1 If time dilates...

2 If time dilates...

"Time dilation" is a very poor name for the actual phenomenon, as it leads people like you to come up with all sorts of nonsense, and sometimes it even confuses people who should know better.

"Time dilation" applies to MEASUREMENTS OF CLOCK TICK RATES by observers in motion relative to the clock, or at a different gravitational potential. "Time" itself [#] never "dilates", and all (good) clocks always tick at their usual rate.

[#] In physics, "time is what clocks measure" [Einstein and others]. For the simple reason that in any experiment that involves time in any way, it is measured by a clock.

Tom Roberts

3 If time dilates...

A good clock is one that keeps time in synchronization with other good clocks. As we are discussing just the clocks, and not signals between them, the comparison must be made between co-located and co-moving clocks.

There is a chicken-egg issue here. The first good clock was the rotation of the earth, and all other good clocks are referenced to that rotation using successively more accurate technology.

Along the way it was found that the earth's rotation actually varies considerably, compared to the accuracy of atomic clocks.

A clock's usual rate is the rate at which it updates itself. A Cs-133 oscillator "ticks" at 9,192,631,770 Hz, but can be divided down to tick at 1 Hz. It is found experimentally that neither relative motion nor difference in gravitational potential affects the tick rate of any good clock -- they do, however, affect how SIGNALS BETWEEN CLOCKS are measured, giving rise to "time dilation" (which, as I have often said, is a very poor name for the actual phenomenon, because time does not "dilate", MEASUREMENTS do).

"Time dilation" is really a geometrical projection, and can have physical consequences. So, for instance, unstable particles traveling at 0.9999 c relative to the lab can travel (on average) 70.7 times further in the lab than their speed*lifetime, due to "time dilation".

Tom Roberts

4 If time dilates...

>	"Time dilation" applies to MEASUREMENTS OF CLOCK TICK RATES by observers in motion relative to the clock, or at a different gravitational potential.

I have a problem with this. Consider a clock with internal working is based on light signals. Consider observer A at rest with this clock at position X. During a certain period, observer A measures that the clock produces 100 counts. During that same period, observer B makes a trip around the clock starting at position X and finishing at position X. Observer B also observers that the clock produces 100 counts.

What this means that the behaviour of the clock is not influenced by any of the two observers.

Next, consider two identical clocks based on light signals. Consider Observer A at rest with these clocks at position X. Both clocks placed in a rocket and the engines of one of the rockets are fired and the rocket moves in a straight line to a point Z At Z the speed the rocket is stopped. The engine is set in reverse and the rocket returns back to position X. At X the two clocks are compared. The stay at home clock shows 1000 counts and the moving clock shows 900 counts. How come. 1. First of all the observer has nothing to do with this result. 2. Secondly, this is not a symmetrical experiment. 3. Thirdly this is a physical issue and the cause is related in the way the clocks are built. Physical investigation reveals that the light path of the moving clock between each count is longer as the light path of the stay at home clock. 4. Mathematics does not solve the issue either. First, we first must agree that the issue is physics. Next, we should study how different parameters influence this behaviour. Finally, you can try to catch this physical behaviour in a law.

>	"Time" itself [#] never "dilates", and all (good) clocks always tick at their usual rate.

Time IMO is an abstract concept. As you can see from above the clock count of clocks can be influenced depending on how they are used. What that means you should not use moving clocks at least you should use clocks in such a way that they move the least.

>	[#] In physics, "time is what clocks measure" [Einstein and others]. For the simple reason that in any experiment that involves time in any way, it is measured by a clock.

A clock measures (counts) clock ticks and we humans convert these ticks in days, hours, minutes and seconds. As such it is better to say that a clock calculates the time. Each clock requires its own conversion.

Nicolaas Vroom.

5 If time dilates...

This replaces the question of what is a good clock by a new question: what means: "keeps time in synchronization" (sorry, this does not answer the question).

To get a better idea please study $ 1.5 Time in the book Gravitation. Specific study Figure 1.9
"Good clock (left) vs bad clock (right) as seen in the maps they give of the same free particles moving through the same region of spacetime."
The world lines of depicted at the left side are straight lines and the world lines at the right side are bent. IMO this paragraph is not very practical.

