train - tunnel paradox

[somanystylez]

Hi guys,

 

I was recently analyzing the famous train and tunnel paradox which is based on length contraction. If somebody isn't familiar to it, here's the link:

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So in the example there are two guillotines and the most important thing is that all observers agree that none of them hits the train.

The first observer is at rest with respect to the tunnel and in his reference frame the guillotines went off simultaneously, but the train got contracted so nothing happened to the train.

The second observer is moving towards the first guillotine and away from the second so in his reference frame the first guillotine went off and the second followed, so nothing happened to the train because enough time passed that the front parts came off the tunnel and the rear parts followed.

 

The point that is troubling me here is the situation in which we imagine a third observer that has the same velocity as the one located in the train, but isn't moving towards the first guillotine and away from the second. Let's say he's moving towards both of them (he is outside of the tunnel). What situation will happen in his reference frame? After all if he is moving towards both of them, he should see them simultaneously, but 'before' the ground observer sees them, and the tunnel will still get length contracted.

 

I hope you understand my question, thanks for reading. Regards

[swansont]

The point that is troubling me here is the situation in which we imagine a third observer that has the same velocity as the one located in the train, but isn't moving towards the first guillotine and away from the second. Let's say he's moving towards both of them (he is outside of the tunnel). What situation will happen in his reference frame? After all if he is moving towards both of them, he should see them simultaneously, but 'before' the ground observer sees them, and the tunnel will still get length contracted.

 

I hope you understand my question, thanks for reading. Regards

 

An observer with the same velocity as someone on the train is in the same frame. They can synchronize clocks and will have the same simultaneity — they will agree on what time each blade dropped.

[somanystylez]

An observer with the same velocity as someone on the train is in the same frame. They can synchronize clocks and will have the same simultaneity — they will agree on what time each blade dropped.

 

But the point here is that the direction of their velocity relative to those 2 blades isn't the same, so they techincally don't have the same velocity (the direction of the velocity is different).

[swansont]

But the point here is that the direction of their velocity relative to those 2 blades isn't the same, so they techincally don't have the same velocity (the direction of the velocity is different).

 

It won't matter. The choice of the observer at the midpoint is so you can see that the two blade drops are not simultaneous (or are, in the other frame) without a lot of math. Having an observer at some other location makes the problem more intricate but won't change the answer. In analyzing the scenarios, you account for the finite speed of light; that's part of Einstein clock synchronization and simultaneity, but that analysis is omitted from the example by using a symmetry argument.

[DimaMazin]

Modern physics without any paradox can answer this question .

 

Link removed

Edited July 6, 2013 by hypervalent_iodine