1 Why is there more than one explanation for the Twin Paradox

Is the concept geometrical projections equivalent with something mathematical?

Does this also indicate that both "time dilation" and "length contraction" are not something physical? In the sense that when you heat an iron rod its length becomes longer?

But what about a moving clock i.e. when two clocks are moved along different path and when they meet the number of ticks is different?

Nicolaas Vroom

2 Why is there more than one explanation for the Twin Paradox

But the question is...When did the number of ticks become different? At what time did the number of ticks become different?

1) right away

2) a little while later

3) a week later

4) sometimes

5) all the time

6) the first tick

I gotta get into my car and go varrrooooooooooooommmm.

3 Why is there more than one explanation for the Twin Paradox

El domingo, 13 de agosto de 2017, 11:23:15 (UTC-3), Nicolaas Vroom escribió:

>	On Monday, 7 August 2017 16:22:34 UTC+2, tjrob137 wrote:

> >	On 8/4/17 8/4/17 - 6:22 PM, Thomas 'PointedEars' Lahn wrote:

> > >

Tom Roberts wrote:

> > >>

[...]

> > >

*time dilation* (a *proper* scientific term that, in contrast to other scientific terms, for unknown reasons you ridiculously liked to put in double-quotes, as if it were not).

> >

I put "time dilation" and "length contraction" in quotes because they are VERY POOR names for the phenomena they refer to. That is, for "time dilation" time does NOT actually dilate, and for "length contraction" lengths do NOT actually contract -- those phrases refer to the clock or object in question, which in all cases is UNAFFECTED. Both "time dilation" and "length contraction" are really geometrical projections that affect how observers moving relative to an object will MEASURE the object, and the phrases do not capture this fact at all -- at face value they imply that the object itself is somehow changed, but it isn't.

>	Is the concept geometrical projections equivalent with something mathematical? Does this also indicate that both "time dilation" and "length contraction" are not something physical? In the sense that when you heat an iron rod its length becomes longer?

It is a geometrical projection that has physical consequences. Like if you try to pass a ladder through a door, the geometrical orientation of the ladder projects the ladder onto the door. If the projection is less than the door width, you can pass the ladder through the door.

4 Why is there more than one explanation for the Twin Paradox

I do not fully understand. You can pass a ladder of 5 by 20 by 200 cm through a hole of 6 by 21 cm. If you have a box of 20 * 20 by 200 cm you cannot pass that box through that same hole,

> >	But what about a moving clock i.e. when two clocks are moved along different path and when they meet the number of ticks is different?

IMO that is something physical

> >	Nicolaas Vroom

5 Why is there more than one explanation for the Twin Paradox

> >	Acceleration most definitely is NOT the root cause:

>

I do not understand this. (See bootom) In any experiment where you want to test the behaviour of identical clocks with different speeds (the initial condition considered being that all the clocks are at rest) there are always accelerations involved specific if the final condition is that all the clocks meet at the same point.

Yes, there is usually accelerations involved. But its not the "accelerations" per se that makes the discrepancy; its the (instantaneous) speed. And even that is not necessary; we only need to know its trajectory (path) (and hence we know its speed; no need of the acceleration). That is what we mean by "acceleration has no effect". Its like a subtle play on words, if you would like.

That said, some versions of the twin paradox (TP) have no accelerations (the triplet version) and yet there is time dilation (TD). So again we see that accelerations are not the "root cause".

>	The condition of the experiment should be such that after all the clocks meet again they should all tick at the same rate.

Yes, and that's what we try to use/attain. If the returning clock no longer functions as its supposed too, we deem it "not a good clock" or "broken".

>

> >	2. The triplet paradox, in which there is no acceleration, gives the same result as the twin paradox with instantaneous frame changes.

>	In a real triplet experiment there are also accelerations involved,

No there arent.

>	except they are outside the direct scope(?) of the experiment.

Perhaps, but its irrelevant what the scientist had for breakfast; its irrelevant what we do with the clock after the experiment is done. During the experiment (the scenario), there are no accelerations whatsoever.

>	The point of the experiment is that: the longer the duration of the full experiment (with constant speeds) the larger the final difference between the clocks (or the more the staying at home twin has aged)

Yes, thats about it.