$16.4 "The rods and clocks used to measure space and time intervals" at page 393 seems more practical. Here we read:
"One must then determine the accuracy to which a given rod or clock is ideal under given circumstances by using the laws of physics to analyze its behaviour"
This is something like the chicken-egg problem. The laws of physics are a description of the experiments in order to study physical processes i.e. the behaviour of clocks.

At that same page we can also read:
"Of course any clock has a breaking point beyond which it will function properly (Box 16.3) But that breaking point depends entirely on the construction of the clock - and not at all on any 'universal influence of acceleration on the march of time.' Velocity produces a universal time dilation; acceleration does not". No comment.

At page 396:
"In principle, one can build ideal rods and clocks from the geodesic world lines of free-falling test particles and photons. (See Box 16.4)"
At page 397:
"Box 16.4 'Ideal rods and clocks built from geodesic world lines' (3) Light rays (null geodesics) bounce back and forth between the parallel world lines; each round trip constitutes one tick"

What this paragragh describes as an ideal clock is a clock using light signals between two mirrors. The same type of clock as used in my previous posting in this thread. What is important that this clock should be used in a local Lorentz rest frame.

The question is exactly how do we know that we have a local Lorentz rest frame and what happens if that is not the case. IMO if the clock operates not in Lorentz rest frame (moves) the clock ticks slower but that does not mean that it is not an ideal clock.

>	A clock's usual rate is the rate at which it updates itself. A Cs-133 oscillator "ticks" at 9,192,631,770 Hz, but can be divided down to tick at 1 Hz. It is found experimentally that neither relative motion nor difference in gravitational potential affects the tick rate of any good clock

To get an idea about the behaviour of atomic clock please read Box 16.3 "Response of clocks to acceleration and to Tidal Gravitational Forces" at page 396 of the Book Gravitation.

Nicolaas Vroom

6 If time dilates...

No. Rather you have a problem with recognizing the distinction between two different physical situations, and how they are modeled in physics.

>	[...] the behaviour of the clock is not influenced by any of the two observers.

Yes. Why would one think otherwise?

>

Next, consider two identical clocks based on light signals. Consider Observer A at rest with these clocks at position X. Both clocks placed in a rocket and the engines of one of the rockets are fired and the rocket moves in a straight line to a point Z At Z the speed the rocket is stopped. The engine is set in reverse and the rocket returns back to position X. At X the two clocks are compared. The stay at home clock shows 1000 counts and the moving clock shows 900 counts. How come.

Because the path through spacetime of the traveling clock is shorter than the path of the stay-at-home clock; for such timelike paths, path length is elapsed proper time, which is what clocks display. This is NOT "time dilation", this is a DIFFERENT physical situation, and a DIFFERENT geometrical property.

"Time dilation" is a geometrical projection of some timelike interval onto a specific clock's path. It is directly analogous to the slope of a line in a Euclidean plane (e.g. the value of each depends on which coordinate axes you use).

Elapsed proper time is path length. A triangle ABC in a Euclidean plane has two paths between points A and B: AB and ACB; they OBVIOUSLY have different path lengths. In SR, the twin paradox with instantaneous accelerations is a triangle (in a space-time plane).

>	1. First of all the observer has nothing to do with this result. 2. Secondly, this is not a symmetrical experiment.

Yes to both.

>	3. Thirdly this is a physical issue and the cause is related in the way the clocks are built.

No. The difference depends on the GEOMETRY, not the clocks or how they were built.

>	Physical investigation reveals that the light path of the moving clock between each count is longer as the light path of the stay at home clock.

Nope. You miscalculated. The path length through spacetime for every light ray is ZERO. So they are the same for the two light clocks. They are also UNRELATED to the clock's elapsed proper times (which are nonzero).

Note that if you PROJECT the light's path onto an inertial frame, the distance you get will depend on which frame you use. (You have implicitly done this, without recognizing its importance.)

>	4. Mathematics does not solve the issue either.

Hmmm. GEOMETRY solves the issue, and is a field of mathematics.

>	First, we first must agree that the issue is physics.

Hmmm. Geometry is part of physics, in that EVERY physical theory uses some geometry at its base, to model the spatial-temporal relationships of the world. But the relationships involved are GEOMETRICAL.

