# Neutral simultaneity for two frames.

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If we want to accelerate very long train,

instantly accelerating each railway carryage into a moving frame at v, then we should accelerate them simultaneously in neutral simultaneity.

t =to + (gamma -1)*x/(v*gamma)



Edited by DimaMazin

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Once the cars start moving, their accelerations won't be simultaneous in their reference frame anymore. The front cars will be accelerating earlier than the rear cars, so the cars will be pulled away from each other.

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You can do it if all the parts of the train can change speed instantly.

Say you have a train of proper length L, at rest on some tracks, and instantly accelerate each part of it to velocity v so that it has a proper length of L in its new frame. There's a frame of reference in between those two, where the tracks + rest train are moving in one direction at some velocity -u, and after the train accelerates, it's moving in the opposite direction but same speed +u, so that the length contraction factor before and after are the same. This is the frame in which all parts of the train would accelerate simultaneously. You can find u using the composition of velocity formula, so that v is the composition of u and u.

Is that what you're talking about, and does this match your result?

I suppose that if you did this repeatedly using small accelerations, in limit form you'd get Born rigid motion?

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3 hours ago, md65536 said:

You can do it if all the parts of the train can change speed instantly.

Accelerating all of the cars in a train instantly in the ground's reference frame would result in a chain of length-contracted cars separated by "uncontracted" distances. The couplings between the cars would all break.

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There's a frame of reference in between those two, where the tracks + rest train are moving in one direction at some velocity -u, and after the train accelerates, it's moving in the opposite direction but same speed +u, so that the length contraction factor before and after are the same. This is the frame in which all parts of the train would accelerate simultaneously.

But that's not the ground frame. There are also complications between -u and +u, so the couplings would have to be flexible. Either that or each car would have to be pre-programmed with its own specific acceleration schedule. In the ground frame, the back end of the train has to initially accelerate more quickly than the front end, because the distances between the cars need to shrink along with the cars' lengths.

Edited by Lorentz Jr
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Unfortunately a simulataneous acceleration of a train would impossible taking into consideration the speed limit of information exchange.

This thought experiment would be accurately described via the Rigid Rod under GR.

In essence let's make your train one light year hypothetically. If the force for acceleration starts at say the engine. The tail end would not accelerate until one year later. Thats assuming the medium is ideal enough to allow the signal to propagate at c. Which is your speed limit.

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3 hours ago, Lorentz Jr said:

Accelerating all of the cars in a train instantly in the ground's reference frame would result in a chain of length-contracted cars separated by "uncontracted" distances. The couplings between the cars would all break.

But that's not the ground frame. There are also complications between -u and +u, so the couplings would have to be flexible. Either that or each car would have to be pre-programmed with its own specific acceleration schedule. In the ground frame, the back end of the train has to initially accelerate more quickly than the front end, because the distances between the cars need to shrink along with the cars' lengths.

Right, the parts of the train aren't accelerated simultaneously in the ground frame, only the in-between frame. The parts are each accelerated instantly but not simultaneously, in other frames. In the ground frame, the train starts at its proper length and ends up length-contracted; the rear of the train must accelerate first. In the post-acceleration train's frame, the train starts length-contracted and ends at rest at its proper length; the front of the train must accelerate first.

This isn't a question of practicality, it's mathematical. If an object can be made to accelerate all at once from -u to +u, it doesn't get pulled apart (in any frame) or physically squished, just length-contracted. If you want to debate whether a real train can do this, you should probably find out what v is before deciding if it can handle it, because in practical cases v is small enough that length-contraction is negligible.

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8 hours ago, Lorentz Jr said:

Once the cars start moving, their accelerations won't be simultaneous in their reference frame anymore. The front cars will be accelerating earlier than the rear cars, so the cars will be pulled away from each other.

Correct. But not in my case. Because in my case  the force of acceleration propagates from backward car to forward car at such velosity (I will define it) when the cars do not interact each other. There is no interaction between the cars therefore it is called by simultaneity. I have described the simultaneity by equation.

4 hours ago, Mordred said:

Unfortunately a simulataneous acceleration of a train would impossible taking into consideration the speed limit of information exchange.

This thought experiment would be accurately described via the Rigid Rod under GR.

