.

>

Always good to describe a problems two ways to best communicate a thought. B sends a sample of 1000 pules to A from his atomic clock to test for time dilation caused by G time dilation. There is not a violation to causality here. However for G red shift to change measurements of time dilation it must change 1000 pulses to 999 or 1001 pulses which is a clear violation to causality.

You are again making the wrong assumption that time translation invariance had to apply. In Schwarzschild coordinates, time translation invariance applies, making all 1000 pulses take the same coordinate time interval to propagate from B to A. So that redshift only can be explained by different ratios of the proper times of the two clocks to coordinate time.

However, in GR, there is no reason why not to apply coordinates without time translation invariance. Take again the following coordinates:

T = sqrt(1 - rs/r) t R = r Theta = theta Phi = phi

You will see that the second pulse from B to A takes a little more coordinate time T to propagate than the first pulse, the third pulse takes again a little more coordinate time than the second one, and so on. Let Delta T_B denote the coordinate time interval it takes to emit all 1000 pulses from clock B. And let Delta T_A denote the coordinate time interval it takes to receive all 1000 pulses at clock A. Then the relation is

Delta T_A = 1.001 * Delta T_B

So, in a coordinate time interval of length Delta T_B, clock A receives only 999 pulses, not 1000. The 1000th pulse comes a little later.

A further analysis shows up that when we consider pulses propagating in the opposite direction, namely inwards from clock A to clock B, the propagation time interval of those pulses becomes shorter and shorter, and after a finite coordinate time T, it hits zero. In other words: the radial coordinate R becomes timelike. This simply means that the coordinates (T, R, Theta, Phi) have a coordinate singularity in future direction, outside the black hole. This implies that their range of validity (their "map") is even more limited than the one of Schwarzschild coordinates (which is limited to r > rs). But within this range, the coordinates (T, R, Theta, Phi) are - according to GR - as good as any other coordinate system.

>	Keep in mind G red shift is information on a laser beam of light that can not go back in time to change the atomic clock as it is just a wave of information of 1000 pulses. There is no Doppler effect to hide pulses.

But there is a lack of time translation invariance (in the coordinates (T, R, Theta, Phi)) that allows the 1000 pulses to stretch, from Delta T_B to

Delta T_A = 1.001 * Delta T_B

78 The two postulates in Special Relativity

Wouldn't that be r = infinity?

>	and why should we believe that these are unique (i.e., that they're the *only* coordinates "natural to an observer in a low gravitational far from the system of interest")?

There should be an infinite number of coordinates that are at r < infinity but still large enough to be insignificantly different from r = infinity by our measurement techniques.

>	And, how do we know that the GE coordinates cover all "interesting" regions of spacetime.

But the GE coordinates are essentially where WE are, and we're in peril if we aren't there.

>	For example, can you prove that GE coordinates don't have any coordinate singularities outside the event horizon? -- jt]]

What about a circular orbit at r = 1.5*r_schw?

Gary

79 The two postulates in Special Relativity

On 12/18/15 12/18/15 1:14 AM, Gerry Quinn wrote:

>

[...] it seems to me that you can start by looking at things through 'god's eye' coordinates, a.k.a. coordinates natural to an observer in a low gravitational far from the system of interest. In these flat spacetime coordinates, light slows and bends in gravitational fields. But so long as you consider only regions outside event horizons, you can describe any physical system in a way that is consistent with any system of GR curved coordinates.

This is just plain not true. You cannot apply such "flat coordinates" to any manifold of GR containing mass or energy, as such manifolds are not flat. Remember "flat" is a property of the metric, not the coordinates, and the metric is a tensor (field) and therefore independent of coordinates.

What you seem to be thinking of is a completely different formulation of gravity as a spin-2 field on a flat manifold. This is a MUCH bigger difference than mere selection of coordinates as you say. This model can account for many properties of GR, but in particular it can be compared to GR only in regions in which gravitation is weak (so you can put the manifolds of the two models into 1-to-1 correspondence with negligible error, and thus compare them). This comparison fails wherever gravity is not weak, and that can happen well outside any event horizons.

>	There is no causality violation in either description.

This depends IN DETAIL on what one means by "causality". The casual notion of "this caused that" is both hopelessly naive and completely useless. So what do you mean?

In relativity, causality is the property that at any given event in the manifold, the fields depend only their values at events within the past lightcone of the event in question. How they depend is an aspect of the specific fields being discussed, and their properties and interactions.

>	If B moves in close to a black hole for a while and comes back again, he will have aged less than A, according to either formulation. But there are no 'missing ticks'. In the flat spacetime formulation, that's because light and time slowed down where he was.

It OUGHT to be obvious that mere coordinate choice cannot possibly do that -- it requires a physical process to make "light and time [be] slowed down".

>	In the curved spacetime formulation, light and time go at the same speed everywhere, but spacetime is distorted. So when he meets up again with A, he finds less time passed on the route he took.

Note that in neither model are there any "missing ticks". In GR the integrated proper time (= tick count) over the two paths is different; in the other model B's clock physically ticked slower for much of his path. But nobody could possibly notice that some ticks were "missing".

>	And when they meet, the number of ticks observed by both parties will be identical.

I think you meant to say that A and B can have different tick counts (elapsed proper times) when they meet, but the two models agree on what those counts are.

>	Remember, in relativity it's very important to talk only about local measurements

Hmmm. One can discuss non-local "measurements" as long as one specifies how they are performed with sufficient clarity and precision. Of course the actual act of measurement takes place at a single event and is thus inherently "local", so by "non-local measurement" one really means combining measurements performed at different events.

>	so you can't safely add the ticks until A and B meet,

I think you mean "count the ticks on clocks A and B, ending when they meet". One can certainly compare the clock readings of two clocks, but then, one must specify HOW they are compared; this is simple when the clocks are co-located, but when they aren't this would be a "non-local measurement" that must be specified in more detail. Note this applies to both the beginning and the end of the interval over which they are to be compared.

>	[... further discussion which I cannot decipher at all]

>	Also, note that energy conservation applies in asymptotically flat spacetimes in GR, but is not necessarily applicable when only part of such a spacetime is considered.

Energy conservation in GR is subtle and complicated. But if you follow your own dictum above, "talk only about local measurements", then it is easy: energy and momentum are locally conserved at every event in the manifold.

>	[[Mod. note -- Your description doesn't tell me how to define your "god's eye" (GE) coordinates. Let's be specific. What's your operational definition of GE coordinates for Schwarzschild spacetime, [...]

He intends the "GE" coordinates to be "flat", which simply is not possible in Schw. spacetime.

Tom Roberts

80 The two postulates in Special Relativity

>

But now consider things in e.g. Kruskal coordinates. With passing Kruskal coordinate time v, a rod with two ends for which r = const applies each is shrinking more and more. This is in full compliance with the rod atoms' positions being determined by equilibrium between gravitational force and interatomic forces: the gravitational field is not static in Kruskal coordinates, but rather changing by coordinate time v. So, the equilibrium positions of the rod atoms are changing, too, making the rod being shrinking.

Another remark: considering the Schwarzschild solution in Kruskal coordinate is similar to considering a uniformly accelerating rocket in SR. Instead of Kruskal coordinates (u,v), there are the coordinates of the inertial frame (X,T) where the rocket is initially resting in, and instead of the Schwarzschild coordinates (r,t), there the so-called Rindler coordinates (x,t) that can be imagined as defining the accelerated frame of reference of the rocket:

81 The two postulates in Special Relativity

82 The two postulates in Special Relativity

83 The two postulates in Special Relativity

84 The two postulates in Special Relativity

A(nother) problem with this argument is the use of the phrase "gravitational red shift" as if it were unique. Let's suppose we specify a pair of observers A and B, with A close to a black hole and B far away, and have A send out time-tagged once-per-second radio pulses. If B receives A's once-per-second pulses at a rate of one pulse per 2 seconds, I think you're arguing that (we should defined) the gravitational redshift from A to B is (to be) a factor of 2.

The problem is, what if B receives each pulse more than once... and the different arrival times are associated with different arrival rates?

For example, consider the following scenario (times in hh:mm:ss):
at B-clock-reading 15:15:00, B receives A's 12:00:00 pulse
at B-clock-reading 15:15:02, B receives A's 12:00:01 pulse
at B-clock-reading 15:15:04, B receives A's 12:00:02 pulse
at B-clock-reading 15:15:06, B receives A's 12:00:03 pulse
but B is a patient observer, and keeps listening. A bit later, ... at B-clock-reading 19:38:00, B receives A's 12:00:00 pulse again
at B-clock-reading 19:38:05, B receives A's 12:00:01 pulse again
at B-clock-reading 19:38:10, B receives A's 12:00:02 pulse again
at B-clock-reading 19:38:15, B receives A's 12:00:03 pulse again
and still later, ...
at B-clock-reading 23:12:00, B receives A's 12:00:00 pulse again from direction-on-the-sky #1
at B-clock-reading 23:12:11, B receives A's 12:00:01 pulse again from direction-on-the-sky #1
at B-clock-reading 23:12:22, B receives A's 12:00:02 pulse again from direction-on-the-sky #1
at B-clock-reading 23:12:33, B receives A's 12:00:03 pulse again from direction-on-the-sky #1
while at the same time, ...
at B-clock-reading 23:12:00, B receives A's 12:00:00 pulse again from direction-on-the-sky #2
at B-clock-reading 23:12:07, B receives A's 12:00:01 pulse again from direction-on-the-sky #2
at B-clock-reading 23:12:14, B receives A's 12:00:02 pulse again from direction-on-the-sky #2
at B-clock-reading 23:12:21, B receives A's 12:00:03 pulse again from direction-on-the-sky #2
at B-clock-reading 23:12:28, B receives A's 12:00:04 pulse again from direction-on-the-sky #2

What would you say is the gravitational redshift from A to B?

(If this scenario seems implausible, consider that there can be multiple propagation paths from A to B, e.g., going clockwise vs counterclockwise around a spinning black hole. In general each path will have its own time-delay.)

As noted by another poster earlier in this thread, to uniquely define gravitational redshift requires specifying not a pair of *observers*, but rather a pair of *events* AND a propagation path between them.

This means that "gravitational redshift" is NOT an attribute of a position or event. - show quoted text -

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87 The two postulates in Special Relativity

You are over thinking the problem. There is a rigid rod between A and B . The rigid rod is hollow to provide a means for a laser light within the hollow rigid rod to communicate clock pulses. This hopefully eliminates all possible options to avoid a conflict with causality. I would have a marked preference for saying "assume ideal conditions" and leave it at that. However if the ideal condition need to be spelled out then so be it. Please do not rotate the system leading to SR effects.