>	Next, we should study how different parameters influence this behaviour. Finally, you can try to catch this physical behaviour in a law.

We already have -- the phenomena known as "time dilation", "length contraction" and the different elapsed proper times over different paths are all well modeled by Minkowski geometry. In particular, they are all completely independent of how clocks and rulers are implemented.

The corresponding law is:

All physical phenomena are locally Lorentz invariant (LLI).

To date nobody has found any exception to this law. And A LOT of people have looked, HARD -- there is a Nobel Prize for anyone who finds an exception.

So all the fools and idiots around here who claim in various ways that "SR is wrong" would have received a Nobel Prize if their criticisms were well founded. They aren't. Not even close.

>>	"Time" itself [#] never "dilates", and all (good) clocks always tick at their usual rate.

>	Time IMO is an abstract concept.

Not in physics. In physics, "time is what clocks measure" [Einstein and others], for the simple reason that in every experiment involving "time", it is measured by a clock.

The "abstract" issues you are thinking of are UNRELATED TO PHYSICS.

>	As you can see from above the clock count of clocks can be influenced depending on how they are used.

Hmmm. Say, rather, that a clock's tick count is a measure of its elapsed proper time, and that is inherently related to the clocks' path through spacetime.

>	What that means you should not use moving clocks at least you should use clocks in such a way that they move the least.

Hmmm. It really means that you should use clocks to measure WHAT YOU WANT TO MEASURE, and not something else. This of course applies to all instruments, not just clocks.

>>	[#] In physics, "time is what clocks measure" [Einstein and others]. For the simple reason that in any experiment that involves time in any way, it is measured by a clock.

>	A clock measures (counts) clock ticks and we humans convert these ticks in days, hours, minutes and seconds.

Hmmm. The clock does also -- essentially all clocks offer an output in seconds, and the arithmetic to convert to hours, days, etc. is trivial and unrelated to physics (it is related to human history).

Tom Roberts

7 If time dilates...

I forgot to point out that unlike "time dilation", path length does NOT depend on which coordinate axes you use. In both Euclidean geometry and SR, path length is an invariant.

Tom Roberts

8 If time dilates...

>

"Time dilation" is a geometrical projection of some timelike interval onto a specific clock's path. It is directly analogous to the slope of a line in a Euclidean plane (e.g. the value of each depends on which coordinate axes you use). Elapsed proper time is path length. A triangle ABC in a Euclidean plane has two paths between points A and B: AB and ACB; they OBVIOUSLY have different path lengths. In SR, the twin paradox with instantaneous accelerations is a triangle (in a space-time plane).

It is better to invoke that a clock second is not a universal interval of TIME.

>

> >	1. First of all the observer has nothing to do with this result. 2. Secondly, this is not a symmetrical experiment.

>	Yes to both.

> >	3. Thirdly this is a physical issue and the cause is related in the way the clocks are built.

>	No. The difference depends on the GEOMETRY, not the clocks or how they were built.

9 If time dilates...

Why not "two identical clocks based on pendulums", poor idiot?

10 If time dilates...

Of course is _IS_ -- with the normal meanings of those words, one second elapsed on a clock _IS_ a universal interval of time. That is, 9,192,631,770 cycles of the Cs-133 ground-state hyperfine transition is ALWAYS one second. After all, that's what we mean by the phrase "one second".

You keep trying to re-define the meanings of words you don't understand. That's hopeless.

Of course one must remember that a clock inherently measures intervals along its own worldline, so this "universality" applies to each clock only along its worldline. For a clock moving inertially, that is its rest frame.

As usual, be sure to use an instrument to measure what you want to measure, and not something else. In general that means you need to use a clock co-moving and co-located with whatever defines the time interval you want to measure. If both ends of the time interval are not defined to be along the clock's worldline, than it inherently cannot be used to measure that interval.

Tom Roberts

11 If time dilates...

What you said, that a clock second is a universal interval of time, is true only if a cycle of the Cs-133 represents a universal interval of time--but it does not. The GPS proved that you are wrong. The GPS second is adjusted to have 4.1+ cycles. That means that a cycle of the Cs-133 is not a universal interval of time.

12 If time dilates...

You are supposed to read what I write. Implicit but unstated in your claim here is measuring a time interval that is NOT defined on the worldlines of the two clocks you are comparing.