In essence let's make your train one light year hypothetically. If the force for acceleration starts at say the engine. The tail end would not accelerate until one year later. Thats assuming the medium is ideal enough to allow the signal to propagate at c. Which is your speed limit.

Each railway carryage can have its engine. Therefore force of acceleration does not need to be transferred.

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2 hours ago, md65536 said:

If an object can be made to accelerate all at once from -u to +u, it doesn't get pulled apart (in any frame) or physically squished, just length-contracted.

It will start out contracted and then get squished halfway through because it loses its contraction. That's what I meant by complications.

Accelerating all at once is just the limit of accelerating quickly. It doesn't mean nothing happens in between.

15 hours ago, DimaMazin said:
instantly accelerating each railway carryage into a moving frame at v

t =to + (gamma -1)*x/(v*gamma)

Except each car will crash into the one in front of it because the car in front isn't contracted yet.

Edited by Lorentz Jr
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3 hours ago, DimaMazin said:

Correct. But not in my case. Because in my case  the force of acceleration propagates from backward car to forward car at such velosity (I will define it) when the cars do not interact each other. There is no interaction between the cars therefore it is called by simultaneity. I have described the simultaneity by equation.

Each railway carryage can have its engine. Therefore force of acceleration does not need to be transferred.

The communication between every engine would also be affected so you still wouldn't have simultaneous acceleration not under rigorous treatment with  GR being applied.

Edited by Mordred
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17 hours ago, DimaMazin said:

If we want to accelerate very long train,

This problem is a classic example of forgetting that both SR and GR are point function theories.

Difficulties can easily arise if you try to apply either to 'bodies' or systems that are too large to be considered as 'point partcles'.

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49 minutes ago, Mordred said:

The communication between every engine would also be affected

Unless you calculate the acceleration required for each car as a function of its proper time before starting and pre-program it into the engine. Then start the engines from a standstill using synchronized triggers. 🙂

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Proper time would follow the wordline between engines so you still have the same problem

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34 minutes ago, studiot said:

This problem is a classic example of forgetting that both SR and GR are point function theories.

Difficulties can easily arise if you try to apply either to 'bodies' or systems that are too large to be considered as 'point partcles'.

It's not a problem if we consider only the the kinematics of the system, and treat the train as a set of particles, and consider only as many particles as needed. Usually one at the front of the train and one at the back is enough for most things. The solution to Bell's spaceship paradox is the same if you consider one large metal ship, or 2 small ships with an imaginary string between them. Einstein used trains in thought experiments without problems.

Considering only kinematics, the forces on the train and communication between the parts is irrelevant. Things like lengths and speeds are what's important.

3 hours ago, Lorentz Jr said:

It will start out contracted and then get squished halfway through because it loses its contraction. That's what I meant by complications.

Accelerating all at once is just the limit of accelerating quickly. It doesn't mean nothing happens in between.

I think this is wrong but I'm not certain.

If it squishes (like, physically crumples) in that one frame, that must happen in all frames. I don't see how that's possible in the moving train's frame, where the train is simply stretching out from length-contracted to rest length. Are you saying that what I described will crush the train with high v, or that I made some other mistake?

Also, if the train "loses contraction" only for an instant, the effects of the "squishing" would be causal, and there's no time for the effects to propagate.

Also, the "squishing" seems to imply that you can't accelerate an object without either stretching or compression strain on the object (you can only minimize it with gradual acceleration), do you agree? However, Born rigid acceleration is possible without spacial strain.

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56 minutes ago, md65536 said:

It's not a problem if we consider only the the kinematics of the system, and treat the train as a set of particles, and consider only as many particles as needed. Usually one at the front of the train and one at the back is enough for most things. The solution to Bell's spaceship paradox is the same if you consider one large metal ship, or 2 small ships with an imaginary string between them. Einstein used trains in thought experiments without problems.

Considering only kinematics, the forces on the train and communication between the parts is irrelevant. Things like lengths and speeds are what's important.

Kinematic treatments are point particle by nature.

Furthermore in both SR and GR, as far as forces can be considered at all,  the Newtonian condition that internal forces cancel out when considering systems, does not apply.

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5 hours ago, Lorentz Jr said:

Except each car will crash into the one in front of it because the car in front isn't contracted yet.

Theoreticaly no.

Because velosity of the wave of the acceleration = (gamma +1)v/gamma

For example  gamma=2

v=31/2c/2

velosity of wave acceleration=3*31/2c/4

Local forces accelerate the train. Therefore no force travels faster than c.