>

> >	5. The basic calculation is of the elapsed proper time over a (timelike) path through spacetime. When calculated in flat spacetime using an inertial frame, acceleration does not appear in the integral, but speed does.

>	If you want to do it accurate you have to take all the speeds into account involved (starting 'slowly' from zero to v and back at each dt) which implies acceleration.

Yes. And thats done in some literature too. But since its not that interesting and does not add to the understanding, we tend to jump over it.

>	The root cause is that the physical behaviour of clocks is affected by speed.

Perhaps, or perhaps not. "causes" in physics are irrelevant. We have a model, describe by formulas. The formulas predict the end results.
The gamma factor 1/sqrt(1 - v²(t)) contains but the speed, not the acceleration and this suffices to find the elapsed time (change in value).

6 Why is there more than one explanation for the Twin Paradox

Yes it figures. You should try any book on Geometry.

>	You can pass a ladder of 5 by 20 by 200 cm through a hole of 6 by 21 cm. If you have a box of 20 * 20 by 200 cm you cannot pass that box through that same hole,

Take your 50x300cm ladder through a 70x200 cm door. The geometrical projection of the ladder onto the door has to be less than 70x200cm to pass through. If you take it horizontal, 200 > 70 means it will not pass. You rotate it so its geometrical projection is 50x60cm and the ladder goes through without a problem.

That it means the ladder length changed from 300cm to 60cm? Of course not, only its orientation in space did.

Similarly, the traveling twin clock rate does not change in its path through spacetime, but its geometrical projection does.

7 Why is there more than one explanation for the Twin Paradox

I do not understand this. (See bootom) In any experiment where you want to test the behaviour of identical clocks with different speeds (the initial condition considered being that all the clocks are at rest) there are always accelerations involved specific if the final condition is that all the clocks meet at the same point.

>	1. Good clocks are unaffected by acceleration (as long as they are not broken by it). Experiments show that the timekeeping mechanism governing muon decay is not affected by a proper acceleration of 10^18 g (!).

The condition of the experiment should be such that after all the clocks meet again they should all tick at the same rate.

>	2. The triplet paradox, in which there is no acceleration, gives the same result as the twin paradox with instantaneous frame changes.

In a real triplet experiment there are also accelerations involved, except they are outside the direct scope(?) of the experiment. The point of the experiment is that: the longer the duration of the full experiment (with constant speeds) the larger the final difference between the clocks (or the more the staying at home twin has aged)

>	5. The basic calculation is of the elapsed proper time over a (timelike) path through spacetime. When calculated in flat spacetime using an inertial frame, acceleration does not appear in the integral, but speed does.

If you want to do it accurate you have to take all the speeds into account involved (starting 'slowly' from zero to v and back at each dt) which implies acceleration.

The root cause is that the physical behaviour of clocks is affected by speed.

>	In the usual twin paradox, it is not possible for the traveling twin to return without experiencing acceleration.

What the travelling twin B experience IMO is of no importance also not if B truelly ages. What is important the clock B uses on the trip.

Nicolaas Vroom

8 Why is there more than one explanation for the Twin Paradox

> >	Acceleration most definitely is NOT the root cause:

>

I do not understand this. (See bootom) In any experiment where you want to test the behaviour of identical clocks with different speeds (the initial condition considered being that all the clocks are at rest) there are always accelerations involved specific if the final condition is that all the clocks meet at the same point.

Yes, there is usually accelerations involved. But its not the "accelerations" per se that makes the discrepancy; its the (instantaneous) speed. And even that is not necessary; we only need to know its trajectory (path) (and hence we know its speed; no need of the acceleration). That is what we mean by "acceleration has no effect". Its like a subtle play on words, if you would like.

That said, some versions of the twin paradox (TP) have no accelerations (the triplet version) and yet there is time dilation (TD). So again we see that accelerations are not the "root cause".

>	The condition of the experiment should be such that after all the clocks meet again they should all tick at the same rate.

Yes, and that's what we try to use/attain. If the returning clock no longer functions as its supposed too, we deem it "not a good clock" or "broken".