Actually, the GPS demonstrates that I am right, in the context of GR.

As I repeatedly point out, to compare tick rates between a satellite clock and a ground clock you must use SIGNALS, and you MUST consider how gravitation affects the measurements of those SIGNALS.

If, instead of tick rates you want to compare elapsed proper times, then you MUST consider how gravitation affects the lengths of the clocks' paths.

Tom Roberts

13 If time dilates...

The problem I have is with the idea that observers influence the behaviour of clocks.

> >	[...] the behaviour of the clock is not influenced by any of the two observers.

>	Yes. Why would one think otherwise?

See the above sentence. Different moving observers, observing the same clock, IMO, is not a very good scientific practice.

> >	At X the two clocks are compared. The stay at home clock shows 1000 counts and the moving clock shows 900 counts. How come.

>

Because the path through spacetime of the traveling clock is shorter than the path of the stay-at-home clock; for such timelike paths, path length is elapsed proper time, which is what clocks display. This is NOT "time dilation", this is a DIFFERENT physical situation, and a DIFFERENT geometrical property.

My remark is not about "time dilation" (which is a tricky concept) but only about clock counts. That is what is observed.

> >	3. Thirdly this is a physical issue and the cause is related in the way the clocks are built.

>	No. The difference depends on the GEOMETRY, not the clocks or how they were built.

The geometry of what? IMO of the construction of the clocks.

> >	Physical investigation reveals that the light path of the moving clock between each count is longer as the light path of the stay at home clock.

>

Nope. You miscalculated. The path length through spacetime for every light ray is ZERO. So they are the same for the two light clocks. They are also UNRELATED to the clock's elapsed proper times (which are nonzero). Note that if you PROJECT the light's path onto an inertial frame, the distance you get will depend on which frame you use. (You have implicitly done this, without recognizing its importance.)

What you are using is the path length mathematical defined as: 1) In general as: s^2 = r^2 + i^2*t^2
2) In the case of a clock at rest, as: s^2 = x^2 + i^2*t^2
3) In the case of a moving clock as: s^2 = (x^2 + y^2) + i^2*t^2
In (1) because r is the physical length of a light ray s becomes zero. s is not a physical quantity you can measure. It is a calculated number, which uses a complex number. i^2 = -1

In order to understand the behaviour of a clock the difference between (2) and (3) is important.
The physical length of the lightray in (2) involves x i.e. the distance between the mirrors.
The physical length of the lightray in (3) involves both x and y i.e. the distance x between the mirrors and the distance y moved.
When the total physical length of the light ray is l Using (2) the clock count c2 = l/x and using (3) the clock count c3 = l/sqr(x^2+y^2)
That means c3 (moving clock) is smaller than c2 (clock at rest)

This is the behaviour for a clock where the direction of the light signal is perpendicular to the direction of movement (Lorentz transformation). For a clock with the light signal in the same direction as the movement, the behaviour is different.

What this means, is that a clock is a mechanical device and its function depends on the construction of the clock. What is also important that in order to understand the functioning of this clock no other laws of nature are required except the assumption that the speed of light is the same (locally) in all directions.

> >	4. Mathematics does not solve the issue either.

>	Hmmm. GEOMETRY solves the issue, and is a field of mathematics.

Simple mathematics based on how the clock physical is constructed describes the operation of the clock (and its limitations). In fact, the mathematics for each clock is different.

>	The corresponding law is: All physical phenomena are locally Lorentz invariant (LLI). To date nobody has found any exception to this law. And A LOT of people have looked, HARD -- there is a Nobel Prize for anyone who finds an exception.

I'm in no way arguing that that is not true. I'm only saying that by simple investigating of how the clock is constructed you can find the mathematics that describes its behaviour. No complex numbers are required.
In process-control a similar issue exists where Laplace transformations (which involves complex numbers), are used, as a temporary tool, to describe the (intermediate) behaviour of industrial processes.

>	Not in physics. In physics, "time is what clocks measure" [Einstein and others], for the simple reason that in every experiment involving "time", it is measured by a clock.

> >	A clock measures (counts) clock ticks and we humans convert these ticks in days, hours, minutes and seconds.