With all this in place there is gravitational time dilation , 1/2 to B. This is fine and will not violate causality when A receives clock pulses from B at 1/2 their normal rate. However we are obligated to add gravitational red shift time dilation according to the equivalence principle by an imperative Doppler effect that is inherent in the equivalence principle. If there is a rigid rod between A and B how can a Doppler effect be accommodated without violating causality? Gravitational time dilated B is sending 1/2 rate pulses. Once B sends 1/2 pulses how can A hear 1/3 the pulses to accommodate gravitational red shift in addition to gravitational time dilation. How can one hide pulses inside a rigid hollow rod without violating causality.

The only way I see out of this is to say use gravitational time dilation or gravitational red shift but not both. In short gravitational time dilation and gravitational red shift are the same and therefore should not be added together as this would be redundant leading to a violation of causality. Somewhat like adding simultaneity of time to length contraction in special relativity leading to a double gamma. A mistake I have noticed more than once.

88 The two postulates in Special Relativity

John Heath wrote:

>	You are over thinking the problem. There is a rigid rod between A and B . The rigid rod is hollow to provide a means for a laser light within the hollow rigid rod to communicate clock pulses.

I'll assume that you meant that the rigid rod should be "straight", i.e., [this is my operational definition of "straight"] that with a suitable alignment of the laser, the laser light does NOT touch the inside walls of the rod.

My question is, why should there be only ONE such rod between A and B? Or more precisely, what if we can place (say) TWO such rods (both rigid and "straight" by the definition I just gave) between A and B... and the redshift of the light arriving at B from A through rod #1 differs from the redshift of the light arriving at B from A through rod #2.
[For example, the two rods might pass on either side of a massive body (say a star, galaxy, or black hole) which is acting as a gravitational lens. And that massive body might be spinning.]
How then should we define "the gravitational redshift from A to B"?

My argument is that such a situation shows that we can't (uniquely) define such a quantity: gravitational redshift is (in general) *not* an attribute of a pair of observers, but rather of a pair of *events* *and* a particular (light-) propagation path between them.

>	Please do not rotate the system leading to SR effects.

Hmm. If A is close to a spinning black hole and B is far away, it's a bit tricky to define what you mean by "do not rotate the system". But we can certainly say that the observer who is far from the black hole isn't rotating with respect to a (local) inertial reference frame.

-- -- "Jonathan Thornburg [remove -animal to reply]" Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA "There was of course no way of knowing whether you were being watched at any given moment. How often, or on what system, the Thought Police plugged in on any individual wire was guesswork. It was even conceivable - show quoted text -

89 The two postulates in Special Relativity

The curvature of spacetime near the earth is quite small: only about a part per million (i.e. the trajectories of the moon and other satellites deviate from straight lines by about 1 part per million).

What do I mean by "a part per million from a straight line", when these objects obviously follow geodesic paths? I mean that in earth-fixed coordinates their path is a helix with radius about a million times smaller than the length of its period (coordinates with c=1).

>>	We use them for most engineering purposes, with accuracy tolerances which are loose enough that we can ignore the curved-spacetime effects. But if we want high accuracy, we can't ignore those effects, and we can't use GE coordintes (or even *define* coordinates with the GE properties).

>	Why not? So long as the topology is the same, changing coordinates is just changing the numbers we assign to any point in spacetime.

It is in general not possible to apply your GE coordinates to a curved manifold, regardless of topology. They can only be applied to a "small" region, where "small" is defined by the error acceptable to your application.

For instance, in 2 dimensions, it is not possible to cover the sphere with ANY coordinate system, much less the 2-d analog of your GE coordinates. Indeed, on the surface of the earth, the errors inherent in using GE coordinates are quite noticeable for regions only a few miles in size (in Chicago, wherever surveyor's regions meet along a main street, all the cross streets are offset by 20-30 feet).

>	it is no more difficult in principle to assume that the meter sticks change in length etc. depending on the gravitational potential than to assume that spacetime is curved under the same conditions.

I doubt this very much. Elsewhere I have posted the algorithm for computing the redshift of an EM signal. Given a curved metric of spacetime, it is straightforward (albeit tedious) to do the calculation. I doubt you could do it at all by assuming that rulers change length and clocks change tick rates.

In particular, how could you ever determine or verify that spacetime is flat (as you assume), when rulers and clocks cannot be trusted?

Indeed, if I construct a 3-d latticework of 1-meter rods, and they don't meet up at the corners, it seems simplest to take this as an indication that space is curved, not that rods constructed to be 1 meter long are not.

It seems to me that you are taking an "armchair" attitude here, and have never actually tried to apply your GE coordinates and varying rulers and clocks to the Schwarzschild manifold of GR. I think that if you try, you will find it MUCH more difficult than you imagine -- Chicago streets seem to me to be a strong indication of that: imagine trying to survey what was back then a trackless wilderness, using rulers that vary in length....

>	[...] pathology such as singularities.

Singularities are not really "pathological". They merely represent places where the theory breaks down (does not apply). EVERY theory has limits to its domain; GR is one of the few that can compute at least some of those limitations (most theories are mute on the subject of where/when they don't apply; usually one must go outside the theory to determine this).

For instance, in 3-d Euclidean space we don't reject cylindrical and spherical coordinates merely because they have singularities -- rather, we simply don't apply them there. Ditto for the curvature singularities of GR.

Tom Roberts

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91 The two postulates in Special Relativity

Dr Thornburg please allow my words to trap you in a corner. If you resist a delicate point of a possible violation to causality when adding gravitational red shift to gravitational time dilation could be lost. You need to be trapped in the same corner as I am to stand in my shoes to see a possible violation to causality. With this in mind allow my words to trap in a corner willingly without resistance.

A is time dilated sending 10 pulses per second. B receives 9 pulses per second as B is not time dilated. We are fine as causality is not violated as gravitational time dilation justifies this. However when we are required to add gravitational red shift to gravitational time dilation a problem pops up with causality. B must now hear 8 pulses per second not 9. Where can 1 pulse per second be hiding if the distance between A and B is fixed. A is sending 10 pulses per second , 9 pulses per second according to Bs clock , but B is hearing 8 pulses per when grt5avitational red shift is added to gravitational time dilation. How can this happen without violating causality?

92 The two postulates in Special Relativity

Why do you think anything breaks down if particles simply keep following a nice continuous trajectory when thy cross the Schwarzschild radius? (And waves likewise.) There is nothing special happening to anything at that radius (nor at a 10% smaller radius).

Do you have anything to offer as an indication of "break down" except for the accidental choice of some coordinate function?

>	- and if we accept this, we do not have any particularly fundamental problems about black holes in terms of thermodynamics etc.

And why *would* we have such problems if we define the "breakdown" at a 10% smaller radius? So again, what do you have to offer as special behavior of physics near the Schwarzschild radius?

>	But the geometric theory has allowed the Schwarzschild singularity to be defined away as a coordinate singularity, and solutions continued inward from it.

But the coordinate theory *also* allows you to take slightly (or radically) different coordinates for which the coordinate functions are defined further inwards. It is exactly a shortcoming of your cherished coordinates that they break down at all kind of arbitrary points where nothing strange happens to the laws of physics at all.

And whether you "believe" that GR breaks down is uninteresting if you fail to mention any indication that the laws of physics change at that point (i.e. they should start to differ from GR).

...

>	The end result, though, is an intractable central singularity that makes no sense whatsoever in terms of thermodynamics,

So then why don't you call a spade a spade and say that *there* is the point where GR breaks down? And if you don't want to, why do you bring up this fact? It actually weakens your case! Your post tells us that: 1) Inside the Schwarzschild radius GR is still consistent. 2) Things become intractable at a central singularity 3) But according to you GR breaks down not at 2) but at 1)

You are not just forgetting to give arguments for your claim, it seems more like you give counter-arguments!

-- Jos

93 The two postulates in Special Relativity

>

..

> >	I believe the Schwarzschild singularity is actually the breakdown point of GR

>

Why do you think anything breaks down if particles simply keep following a nice continuous trajectory when thy cross the Schwarzschild radius? (And waves likewise.) There is nothing special happening to anything at that radius (nor at a 10% smaller radius). Do you have anything to offer as an indication of "break down" except for the accidental choice of some coordinate function?

Obviously I don't believe they keep following such a trajectory.

"There is nothing special happening to anything..." I believe I pointed out the circularity of that argument in the post you are responding to. If GR breaks down at the Schwarzschild radius, then GR's prediction that nothing special is happening there doesn't mean very much.

The choice of coordinates is nothing to do with the breakdown, except insofar as GR allows coordinate choices that in its own terms allow patching of interior solutions (which in my view are spurious, corresponding to no physical reality) to external ones.

I don't believe in any special behaviour of physics anywhere. I think gravity can be described - like the other forces - in terms of a field on a flat background (albeit an effective field, which cannot be fundamental). At the Schwarzschild radius, this becomes topologically incompatible with the geometric theory of gravity, so one of them (at least) must be wrong.

I suppose in a sense I'm saying that both are wrong, as the effective field must itself break down here. The effective field acts like geometric gravity. But unlike geometric gravity, it has a way to fail gracefully, as high-energy underlying processes become observable.

As to the actual mechanics of how such forces might become observable, there are several angles. We can say that ordinary 'low-energy' clocks become time dilated to the point of stopping, so only high-energy clocks remain. We can argue that the intense gravitational time dilation means that the absorption of Hawking radiation by distant observers corresponds to high-energy events at the Schwarzschild radius. And we can argue that decay processes catalysed by high-energy interactions eventually 'start a fire' so to speak, which brings the Schwarzschild region up to a temperature where we'd expect the breakdown of the effective field theory anyway (the so-called 'firewall').

[--]

> >	The end result, though, is an intractable central singularity that makes no sense whatsoever in terms of thermodynamics,

>

So then why don't you call a spade a spade and say that *there* is the point where GR breaks down? And if you don't want to, why do you bring up this fact? It actually weakens your case! Your post tells us that: 1) Inside the Schwarzschild radius GR is still consistent. 2) Things become intractable at a central singularity 3) But according to you GR breaks down not at 2) but at 1) You are not just forgetting to give arguments for your claim, it seems more like you give counter-arguments!

You are misundertanding my argument. I am saying that the central singularity that arises if the equations of geometric gravity are extended into the black hole interior is a monstrosity that doesn't make sense even as the breakdown point of a theory. What sort of new physics can you imagine that will take the place of general relativity there? If we did not have quantum mechanics, we might imagine that matter is somehow crushed out of existence entirely, leaving only its gravitational field as a kind of ghost. But if we hope to be compatible with quantum theory, even this in untenable.