>

> >	2. The triplet paradox, in which there is no acceleration, gives the same result as the twin paradox with instantaneous frame changes.

>	In a real triplet experiment there are also accelerations involved,

No there arent.

>	except they are outside the direct scope(?) of the experiment.

Perhaps, but its irrelevant what the scientist had for breakfast; its irrelevant what we do with the clock after the experiment is done. During the experiment (the scenario), there are no accelerations whatsoever.

>	The point of the experiment is that: the longer the duration of the full experiment (with constant speeds) the larger the final difference between the clocks (or the more the staying at home twin has aged)

Yes, thats about it.

>

> >	5. The basic calculation is of the elapsed proper time over a (timelike) path through spacetime. When calculated in flat spacetime using an inertial frame, acceleration does not appear in the integral, but speed does.

>	If you want to do it accurate you have to take all the speeds into account involved (starting 'slowly' from zero to v and back at each dt) which implies acceleration.

Yes. And thats done in some literature too. But since its not that interesting and does not add to the understanding, we tend to jump over it.

>	The root cause is that the physical behaviour of clocks is affected by speed.

Perhaps, or perhaps not. "causes" in physics are irrelevant. We have a model, describe by formulas. The formulas predict the end results. The gamma factor 1/sqrt(1 - v²(t)) contains but the speed, not the acceleration and this suffices to find the elapsed time (change in value).

9 Why is there more than one explanation for the Twin Paradox

The Twin paradox has nothing to do with Time Dilaton. Time Dilation does not intervene in the explanation of the Twin Paradox.

> >	If you want to do it accurate you have to take all the speeds into account involved (starting 'slowly' from zero to v and back at each dt) which implies acceleration.

>	Yes. And thats done in some literature too. But since its not that interesting and does not add to the understanding, we tend to jump over it.

Actually, it does. Only reductionist imbeciles like Stephane Baune would claim such an idiocy.

10 Why is there more than one explanation for the Twin Paradox

What the experiments show is that atomic clocks (the type of clocks used in scientific experiments) are not affected by acceleration. Tom even put the number just below.

> >	1. Good clocks are unaffected by acceleration (as long as they are not broken by it). Experiments show that the timekeeping mechanism governing muon decay is not affected by a proper acceleration of 10^18 g (!).

>	The condition of the experiment should be such that after all the clocks meet again they should all tick at the same rate.

But they do, the reunited clocks are tested and sure enough they continue to tick at the same rate.

> >	2. The triplet paradox, in which there is no acceleration, gives the same result as the twin paradox with instantaneous frame changes.

>

In a real triplet experiment there are also accelerations involved, except they are outside the direct scope(?) of the experiment. The point of the experiment is that: the longer the duration of the full experiment (with constant speeds) the larger the final difference between the clocks (or the more the staying at home twin has aged)

Again, accelerations do not affect the clock ticking.

> >	5. The basic calculation is of the elapsed proper time over a (timelike) path through spacetime. When calculated in flat spacetime using an inertial frame, acceleration does not appear in the integral, but speed does.

>	If you want to do it accurate you have to take all the speeds into account involved (starting 'slowly' from zero to v and back at each dt) which implies acceleration.

What? Are you unable to read above?

>	The root cause is that the physical behaviour of clocks is affected by speed.

Total nonsense. If the atomic clock rate are not affected by acceleration, why would they be affected by speed?

> >	In the usual twin paradox, it is not possible for the traveling twin to return without experiencing acceleration.

>	What the travelling twin B experience IMO is of no importance also not if B truelly ages. What is important the clock B uses on the trip. Nicolaas Vroom

Yeah right.... This is a waste of time...PLONK

11 Why is there more than one explanation for the Twin Paradox

>	But they do, the reunited clocks are tested and sure enough they continue to tick at the same rate.

Bullshit. Yake the clock from GPS back to Earth, poor idiot - the rate will be different.

12 Why is there more than one explanation for the Twin Paradox

"Similarly, the traveling twin clock rate does not change in its path through spacetime, but its geometrical projection does. "

Does the Pioneer spacecraft represent a travelling twin? In which case can we verify the twin paradox effect by using the signals from the Pioneer? This would sort of settle it.