>	Hmmm. The clock does also -- essentially all clocks offer an output in seconds, and the arithmetic to convert to hours, days, etc. is trivial and unrelated to physics (it is related to human history).

I agree that this conversion is a human endeavour, but the true issue is that a clock does not measure time but physical ticks.

Nicolaas Vroom

14 If time dilates...

Who do you think is making clocks? They are not any moronic avatars of the Great Mystical Essence of the Core. They are human made tools. Of course we're influencing them.

15 If time dilates...

They can't.

The state of motion of the observer doesn't affect the observed object, but it may affect the observer's observations (measurements) of the object.

A simple example: A clock is approaching you very fast. You will visually observe the clock to run fast. Does that mean that the clock is affected in any way being observed by you?

-- Paul

16 If time dilates...

> >	The problem I have is with the idea that observers influence the behaviour of clocks.

>

They can't. The state of motion of the observer doesn't affect the observed object, but it may affect the observer's observations (measurements) of the object. A simple example: A clock is approaching you very fast. You will visually observe the clock to run fast. Does that mean that the clock is affected in any way being observed by you?

Another simple example, maybe even simple enough for such a poor idiot. You're taking a clock and adjusting it. Does this mean that that the clock is affected in any way being adjusted by you?

17 If time dilates...

> >	The problem I have is with the idea that observers influence the behaviour of clocks.

>	They can't. The state of motion of the observer doesn't affect the observed object, but it may affect the observer's observations (measurements) of the object.

I fully agree with you. However, that is not so much the issue. The issue is the sentence:

"Time dilation" applies to MEASUREMENTS OF CLOCK TICK RATES by observers in motion relative to the clock"

This problem is very closely related to the electromagnetic problem of moving an electric object (field) versus a magnetic object (field). Moving an electric object creates a magnetic field and moving a magnetic object creates an electric field.

The moving clock problem is different because it is only the clock that is moving relative to another clock. The observer does not play any role.

However, there is still another problem: is it allowed to call a clock at rest?

Consider you have two clocks. In principle, you can call both clocks at rest. You place clock #2 in a space ship. You start the engines and you take care that the space ship travels from A to B and back to A.
When the space ship returns you compare clock #1 with clock #2 and you will observe that the number of ticks of clock #2 is less than the number of ticks of clock #1.
This is all in agreement with the idea that clock #1 is at rest.

Now you are going to perform a slightly different experiment.
You start with three identical clocks and you place both clock #2 and clock #3 each in a space ship. For the rest, everything is the same and both space ships travel side by side from A to B.
As IF they are both at rest, but they are not.
Half away between A and B (at point P) the captain on board the space ship with clock #3 does something special: he changes the speed of his space ship.
What will happen with his clock #3?
What we already know that before he changed speed (before point P) both clock #2 and clock #3 each run slower as clock #1. There are two possiblities:
1) when the speed will be increased in the direction of point B, the total speed will increase and clock #3 will start to run even more slower as clock #2.
2) when the speed will be increased in the direction of point A, the total speed will decrease and clock #3 will start to run faster as clock #2 (but still slower as clock #1)

What this means from the point of view of clock #2 (considering him self at rest) that this is not a symmetrical situation.

The final lesson is that in order to study physics the most important tool are real experiments.

18 If time dilates...

NOBODY thinks that would happen. You are arguing only with your own misconceptions.

Different observers can measure different values for the tick rate of a given clock, BECAUSE THEY USE DIFFERENT MEASUREMENT PROCEDURES. The differences are in the MEASUREMENTS, not in the behavior of the clock itself.

>	Different moving observers, observing the same clock, IMO, is not a very good scientific practice.

But it happens all the time (e.g. at particle accelerators). So physicists cannot avoid it. The point is to model what happens accurately, and SR does precisely that (among many other things).

>	My remark is not about "time dilation" (which is a tricky concept) but only about clock counts. That is what is observed.

In SR, "time dilation" is straightforward, and not "tricky" at all. But you do need to understand what it is, AND WHAT IT IS NOT.

>>>	3. Thirdly this is a physical issue and the cause is related in the way the clocks are built.

>>	No. The difference depends on the GEOMETRY, not the clocks or how they were built.

>	The geometry of what? IMO of the construction of the clocks.

It is the geometry of spacetime. Clock construction is COMPLETELY irrelevant, as long as the clock is a good one.