So we must have made a mistake - the breakdown point must have been earlier. And there is only one other distinctive place where it could be - the Schwarzschild radius, which must not have been a mere coordinate singularity after all...

(As to whether the patching of interior to exterior solutions is really consistent, to be honest I'm not certain that it is, but I don't think either side would have their views affected by argument on the subject.) - show quoted text -

94 The two postulates in Special Relativity

Again you talk about your "belief". It is not interesting. Your homework is: 1) Give observational proof. 2) Explain how you remove the inconsitencies. About the second point: how can GR breakdown if there is nothing indicating where the Schwarzschild radius is? It cannot be the curvature of space, because at the Schwarzschild radius of a large black hole that is completely different from a small one. Also the presence of other gravitating objects would create asymmetry. You really would not *believe* that for a black hole binary GR breaks down exactly in two spherical regions around each of them without the slightest influence of the other, or do you?

...

>	"There is nothing special happening to anything..." I believe I pointed out the circularity of that argument in the post you are responding to. If GR breaks down at the Schwarzschild radius, then GR's prediction that nothing special is happening there doesn't mean very much.

GR isn't needed for that prediction. Also without GR (or *even more so* without GR) there is no criterion possible that gives you the position of the Schwarzschild radius based on the physical situation of the point where you believe it to be. There is not a specific value of any physical quantity that can serve to position it.

You write that you *believe* that something special is happening at certain boundaries in space but in fact you are fooling yourself because you evade any definition of what those special boundaries are.

>	The choice of coordinates is nothing to do with the breakdown,

Of course not. But you also fail to give us anything else that could have something to do with it. Therefore there cannot be a breakdown.

>	I don't believe in any special behaviour of physics anywhere.

Your *believe* is extremely flexible. You just argued against "There is nothing special happening to anything" being used by others, but now you seem to believe exactly that yourself.

>

I think gravity can be described - like the other forces - in terms of a field on a flat background (albeit an effective field, which cannot be fundamental). At the Schwarzschild radius, this becomes topologically incompatible with the geometric theory of gravity, so one of them (at least) must be wrong.

But you "don't believe in any special behaviour of physics anywhere" so your choice will be that the field on the flat background would be wrong and GR correct.

>	I suppose in a sense I'm saying that both are wrong, as the effective field must itself break down here.

Why? It is on a flat background, you say! So it doesn't have any problem.

>	The effective field acts like geometric gravity. But unlike geometric gravity, it has a way to fail gracefully, as high-energy underlying processes become observable.

But there are no high energy processes activated if you approach the Schwarzschild radius. NB: there also is no large gavitational force field if it is a large black hole (the larger it is, the *weaker* its gravitational field at the Schwarzschild radius.)

>	As to the actual mechanics of how such forces might become observable,

Yes, the mechanism is what you leave out. In everything you wrote until now.

>	there are several angles. We can say that ordinary 'low-energy' clocks become time dilated to the point of stopping, so only high-energy clocks remain.

Those are all meaningless words, especially since you denounce GR. Write down a well-defined theory for what you want to say and perhaps we can discuss it further.

...

>>>	The end result, though, is an intractable central singularity that makes no sense whatsoever in terms of thermodynamics,

>>

So then why don't you call a spade a spade and say that *there* is the point where GR breaks down? And if you don't want to, why do you bring up this fact? It actually weakens your case! Your post tells us that: 1) Inside the Schwarzschild radius GR is still consistent. 2) Things become intractable at a central singularity 3) But according to you GR breaks down not at 2) but at 1) You are not just forgetting to give arguments for your claim, it seems more like you give counter-arguments!

>	You are misundertanding my argument. I am saying that the central singularity that arises if the equations of geometric gravity are extended into the black hole interior is a monstrosity that doesn't make sense even as the breakdown point of a theory.

Here your words are *not even meaningless* I would say. If the singularity doesn't make sense in an existing theory then by the accepted meaning of these words this is synonymous to the theory breaking down.

You are now descending into the rather pointless game of stripping words of there ordinary meaning!

>

What sort of new physics can you imagine that will take the place of general relativity there? If we did not have quantum mechanics, we might imagine that matter is somehow crushed out of existence entirely, leaving only its gravitational field as a kind of ghost. But if we hope to be compatible with quantum theory, even this in untenable.

On the contrary, things that are classically a singular point, could become manageable in quantum theory. Even in other theories, there might be some region where the theory changes gradually. This could be just outside the classical point of singularity, but far inside the Schwarzschild radius.

>	So we must have made a mistake - the breakdown point must have been earlier.

So that could be just outside the classical point of singularity, but still far inside the Schwarzschild radius.

>	And there is only one other distinctive place where it could be - the Schwarzschild radius,

That is not distinctive at all! You failed miserably until now to define what distinguishes the Schwarzschild radius from any other point in space.

-- Jos

95 The two postulates in Special Relativity

Work by Samir Mathur and others suggest that the Schwarzschild radius points (or just outside them) have structure:

96 The two postulates in Special Relativity

>>>	Why do you think anything breaks down if particles simply keep following a nice continuous trajectory when thy cross the Schwarzschild radius? (And waves likewise.) There is nothing special happening to anything at that radius (nor at a 10% smaller radius).

The coordinate "r" in the Schwarzschild solution is essentially the radial distance from the center of the (uncollapsed) spherical mass WHEN r is sufficiently large, and "t" is the time coordinate when r is greater than 1. But for r < 1, r becomes the time coordinate, and t becomes one of the three spatial coordinates. So when r is 10% smaller that 1, it is NOT a "radius", it is a time. And r = 0 is NOT the "center" of the blackhole.

I'm one of the few people who believe that the r < 1 solution to the quadratic equation obtained in the Schwarzschild derivation is just a spurious mathematical result, with no physical significance in our universe. The "center" of the blackhole is at r = 1, and there is nothing "inside" of that ... there IS no "inside" of that.

I realize I'm a member of a tiny minority holding this view, but I'm in very good company: some years ago (after I had arrived at my view), I found out that Dirac had the same view. Made my day!

97 The two postulates in Special Relativity

You attempt to make a distinction without a difference.

"Gravitational redshift" and "gravitational time dilation" are the same phenomenon, and nobody in their right mind would "add" them.

See my earlier post on how to compute them -- one uses exactly the same algorithm for both, which is why I say they are the same phenomenon. You just apply different words as labels to a single phenomenon. The physics, of course, is completely independent of your labels.

Tom Roberts

98 The two postulates in Special Relativity

They want the "firewall" to be located at some "horizon" (p. 13, "Conclusions") but they write that is is: "not determined by any local feature but by a global property." They even admit that: (p. 14) "..we pass through Rindler horizons all the time and do not burn up or experience obvious new physics."

So then the burden is on the authors to show that there can be a consistent definition of where we will, and where we *will not* see this new physics happening.

It must in particular be applicable to combined Rindler- Schwarzschild situations for multiple black holes and masses with all kind of accelerations. And it must explain *why* this should happen despite the absence of "any local feature" (a fact that they admit.)

Their answer, "We believe that this is due to an essential difference.." (p. 14) is not accompanied by any explanation. It doesn't look much better than the "we believe" arguments that people in this thread are making.

-- Jos

99 The two postulates in Special Relativity

Those are the coordinate functions used in that case. So how does that prove that anything strange is the matter with space? You mention only a peculiarity of your chosen coordinates. So I could elaborate:

"There is nothing special happening to anything at the Schwarzschild radius, nor at a 10% smaller r in those coordinates, nor in the region going further inwards (which is another direction than decreasing r)."

A region "further in" should be in the direction following the space-like coordinate that goes further in. You can draw a curve going in space-like direction regardless of the coordinates you have chosen.

So where do you see anything that blocks you from drawing the curve further inwards?

..

>	I'm one of the few people who believe that the r < 1 solution to the quadratic equation obtained in the Schwarzschild derivation is just a spurious mathematical result,

Why would it matter what the coordinates do? You do not answer the question what would be preventing us from constructing a space-like curve inwards.

-- Jos

100 The two postulates in Special Relativity

You seem to not understand the difference between coordinates and the geometry or physics -- neither geometry nor physics can depend on the coordinates used. Your statements are inextricably bound to the usual Schwarzschild coordinates, and simply do not apply to the manifold itself. The physics and geometry are in the manifold, not the coordinates.

Technically the Schw. solution clearly has no relevance to the universe we inhabit (the world we inhabit is nowhere close to being static and spherically symmetric). But it is not unreasonable to expect that solution to approximate certain regions of our universe -- indeed we observe that it does apply to our solar system outside the solar surface. I see no reason to think this would not apply to isolated objects smaller than their Schw. radius -- certainly GR remains valid for such objects (within the approximation of applying GR to just a region of the universe). Indeed there are many objects observed that are consistent with being black holes, and for which no alternative description has been found.

>	The "center" of the blackhole is at r = 1, and there is nothing "inside" of that ... there IS no "inside" of that.

This is just not so. The manifold extends inside the horizon, and the physics and geometry are in the manifold. Yes, the coordinates you use do not extend inside, but that does not AND CAN NOT affect the manifold, the physics, or the geometry.

>	I realize I'm a member of a tiny minority holding this view, but I'm in very good company: some years ago (after I had arrived at my view), I found out that Dirac had the same view. Made my day!

I'll bet that was an opinion that he formed long before the complete geometry was known.

Tom Roberts

101 The two postulates in Special Relativity

Thank you.

102 The two postulates in Special Relativity

On 1/12/16 1/12/16 4:56 PM, Gerry Quinn wrote:

>	In article , tjroberts137 @sbcglobal.net says...

>>

It is in general not possible to apply your GE coordinates to a curved manifold, regardless of topology. They can only be applied to a "small" region, where "small" is defined by the error acceptable to your application. For instance, in 2 dimensions, it is not possible to cover the sphere with ANY coordinate system, much less the 2-d analog of your GE coordinates. Indeed, on the surface of the earth, the errors inherent in using GE coordinates are quite noticeable for regions only a few miles in size (in Chicago, wherever surveyor's regions meet along a main street, all the cross streets are offset by 20-30 feet).

>	Those errors arise from using them incorrectly.

No. The surveyors correctly applied Euclidean geometry. The errors arise from the MISMATCH between their assumption of Euclidean geometry and the actual curved geometry of the surface of the earth.

Your "GE coordinates" will have the same problem.

>	You are assuming, just as Jonathan did, that I think that orthogonal straight lines, measured according to your operational definition (which in the case of your Chicago example presumably means great circles) must under all conditions form a rectilinear grid. I do not say that.

