Time dilation and expansion in accelerated motion

[Jorrie]

Not quite

I think pervect dealt with both problems here.

Yes, pervect dealt with it, but only saying that there is insufficient information in the original question regarding the bar's properties. If we idealize the bar (perfectly rigid) and look at relativistic effects only, it should be solvable.

 

[nakurusil]

But what about Experiment 2?
My question is what is the difference between the recorded proper times (if any) between the two probes and what is the proper acceleration profile for the probe on the trailing end of the rod.

As pervect explained, your second problem is not sufficiently constrained. We need to add the following constrains (and maybe more) in order to answer it.

A. IF the rod is infinitely rigid (a totally unphysical condition) AND IF you ignore any gravitational field the acceleration profiles will be identical and the recorded proper time by the two clocks will be identical.

b. IF the rod is a real rod (finite rigidity) and IF you are still ignoring all gravitational shift effects, then the speed profiles will be different.
-If the rod is pushed, the rear end will reach cruising speed faster
-If the rod is pulled, the front end will reach cruising speed faster

The two clocks will record different proper time in this case.

 

[Jorrie]

Agreed

... IF the rod is infinitely rigid (a totally unphysical condition) AND IF you ignore any gravitational field the acceleration profiles will be identical and the recorded proper time by the two clocks will be identical.

I agree with your assessment. It boils down to that fact that in this unphysical situation, the results will be the same as in MeJennifer's experiment #1 (independent probes accelerating at a constant rate).

It is however interesting to note that the very clocks used in recording those times and profiles will not be synchronized in the new inertial frame (after the acceleration has stopped, using Einstein's method). The front clock will be ahead of the rear clock, I reckon.

 

[nakurusil]

I agree with your assessment. It boils down to that fact that in this unphysical situation, the results will be the same as in MeJennifer's experiment #1 (independent probes accelerating at a constant rate).

It is however interesting to note that the very clocks used in recording those times and profiles will not be synchronized in the new inertial frame (after the acceleration has stopped, using Einstein's method). The front clock will be ahead of the rear clock, I reckon.

Einstein's synchronisation method applies to inertial motion only.

 

[Jorrie]

Einstein's synchronisation method applies to inertial motion only.

After the acceleration has stopped the two clocks are in inertial motion once again, so they can be re-synchronized. The front clock will have to be adjusted backwards.

 

[nakurusil]

After the acceleration has stopped the two clocks are in inertial motion once again, so they can be re-synchronized. The front clock will have to be adjusted backwards.

You are talking my case b, correct? If yes, then I agree.

 

[Jorrie]

Not quite

You are talking my case b, correct? If yes, then I agree.

Nope - I'm talking about the unphysical situation of your case a, where MeJennifer's experiment 2 will show identical recorded times and accelerations. Yet, after the acceleration, the clocks used in those recordings will no longer be in sync in the final inertial frame.

I think the normal desynchronization vL/c^2 after a change in velocity of v would apply.

 

[Demystifier]

For your info, relativity is also considered experimental physics too. The twin paradox has recently been experimentally tested to be true. There can be no science without experimental observation. On the other hand, I am sure you have heard about the theory of elasticity? That is theoretical physics, right?

You have not understood my point. (Or do you pretend that you did not?)

Take elasticity for example.
If you study general principles of the theory of relativity, you are doing theorethical physics. This is something I am interested about.
But if you apply this theory to a motion of a rod made of specific material and moving with specific accelerations, then you are doing phenomenology. This is not something I am particularly interested about.

Although you are right that there is no science without the experimental observations, it does not mean that every scientist should study experimental observations.

 

[Garth]

Although you are right that there is no science without the experimental observations, it does not mean that every scientist should study experimental observations.

I find that statement difficult to agree with, even as a theoretical physicist.

Garth

 

[Boustrophedon]

Explanation based on sound SR principles...

Let's try and clarify things by going back to basic SR principles. You're probably all familiar with the following train embankment demo. The length of a stationary single carriage is marked off on the platform before the train is speeded up from a distant point to pass the platform at constant velocity. Explosive charges are detonated on the platform at each end of the marked length, simultaneously by synchronised clocks on the platform. It is subsequently found that the burn marks on the train are further apart than one carriage length ( by the usual Lorentz factor ).

If we reverse the situation so that instead charges are set off at each end of a single moving carriage, simultaneously by synchronised clocks on the train, then they will leave burn marks on the platform further apart than the marked carriage distance. Now we also know that if the carriage ends of the moving train are marked on the platform simultaneously by observers with synchronised clocks, the marked distance will be shorter. So we have similar, equivalent evidence that on the one hand the carriage is longer, and on the other that it is shorter, than when stationary.

When the distance is marked using simultaneity for train clocks, the carriage seems to have increased in length, but using simultaneity by platform clocks it appears to have decreased. Of course the explanation is simple. What appears "simultaneous" aboard the train is clearly a case of the rear charge going off first due to the forward clocks having been turned back during a synchronisation procedure, so a platform observer is not the least surprised or perplexed that the front mark is further on than one length. He does not suppose that the carriage "got longer".

In a similar way, the train rider sees the platform recorder ahead make his mark before the one behind does so, due to the platform clocks ahead being progressively set forward, and can thus see all too easily how those on the platform have recorded the front before the rear to get too short a length.
Note that this is precisely how SR deals with moving lengths. It is of the utmost importance to realize that nothing whatever has happened to the train itself. The whole of the disagreement over lengths between inertial observers is due to the proportional difference in simultaneity.

Thus if we have an adjacent parallel set of rails with two engines, one keeping pace with the front end of the carriage and behind it, another keeping up with the rear end, exactly the same measurements and marks would obviously be recorded for the distance between the trains.
Moreover, because as has been shown, the train itself is unaffected as it gains speed, the "proper" accelerations of front and rear are identical.

Remember that "proper" refers simply to things "as measured by a co-mover" - so the apparent difference in front/rear acceleration is not the proper acceleration but actually the acceleration as reckoned by pairs of platform observers who mark off a diminishing length progressively along the platform. It follows automatically according to such a correct SR analysis that the two engines will also have identical proper acceleration when keeping alongside the ends of the carriage. Thus in MeJennifer's problem the two experiments will give identical results.

What is surprising, and possibly quite shocking, is that quite a few textbooks, some with eminent authors, get this analysis wrong and perpetuate bizarrely antiquated notions connected with "Born rigidity".

 

[nakurusil]

Nope - I'm talking about the unphysical situation of your case a, where MeJennifer's experiment 2 will show identical recorded times and accelerations. Yet, after the acceleration, the clocks used in those recordings will no longer be in sync in the final inertial frame.

I think the normal desynchronization vL/c^2 after a change in velocity of v would apply.

Hmmm, I am not sure about that. Can you try to put some math behind your statement? We are talking the frame comoving with the rod.
We might be talking about different things, when I talk about the clocks being synchronised , I am talking about them ticking at the same rate.
I sense that you are talking about what an observer wrt which the rod moves at v will see the two clocks indicating. If the length of the rod is L , then , indeed he will see the clocks differing by vL/c^2. Light doesn't propagate instantaneously :-)

 

[Jorrie]

Where?

Thus if we have an adjacent parallel set of rails with two engines, one keeping pace with the front end of the carriage and behind it, another keeping up with the rear end, exactly the same measurements and marks would obviously be recorded for the distance between the trains.
Moreover, because as has been shown, the train itself is unaffected as it gains speed, the "proper" accelerations of front and rear are identical.

Everything you said up to the statement "Thus if we have an adjacent parallel set of rails with two engines, one keeping pace with the front end of the carriage and behind it, another keeping up with the rear end, exactly the same measurements and marks would obviously be recorded for the distance between the trains" is stock-standard SR and not disputed (unless I missed something).

However, your "Moreover, because as has been shown, the train itself is unaffected as it gains speed, the "proper" accelerations of front and rear are identical" places the rest of your argument under suspicion. Where has it been shown?

You cannot use the arguments of the train before and after acceleration to show anything about the conditions during acceleration. Simultaneity changes constantly during acceleration. So try again.

Jorrie

 

[nakurusil]

However, your "Moreover, because as has been shown, the train itself is unaffected as it gains speed, the "proper" accelerations of front and rear are identical" places the rest of your argument under suspicion. Where has it been shown?

Jorrie

Good catch. He might be thinking about an infinitely rigid train. No springs between cars

 

[Jorrie]

Semantics!

Hmmm, ...
We might be talking about different things, when I talk about the clocks being synchronised , I am talking about them ticking at the same rate.

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. 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

 

[Jorrie]

I think he is

Good catch. He might be thinking about an infinitely rigid train. No springs between cars

This is, however, not the issue! In treating relativistic effects, one may ignore non-relativistic effects for clarity. His premise is wrong on pure relativistic grounds.

 

[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.