Relativity of simultaneity, time dilation misunderstanding

• I

Main Question or Discussion Point

Hi everybody,
I'm new on this forum so I apologize in advance if I don't respect some formalities (and sorry for my English).

It is known that in the perspective of the stationary observer the events in the back and in the front of the moving spaceship are not simultaneous. If I understand well the clock in the back is advanced compared to the clock in the front. So, first you have the tick in the "back clock" and only after some time you have the same tick in the "front clock" (in the perspective of the stationary observer).

In order to have this "time shift" between the events in the front and in the back of the spaceship I expect that there is some time-dilation-rate difference while the acceleration (the "back clock" must run faster while the acceleration, in order to obtain the final post-acceleration time-shift described above). But, the SR calculations give the opposite results, and this is that the front clock runs faster while the acceleration.

What am I missing. Thanks in advance

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PeroK
Homework Helper
Gold Member
Hi everybody,
I'm new on this forum so I apologize in advance if I don't respect some formalities (and sorry for my English).

It is known that in the perspective of the stationary observer the events in the back and in the front of the moving spaceship are not simultaneous. If I understand well the clock in the back is advanced compared to the clock in the front. So, first you have the tick in the "back clock" and only after some time you have the same tick in the "front clock" (in the perspective of the stationary observer).

In order to have this "time shift" between the events in the front and in the back of the spaceship I expect that there is some time-dilation-rate difference while the acceleration (the "back clock" must run faster while the acceleration, in order to obtain the final post-acceleration time-shift described above). But, the SR calculations give the opposite results, and this is that the front clock runs faster while the acceleration.

What am I missing. Thanks in advance
The leading clock is behind the rear clock by a fixed amount. Both are time dilated by the same factor. So, they remain out of sync by the same amount.

By considering the initial acceleration of the ship you are complicating things. For example, if the ship accelerates from rest, who says initially synchronised clocks in the ship remain synchronised? Also, as the ship is length contracting as it accelerates, the two ends of the ship cannot have the same velocity/acceleration profile in the original reference frame.

Until you have really understood the basics of SR, it is best to re-assess the situation after each period of acceleration, once everything has returned to an inertial reference frame.

sha1000 and SiennaTheGr8
By considering the initial acceleration of the ship you are complicating things. For example, if the ship accelerates from rest, who says initially synchronised clocks in the ship remain synchronised? Also, as the ship is length contracting as it accelerates, the two ends of the ship cannot have the same velocity/acceleration profile in the original reference frame.
So after acceleration the clocks on both ends of the ship are no longer synchronized even in the reference frame of the ship? If it's like this so I have my answer.
Thank you for the thread, I'll take a look at it.

PeroK
Homework Helper
Gold Member

So after acceleration the clocks on both ends of the ship are no longer synchronized even in the reference frame of the ship? If it's like this so I have my answer.
Thank you for the thread, I'll take a look at it.
Yes, even in the rest frame of the ship. You have something similar to gravitational time dilation between the two ends of the ship.

Yes, even in the rest frame of the ship. You have something similar to gravitational time dilation between the two ends of the ship.
Actually after some thinking I still have some problems with my understanding. I'll try to explain myself:

I always considered that the length contraction is just the space contraction depending only on the velocity and that there is no need to think about it. But, when I learned about Bell's "physical interpretation" of length contraction I got very confused. If I understand well, Bell and many others say that the length contraction is a result of different coordinate-acceleration rate of the back and the front of the spaceship. This means that the length contraction is not about the final velocity v of the spaceship but actually depends on the way it was accelerated, in other words if one somehow manage to accelerate every fundamental particle of the spaceship with the same coordinate-acceleration rate there will be no length contraction (I'm exaggerating but you get the idea).

So here comes my confusion about simultaneity. If we take two twins and give them the poison, then we place them on the spaceship (one in the back and another in the front). Afterwards we accelerate the spaceship to the speed v. Only by taking into account the final velocity we know that due to the relativity of simultaneity: events in the back happen before than the events in the front (am i right on this?), so in the perspective of the stationary frame the twin in the back dies before the twin in the front. But what does it means? This means that somehow the twin in the back "aged" more than the twin in the front. My intuition tells me that the only explanation comes from the acceleration process and the time somehow runs faster in the back of the spaceship while the acceleration. But the SR calculations tells us that time runs faster in the front of the spaceship, so it's actually the opposite.