Wikipedia

"Pioneer 10 crossed the orbit of Saturn in 1976 and the orbit of Uranus in 1979.[47] On June 13, 1983, the craft crossed the orbit of Neptune, the outermost planet, and so became the first human-made object to leave the proximity of the major planets of the Solar System. The mission came to an official end on March 31, 1997, when it had reached a distance of 67 AU from the Sun, though the spacecraft was still able to transmit coherent data after this date"

13 Why is there more than one explanation for the Twin Paradox

Well, bring it back and check it here on Earth. That would be a travelling twin scenario.

14 Why is there more than one explanation for the Twin Paradox

But after it went through the door via orientation can it be contained in a 70x200x200 cm barn briefly with both barn doors close simultaneously? I think not.

15 Why is there more than one explanation for the Twin Paradox

> >

Take your 50x300cm ladder through a 70x200 cm door. The geometrical projection of the ladder onto the door has to be less than 70x200cm to pass through. If you take it horizontal, 200 > 70 means it will not pass. You rotate it so its geometrical projection is 50x60cm and the ladder goes through without a problem.

>	But after it went through the door via orientation can it be contained in a 70x200x200 cm barn briefly with both barn doors close simultaneously? I think not.

If you are referring to the pole and barn paradox, then the ladder has to be traveling at v=0.8c, for example. At that speed, an observer in the barn will see the ladder to be length contracted and, for sure, to be fully contained inside the barn with its doors closed. The situation for the observer with the ladder is different. For him the ladder has the same length it had before moving, but it will pass through the barn unharmed, since the doors for that observer do not close at the same time (due to relativity of simultaneity)

16 Why is there more than one explanation for the Twin Paradox

Okay

>	Yes, and that's what we try to use/attain. If the returning clock no longer functions as its supposed too, we deem it "not a good clock" or "broken".

Okay

> >	except they are outside the direct scope(?) of the experiment.

>	Perhaps, but its irrelevant what the scientist had for breakfast; its irrelevant what we do with the clock after the experiment is done. During the experiment (the scenario), there are no accelerations whatsoever.

I agree with your final remark, but considering the experiment in total there are accelerations involved.

> >	The point of the experiment is that: the longer the duration of the full experiment (with constant speeds) the larger the final difference between the clocks (or the more the staying at home twin has aged)

>	Yes, thats about it.

But important

> >	If you want to do it accurate you have to take all the speeds into account involved (starting 'slowly' from zero to v and back at each dt) which implies acceleration.

>	Yes. And thats done in some literature too. But since its not that interesting and does not add to the understanding, we tend to jump over it.

Okay. Interesting

> >	The root cause is that the physical behaviour of clocks is affected by speed.

>	Perhaps, or perhaps not. "causes" in physics are irrelevant.

The causes in physics are the actual descriptions of the processes that take place. It is a light which is reflected between two mirrors at rest versus two mirrors which both have a speed v. Generally speaking the path in the second case (moving) is longer then the first case (at rest). This physical explains why there is a difference between the two clocks.

>	We have a model, describe by formulas. The formulas predict the end results. The gamma factor 1/v(1 - v²(t)) contains but the speed, not the acceleration and this suffices to find the elapsed time (change in value).

When you start with the physical model you can derive based on some simple mathematics the gamma factor. The final part is to test the gamma factor based on actual experiments. When they agree all the steps leading to the final formula are correct.

Nicolaas Vroom

17 Why is there more than one explanation for the Twin Paradox

Hmmmm. Note that muons experiencing 10^18 g as they go around a ring have the same lifetime measured in the lab as muons that travel at the same speed along a straight line with essentially no acceleration. So acceleration does not affect the timekeeping mechanism of muon decay. GPS satellite clocks are likewise unaffected by their acceleration, giving us confidence to apply the same idea to all clocks: they are unaffected by acceleration. And that is how SR and GR model it.

>	In any experiment where you want to test the behaviour of identical clocks with different speeds (the initial condition considered being that all the clocks are at rest) there are always accelerations involved specific if the final condition is that all the clocks meet at the same point.

No. You are assuming things which are not present.

