Time dilation and expansion in accelerated motion

[nakurusil]

Indeed we are! I read synchronized clocks to mean showing the same time simultaneously in an inertially moving frame, i.e., Einstein's method of clock synchronization.

Clocks at the two ends of a lengthwise acceleration rod will not stay in sync.

...from the PoV of a non-comoving frame. I think MeJennifer''s scenarios 1 and 2 are being set up from the PoV of an observer that rides inside the rocket. At least this is how I read the text.

The line of simultaneity on a Minkowski spacetime diagram will constantly change. If no attempt is made, during the acceleration to keep them synchronized, then after the acceleration, a rather large adjustment in their synchronization might be required!

Jorrie

Sure, from the PoV of a non-comoving frame.

 

[MeJennifer]

...from the PoV of a non-comoving frame. I think MeJennifer''s scenarios 1 and 2 are being set up from the PoV of an observer that rides inside the rocket. At least this is how I read the text.

Note that the experiment is defined in terms of proper acceleration and proper time intervals. Furthermore since the elapsed times are recorded and then compared, we compare the proper durations undisturbed by synchronization issues. There is no point of view since the setup only measures and compares Lorentz invariant properties.

 

[nakurusil]

Note that the experiment is defined in terms of proper acceleration and proper time intervals. Furthermore since the elapsed times are recorded and then compared, we compare the proper durations undisturbed by synchronization issues. There is no point of view since the setup only measures and compares Lorentz invariant properties.

Thank you, you are confirming what I said. You also got the answers to your scenarios 1 and 2. Did you notice that?

 

[country boy]

Here's another version of the problem:

Experiment 3: The two rockets are not connected, but the front rocket sends light pulses to the back rocket at time intervals T. The back rocket adjusts its motion to keep the received time intervals equal to T. The front rocket accelerates. What are the recorded profiles for each rocket?

 

[MeJennifer]

Thank you, you are confirming what I said. You also got the answers to your scenarios 1 and 2. Did you notice that?

Well in experiment 2 I don't think it is that simple.

It seems to me that the trailing end of the rod's acceleration is modulated by some sort of wave due to inertia. The metal bar will undergo a series of compressions and expansions. Furthermore the waves in the backward direction will modulate the constant proper acceleration, so it is interesting to see how we can even attempt to keep it constant.

For starters, it seems to me that we can say that the proper elapsed time for the trailing clock must be less than in the case of an unphysical Born ridgid situation.

Perhaps we can make a simple model by adding a speed of propagation for the rod and a compression rate.

 

[nakurusil]

Well in experiment 2 I don't think it is that simple.

It seems to me that the trailing end of the rod's acceleration is modulated by some sort of wave due to inertia. The metal bar will undergo a series of compressions and expansions.

This is "Born rigidity". I mentioned it to you. The bar will not undergo any "series of compressions and expansions"

If it is pushed, it will undergo compression.
If it is pulled, it will undergo expansion.
It is all in my post.

 

[MeJennifer]

This is "Born rigidity". I mentioned it to you. The bar will not undergo any "series of compressions and expansions"

If it is pushed, it will undergo compression.
If it is pulled, it will undergo expansion.
It is all in my post.

What do you mean "this is Born rigidity"?
Please read what I wrote, nowhere in my experiment did I mention that we assume Born rigidity.
Clearly Born rigidity is unphysical.

 

[nakurusil]

What do you mean "this is Born rigidity"?
Please read what I wrote, nowhere in my experiment did I mention that we assume Born rigidity.
Clearly Born rigidity is unphysical.

This is "Born rigidity theory". It is very far from being unphysical, quite the opposite, it describes very realistically how rigid bodies behave. You should try reading it sometime.

 

[MeJennifer]

This is "Born rigidity theory". It is very far from being unphysical, quite the opposite, it describes very realistically how rigid bodies behave. You should try reading it sometime.

