Question about Brian green book THE FABRIC OF THE COSMOS

[lnsanity]

On page 56 last paragraph Brian give example of a train paradox where two person have clock and there is two observer on on the train the other outside. They agree to set there clock at 12:00 when they see the light open witch is placed between them.

From there perspective each clock will be set at 12:00 but from the outside observer perspective it may be different if say 12:00 and 12:02 my question is what append if we stop the train and the outside observer keep watching both clock at the same time ? Will he see them synchronize 1 slow down the other speed up ? or only the one being will speed up ? or none of that they stay both desynchronized ? Think carefully because I have more dificult question coming up ! (by the way I am asking the question because I don't know the answer...)

 

[JesseM]

Depends on the details of how they decelerate, but if both ends of the train instantaneously decelerate from v to 0 in the outside observer's frame, and they do so simultaneously in the outside observer's frame, then after they come to rest both clocks will be ticking at the same rate as the outside observer's clock, but the two clocks at either end will remain out-of-sync by the same amount as they were when the train was moving, since neither one jumps forward or backward at the moment of the deceleration.

 

[lnsanity]

Depends on the details of how they decelerate, but if both ends of the train instantaneously decelerate from v to 0 in the outside observer's frame, and they do so simultaneously in the outside observer's frame, then after they come to rest both clocks will be ticking at the same rate as the outside observer's clock, but the two clocks at either end will remain out-of-sync by the same amount as they were when the train was moving, since neither one jumps forward or backward at the moment of the deceleration.

But from the inside perspective view they never desynchronize? So when they stop they always stay in the same frame of reference so from there perspective the clock should stay synchronize ?

Imagine its a digital clock and instead of setting there clock at 12:00 they stop the clock at whatever time it is imagine when they stop its exactly 13:00 so they are inside the train they can even take a picture but the outside viewer take a picture too, on its picture its 13:00:01 on one of the clock but if you stop the train the clock and picture will still be at 13:00 for the people inside the train since they stopped it... how could it be ?? when they stop they become on the same frame of reference as the outside viewer... Once the train stop they are on the same frame of reference they can't see different things ?

 

[JesseM]

But from the inside perspective view they never desynchronize?

What do you mean by "inside perspective"? Do you mean the inertial frame where the train was originally at rest (which continues to move inertially when the the two ends of the train change velocity, so it sees the train start to move), or do you mean some kind of non-inertial frame where each part of the train remains at rest at all times? If the latter, non-inertial frames are tricky, there's a variety of ways to construct a coordinate system where an accelerating object is at rest, and you also can't assume that normal SR rules (like the relation between velocity and the tick rate of a clock) still apply in non-inertial frames.

Imagine its a digital clock and instead of setting there clock at 12:00 they stop the clock at whatever time it is imagine when they stop its exactly 13:00 so they are inside the train they can even take a picture but the outside viewer take a picture too, on its picture its 13:00:01 on one of the clock but if you stop the train the clock and picture will still be at 13:00 for the people inside the train since they stopped it...

Why do you think it'd be different? If the clocks each stop when their end of the train decelerates, all frames will agree about what times show on the clocks when they stop (different frames can't disagree about local facts like what a clock reads at the moment it changes velocity). Keep in mind that in the inertial frame where the train was at rest before any part decelerated, the two ends decelerate at different times (rather than simultaneously as in the outside observer's frame) because of the relativity of simultaneity.

 

[lnsanity]

What do you mean by "inside perspective"? Do you mean the inertial frame where the train was originally at rest (which continues to move inertially when the the two ends of the train change velocity, so it sees the train start to move), or do you mean some kind of non-inertial frame where each part of the train remains at rest at all times? If the latter, non-inertial frames are tricky, there's a variety of ways to construct a coordinate system where an accelerating object is at rest, and you also can't assume that normal SR rules (like the relation between velocity and the tick rate of a clock) still apply in non-inertial frames.

Why do you think it'd be different? If the clocks each stop when their end of the train decelerates, all frames will agree about what times show on the clocks when they stop (different frames can't disagree about local facts like what a clock reads at the moment it changes velocity). Keep in mind that in the inertial frame where the train was at rest before any part decelerated, the two ends decelerate at different times (rather than simultaneously as in the outside observer's frame) because of the relativity of simultaneity.

The inside perspective is the perspective of the 3 people inside the train while it is moving, when the train stop there clock from there perspective is always synchronized. But the outside viewer saw something else, so now if the train stop what will see the outside viewer ?? since the clock as always be synchronized from the point of view of people inside the train...

 

[JesseM]

The inside perspective is the perspective of the 3 people inside the train while it is moving, when the train stop there clock from there perspective is always synchronized.

In relativity when you talk about someone's "perspective" about when events happen or whether some clocks are synchronized, you're talking about a coordinate system (reference frame) that assigns time-coordinates to different events. For a person moving inertially there is a unique inertial reference frame where they're at rest so we can call that their "perspective", but for a person who moves non-inertially there's an infinite variety of different non-inertial coordinate systems where they're at rest, and none is more deserving of being called their "perspective" than any other. So for any statement about the "inside perspective" to be meaningful, you need to specify if you're talking about an inertial frame (in which case the train can only be at rest before the decelerations, after that it'll be moving in this frame) or a non-inertial frame, and if it's a non-inertial frame there need to be details about how it's constructed.

But the outside viewer saw something else, so now if the train stop what will see the outside viewer ??

Again it depends on how the acceleration happens. Do the two ends accelerate simultaneously in the outside observer's rest frame, or do they each accelerate when the train's clock at that end read a certain time (simultaneously in the inertial frame where the train was originally at rest), or in some other way?

 

[lnsanity]

In relativity when you talk about someone's "perspective" about when events happen or whether some clocks are synchronized, you're talking about a coordinate system (reference frame) that assigns time-coordinates to different events. For a person moving inertially there is a unique inertial reference frame where they're at rest so we can call that their "perspective", but for a person who moves non-inertially there's an infinite variety of different non-inertial coordinate systems where they're at rest, and none is more deserving of being called their "perspective" than any other. So for any statement about the "inside perspective" to be meaningful, you need to specify if you're talking about an inertial frame (in which case the train can only be at rest before the decelerations, after that it'll be moving in this frame) or a non-inertial frame, and if it's a non-inertial frame there need to be details about how it's constructed.

Again it depends on how the acceleration happens. Do the two ends accelerate simultaneously in the outside observer's rest frame, or do they each accelerate when the train's clock at that end read a certain time (simultaneously in the inertial frame where the train was originally at rest), or in some other way?

OK you don't have is book I get it... they are on the same platform same train they move together like in any example of that classic experiment I don't get why you are asking question like this and you do not mention you did not read the book it would have been simpler if you told me before so I can't recopy the pages of the book but they do everything simultaneous they are in the same time frame relative to each other all the time.

 

[JesseM]

OK you don't have is book I get it... they are on the same platform same train they move together like in any example of that classic experiment I don't get why you are asking question like this and you do not mention you did not read the book it would have been simpler if you told me before so I can't recopy the pages of the book but they do everything simultaneous they are in the same time frame relative to each other all the time.

No, I read the book, but I don't recall him talking about the "perspective" of a non-inertial observer the way you're doing. The example on p. 56-57 only deals with a train moving at constant velocity relative to the platform, not one that decelerates.