>>	1. Good clocks are unaffected by acceleration (as long as they are not broken by it). Experiments show that the timekeeping mechanism governing muon decay is not affected by a proper acceleration of 10^18 g (!).

>	The condition of the experiment should be such that after all the clocks meet again they should all tick at the same rate.

Can't be done. Experiments are what they are, not what you WISH them to be.

>>	2. The triplet paradox, in which there is no acceleration, gives the same result as the twin paradox with instantaneous frame changes.

>	In a real triplet experiment there are also accelerations involved, except they are outside the direct scope(?) of the experiment.

Perhaps, but perhaps the triplets were each born in their inertial frame. In this scenario there is no need for them to be born together. But that's irrelevant -- activities before the experiment started don't matter.

>	The point of the experiment is that: the longer the duration of the full experiment (with constant speeds) the larger the final difference between the clocks (or the more the staying at home twin has aged)

This is a GEDANKEN, not a real experiment. The gedanken certainly behaves that way.

>>	5. The basic calculation is of the elapsed proper time over a (timelike) path through spacetime. When calculated in flat spacetime using an inertial frame, acceleration does not appear in the integral, but speed does.

>	If you want to do it accurate you have to take all the speeds into account involved (starting 'slowly' from zero to v and back at each dt) which implies acceleration.

THIS calculation can handle arbitrary accelerations. But the accelerations do not contribute to the result, only the resulting path and its speed (relative to that inertial frame) contribute. That is, acceleration affects the path but not the calculation itself, but the calculation depends on the path.

>	The root cause is that the physical behaviour of clocks is affected by speed.

No! NOT AT ALL! Experiments show the opposite: speed does not affect the physical behavior of clocks. It only affects how observers MEASURE them. That, however, does not make it "imaginary", or "fictitious", or "illusory", because it can have real physical consequences (such as pion beams 1 km long being useful).

If what you claim were true, Einstein's first postulate of SR could not possibly be valid. But myriad experiments show that SR is valid.

Tom Roberts

18 Why is there more than one explanation for the Twin Paradox

>	No! NOT AT ALL! Experiments show the opposite: speed does not affect the physical behavior of clocks.

Your gedanken experiments only, poor idiot. As for reality, clocks of GPS satellite coun second with different numer of ticks than clocks on Earth. As you've said, experiments are what they are, not

19 Why is there more than one explanation for the Twin Paradox

20 Why is there more than one explanation for the Twin Paradox

>	Note that muons experiencing 10^18 g as they go around a ring have the same lifetime measured in the lab as muons that travel at the same speed along a straight line with essentially no acceleration. So acceleration does not affect the timekeeping mechanism of muon decay.

Acceleration should not have _no_effect_at_all_ on muon decay, merely _unmeasurable_ effects. Are there any sorts of heuristic arguments that one might apply to estimate what level of acceleration might significantly affect muon decay?

By analogy, I was considering singly-ionized helium traveling around a ring. Given Coulomb's law and the dimensions of the helium ion, I imagine that the second electron should be stripped from the helium ion, leaving an alpha particle, at accelerations above, say, 5e21 g or so.

Looking at a table of muon properties, I see nothing obvious that would allow me to perform any sort of "Fermi-estimate" on what accelerations might begin to have a significant effect on muon lifespan.

It seems fun to speculate, however.

21 Why is there more than one explanation for the Twin Paradox

So that means material contraction but your SR brothers (Bodkin and Tom) said that there is no material contraction. Do you agree - show quoted text -

22 Why is there more than one explanation for the Twin Paradox

The computer sends out my post before I was ready. So according to you, the pole is materially contracted but your SR brothers (Bodkin and Tom) said that there is no material contraction. Do you agree with Tom and Bodkin or do you believe that there was material contraction?

23 Why is there more than one explanation for the Twin Paradox

I'am not writing here that they are affected by accelerations. In any such experiments there are always different speeds involved which indistinguishable implies that there are accelerations involved.

Read page 167 of the book GRAVITATION "Exercise 6.3 Twin Paradox (a) show that of all timelike world lines connecting two events A and B the one with the longest lapse of proper time is the unaccelerated one (hint: perform the calculation in the inertial frame of the unaccelerated world line) (b) One twin chooses to move from A to B along the unaccelerated world line. Show that the other twin, by appropriate choice of accelerations can get from A to B in arbitrary small proper time" Also see page 315.