Sure you are always right and we have to read and go back to school.
It is getting old, and frankly, very annoying.

 

[nakurusil]

Sure you are always right and we have to read and go back to school.
It is getting old, and frankly, very annoying.

Tough. I'll give you a preview: the idea is that in real rigid bodies (as opposed to ideal ones) forces propagate at finite speed (the speed of sound). Because of that the part of the rod where the force is applied reaches the cruising speed the fastest:

-if the rod is pushed, it gets compressed (the rear outraces the front)
-if the rod is pulled, it gets extended (the front outraces the rear)
In both cases the clock at the front of the rod and the one at the rear travel at different speeds during the acceleration period, until cruising speed is reached when the force is removed. You can draw your own conclusion about what happens to the clocks in the proper frame of the rod.

No "series of compressions and expansions" though, ok?

 

[Jorrie]

This is "Born rigidity". I mentioned it to you. The bar will not undergo any "series of compressions and expansions"

If it is pushed, it will undergo compression.
If it is pulled, it will undergo expansion.
It is all in my post.

Huh! Are you saying "Born rigidity" means that the rod is compressed or stretched, or do I understand you wrongly? It is surely not the accepted definition of "Born rigidity".

Since you are inclined towards keeping it physical, a sudden start to even a moderate lengthwise acceleration will cause some 'ringing' in the length of a rod, although it might only be for a short time before it dampens out.

 

[Jorrie]

...
-if the rod is pushed, it gets compressed (the rear outraces the front)
-if the rod is pulled, it gets extended (the front outraces the rear)
In both cases the clock at the front of the rod and the one at the rear travel at different speeds during the acceleration period, until cruising speed is reached when the force is removed.

Huh! (again). Your post creates the impression that a pulled/pushed rod is stretched/compressed progressively <edit> more and more </edit> in proper length for as long as a constant acceleration lasts. I hope I have read you wrongly!

 

[Boustrophedon]

Please drop this Born rigidity nonsense.

The concept of "Born rigidity" has no particular relevance in SR. This is because in all the usual thought experiments inertial stresses are excluded from consideration by (a) assuming sufficiently gentle acceleration and/or (b) assuming any elastic distortion is reversable. The mere reference to a "rigid rod" carries implicit indication that only relativistic effects are under consideration.

My argument on the previous page still stands as valid. I don't think Jorrie has understood that the train must have remained unaffected because the longer and shorter "measured" lengths ( gamma*L & L/gamma) are shown to derive purely from the difference in simultaneity between using synchronised train clocks (longer) or synchronised platform clocks (shorter).

With no reason, effect or cause for any variation in lengths on the train, it follows that the proper acceleration is identical at all points along the train.
As I said, accelerations deduced by platform clock observers, who measure shorter and shorter (L/gamma) lengths at higher velocities, will "seem" to be lower at the front than the rear - but they are not measuring "proper" accelerations !

 

[country boy]

I posed "Experiment 3" above to eliminate the vexing rigid rod from the puzzle and see what happens with a purely light-speed connection. This is a realistic problem, since satellites might be coordinated in this way. Does it somehow miss the point of MeJennifer's original question?

 

[Boustrophedon]

Yes it does miss the point of MeJennifer's problem. In order to maintain constant light pulses, the rear rocket would have to slow its acceleretion, thus falling increasingly behind and yielding entirely different telemetry.

 

[pervect]

Huh! Are you saying "Born rigidity" means that the rod is compressed or stretched, or do I understand you wrongly? It is surely not the accepted definition of "Born rigidity".

Since you are inclined towards keeping it physical, a sudden start to even a moderate lengthwise acceleration will cause some 'ringing' in the length of a rod, although it might only be for a short time before it dampens out.

Yep. Exactly.

 

[Jorrie]

Diametrically opposing views

Yes it does miss the point of MeJennifer's problem. In order to maintain constant light pulses, the rear rocket would have to slow its acceleretion, thus falling increasingly behind and yielding entirely different telemetry.