If you don't say that, at least locally and at every point, then you don't understand what a manifold is. A manifold is BY DEFINITION locally equivalent to a Euclidean space. And in Euclidean space orthogonal straight lines do form a rectangular grid.

>

Imagine flat creatures living on the surface of a sphere, unaware of a third dimension. They might hypothesise that their space is curved. Or they might hypothesise that it is embedded in a higher dimensional space, and some force causes their meter sticks to bend to conform to a sphere. If they believed in the latter, they could still define a two parameter coordinate system (e.g. latitude and longitude), and there is no reason why they could not convert such coordinates to 3D coordinates, make calculations, convert them back again, and build roads with perfect accuracy.

Sure. But those coordinates are not your "GE coordinates", because latitude and longitude do NOT yield geodesics. If they try to use geodesics ("straight lines"), they will find inconsistencies and problems in sufficiently large regions.

>>	It seems to me that you are taking an "armchair" attitude here, and have never actually tried to apply your GE coordinates and varying rulers and clocks to the Schwarzschild manifold of GR. [...]

>	An armchair attitude is appropriate, given that we are discussing theory, not the taking of measurements.

I meant "armchair" not in the sense of thinking mathematically, but in the sense of NOT applying mathematics. Because you haven't tried to apply your "GE coordinates" on Schw. spacetime. You ASSERT it is "no more difficult in principle", but you have not actually TRIED. I strongly suspect your assertion is false, and it would be MUCH more difficult to use your approach.

>	As for verification that spacetime is flat, the only sure way I know at present is to jump into a very large black hole, and find out whether you get incinerated near the Schwarzschild radius, or progress further only to be spaghettified at some point inside.

You are mixing metaphors -- that is not at all "flat".

The issue of whether GR fails at the Schwarzschild radius of a Schw. black hole has been resolved for many decades: GR is valid at the horizon and inside it until the singularity at the "center" is approached.

Whether there exist such objects in the world we inhabit is a completely different issue. As is the issue of whether other physics applies (e.g. some as-yet-unknown quantum theory).

>	Failing that, we can only argue on the basis of what is consistent, including what is consistent with the rest of physics such as quantum theory and thermodynamics. In my view, the geometric theory of gravity cannot easily be made consistent with these.

Yes, consistency of GR and QM is a major current topic.

>	It seems to me that GR is actually a theory which has allowed singularities to be wished away. I believe the Schwarzschild singularity is actually the breakdown point of GR

You are wrong on both points. GR is _KNOWN_ to be well behaved at the horizon of a Schw. black hole. There is no "wishing away of singularities, BECAUSE THERE IS NO SINGULARITY THERE.

It may be that other physics becomes important at or near the horizon, rendering GR only an approximation, or even invalid. But GR itself does not "breakdown" there at all.

>	But the geometric theory has allowed the Schwarzschild singularity to be defined away as a coordinate singularity, and solutions continued inward from it.

This is not "defined away", it is rather the correction of an old mistake. I repeat: THERE IS NO SINGULARITY THERE. It's just that historically people made a poor choice of coordinates that made them THINK there was a singularity there, WHEN THERE WASN'T.

>	The end result, though, is an intractable central singularity that makes no sense whatsoever in terms of thermodynamics, or physics in general.

Hmmmm. Other theories of physics may indeed need to be modified to be consistent with GR, or GR may need to be modified to be consistent with them. At present, nobody has done so. This is a major area of research.

>	This should be taken as a sign that the interpretation of the Schwarzschild singularity as a coordinate singularity is incorrect, and that conditions there are such that the symmetries of GR, which allow the extension to interior solutions, no longer apply.

I see no reason to expect that.

Remember that "all physics is local" [Einstein and others]. Locally, the horizon is no different from any other point in the manifold. There is no possible local experiment or measurement that can identify the horizon.

>

"But how can that be", you ask? "GR predicts that conditions at the Schwarzschild radius of a large black hole are nothing special. So obviously GR cannot break down there. Your alternative hypotheses are unimaginable!" And therein lies the problem. Internal consistency is not truth, and powerful theories of symmetry cannot imagine their symmetries broken. I think "going outside the theory" is something that proponents of the geometric view of gravity should practice more!

I think you greatly overstate the case. I think not enough is known about how GR relates to other theories of physics, and until more is known about that this will have to remain unresolved.

Tom Roberts

103 The two postulates in Special Relativity

I THINK the paper in which Dirac stated those conclusions was published around 1965 or so. And as I recall, it was the moderator of the sci.physics.foundations newsgroup who told me about Dirac's conclusions (after I had expressed my conclusions on that newsgroup, and acknowledged that I knew I was in a tiny minority with that opinion), and he gave me an on-line link to that paper. I've got that link (and perhaps a printout of the paper) around here somewhere, but I don't know where ... it's probably been about 10 years since I found out about it. - show quoted text -

104 The two postulates in Special Relativity

Hi Nicolaas!

Einstein's two postulates aren't enough on their own to uniquely define the physics of special relativity. We also seem to need a third, "geometrical", postulate, the assumption that spacetime is and remains "flat" and that the presence or introduction of stationary or moving matter doesn't affect the propagation of light, or the resulting lightbeam geometry.

The physics of how relatively-moving bodies interact in real life is //never// conducted in totally empty space (because the space under consideration has to contain the bodies!), so our third postulate should probably be that the "mathematical" lightbeam geometry derived by SR for empty space is still correct in the presence of physically-real moving masses and observers.

If we don't apply this third postulate, we can imagine a different physics that still obeys the principle of relativity and the law of local lightspeed constancy, without being the 1905 theory.

For instance, we could take Fresnel's early C19th idea of local light-dragging as the basis of a relativistic dragged-light model, eliminate the "aether" terminology and restate it as a geometrical theory where the dragging is a gravitoelectromagnetic effect, use GEM to regulate local lightspeeds and use W.K. Clifford's late C19th concept of "all physics as curvature" to reject the idea of moving-body physics having a valid flat-spacetime solution. We'd then have a different theory of relativity that'd seem to agree with the physical evidence available in 1905, but which wouldn't be Einstein's special theory.

Physicists in 1905 may have believed that two postulates were sufficient to make SR inevitable, but we now have a broader and more sophisticated conceptual vocabulary, which opens up other possibilities. This means that defining SR's position within "theory-space" and distinguishing it from its neighbours requires more parameters.

105 The two postulates in Special Relativity

Yes, the two standard postulates, plus the concept of the "inertial frame" gives special relativity. The "frame" approach assumes that the global lightspeed across a region is the same as the local lightspeed measured anywhere within it, providing SR's required third postulate of flat spacetime.

If we don't make this additional assumption, then there is at least one other way of implementing the principle of relativity for inertial physics. Globally flat geometry plus the principle of relativity gives SR, but a //locally//-constant c pus the principle of relativity seems to lead //either// to special relativity or to a relativistic acoustic metric.

>

One also needs the "hidden postulates" Einstein described in a 1907 paper: a) clocks and rulers have no memory, b) space is homogeneous and isotropic, and c) time is homogeneous. Plus one he didn't mention: d) light follows a null geodesic in the spacetime geometry. Note (b) and (c) are part of the definition of inertial frames, and (d) can be derived from that and the second postulate. Note also that it is the instantaneous tick rate of a clock that has no memory, not the counter or indicated time (which is clearly a type of memory).

> >

The physics of how relatively-moving bodies interact in real life is //never// conducted in totally empty space (because the space under consideration has to contain the bodies!), so our third postulate should probably be that the "mathematical" lightbeam geometry derived by SR for empty space is still correct in the presence of physically-real moving masses and observers.

>	Physics is never exact. All that is required is that other effects are small enough to be neglected. Here on earth that is so (see below).

Mmm ... according to Einstein's description of the effects that appear under GR, rotational motion and forcibly accelerated motion both create significant deviations from flat spacetime. The calculated magnitude of those effects for circling bodies was the same as the magnitude of SR effects, leading to the assumption that we could describe the time dilation of a circling clock either as an SR time- dilation effect due to speed, or as a gravitational time- dilation effect due to the apparent radial ("Machian") gravitational field due to rotation. It was assumed that if a central observer didn't rotate with the centrifuge then they could blame the effect on relative motion and SR, but if they rotated with the centrifuge, so that there was no relative motion between the two, they could explain exactly the same result by blaming spacetime curvature.

In 1960, those two arguments were found to be in apparent conflict, because if we allowed the gravitational calculation, the associated intrinsic curvature would be present for both the rotating and the non-rotating observers. This suggested that the gravitational interpretation had priority and that the SR interpretation wasn't fundamental, but was providing a sort of rough "flat approximation" of effects that were intrinsically curved-spacetime phenomena.

In late 1960 the community apparently decided that losing SR wasn't acceptable, and standardised on the "SR" explanation rather than the "curvature-based" one.

If we'd taken the other path and given the GPoR priority over SR, then we'd have lost special relativity and would have had to implement a curved-spacetime replacement, with curvature effects being fundamental not only to relative acceleration and relative rotation, but also to relative velocity.

Nowadays (post-1960), we "know" that gravitational/ distortional effects don't play a part in everyday physics because we "know" that SR is correct and that the GPoR isn't to be taken too seriously. Where the GPoR and SR generate similar predictions for an effect, we say that the SR version is correct and the GPoR version is wrong, and that the success of the SR explanation means that there's nothing left for the GPoR to explain, and therefore no measurable effect due to acceleration (see: "SR clock hypothesis").

But this "knowledge" is based on interpretation rather than raw phenomenology. We believe it because we grew up in a society where SR was the norm.

If in 1960 the community had decided to take the other "fork in the road" and had decided to support the GPoR rather than SR, we'd now be saying with similar certainty that that we "know" that distortional effects are strong in rotation and and acceleration, that we "know" that particle lifetimes in accelerator storage rings support the GPoR rather than SR, and that we "know" that SR isn't correct core theory.

Until we have better reasons for selecting one or other of these two interpretations, I don't think that we can safely say that we "know" that curvature effects are vanishingly weak and too small to worry about in Earth-based physics. I think that people are certainly entitled to argue in favour of that position, but I don't think that the issue has yet been settled.

> >	If we don't apply this third postulate, we can imagine a different physics that still obeys the principle of relativity and the law of local lightspeed constancy, without being the 1905 theory.

>	But the key theoretical characteristic of SR is Lorentz invariance; local lightspeed constancy is required for that, but is itself not very important, theoretically. Without your "third postulate" (or equivalent) you don't have Lorentz invariance, and arrive at an essentially useless theory ...

IMO, The current concept of Lorentz invariance hasn't yet been shown to be essential to relativity theory.