>	But they do, the reunited clocks are tested and sure enough they continue to tick at the same rate.

That is also my understanding The point is that the final readings are different, which implies that something must have happened inbetween.

> > >

2. The triplet paradox,

> >	The point of the experiment is that: the longer the duration of the full experiment (with constant speeds) the larger the final difference between the clocks (or the more the staying at home twin has aged)

>	Again, accelerations do not affect the clock ticking.

But something must have.

> > >

5. The basic calculation is of the elapsed proper time over a (timelike) path through spacetime. When calculated in flat spacetime using an inertial frame, acceleration does not appear in the integral, but speed does.

But this does not explain what the cause is.

> >	If you want to do it accurate you have to take all the speeds into account involved (starting 'slowly' from zero to v and back at each dt) which implies acceleration.

>	What? Are you unable to read above?

> >	The root cause is that the physical behaviour of clocks is affected by speed.

>	Total nonsense. If the atomic clock rate are not affected by acceleration, why would they be affected by speed?

If the atomic clock rate is not affected in some way by something then, when they reunite the reading of the two clocks should be identical, which is in conflict with the results of actual experiments?

> > >

In the usual twin paradox, it is not possible for the traveling twin to return without experiencing acceleration.

> >	What the travelling twin B experience IMO is of no importance also not if B truelly ages. What is important the clock B uses on the trip.

>	Yeah right.... This is a waste of time...PLONK

My problem is that I want to understand something. I want to understand why there is a different in clock readings between a stay at home clock versus a moving clock. You can never explain that simply based on the lorentz transformations. because the lorentz transformations are also a description of a process and it is that process that I want to understand. And because the difference between the two clocks is distance the cause must be related to speed and or acceleration. (But that does not mean there are two explanations)

Nicolaas Vroom

24 Why is there more than one explanation for the Twin Paradox

So do the exercise. Then LOOK at the formulas you used -- acceleration does not appear in them. If you follow the hint, you'll find that speed relative to that frame does appear.

>	[Twin paradox] The point is that the final readings are different, which implies that something must have happened inbetween.

Yes! They traveled different paths between the same endpoints; paths with different path lengths (elapsed proper times). NOTHING "happened" to the clocks, just to the PATHS.

>>	Again, accelerations do not affect the clock ticking.

>	But something must have.

No. "Something" happened TO THE PATHS.

>	If the atomic clock rate is not affected in some way by something then, when they reunite the reading of the two clocks should be identical, which is in conflict with the results of actual experiments?

You repeatedly ignore the PATHS. Clocks measure the path length of their trajectory through spacetime, and when they follow different paths they can measure different path lengths. For timelike paths, path length is just elapsed proper time.

>	I want to understand why there is a different in clock readings between a stay at home clock versus a moving clock.

See above. The difference in clock readings is related to the different paths they followed, not any effect on the clocks themselves.

>	You can never explain that simply based on the lorentz transformations. because the lorentz transformations are also a description of a process and it is that process that I want to understand.

That "process" is simple geometry: different paths can have different path lengths, and each clock measures the path length of its trajectory through spacetime.

Tom Roberts

25 Why is there more than one explanation for the Twin Paradox

26 Why is there more than one explanation for the Twin Paradox

"The situation for the observer with the ladder is different. For him the ladder has the same length it had before moving, but it will pass through the barn unharmed, since the doors for that observer do not close at the same time (due to relativity of simultaneity)".

Indeed nothing material happens to the ladder, so yes I agree with Tom and Bodkin. If you were riding with the ladder, you would experience nothing out of the ordinary. For you, however, the doors of the barn would not close simultaneously: the front door (the one the ladder tip crosses when leaving the barn) would close first (just before the ladder reaches it) and later the back door would close (just after the ladder tail enters the barn).

27 Why is there more than one explanation for the Twin Paradox

It has been explained before to you and tyhis will be my last one. Both clocks at the end of the gedanken show the accumulated reading (total number of ticks) due to their respective paths through spacetime and, since those path are clearly different, those reading should also be different and they are.