I'm afraid we seem to have diametrically opposing views on this!

I believe that in your train experiment the proper acceleration varies across the length of the "rigid" train, because the proper time varies. During acceleration, clocks in the front will gain time on clocks in the rear, just like the higher clock in the Harvard tower experiment gained time on the lower clock.

On the other hand, in Country Boy's constant period light experiment, I think the proper accelerations will have identical profiles, barring a simple time lag between the front and the rear ship, due to the speed of light.

It is true that the rear ship will fall increasingly farther behind the lead ship, because it started accelerating later and will always have a lower speed. It does not have to slow its proper acceleration relative to the lead ship, as you stated it.

BTW, am I right in feeling that you seem to oppose much of mainstream relativity?

 

[Boustrophedon]

Don't jump to conclusions...

Jorrie writes:

I believe that in your train experiment the proper acceleration varies across the length of the "rigid" train, because the proper time varies. During acceleration, clocks in the front will gain time on clocks in the rear

This is a crucial error of reasoning. The forward clock does not "go faster". You are running together two separate things. The clock couldn't "know" how far away the observer is to decide how much faster to go !


What happens is that the clocks continue at the same rate but the shift in simultaneity for rear observers means that they perceive as simultaneous the front clock at a progressively later time ( compared to their own clock ) during acceleration so that it appears to be gaining. Correspondingly the front observer's simultaneity also shifts so that the rear clock appears to be falling behind his own.

Obviously when they re-synchronise clocks either the front clock has to be turned back or the rear clock turned forward or some combination of both.
Since what you like to call the "proper time" is the elapsed period on a standard clock without any readjustment or tampering then the "proper times" are identical and so are the accelerations.

Of course when the've re-synchronised at constant v then the train is as equally valid an inertial system as the platform and can legitimately claim that the platform clocks are unsynchronised with the clocks ahead set forward.

 

[nakurusil]

Huh! (again). Your post creates the impression that a pulled/pushed rod is stretched/compressed progressively <edit> more and more </edit> in proper length for as long as a constant acceleration lasts. I hope I have read you wrongly!

Correct, I have explained this several times. Apparently you have a problem with that and you seem to be in the camp of "alternating compressions / expansions"

 

[nakurusil]

Huh! Are you saying "Born rigidity" means that the rod is compressed or stretched, or do I understand you wrongly? It is surely not the accepted definition of "Born rigidity".

Since you are inclined towards keeping it physical, a sudden start to even a moderate lengthwise acceleration will cause some 'ringing' in the length of a rod, although it might only be for a short time before it dampens out.

Forget about how it is named, concentrate on the physics of the problem.
If you apply the force as a step function you will get some ringinging. If you use a different profile (like a ramp) you will get "less" ringing. The point is that ringing disappears after the short transitory regime. What steady effect do you get after the ringing has disapperared ? Compression for pushing and extension for pulling, ok?
It is the difference of the speeds at the two ends of the rod that desynchroizes the clocks for the case of a non-infinitely rigid rod, I thought that you understood and that you agreed with me in an earlier post. This is the problem at hand.

 

[ZapperZ]

Again, as in another thread that was recently locked, this thread seems to be going around in circle, and doing that for a rather lengthy period of time.

I will also re-emphasize that if you wish to argue this based on non-standard physics, then PF is the wrong place to do it, as I'm sure you would have already been aware of since you have read the PF Guidelines very closely and memorized it by heart now. We have let threads like this go on a bit longer than we should simply because we hope that some things can be straightened out. It is obvious that based on how long this thread has gone on, and the number of times things keep going back to the same thing, it isn't going to progress that way.

Therefore, I'm sticking a fork into this one and declare it done. Take note that if a similar thread is started and going along the same trend, it will be deleted without warning and approprate actions against the relevant members will be taken.

Zz.