The principle of relativity seems to require that there be a "Lorentzlike" factor involved, expressable as the ratio [1 - vv/cc]^x, where the exponent has a value in the range 0.5 to 1 ... but it doesn't tell us what that exponent's value ought to be.

* If we assume that the existence and motion of particles has zero effect on the lightbeam geometry of a region, we can set x=0.5 and get the unique flat-spacetime solution of special relativity. * If we assume that the recoverable kinetic energy of a system is expressed as a physical spacetime distortion between moving bodies, then we need a value of x that's greater than 0.5, but no greater than 1. * If we require the theory to also produce the classical counterpart of Hawking radiation (for compatibility with QM), we seem to require x to be equal to one.

Assuming flat spacetime gives a straightforward way of immediately ruling out all possibilities apart from x=0.5 ... which is certainly convenient ... , but that doesn't necessarily mean that x=0.5 is the right answer.

>	... (examples of other useless theories below).

> >

For instance, we could take Fresnel's early C19th idea of local light-dragging as the basis of a relativistic dragged-light model, eliminate the "aether" terminology and restate it as a geometrical theory where the dragging is a gravitoelectromagnetic effect, use GEM to regulate local lightspeeds and use W.K. Clifford's late C19th concept of "all physics as curvature" to reject the idea of moving-body physics having a valid flat-spacetime solution. We'd then have a different theory of relativity that'd seem to agree with the physical evidence available in 1905, but which wouldn't be Einstein's special theory.

>

I don't think that any of this leads anywhere useful, for the simple reason that here on earth spacetime curvature is quite small (on the order of 1 part-per-million). Of course some experiments are sensitive enough to detect that, but the great majority are not. This is easy to compute: in coordinates fixed to the earth, the moon follows a helical path with radius 1.3 light-sec and period 27.3 light-days. That helix differs from a straight line by about 0.5 ppm. Somewhat larger values apply to falling rocks near the surface.

I think you've just produced an excellent argument for why it can be dangerous to artificially set the strength of "puny" effects to zero. If we tried to construct a theory of gravity, and said that the moon's deviation from a straight line was only about 0.5ppm, and that the deviation was too small to be taken seriously, and should be set to zero ... and we then based a gravitational theory on the assumption that it //was// zero ... we would be liable to get a very bad theory.

It's often the job of theoretical physics to fixate on effects that are so small as to be undetectable or nearly-undetectable, but which should (or might) exist, and to calculate the consequences, not just of the effects themselves, but of the design changes that we make to theories to accommodate those imperceptibly-small effects.

It's the job of theoretical physics to try to be ahead of the experimental data. If we're operating in a region where the theoretical inputs and outputs are all well within the range that can be easily measured and verified, then we're probably not doing theoretical physics but engineering.

> >

Physicists in 1905 may have believed that two postulates were sufficient to make SR inevitable, but we now have a broader and more sophisticated conceptual vocabulary, which opens up other possibilities. This means that defining SR's position within "theory-space" and distinguishing it from its neighbours requires more parameters.

>	Hmmmm. I don't think those "neighbors" are useful at all.

Knowing which set of Lorentzlike equations is the correct one impacts on some interesting issues, ranging from horizon physics, to the problem of how to reconcile GR with QM, to whether or not we can ever build a warp drive.

SR's "near neighbours" where the Lorentzlike difference is small are probably not all that interesting (except as a proofs of concept), but the solution at the farthest end of the range from SR (x=1 rather than 0.5), with nominal relationships that are redder and shorter than SR's by one complete extra Lorentz factor, is IMO rather intriguing.

If future experiments turn out to confirm that this "redder" solution is more accurate than the SR version, then modifying GR to accept the revised equations would seem to solve the black hole information paradox. That would be a useful thing.

>

You did not mention the infinite set of aether theories which are experimentally indistinguishable from SR. These are theories in which the round-trip vacuum speed of light is isotropically c in every inertial frame, but the one-say speed of light differs from c; how it differs distinguishes these theories from one another. This set includes Lorentz Ether Theory (LET), the Tangherlini transforms, and an infinite number of even less well known theories. Except for SR, none of them are useful theoretically, as they do not obey Lorentz invariance. These are discussed by Zhang, were he calls them "Edwards frames". Zhang, _Special_Relativity_and_its_Experimental_Foundations_.

You're right, I'm less interested in theories that are completely identical to SR, or completely experimentally indistinguishable from SR, and which don't obviously lead to any new physics.

The switch from a flat SR approach to a relativistic acoustic metric isn't in that category, though - it'd seem to reinstate the GPoR as a proper principle, it'd seem to fix most or all of the outstanding problems with GR including the incompatibility with QM, it'd lead to GR being extendable down to the realm of particle physics, it'd change the way that we think about gravitational horizons, and it'd allow experimental verification (or disproof) using lab-scale physics.

I had a look though as much of the relevant parts of that Zhang book as I could using Google Books preview, but I didn't see anything that seemed to me to be in this league.

BTW, in the Zhang book, the term "SR test theory" seems to be used to mean "a theory to be compared against SR", whereas in all the papers I've seen, it usually means "the principles and procedures of how we should go about comparing SR against other theories".

I've always used this second definition - if you're more familiar with the first, from Zhang's book, then some of my older posts may seem rather confusing.

Eric

106 The two postulates in Special Relativity

Aren't there at least three or four postulates to begin with? Or, isn't there at least two or three postulates entangled just in #1 above?

Something like:

0. Motion is not many-body, multiple-state or multiple-field-field related but arises only due to universe being composed of space and time describable in terms as inertial frames. 2. The laws of physics take the same form in all inertial frames (described in terms of increments, and increments orf increments of the assumed space and time). 3. In any given inertial system the velocity of light c is the same whether the light be emitted by a body at rest or by a body in uniform motion.

Ralph

107 The two postulates in Special Relativity

Eric,

In order to unravel what you mean with GPoR (General Principle of Relativity) I found this link (Search "Eric Baird GPoR")

108 The two postulates in Special Relativity

>	If we'd taken the other path and given the GPoR priority over SR, then we'd have lost special relativity

Why is that? If SR worked as well as the other approach you simply would have had the luxury to keep both of them!

>	and would have had to implement a curved-spacetime replacement, with

curvature effects being fundamental not only to relative acceleration and relative rotation, but also to relative velocity.

Why the latter? Constant velocity can never transform flat coordinates to a non-flat situation. So you would not have had to implement that (nor even have been able to do so, in fact).

-- Jos

109 The two postulates in Special Relativity

Dne 16/05/2016 v 05:02 Nicolaas Vroom napsal(a):

>

This text raises the following question: How important are observers related to the study of science? IMO generally speaking zero. For medicine this is 100%. The laws of "nature" are independent of humans. What is important are the concepts of speed and acceleration. What is also important that you first start from a fixed reference coordination system. When that leads to contradiction you can try something else. When you start from a fixed frame all observers fixed to the frame are the same and there are no moving clocks involved. It is like placing the Sun in the center of the solar system and not the earth.

As experimental information and feedback in science is get from ( generalized ) observers, the statement their importance is zero is .... ... interesting.

The consequence would be physics can be reduced to the theoretical physics and no examination is needed.

-- Poutnik ( The Pilgrim, Der Wanderer ) Knowledge makes great men humble, but small men arrogant.

110 The two postulates in Special Relativity

Again I would like to comment on this text but in a more general(?) way.

Consider the following experiment. At point A you have a lightsource and a photon detector. At point B a distance x away, there is a mirror. With the lightsource you emit a flash at A which is reflected with the mirror at B and detected with the photon detector at A. All this sounds reasonable. Next you place a second mirror at C. The distance A-B = B-C = x You also place a mirror at A. At A in stead of one flash you simultaneous emit two flashes. The first flash goes from A to B back to A (reflection) to B and back to A. The second flash goes from A to C (reflection) and back to A.

Question: Are the two flashes finally arriving at A simultaneous? IMO because the distance is identical 4*(A-B) = 2*(A-C) they will arrive simultaneous. But there is more: you can move this setup in any direction horizontal and the answer will be the same. Ofcourse such an experiment in reality is extremely difficult and the accuracy not very reliable.

Next we perform the same experiment but now in vertical direction. Point A is at the top and point C at the bottom. There are two possible outcomes in principle:
1) The two final flashes arrive simultaneous.
2) The two final flashes do not arrive simultaneous. The one which goes via the bottom first.

When the result is (1) the speed of light is constant and you can describe the experiment using SR.
When the result is (2) the speed of light is not constant and you must describe the experiment using GR. (GPoR)

Any comments?

Nicolaas Vroom

111 The two postulates in Special Relativity

Dne 20/05/2016 v 04:43 Poutnik napsal(a):

>

[[Mod. note -- 1. I apologise for the delay in processing this article, which arrived at my moderation inbox on monday 2016-05-16. 2. It's very important to distinguish between the following different meanings of the word "observer": - an inertial reference frame in the context of special relativity - a *macroscopic* observer in the context of quantum mechanics ("an observation collapses the wave function") - a worldline in general relativity - a coordinate system in general relativity -- jt]]

---------------------------------

>>

>	As experimental information and feedback in science is get from ( generalized ) observers, the statement their importance is zero is .... .... interesting.

- show quoted text -

112 The two postulates in Special Relativity

Your description is incomplete, as you did not specify the distance A to C.

If I suppose that the distance A-C is twice A-B, then your description is still incomplete; if I further suppose that all components are at rest in an inertial frame in a region in which gravitation is negligible, then the two flashes arrive at A simultaneously. [These further suppositions permit me to apply SR in a simple and obvious manner.]

>	IMO because the distance is identical 4*(A-B) = 2*(A-C) they will arrive simultaneous.

Your description did not say this, but it is my first supposition in the second paragraph above. Apparently you are assuming (but did not say) that A, B, and C are lined up along a straight line, with B midway between A and C. How the two flashes are kept separate and follow their specified paths is not mentioned, but this is a detail we can ignore.

>	But there is more: you can move this setup in any direction horizontal and the answer will be the same.

Perhaps. If the further suppositions above are valid this is true for any meaning of "horizontal", but if they do not hold this might not, either.

>	Ofcourse such an experiment in reality is extremely difficult and the accuracy not very reliable.

Let's keep this a gedanken.

>	Next we perform the same experiment but now in vertical direction.

If the further suppositions above are valid, then "vertical" has no real meaning and is the same as "horizontal".

So I assume this means you don't want to make my further suppositions above, and want to consider gravity to be important. This opens a very large can of worms as one must apply GR.... As a simple example, there is now no definite meaning to "distance A-B", and you must specify how it is to be measured (i.e. along which spacelike geodesic; this is directly related to choosing a time coordinate...). Remember that above I had to suppose all components were at rest in some inertial frame, which resolves this ambiguity for SR, but not for GR with non-negligible gravity.