28 Why is there more than one explanation for the Twin Paradox

>

It has been explained before to you and tyhis will be my last one. Both clocks at the end of the gedanken show the accumulated reading (total number of ticks) due to their respective paths through spacetime and, since those path are clearly different, those reading should also be different and they are.

A lie, as expected from relativistic trash. Yes, the readings should be different. No, they are not (check it at GPS).

29 Why is there more than one explanation for the Twin Paradox

Okay But muon decay is a physical process which has its own (quantum mechanical) rules. Let us emphasize the experiments mentioned at page 167 of the book GRAVITATION in chapter 6 (Accelerated observers) which are about to the Twin paradox.

>	GPS satellite clocks are likewise unaffected by their acceleration, giving us confidence to apply the same idea to all clocks: they are unaffected by acceleration.

And that is only true if these clocks work based on muon decay and I doubt that. Anyway GPS clocks require continuous synchronisation and there must be a reason why.

>	And that is how SR and GR model it.

IMO SR, GR and Newton's supply the descriptions in mathematical form how the universe changes and evolves. The cause are primarily forces.

> >>	1. Good clocks are unaffected by acceleration (as long as they are not broken by it). Experiments show that the timekeeping mechanism governing muon decay is not affected by a proper acceleration of 10^18 g (!).

> >	The condition of the experiment should be such that after all the clocks meet again they should all tick at the same rate.

>	Can't be done. Experiments are what they are, not what you WISH them to be.

What I understand of all the experiments is when you start the experiments you should test that all clocks tick at the same rate and when the experiment is finished you should test again. Muon decay is a different process.

> >>	5. The basic calculation is of the elapsed proper time over a (timelike) path through spacetime. When calculated in flat spacetime using an inertial frame, acceleration does not appear in the integral, but speed does.

> >	If you want to do it accurate you have to take all the speeds into account involved (starting 'slowly' from zero to v and back at each dt) whichimplies acceleration.

>

THIS calculation can handle arbitrary accelerations. But the accelerations do not contribute to the result, only the resulting path and its speed (relative to that inertial frame) contribute. That is, acceleration affects the path but not the calculation itself, but the calculation depends on the path.

Okay

> >	The root cause is that the physical behaviour of clocks is affected by speed.

>	No! NOT AT ALL! Experiments show the opposite: speed does not affect the physical behavior of clocks.

Speed affects the innerworking and the positions of the dials on the clock using light signals. This is equivalent as the number of revolutions or ticks of the clocks.

>	It only affects how observers MEASURE them.

Observing the time on the clock, the event of looking, has nothing to do with the physical behaviour of a clock. (It is the same as when you open the box)

>

That, however, does not make it "imaginary", or "fictitious", or "illusory", because it can have real physical consequences (such as pion beams 1 km long being useful). If what you claim were true, Einstein's first postulate of SR could not possibly be valid. But myriad experiments show that SR is valid.

For a clock, based on the speed of light, it is important that the speed of light is constant. The more there is a discrepancy the less accurate this clock is,

>	Tom Roberts

Thanks

Nicolaas Vroom

30 Why is there more than one explanation for the Twin Paradox

But you said according to the barn observer the pole is completely inside the barn briefly with both doors closed simultaneously. This is only possible if the pole is materially contracted.

31 Why is there more than one explanation for the Twin Paradox

I fully agree that in the formula there is no acceleration, but that does not mean that in the experiment there is no acceleration involved.

> >	[Twin paradox] The point is that the final readings are different, which implies that something must have happened inbetween.

>	Yes! They traveled different paths between the same endpoints; paths with different path lengths (elapsed proper times). NOTHING "happened" to the clocks, just to the PATHS.

This all depents about the definition of a path. IMO when you go from A to B in a straight line with different speeds then in each case the path length is the same but the final clock reading in each case will be different. If in the definition of path length also duration is included then the path length will be different, but the result will be the same: the final clock reading will be different. This implies that the # of counts or the position of the dials will be different i.e. something different "happened" to each clock.

> >	If the atomic clock rate is not affected in some way by something then, when they reunite the reading of the two clocks should be identical, which is in conflict with the results of actual experiments?