>	What you are using is the path length mathematical defined as: [...]

NO. I have no idea where you got that, but it is very confused. Nobody today uses imaginary quantities like that. Get a MODERN textbook -- ancient ones use archaic terms and concepts, and will be VERY confusing to a modern reader.

>	s is not a physical quantity you can measure. It is a calculated number,

NO. Your s is supposed to be the path length of the (timelike) path traversed by the clock; s is DIRECTLY measured by the elapsed time of the clock.

Given the parameters of the path relative to some inertial frame, we can calculate s, and compare to what the clock shows. That's how we KNOW that SR is an excellent model.

Your (2) and (3) are muddled and incorrect. They do NOT represent what you say they represent. YOU ARE CONFUSED.

>	The physical length of the lightray in (2) involves x i.e. the distance between the mirrors.

You are using PUNS. When I say "path length" I mean in spacetime. Your x and the distance between mirrors are only in space. The path through spacetime involves more than that. Get a good, modern textbook and LEARN about this.

>>	Hmmm. GEOMETRY solves the issue, and is a field of mathematics.

As I said above, I mean the geometry of SPACETIME. The clock is irrelevant, because the spacetime geometry applies identically to EVERYTHING, including all types of clocks.

>	Simple mathematics based on how the clock physical is constructed describes the operation of the clock (and its limitations). In fact, the mathematics for each clock is different.

Not so, for the geometry of SPACETIME.

>	I'm only saying that by simple investigating of how the clock is constructed you can find the mathematics that describes its behaviour.

But the behavior IN SPACETIME is the same for all clocks, independent of their internal construction.

It is this behavior IN SPACETIME that is the subject of SR; SR does NOT study the construction of clocks, it studies HOW GOOD CLOCKS BEHAVE. And we find that ALL good clocks behave the same, independent of their construction.

>	the true issue is that a clock does not measure time but physical ticks.

This is supposed to be physics, and not some abstract debating society. In physics, "Time is what clocks measure" [Einstein and others], because in every experiment involving time, it is measured with a clock.

You keep trying to talk about "time" as something else [#]. All you do is confuse yourself, because other than the definition I just gave, there is no good meaning for the word "time". Certainly to humans, time is VERY subjective and highly variable (e.g. it appears to stop when we sleep, and resumes when we wake; comparing to clocks we find that time did not actually stop at all).

[#] Google "define: time" -- all you get are circular definitions. Ditto for using a dictionary. Time is something to be experienced, not defined. In physics, that experience is encapsulated in clocks. Indeed that is also true in our everyday lives.

Tom Roberts

19 If time dilates...

It does not matter. This is relativity, and all that matters is the RELATIVE motion between clock and observer.

>	This problem is very closely related to the electromagnetic problem of moving an electric object (field) versus a magnetic object (field).

That "problem" was resolved over a century ago. That's what relativity is all about.

>	However, there is still another problem: is it allowed to call a clock at rest?

It's not a problem once you understand that there is no "absolute space" or "absolute rest", there is only "at rest relative to this coordinates". That is one of the basic lessons of relativity, from over a century ago.

You are floundering because you attempt to use everyday concepts in physics. Those everyday concepts are not nearly precise enough to discuss physics, which is both complicated and subtle. At scales outside our everyday experiences the world behaves VERY different from what we experience every day.

>

[...]

You keep repeating the same mistakes. Get a good, MODERN textbook and STUDY.

Tom Roberts

20 If time dilates...

>	You keep repeating the same mistakes. Get a good, MODERN textbook and STUDY. Tom Roberts

Can you give me two titles of a good MODERN textbook?

Why do you use the word MODERN?

Nicolaas Vroom

21 If time dilates...

Yes, it is the very issue.

>	The issue is the sentence: "Time dilation" applies to MEASUREMENTS OF CLOCK TICK RATES by observers in motion relative to the clock"

I would rephrase the statement a bit:

"Time dilation" applies to MEASUREMENTS OF TICK RATES OF CLOCKS in motion relative to the observer.

The tick rate of the observed clock is not affected in any way, only the observer's _measurements_ of the tick rates are affected.