To proceed, let me make these further assumptions (which I suspect are what you have in mind); remember this is a gedanken:
* the experiment is performed on the surface of the earth
* the earth is a perfect sphere with its usual mass
* all other massive objects are ignored, as is the atmosphere
* all components are supported against gravity, on the surface
* horizontal means a constant altitude from the surface * vertical means along a radius from the center of the earth
* the metric is static (follows from the above assumptions)
* the time coordinate is the timelike Killing vector
* all distance measurements are made along spacelike geodesics orthogonal to the time coordinate
* All components are very close together compared to the radius of the earth. In particular, within the apparatus the difference between an initially horizontal spacelike geodesic and an initially horizontal null geodesic is negligible (note that neither is the "horizontal distance", but this assumption also makes the difference to that be negligible).

Explanation of this last: if two points have identical altitudes, the (constant-time) spacelike geodesic along which the distance between them is measured does not have that altitude everywhere between them, and there is no such thing as a "horizontal plane"; this assumption makes the effect of that be negligible within the apparatus and permits me to use a horizontal plane there.

[These deal with the major worms; I'll ignore any others.]

First let me consider a simpler physical situation: A still has a pulsed light source and detector; there are mirrors at D and E which are always a distance x from A, but their positions (orientations wrt A) can vary; A can always send a pulse to both D and E and detect the two reflected pulses (i.e. the mirrors are always adjusted to make this so, as is the detector orientation).

If A, D, and E are all in a horizontal plane, then the pulses arrive at A simultaneously. If they are not in a horizontal plane, then the pulses in general do NOT arrive simultaneously at A (for certain specific situations they can, such as D-A-E forming a vertical "V").

Consider A-D horizontal, and A-E vertical, with E above A. Remember the distance A-D = A-E, and both distances are measured simultaneously in the above coordinates. The pulse A->E->A will arrive before the pulse A->D->A. If E is vertically below A, then A->E->A will arrive after A->D->A.

For your physical situation with A, B, and C along a straight line with B midway between A and C, and the light traverses A-B four times and A-C twice: if the line is horizontal the pulses arrive simultaneously; if A-C is vertically upward, A->C->A arrives before A->B->A->B->A; if A-C is vertically downward, A->C->A arrives after A->B->A->B->A.

Note all these non-simultaneous arrivals come far too close together to actually measure in a real experiment with x less than a km or so. So this must remain a gedanken unless possibly an interferometer setup can be invented; the basic problem is comparing horizontal and vertical distances to the required accuracy without using light (use light and the result is fore-ordained).

>	There are two possible outcomes in principle: 1) The two final flashes arrive simultaneous. 2) The two final flashes do not arrive simultaneous. When the result is (1) the speed of light is constant and you can describe the experiment using SR.

Not necessarily (see below).

>	When the result is (2) the speed of light is not constant and you must describe the experiment using GR.

If gravitation is not negligible, you cannot use SR and must use GR. Even if you happen to luck out and the flashes arrive simultaneously.

Tom Roberts

113 The two postulates in Special Relativity

I have to apoligize. I should have drawn a sketch

'  A--------------B--------------C
'Light           Mirror        Mirror

'  E0------------->
'  <---------------  From A to B to A to B
'  --------------->
'  E1<-------------
'  E0---------------------------->
'  E2<----------------------------   from A to C to A

> >	At A in stead of one flash you simultaneous emit two flashes. The first flash goes from A to B back to A to B and back to A. The second flash goes from A to C (reflection) and back to A. Question: Are the two flashes finally arriving at A simultaneous?

>	Your description is incomplete, as you did not specify the distance A to C.

All is in horizontal plane on surface of the earth
The two original lightflashes are at E0.
Via B the second detection at A is at E1
Via C the first detection at A is at E2
The question is are E1 and E2 simultaneous.

>

If I suppose that the distance A-C is twice A-B, then your description is still incomplete; if I further suppose that all components are at rest in an inertial frame in a region in which gravitation is negligible, then the two flashes arrive at A simultaneously. [These further suppositions permit me to apply SR in a simple and obvious manner.]

I agree with you in the horizontal setup

>

> >	IMO because the distance is identical 4*(A-B) = 2*(A-C) they will arrive simultaneous.

>

Your description did not say this, but it is my first supposition in the second paragraph above. Apparently you are assuming (but did not say) that A, B, and C are lined up along a straight line, with B midway between A and C. How the two flashes are kept separate and follow their specified paths is not mentioned, but this is a detail we can ignore.

I agree.

> >	But there is more: you can move this setup in any direction horizontal and the answer will be the same.

>	Perhaps. If the further suppositions above are valid this is true for any meaning of "horizontal", but if they do not hold this might not, either.

I agree

> >	Next we perform the same experiment but now in vertical direction.

>	If the further suppositions above are valid, then "vertical" has no real meaning and is the same as "horizontal".

No that's not I have in mind. The idea is that the whole set up is in a vertical direction and that the light signal first travels towards the center of the earth.

>

So I assume this means you don't want to make my further suppositions above, and want to consider gravity to be important. This opens a very large can of worms as one must apply GR.... As a simple example, there is now no definite meaning to "distance A-B", and you must specify how it is to be measured (i.e. along which spacelike geodesic; this is directly related to choosing a time coordinate...). Remember that above I had to suppose all components were at rest in some inertial frame, which resolves this ambiguity for SR, but not for GR with non-negligible gravity. To proceed, let me make these further assumptions (which I suspect are what you have in mind); remember this is a gedanken:

Sorry SNIP

I like all the technical subtleties you bring into this discussion but I do not know if they are necessary.

>

Explanation of this last: if two points have identical altitudes, the (constant-time) spacelike geodesic along which the distance between them is measured does not have that altitude everywhere between them, and there is no such thing as a "horizontal plane"; this assumption makes the effect of that be negligible within the apparatus and permits me to use a horizontal plane there. First let me consider a simpler physical situation: A still has a pulsed light source and detector; there are mirrors at D and E which are always a distance x from A, but their positions (orientations wrt A) can vary; A can always send a pulse to both D and E and detect the two reflected pulses (i.e. the mirrors are always adjusted to make this so, as is the detector orientation). If A, D, and E are all in a horizontal plane, then the pulses arrive at A simultaneously.

I agree

>

If they are not in a horizontal plane, then the pulses in general do NOT arrive simultaneously at A (for certain specific situations they can, such as D-A-E forming a vertical "V"). Consider A-D horizontal, and A-E vertical, with E above A. Remember the distance A-D = A-E, and both distances are measured simultaneously in the above coordinates.

I have difficulties in understanding this sentence.

>	The pulse A->E->A will arrive before the pulse A->D->A.

In this case A is "high" above the surface of the earth and so is D

>	If E is vertically below A, then A->E->A will arrive after A->D->A.

In this case A is at the surface of the flat earth and so is D

In this case gravity has to be considered. Tricky IMO this example is much more complex than I have in mind.

>	For your physical situation with A, B, and C along a straight line with B midway between A and C, and the light traverses A-B four times and A-C twice: if the line is horizontal the pulses arrive simultaneously; if A-C is vertically upward, A->C->A arrives before A->B->A->B->A;

Both A-C and A-B are upward.

>	if A-C is vertically downward, A->C->A arrives after A->B->A->B->A.

Both A-C and A-B are downward. This is the situation I have in mind.

The issue is that when you perform such an experiment gravity is involved and SR is not sufficient.
The center idea is that incase of AB 4 times the same path (length) is considered. In the case of AC this is also the situation.
However (downward) the difference is that in the case of AB two times a path AB is considered and in the case of AC two times the path BC is considered.
AB is rougly speaking high above the surface and BC low above the surface. The issue is if this has any relation with the speed of light.
When the speed increases going from top to bottom this will mean that light via C arrives earlier than light via B (at A)
When the speed decreases going from top to bottom this will mean that light via C arrives later than light via B (at A)

>

Note all these non-simultaneous arrivals come far too close together to actually measure in a real experiment with x less than a km or so. So this must remain a gedanken unless possibly an interferometer setup can be invented; the basic problem is comparing horizontal and vertical distances to the required accuracy without using light (use light and the result is fore-ordained).

I fully agree with you. Such an experiment is in practice very difficult to perform. The whole issue is that, no clock is involved. However that is not totally true. The signal ABABA services as a clock for the signal ACA.

> >	There are two possible outcomes in principle: 1) The two final flashes arrive simultaneous. 2) The two final flashes do not arrive simultaneous. When the result is (1) the speed of light is constant and you can describe the experiment using SR.

>	Not necessarily (see below).

> >	When the result is (2) the speed of light is not constant and you must describe the experiment using GR.

>	If gravitation is not negligible, you cannot use SR and must use GR. Even if you happen to luck out and the flashes arrive simultaneously.

Exactly. You have to use GR for the vertical set up. That is what I have in mind to challenge that the speed of light is constant.

However there is more it places the importance of GR above SR. And you can ask yourself the question how important is the third postulate proposed by Eric Baird.

>	Tom Roberts

Thanks

Nicolaas Vroom

114 The two postulates in Special Relativity

' A--------------B--------------C
' Light          Mirror         Mirror

All is in horizontal plane on surface of the earth

And we agree that light A->B->A->B->A arrives at A simultaneously with light A->C->A. (Distance A-B = distance B-C.)

>>>	Next we perform the same experiment but now in vertical direction.

>	The idea is that the whole set up is in a vertical direction and that the light signal first travels towards the center of the earth. [...] In this case gravity has to be considered. Tricky

Not terribly tricky.

The trick is keeping FIRMLY IN MIND what one means by "speed". Remember that in GR the LOCAL speed of light in vacuum is always c when measured in a locally inertial frame. Remember also that the size of such a locally inertial frame depends on the measurement accuracy with which one can make the relevant measurements.

From that we can immediately conclude if the distance A-C is "small" enough, and if the apparatus is in freefall, the two light pulses above will arrive simultaneously at A, regardless of the orientation of the apparatus. (This basically means that the measurement resolution is insufficient to observe the difference in their arrival times.)

But you want to keep the apparatus at rest on earth's surface, and you want to use essentially infinite accuracy. So the apparatus is not at rest in a locally inertial frame. All is not lost, and we can make some conclusions (see below).

>>	if A-C is vertically downward, A->C->A arrives after A->B->A->B->A.

>	Both A-C and A-B are downward. This is the situation I have in mind. The issue is that when you perform such an experiment gravity is involved and SR is not sufficient.