Why velosity of wave of acceleration can be faster than c? Because local forces don't need to wait when light crosses already contracted part of the train.

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5 hours ago, Mordred said:

The communication between every engine would also be affected so you still wouldn't have simultaneous acceleration not under rigorous treatment with  GR being applied.

The experiment can be done on very long spacestation in space between galaxy clusters.

1 hour ago, DimaMazin said:

Theoreticaly no.

Because velosity of the wave of the acceleration = (gamma +1)v/gamma

For example  gamma=2

v=31/2c/2

velosity of wave acceleration=3*31/2c/4

Local forces accelerate the train. Therefore no force travels faster than c.

Why velosity of wave of acceleration can be faster than c? Because local forces don't need to wait when light crosses already contracted part of the train.

I am wrong there. I have confused.

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5 hours ago, md65536 said:

If it squishes (like, physically crumples) in that one frame, that must happen in all frames. I don't see how that's possible in the moving train's frame, where the train is simply stretching out from length-contracted to rest length.

Each car stretches out separately. If two adjacent cars get longer, the car in front has to move forward or the rear one has to move back.

Quote

Also, if the train "loses contraction" only for an instant, the effects of the "squishing" would be causal, and there's no time for the effects to propagate.

Then you run into the problem of propagating the acceleration itself through the length of the car. As studiot said, you have to analyze relativity problems in terms of point events. What happens to extended objects tends to be complicated.

10 hours ago, DimaMazin said:

in my case  the force of acceleration propagates from backward car to forward car at such velosity (I will define it) when the cars do not interact each other. There is no interaction between the cars therefore it is called by simultaneity.

Each railway carryage can have its engine. Therefore force of acceleration does not need to be transferred.

6 hours ago, Mordred said:

The communication between every engine would also be affected so you still wouldn't have simultaneous acceleration not under rigorous treatment with  GR being applied.

5 hours ago, Lorentz Jr said:

Unless you calculate the acceleration required for each car as a function of its proper time before starting and pre-program it into the engine. Then start the engines from a standstill using synchronized triggers. 🙂

5 hours ago, Mordred said:

Proper time would follow the wordline between engines so you still have the same problem

I'm sorry, but that's just nonsense. First of all, it's "world", not "word"; and second, the world line for any one (small) object doesn't follow anything except that object. It's theoretically possible to calculate the accelerations of individual cars as a function of time that will keep the cars lined up correctly (and then convert the accelerations to functions of the cars' proper times), and it's theoretically possible to program an engine to provide the calculated acceleration for that car independently of other cars and engines (and it's easy enough to synchronize multiple starter switches when the train is motionless).

So there's no problem at all in principle. The only possible problem would be that it's probably dangerous and impractical, so no one in their right mind would actually do it unless they prepared the train and cleared its surroundings very carefully. 😄

Edited by Lorentz Jr
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How much GR have you studied ? Under GR coordinate time is the time at each event. The proper time follows the worldline.

What I stated earlier stands

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20 minutes ago, Mordred said:

How much GR have you studied ?

Enough to know that "Proper time would follow the wordline between engines" is meaningless gibberish.

Quote

The proper time follows the worldline.

Which world line? One can construct an infinite number of world lines, and the ones that are relevant to individual cars don't extend "between engines".

Quote

What I stated earlier stands

Sure, buddy. Whatever you say. 🙂

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OK let's examine it. Let's assume the signal is sent by the lead train. Each engine will receive that signal progressively later than the previous engine.

Do you consider that simulateneous ? The speed limit of c will always apply it doesn't matter if the signal is through EM frequencies, or transmitted via particle to particle interactions through the train body (which actually transmits less than c) vibration travels at the speed of sound however a hypothetical perfect rigid rod the speed of sound can be treated at the speed of light.

So do this assign an event at each box car or engine in your train. Assign any engine or box car as the transmitter.

At no point will every event receive the signal simultaneous. That would require instantaneous communication.

Edited by Mordred
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On 12/9/2022 at 1:01 PM, DimaMazin said:

If we want to accelerate very long train, instantly accelerating each railway carryage into a moving frame at v, then we should accelerate them simultaneously in neutral simultaneity.