>	You repeatedly ignore the PATHS. Clocks measure the path length of their trajectory through spacetime, and when they follow different paths they can measure different path lengths. For timelike paths, path length is just elapsed proper time.

I understand your answer. The issue is when you use atomic clocks in a twin paradox type experiment when they reunite do the clocks show a different time?

Nicolaas Vroom

32 Why is there more than one explanation for the Twin Paradox

I understand that. Part of the problem is described at the pages 21 and 315 of the book GRAVITATION. The two figures are almost identical but they are not. The mathematics is the same, which makes it difficult. For me one problem is to calculate the path length in a real experiment i.e. how can you calculate the clock readings. I think this is very complicated. Let me describe a realistic but difficult example. 1) Take a piece of paper and draw a point at the center. This is our Galaxy as a point mass. 2) Draw an arrow through this point. This is the direction of movement of our Galaxy. 3) Draw a cirkel around this point. This is the trajectory of our Sun. 4) Draw a point some where. This is the position or our Sun. 5) Draw a circle around the Sun. This is the trajectory of our Earth. 6) Draw a point at this trajectory. This is the Earth. 7) Draw a circle around the Earth. This is the trajectory of the Moon. 8) Draw a point at this trajectory. This the Moon. 9) Draw a small ellipse around the Sun. This is trajectory of Mercury. 10) Draw a point at this ellipse. This is Mercury.

The first issue is where should I draw the points 4, 6, 8 and 10. IMO they should represent simultaneous events, for simplicity in the plane of the paper.

Next draw all the world lines, with time in z dimension. The best way is to make an image in your brain. The position of our Galaxy is considered the origin. 1) The arrow (2) through the origin and point (x0,y0,0) becomes a straight line through the origin and point (x0,y0,z0) identifying the movement of our Galaxy. 2) The circle 3 becomes a spiral, starting at point (4) in the direction of this straight line, showing the movement. 3) Circle 5 (the earth) becomes a spiral around this spiral. 4) Circle 7 (the moon) becomes a spiral around a spiral around a spiral. 5) Circle 9 becomes the same as above. The reason is to study the perihelion shift over a large period.

As such worldlines become extremely complex. The same is true if you want to calculate the readings of the clocks (or the proper time) which follow these worldlines. These calaculations are also difficult.

IMO the only solution is only to use one fixed clock. This IMO makes certain issues much simpler (I expect). This, maybe, eliminates the concept of worldlines all together if your object is to study the evolution of the planet mercury.

Nicolaas Vroom

33 Why is there more than one explanation for the Twin Paradox

On the contrary, in the case of the twin paradox (which is the subject of this thread) you do not need to calculate the clock readings (even if that is quite easy to do with simple geometrical diagrams). You only need to compare the clocks readings when they reunite (the clocks then are side by side and you only need to look at the clocks displays).

34 Why is there more than one explanation for the Twin Paradox

Which clock contains the correct time?

35 Why is there more than one explanation for the Twin Paradox

When you want to understand the twin paradox you have to understand the concept of worldline and propertime of the moving twin (at least that is the message I get based on the different postings)

That is why I showed the example based on the movement of Our Galaxy, the Sun, the Earth (or Marcury) and the Moon to demonstrate that it is very complicated to calculate the length of such a worldline.

I do not think there are simple geometrical diagrams. It is easy to observe the readings but they are difficult to predict in general!

Anyway it is much more then a thought experiment.

>	Which clock contains the correct time?

That is a very good question. I do not know. That is why I think you should study all from one reference frame and use only one clock. (And in some sense to forget the whole concept of worldlines, except if there is some other reason to use it)

Nicolaas Vroom

36 Why is there more than one explanation for the Twin Paradox

well, if your watch is running slow..it means you have the incorrect time.

37 Why is there more than one explanation for the Twin Paradox

It simply not possible for the Twins Paradox without at least a 'third observer'.

Get on your mark, get set....GO!!!!

38 Why is there more than one explanation for the Twin Paradox

"Wait a second, where you're going?"

"I'm going on a rocket and then I'll return, I only moved a second!"

"No, come back here, the time is already running slow..no need to make that long trip."