Yes. But very general things are known about GR. For this conclusion I simply applied the analysis of the Shapiro time delay -- B-C is below A-B, and thus from the perspective of an observer at A, light traversing B-C is delayed more than light traversing A-B. Hence I can make this conclusion without performing a detailed calculation.

But I would NOT claim "light travels slower B-C than A-B". That would be a PUN on "speed", because we normally reserve that word for measurements in locally inertial frames. And also because we did not measure it.

Interesting observation: as in QM, in GR it is usually not possible to discuss quantities which were not measured. Here the delays of pulses are measured (compared) and I can make definitive statements about them; but their speed is NOT measured, and I cannot make definite statements. It is remarkable that the two major revolutions in physics of the 20th century, quantum mechanics and relativity, share this emphasis on measurements. But the reasons for this similarity are QUITE different: in QM it is because such quantities have no definite value, while in GR it happens because such statements invariably involve a choice of coordinates, and such choices are arbitrary (coordinate-dependent quantities need not reflect the underlying physical processes as they also involve aspects of the coordinate choice).

Why are measurements so "special" in GR? -- because they are necessarily independent of coordinates. That is, every measurement projects the quantity being measured onto the measuring instrument. As you were taught in kindergarten, the ruler must be aligned with the object to measure its length (the ruler projects onto itself, and if not aligned the projection will not be the desired result); this is inherently a very general aspect of measuring instruments.

>	You have to use GR for the vertical set up. That is what I have in mind to challenge that the speed of light is constant.

Hmmmm. As I said above: keep FIRMLY IN MIND what you mean by "speed". When you try to say "the speed of light is not constant" you are using a PUN on "speed". The vacuum speed of light measured in a locally inertial frame is c, everywhere and everywhen. But if you choose to divide a distance by a flight time and call the result "speed", even when the measurements are not in a locally inertial frame, then OF COURSE you can obtain a result not equal to c. Indeed GR predicts this (c.f the Shapiro time delay -- if you insist on calling the result "speed" then of course it is not equal to c; that's why it is termed a DELAY and not a "reduction in speed").

>	However there is more it places the importance of GR above SR.

Yes, of course. The only reasons SR is still taught are a) because it is the local limit of GR, and b) is ENORMOUSLY less difficult to apply [#].

Moreover, most ordinary measurements are made in a locally inertial frame in which SR can be applied with negligible error. This includes every aspect of our daily lives, every elementary- particle experiment, and almost all optical experiments performed on a table.

[#] Remember the details I gave earlier in this thread, for the horizontal situation where the light path does not correspond to a spacelike geodesic between endpoints A-C -- so what does "distance" mean when attempting to apply the definition of speed? No matter what you do, you will have to CHOOSE coordinates (or at least a foliation of spacetime into space and time), and the result will depend on your choice.

>	And you can ask yourself the question how important is the third postulate proposed by Eric Baird.

He proposed adding "flat spacetime" -- that is inherent in applying SR and presuming it to be exact. But as the local limit of GR it can be a very useful and accurate approximation in many physical situations of interest.

Tom Roberts

115 The two postulates in Special Relativity

Sorry I have to skip this part.

> >>	if A-C is vertically downward, A->C->A arrives after A->B->A->B->A.

> >	Both A-C and A-B are downward. This is the situation I have in mind. The issue is that when you perform such an experiment gravity is involved and SR is not sufficient.

>

Yes. But very general things are known about GR. For this conclusion I simply applied the analysis of the Shapiro time delay -- B-C is below A-B, and thus from the perspective of an observer at A, light traversing B-C is delayed more than light traversing A-B. Hence I can make this conclusion without performing a detailed calculation.

In order to refresh my mind about the Spapiro effect I have studied paragraph 15.6 (page 204) from the book 1:"Introducing Einstein's Relativity" by Ray d'Inverno and page 1106 etc of the book 2:"Gravitation."

Consider dropping a ball A from the top of a tower with height h. The ball is reflected completely without any friction. T1 is the moment when the ball A is back at the top Consider dropping a second ball B simultaneous with A from the top, however this ball is reflected at height h/2. When ball B is back at the top the ball is immediate dropped again. T2 is the moment when ball B is back at the top for the second time. Question is T1=T2 or T1T1 ? IMO T1 What you claim that when photons are used this is not the case: T1>T2. Your argumentation is based on the Shapiro effect. Book 1 at page 205 writes: "Time delay of light signals is intimately connected with light bending." The problem is when you send a light signal from a point in space straight towards earth and simultaneous from the same distance but now the path passes close to an object than this path will be bended and will arrive later or delayed compared with the first. The primary reason is that the path is longer. I remember that the same phenomena has been detected, with the aid of gravitational lensing around galaxies and with the aid supernovae.

But that is not what I want. I'am interested in the behavior of a light signal with goes "undisturbed" straight towards to the (center of) the earth. For example starting half way between the Moon and the Earth.

The initial speed can be "c". The first question is will this speed increase or decrease or decrease when the photons travel towards the earth.

>	But I would NOT claim "light travels slower B-C than A-B". That would be a PUN on "speed", because we normally reserve that word for measurements in locally inertial frames. And also because we did not measure it.

I'am not that "strict". If you compare two light signals, which both travel over the same distance and the first arrives before the second than the speed of the first is higher than the second without any indication what the actual speed is.

>	Interesting observation: as in QM, in GR it is usually not possible to discuss quantities which were not measured. Here the delays of pulses are measured (compared) and I can make definitive statements about them; but their speed is NOT measured, and I cannot make definite statements.

I agree with this, but I do not think this is particular related to GR. IMO there is a hugh difference for the laws that are relevent at macro niveau versus micro niveau. You "can not" use GR to predict earthquakes.

>

It is remarkable that the two major revolutions in physics of the 20th century, quantum mechanics and relativity, share this emphasis on measurements. But the reasons for this similarity are QUITE different: in QM it is because such quantities have no definite value, while in GR it happens because such statements invariably involve a choice of coordinates, and such choices are arbitrary

This whole discussion is very tricky. Suppose you want to simulate a whole galaxy. To do that you have to measure the position of the stars involved over a series of intervals. In order to do that you need one coordinate system. When the positions are known the next step is to calculate the masses of the stars in the galaxy, using a certain model. However in order to measure the position of a single star light signals are involved which have to be corrected because the signals are bended by masses of stars inbetween this single star and the measuring instrument. In fact you have to take the behaviour of photons (QM?) into account if you want to do this very accurate.

>

Why are measurements so "special" in GR? -- because they are necessarily independent of coordinates. That is, every measurement projects the quantity being measured onto the measuring instrument. As you were taught in kindergarten, the ruler must be aligned with the object to measure its length (the ruler projects onto itself, and if not aligned the projection will not be the desired result); this is inherently a very general aspect of measuring instruments.

For me a much more important issue is the relation of a measurement versus a calculation. Went you want to know the order of the runners in a maraton this is a (direct) measurement. The first one arriving runs the fastest. When you want to know the speed of each runner this is a calculation because it depents on two measurements.

>	The vacuum speed of light measured in a locally inertial frame is c, everywhere and everywhen. IMO this is a calculation. When you declare c

a constant this make certain things simpler and but also introduces others: What is a meter or what is a second.

>

But if you choose to divide a distance by a flight time and call the result "speed", even when the measurements are not in a locally inertial frame, then OF COURSE you can obtain a result not equal to c. Indeed GR predicts this (c.f the Shapiro time delay -- if you insist on calling the result "speed" then of course it is not equal to c; that's why it is termed a DELAY and not a "reduction in speed").

When you study Fig 15.13 book 1 the shortest distance is called D. In fig 40.3 book 2 this is the distance slightly larger than b. For me the important question is the speed of light constant from transmitter to reflector? Is the speed the highest at the shortest distance near the Sun? To answer that question IMO you have to divide the path in for example 10 smaller parts with the same length and investigate each. In the experiment I propose I try to answer that same question very close to the earth by comparing two signals without the aid of a clock and "no" mathematics.

Thanks Tom.

Nicolaas Vroom

116 The two postulates in Special Relativity

Is the speed the highest at the shortest distance near the

>	Sun? To answer that question IMO you have to divide the path in for example 10 smaller parts with the same length and investigate each. In the experiment I propose I try to answer that same question very close to the earth by comparing two signals without the aid of a clock and "no" mathematics.

Suppose there was self aware matter that could answer these questions? I put it to you that we are self aware matter and if it does not seem to be logical from our shoes then all efforts should be made to make sense of it. Myself having lucked out as being self aware matter for a brief period of time can say the consistency of the speed of light is only true for measurements the observer not reality in the larger picture. Your only obligation to fulfill the postulate of SR is to measure the speed of light to be c. This is not the same as saying the speed of light is constant at c. If one lived in a hot air balloon it is never a windy day and one could conclude that the speed of sound is constant at 1000 feet per second. If we are a product of a vacuum we would be under the same illusion that the speed of light is constant. However a hot air balloon Einstein would never be noted as a hero in physics as every hot air balloon person would be is aware that temperature effects time. A hot air person , cloud in the sky , will know intuitively to leave earlier to arrive on time on a cold day. Temperature effects time. What seems obvious to a cloud in the sky could lead to misunderstanding to us as solids so we celebrate Einstein as a hero in physics. A vacuum sets time for us in the same way the temperature effects time for a cloud in the sky. Both the cloud gas and ourselves solids think the speed of sound for clouds and the speed of light is constant by measurements made in both cases. In both cases we are wrong for the same reasons. There is no way the speed of light is c near a black hole as this would violate the postulate the laws physics are the same for all Frames of reference. The speed of light only measures c for the same reason the speed of sound always measure 1000 feet per second for a hot air balloon.

117 The two postulates in Special Relativity

The concept of "self aware matter" is out side the physical reality which makes any discussion immediate tricky.

>	Your only obligation to fulfill the postulate of SR is to measure the speed of light to be c. This is not the same as saying the speed of light is constant at c.

The current topic in the discussion is the speed of light. What I try to answer is the question: is this speed always the same or is this speed variable. Specific I want to find out "if" and "what" the influence of matter or gravity is. The influence of vacuum should also be considered. What I presently do not want to discuss is the actual (average?) value of the speed of light. In order to study the behaviour of photons, I propose an experiment (using light, a tower and mirrors). See previous postings. The current discussion is to predict the outcome of this experiment. My understanding is that the speed will increase when the photons approach the earth. In fact when you send a light signal from the sun towards the earth, first the speed will decrease and than increase.

The problem with this whole discussion is that it belongs more in the newsgroup :Sci.physics.foundations. However at this moment this is impossible, because the newsgroup is temporary "out of order".