17 hours ago, Mordred said:

Unfortunately a simulataneous acceleration of a train would impossible taking into consideration the speed limit of information exchange.

13 hours ago, DimaMazin said:

Correct. But not in my case. Because in my case  the force of acceleration propagates from backward car to forward car at such velosity (I will define it) when the cars do not interact each other. There is no interaction between the cars therefore it is called by simultaneity.

Each railway carryage can have its engine. Therefore force of acceleration does not need to be transferred.

10 hours ago, Mordred said:

The communication between every engine would also be affected so you still wouldn't have simultaneous acceleration

9 hours ago, Lorentz Jr said:

Unless you calculate the acceleration required for each car as a function of its proper time before starting and pre-program it into the engine. Then start the engines from a standstill using synchronized triggers. 🙂

1 hour ago, Mordred said:

OK let's examine it. Let's assume the signal is sent by the lead train.

What signal? Who said anything about a signal? Other than you, of course.

An array of starter switches can be positioned, one near each car of the train, connected to synchronized timers, so they're all timed to start the engines simultaneously in the ground frame. Then the pre-programmed engines can accelerate their cars, each according to its own previously calculated schedule, with no further input.

As I already mentioned, it's probably a silly and even dangerous thing to do in real life, and I don't think DimaMazin's timing function would work correctly. But there are no signals involved after the initial setting of the timers, so your comments about signals are immaterial.

Edited by Lorentz Jr
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2 hours ago, Mordred said:

How much GR have you studied ? Under GR coordinate time is the time at each event. The proper time follows the worldline.

What I stated earlier stands

I agree this is irrelevant nonsense and you're incorrectly applying definitions that have no bearing on the issue.

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21 minutes ago, Lorentz Jr said:

What signal? Who said anything about a signal? Other than you, of course.

An array of starter switches can be positioned, one near each car of the train, connected to synchronized timers, so they're all timed to start the engines simultaneously in the ground frame. Then the pre-programmed engines can accelerate their cars, each according to its own previously calculated schedule, with no further input.

As I already mentioned, it's probably a silly and even dangerous thing to do in real life, and I don't think DimaMazin's timing function would work correctly. But there are no signals involved after the initial setting of the timers, so your comments about signals are immaterial.

Ah so now we're changing goalposts. I was showing the problems of Born rigidity. Either way there are no rigid objects under GR.

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4 hours ago, Lorentz Jr said:

Each car stretches out separately. If two adjacent cars get longer, the car in front has to move forward or the rear one has to move back.

I've thought about it more and I still think my first reply is correct. The issue is, if there's an instant change in velocity, does length contraction apply to all of the velocities in between as if it accelerates through them all in an instant, and I say it doesn't. SR doesn't predict the effects of acceleration, rather it is an assumption that acceleration doesn't have an effect, only velocity itself does (the "clock postulate"). SR neither says that the train would survive the acceleration, nor that it wouldn't. It says the train would be contracted at the beginning velocity, and also at the end, but not what strains would happen to the train in the zero length of time in between. So, whether the train can accelerate instantly or not is an assumption we have to make, not one we can derive from SR itself. If the train parts can instantly accelerate from 0 to v, then I think my answer works, and if not then it doesn't, and SR doesn't change that.

But yes, if there's any frame in which a train is moving and then all parts of it simultaneously stop, SR says its new proper length is smaller than it was, so it physically must get squished. Going from -u to +u instantaneously doesn't have a moment when it is at rest, so SR does not by itself say it will behave as if at rest in that case.

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32 minutes ago, md65536 said:

I agree this is irrelevant nonsense and you're incorrectly applying definitions that have no bearing on the issue.

Nope just examining the situation under GR I do believe this is the relativity forum unless things have changed. I know you ate familiar enough with relativity to recognize the rigid rod conjectures in regards to relativity

32 minutes ago, md65536 said:

I agree this is irrelevant nonsense and you're incorrectly applying definitions that have no bearing on the issue.

I was making Lorentz aware that proper time differs from coordinate time in regards to

9 hours ago, Lorentz Jr said:

Unless you calculate the acceleration required for each car as a function of its proper time before starting and pre-program it into the engine. Then start the engines from a standstill using synchronized triggers. 🙂

Each engine clock will be in coordinate time.

Anyways it will be interesting when the train tries to turn.... so far the examination has been strictly linear.

Edited by Mordred

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