22 If time dilates...

23 If time dilates...

In this document, you write:
Event E1: clock A and clock A' are adjacent.
Event E2: clock A and clock B' are adjacent.
Event E3: clock B and clock A' are adjacent.

1) The situation of Event E1 is shown in Figure 1 I expect that this is the moment that all clocks A, B, A' and B' are reset.

2) At Event E2 clock A and clock B' are adjacent but at the same time also clock B and clock A' are adjacent. This is because the distance is the same.
2a) My assumption is that when this happens both clock A and clock B will show the same time or clock counts. With clock A, I mean an observer near clock A to write down the time.
2b) My assumption is that when this happens both clock A' and clock B' will show the same time or clock counts.

More I can not say, because you have to perform the full twin experiment That means, for example, you have to stop the train in Frame K' and you have to take care that you go back to the same situation (with a speed -v) as depicted in Figure 1.

My prediction will be that the clock count of the train in the frame K' at point A' will be less than the clock in frame K at point A.

This is what I will write at this moment because I'm not sure if we are in synchronisation. I'm awaiting your comments

24 If time dilates...

This is what Tom Roberts wrote in the tread: "the self destruction of a newsgroup"

* On Tuesday, 17 December 2019 17:10:24 UTC+1, tjrob137 wrote: * On 12/17/19 8:44 AM, Nicolaas Vroom wrote: * * IMO the most important issue to understand science is not * * mathematics but first physics based on observations and experiments. * * Fair enough. But math is the language of physics, and cannot be avoided. * When you discuss gedankens, all you have is the math of SR. * * Have a look at page 68 of the book Space-Time physics second * * edition.[...] * * I don't have the book, and that's 'way too complicated to bother with. * Your misconceptions are very basic and don't need complicated scenarios.

IMO the Space-Time physics is an excellent book. The same with the book GRAVITATION by MTW. Both books were advised to read.

However, both books raise certain questions and if these answers are not in these books how can you find the answers and who can give the answers.

>	General Relativity From A to B, by Geroch Special Relativity and Classical Field Theory, by Susskind

> >	Why do you use the word MODERN?

>	Because older materials use “bridge concepts” that attempted to make relativity somewhat similar to classical physics (things like “relativistic mass”),

I always learned that there are two concepts m0 and m. The difference between these two is the factor lambda. Is this still considered correct?

>	or tried pedagogical stunts that only made things more confusing (like calling teaching puzzles “paradoxes”).

Is the concept of twin paradox still okay? You have also something like the ladder paradox? What about Length contraction paradox? (Ehrenfest paradox?, Bell's spaceship paradox?)

>

It’s better to use newer books that make a cleaner break with the past and present things as they’ve been understood lately, meaning in the last 40-50 years. This means, for example, that Einstein’s books on his own theory are actually not the best resources. Neither is Born’s book or French’s book.

What about his article: On the Electrodynamics of Moving Bodies - by A. Einstein 1905?

Anyway who decides about these issues?

Nicolaas Vroom

25 If time dilates...

Scientists are totally out in left field with their idea of slow Gamma math time. If you do not believe me, multiply anything at all by gamma, 1/sqrt(1-v^2/c^2). If you multiply anything by 1/(less than 1), you end up with a greater value than you started with, not a smaller value. The slow math time that scientists so adore comes from the numerator of Lorentz's term in his equation for t', the term (t-vx/c^2). As v approaches c, t' approaches 0, meaning the clock in S' is slower than the clock in S. Multiplying by gamma increases t' from what it would be as calculated from (t-vx/c^2) alone.

>	Sure it does. Time slows down from its C speed by two ways. The strength of gravity and speed of the atom.

26 If time dilates...

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It’s better to use newer books that make a cleaner break with the past and present things as they’ve been understood lately, meaning in the last 40-50 years. This means, for example, that Einstein’s books on his own theory are actually not the best resources. Neither is Born’s book or French’s book.

>	What about his article: On the Electrodynamics of Moving Bodies - by A. Einstein 1905? Anyway who decides about these issues? Nicolaas Vroom

The book "Einstein's Theory of Relativity" is not considered one of the best resources to study physics (Stellar Mechanics). I bought this book a long time ago and I started to read the book again because I wanted to know why this book is no good. In fact, I was a little surprise, because this book is very clear and very easy to read. I'm not saying that it is easy.