118 The two postulates in Special Relativity

119 The two postulates in Special Relativity

>	In article <04c3fc41-22cb-43aa-b594-84fb25c038ae@googlegroups.com>, Nicolaas Vroom writes: > Op woensdag 22 juni 2016 03:23:17 UTC+2 schreef John Heath:

>>	When you study: https://en.wikipedia.org/wiki/Speed_of_light you can read: "the metre was redefined in the SI Units as the distance travelled by light in vacuum in 1/299792458 of a second." The problem with this defintion is when the speed is not constant the length of a metre also changes.

>	If the speed of light is not constant, there would be many other worries besides problems with the definition of the metre!

Very few, actually. The speed of light is both a *concept* (let's call it c0=1 for simplicity) and a measured quantity 'c' (though via the SI the latter has to be done indirectly).

The *experimentally* established mass of the photon is smaller than 10^-18 eV [1] - everything below that is simply terra incognita. It could be that the photon had a mass of, say 4*10^-21 eV. That would lead to not only to a speed of light different from c0 but also a *frequency dependent* speed of light.

Not a problem there, obviously, as this might actually be the case for all that we know.

Now, the *concept* of a finite speed limit in the Universe is fully independent of any actual physical realisation or, indeed, experimental proof.

If it turned out that 'real' light is not quite the 'conceptual light' and that the photon has a mass, very few actual things would change. So few, that with all our rather well developed measurement devices we are currently not able to measure the effects of a massive photon, provided the mass is smaller than said 10^-18 eV.

[1] Interestingly enough, the mass of the graviton (or in absence of a quantum theory of gravity, the dispersion of gravitational waves) is known better than that - m_g < 1.2e-22 eV. Still, we call it 'speed of light' and not 'speed of gravity', because the for the ART, it is the *concept* that matters, not so much the actual speed. -- Space - The final frontier

120 The two postulates in Special Relativity

121 The two postulates in Special Relativity

122 The two postulates in Special Relativity

What is physical wrong with the idea that the speed of light (radiation) is not always the same? (can vary). The same with any particle? The opposite would be amazing. Why should the speed be constant

As I said before this whole discussion belongs more in the newsgroup: sci.physics.foundations. When consider the above definition of a metre you must also define what a second is and such a second must also be a physical constant process. We know by experiment that that is also difficult to establish. A whole different physical issue the speed of gravition. It is physical possible that this speed is much more "fixed" (stable?) than the speed of light. In principle such a speed (if constant) is a better starting point to define a metre. (But is has its own problems)

> >

What is important as part of this discussion: what is the definition of a vacuum. Accordingly to: https://en.wikipedia.org/wiki/Vacuum : "Vacuum is space void of matter" But that does not exist in outerspace. In fact the whole universe is filled with photons, which makes any definition based on vacuum misleading(?)

>	No; you can always discuss the limit of a true vacuum.

The point is when you use the concept "vacuum" in a defintion than the concept vacuum should also clearly be defined. I doubt it is. A different issue is than also always when you consider the speed of light in any discussion it should be in a vacuum. The point is when the physical state between the Sun and the earth is not a vacuum than you cannot use the definition in order to measure distance. (Of course for most applications you can)

> >

A different reason, why the issue is important, is the program "VB light" See: https://www.nicvroom.be/VB%20Light%20operation.htm In this program light rays around matter are simulated, specific to study: "The bending of light around matter". What this simulation shows (based on Newton's Law) that the speed of light (photons) is not constant.

>	You can't expect to learn anything based on Newton's laws. We know that they are wrong. Yes, they are good approximations in some limits, but you have to know what those are before you can safely use Newton's laws.

I agree quantitatif that you are right. The point I want to make is that using Newton's Law you can see that the speed is not always the same, which raises an issue to be discussed.

>	The point is that any LOCAL measurement of the speed of light always gives the same value.

As I stated before it is primarily not my strategy to calculate the speed of light. What I want to challenge is the idea that this speed is not always the same. To do that I use one observer, two light sources, a tower, and two mirrors at different heights. The question is what is the outcome of the two experiments.

Nicolaas Vroom.

123 The two postulates in Special Relativity

>	My understanding is that the speed will increase when the photons approach the earth. In fact when you send a light signal from the sun towards the earth, first the speed will decrease and than increase.

You mean, you want to consider the combined gravitational field of Sun and Earth. The first thing you have to note then is that there is no known exact solution of GR field equations for a gravitational field with more than one centre of gravity. For one single centre of gravity, there is Schwarzschild solution, but for two or more centres of gravity, there is no exact solution known. And due to non-linearity of GR, you cannot simply construct such as solution by combining two Schwarzschild solutions.

However, you could argue that an eventual solution for two centres of gravity, like Sun and Earth, should in some way look similar to a combination of two Schwarzschild solutions, at least in that way that one should be able to find a coordinate system in which the speed of light, measured with respect to that coordinate systems, shows the behaviour you described.

>	The problem with this whole discussion is that it belongs more in the newsgroup :Sci.physics.foundations. However at this moment this is impossible, because the newsgroup is temporary "out of order".

Assumed, in spf would someone reply to you who has good knowledge in GR, his answer might probably be similar to the answers you got here. So, it wouldn't make any difference.

>	When you study: https://en.wikipedia.org/wiki/Speed_of_light you can read: "the metre was redefined in the SI Units as the distance travelled by light in vacuum in 1/299792458 of a second." The problem with this defintion is when the speed is not constant the length of a metre also changes.

As far as the variability of the speed of light due to gravitational effects is concerned, the metre definition is not touched in any way: to define the metre, one uses the speed of light measured with respect in a local inertial frame, which is applied in a small spacetime region limited enough to neglect gravitational effects and to apply the SR-limit of GR.

As far as an eventual variability of the speed of light is concerned that might occur even in a local inertial frame due to an eventual failure of GR and SR, the "problem" you described is not different from the "problem" any other metre definition would cause, and the definition of the unit of any other quantity causes. As you can read here:

124 The two postulates in Special Relativity

This IMO raises an issue when you want to study the merging of two black holes using GR.

>

However, you could argue that an eventual solution for two centres of gravity, like Sun and Earth, should in some way look similar to a combination of two Schwarzschild solutions, at least in that way that one should be able to find a coordinate system in which the speed of light, measured with respect to that coordinate systems, shows the behaviour you described.

As such we both agree.

> >	When you study: https://en.wikipedia.org/wiki/Speed_of_light you can read: "the metre was redefined in the SI Units as the distance travelled by light in vacuum in 1/299792458 of a second." The problem with this defintion is when the speed is not constant the length of a metre also changes.

>

As far as the variability of the speed of light due to gravitational effects is concerned, the metre definition is not touched in any way: to define the metre, one uses the speed of light measured with respect in a local inertial frame, which is applied in a small spacetime region limited enough to neglect gravitational effects and to apply the SR-limit of GR.

I agree with you, however this becomes an issue when light years are considered.

Sorry, I skipped a lot of your text but it is very worthwhile reading.

>

But even that is not really necessary. One could as well argue that there should be a speed of light, let's call it c0, that would be the speed of light in a hypothetical perfect vacuum. Then one could postulate that this speed c0 is always the same, in all inertial frames, and conclude that SR effects occur at velocities near this speed. From the fact that we observe SR effects near the real speed of light that we can factually measure in a real vacuum, let's call it c', we then can conclude that both speeds, c0 and c', are very close to each other.

I fully agree with you. The problem is more or less that in SR we start from the idea that the speed of light is constant (and in all directions the same) and equal to c. In reality this picture is much more complex.

> >

A different reason, why the issue is important, is the program "VB light" See: https://www.nicvroom.be/VB%20Light%20operation.htm In this program light rays around matter are simulated, specific to study: "The bending of light around matter". What this simulation shows (based on Newton's Law) that the speed of light (photons) is not constant.

>

It shows that in Newtonian Gravity, the speed of light is variable. Or more precisely: in Newtonian Gravity amended by some assumptions on how light is influenced by gravity. However, since Newtonian Gravity is known to be wrong, except in non-relativistic regime, this result shows little about reality. At best, is *suggests* that also in a relativistic theory of gravity, i.e. in GR, the speed of light should be variable in some way.

I fully agree. Specific I like the subtleties in your comments.

>	And indeed, in GR, the speed of light turns out to be variable in some way. Namely in that way, that the speed of light measured with respect to a general coordinate system is variable. But not the speed of light measured with respect to a local inertial frame.

I doubt how important the last is. What is the point when local implies a very small region, while in general what we want is to study the evolution of the universe.

Nicolaas Vroom.

125 The two postulates in Special Relativity

>>>	When you study: https://en.wikipedia.org/wiki/Speed_of_light you can read: "the metre was redefined in the SI Units as the distance travelled by light in vacuum in 1/299792458 of a second." The problem with this defintion is when the speed is not constant the length of a metre also changes.

>>	If the speed of light is not constant, there would be many other worries besides problems with the definition of the metre!

>	What is physical wrong with the idea that the speed of light (radiation) is not always the same? (can vary). The same with any particle? The opposite would be amazing. Why should the speed be constant

According to all our obversations, the speed of light is constant in situations where the SR-limit of GR is applicable, i.e. where gravitational effects can be neglected. So, obviously, it would be physically wrong to say that the speed of light would vary in those situations.

Or did you want to ask for a theoretical explaination for the constancy of the speed of light? Within the framework of Relativity (no matter if SR or GR), the constancy of the speed of light is a fundamental postulate, i.e. it is considered as a fundamental property of nature. So, it cannot be explained (in the sense that it could be derived from a more fundamental principle).

This, however, is no lack of Relativity: every imaginable physical theory is based on fundamental assumptions that are not explained themselves. Take e.g. Newtonian Mechanics: there, the fundamental assumptations are that the three Newtonian axioms apply and that simultaneity is absolute (or in other world: Galilei invariance applies). Newtonians Mechanics does not explain why the three axioms apply or why simultaneity is absolute, it consider both as fundamental properties.

Relativity instead makes the fundamental assumption that the speed of light is constant and Lorentz invariance applies (globally in SR and locally in GR). Before SR was founded it 1905, there was Lorentzian Ether Theory (LET) that "explained" the constancy of the speed of light by the ether influencing yardsticks and clocks when moving relative to the ether. However, this wasn't a real explaination: this mechanism was more complex than the assumption that the speed of light is constant, and therefore did not match the requirement that explainations have to be simple.

>	As I said before this whole discussion belongs more in the newsgroup: sci.physics.foundations. When consider the above definition of a metre you must also define what a second is

This is done: