Time dilation and expansion in accelerated motion

[nakurusil]

I think that the confusion comes from another angle (sometimes mentioned in conjunction with a more elaborate form of the Bell's paradox):

It does make a difference whether a rocket is pushed or pulled. Since forces do not propagate instantaneously in solid (they propagate at the speed of sound), the rear of a rocket (where the engine is located) will attain crusing speed before the front.
If the rocket has the engine towards the front, then the above situation is reversed.

 

[Jorrie]

Not quite the problem!

I think that the confusion comes from another angle (sometimes mentioned in conjunction with a more elaborate form of the Bell's paradox): ...

The issue here is essentially the relativistic difference, as viewed from a static frame, between the pushed and the pulled 'rigid' bar. We know that it is unphysical, since no proper bar can work like that, but the relativistic effects can be analyzed from whatever inertial frame we choose.

Unfortunately, I think we have not addressed MeJennifer's original question!

If we do not touch, (meaning attempt to synchronize) the clocks at the nose and at the tail of the 'perfectly rigid bar', how would they record the actual time of acceleration respectively?

Next, if I recall correctly, would the accelerometer at the back record a different acceleration profile against time than the accelerometer at the front?

Have fun - Jorrie

 

[pervect]

Sorry that I got this thread confused with the Bell spaceship thread - though the two issues are IMO fundamentally related.

When I get some time I'll try to address some of the other points raised, unfortunately real life is making some demands on my time at the moment.

Basically, my current position is that with about five authors making the same or very similar claims, I don't believe there's much question about where the "mainstream opinion" lies.

 

[quantum123]

Quantum123, let me also remind you that there are many aspects of physics such as:
1. foundations of physics
2. mathematical physics
3. theoretical physics
4. physics phenomenology
5. applied physics
6. experimental physics

Your interests may be based mainly on 4 and 5, while mine are mainly 1 and 3. But all these things belong to physics.

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?

 

[nakurusil]

The issue here is essentially the relativistic difference, as viewed from a static frame, between the pushed and the pulled 'rigid' bar. We know that it is unphysical, since no proper bar can work like that, but the relativistic effects can be analyzed from whatever inertial frame we choose.

Unfortunately, I think we have not addressed MeJennifer's original question!

If we do not touch, (meaning attempt to synchronize) the clocks at the nose and at the tail of the 'perfectly rigid bar', how would they record the actual time of acceleration respectively?

Next, if I recall correctly, would the accelerometer at the back record a different acceleration profile against time than the accelerometer at the front?

Have fun - Jorrie

I think pervect dealt with both problems here.

 

[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?