Where is the problem? Was Bell wrong trying to give the physical interpretation of the length contraction and there is no need to think about this questions? Or was Bell right and we can actually give physical interpretations for all SR phenomena (like my simultaneity question)? Or I have a serious misunderstanding of SR and Bell's interpretation (this is more probable :) )

A.T.
...if one somehow manage to accelerate every fundamental particle of the spaceship with the same coordinate-acceleration rate there will be no length contraction...
The particles (or the fields via which they interact) would still contract, so the spaceship would break, because the contracted particles/fields could not span the fixed total length anymore. This is basically what happens with the rope in Bell's spaceship scenario

sha1000
The particles (or the fields via which they interact) would still contract, so the spaceship would break, because the contracted particles/fields could not span the fixed total length anymore. This is basically what happens with the rope in Bell's spaceship scenario
Thanks for response.

When you talk about the field contraction are you referring to the Lorentz's work about the contraction of the electric fields?

In this case we can talk about physical interpretations of different SR phenomena. Do you have any clue about my confusion with simultaneity problem which I described above?

A.T.
Do you have any clue about my confusion with simultaneity problem which I described above?
No, I don't understand your confusion. You might be confusing different clock-rates with a fixed offset between two clocks running at the same rate. Or something like that.

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sha1000
So after acceleration the clocks on both ends of the ship are no longer synchronized even in the reference frame of the ship?

No. The clocks stay exactly synchronized in the reference frame of the ship. And the reason for that is a ship janitor that keeps the clocks synchronized all the time.

In the stationary frame the clocks become unsynchronized quite quickly. And the reason for that is the janitor who is messing with the clocks, which would otherwise stay quite well synchronized in the stationary frame.

In case there is no janitor - then clocks become quite quickly unsynchronized in the ship frame. And, as I said, clocks stay quite well synchronized in the stationary frame.

My point is that clocks should be synchronized in a frame, before we can say how much they are unsynchronized in another frame.

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sha1000
pervect
Staff Emeritus
Let's put this another way. If you accelerated every particle in an object with the same coordinate acceleration, under the laws of special relativity the proper length of the object would change. The object would not be a rigid object, it would basically stretch. This is different from the Newtonian behavior. The important part of the message is that the proper length of the objects changes when you accelerate it in the manner you describe, informally we say that the object stretches.

It's also possible to imagine the space-ship moving as a rigid body, so it does not stretch. The technical name for this is "Born rigid motion". But acceleration profile is different for Born-rigid acceleration than the one you described. If you want to move the space-ship as a rigid body, the stern needs to accelerate slightly harder than the bow.

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sha1000
Hi everybody,
I'm new on this forum so I apologize in advance if I don't respect some formalities (and sorry for my English).

It is known that in the perspective of the stationary observer the events in the back and in the front of the moving spaceship are not simultaneous. If I understand well the clock in the back is advanced compared to the clock in the front. So, first you have the tick in the "back clock" and only after some time you have the same tick in the "front clock" (in the perspective of the stationary observer).

In order to have this "time shift" between the events in the front and in the back of the spaceship I expect that there is some time-dilation-rate difference while the acceleration (the "back clock" must run faster while the acceleration, in order to obtain the final post-acceleration time-shift described above). But, the SR calculations give the opposite results, and this is that the front clock runs faster while the acceleration.

What am I missing. Thanks in advance
Both, the front and the back clock display the same acceleration profile when observed independently. The only difference is, that the back clock begins with this acceleration profile earlier, hence begins to accelerate earlier than the front clock.

For the case of the near instantaneous acceleration, one could say that the front clocks remains at rest in the initial frame for a longer period of time, hence ticks at a faster rate for longer before it accelerates and ticks slower because of time-dilation.

We showed that in the case of a near instantaneous acceleration, for a 10 lightseconds sized rocked, the front clock would remain at rest relative to the initial frame, for about 2.087 seconds longer than the back clock.

We also showed that post acceleration, the front clock would be ahead by around 4.17 seconds.

edit: You might ask yourself, who is going to tell the front clock to accelerate, when it would take 10 seconds for a light signal to reach the front clock, once the back clock starts accelerating. Far longer than the 2.08 seconds we calculated.
Since FTL signaling is not possible, in a realistic scenario where we just accelerate the rocket from behind, and let nature do the rest, the front clock would actually be even more ehead than the 4.17s we calculated.
If we wanted to avoid this and put the least amount of stress on the rocket, we would have to place motors with clocks all along the rocket and pre-program the motors to trigger at the correct times. 2.08s later for the front compared to the back. At 1.04s for the middle etc.

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sha1000
Thank you all for your responses. I'll need some time to digest all the information.