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Okay. Two trains travelling towards each other at the speed of light. So, from one train (let's call it train A), the other is moving towards it at the speed of light. The other train shines a torch. They are both moving at the same speed so they both reach train A at the same time.

From train B (the other train), A is moving towards it at the speed of light. It shines the torch, and the torch is moving faster than the train itself (since the train is stationary from it's own frame of reference). So the light should hit train A before train B does.

Obviously both of these scenarios cannot be true, so what happens from each frame of reference?

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No massive object can travel at the speed of light. This question can be framed in terms of trains moving near the speed of light, but then there is no paradox: observers on both trains can agree on the interval between the light reaching train A and the trains meeting. –  dmckee Aug 19 '12 at 18:33
    
I know that they can't ACCELERATE to the speed of light. I'm simply asking about the consequences if they were traveling at the speed of light. –  Bguy92 Aug 19 '12 at 18:47
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@Bguy92 They can't be traveling at the speed of light either, unless they are massless. See my answer below. –  QuantumDot Aug 19 '12 at 19:09
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@Bguy92 the issue is that no massive object, such as a physical torch, can move at the speed of light. Yes, move at, not just accelerate to. And any (necessarily massless) object that does move at the speed of light doesn't have a reference frame. You're asking about an impossible situation, which puts this under the "fictional physics" exclusion of our FAQ. Of course, if you change the question you're asking slightly, it should be okay and in that case I'd be happy to reopen it. (cont.) –  David Z Aug 19 '12 at 19:35
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(cont.) You could ask about objects traveling at slightly less than light speed, or you could ask about something like a photon emitting another photon - but then you would have to reword your question to avoid asking what happens in each frame of reference. Let me know if you'd like help rewording your question. –  David Z Aug 19 '12 at 19:37
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closed as off topic by David Z Aug 19 '12 at 19:31

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1 Answer

As dmckee comments, this questions is 'wrong' since the massive trains can't go at the speed of light.

But we can modify the question a bit to say that our 'trains' are massless. And for simplicity, let's make these 'trains' massless point-particles A and B.

According to relativity, the plane of simultaneous events of train A is light-like, and also contains A's world-line. Therefore, the event of shining the torchlight (emission of a massless photon), the collision of the light with B, and the collision of A and B are all simultaneous, in A's reference (which we can't boost into in the first place)

But non-trivial dynamical systems must carry a mass so this question is plainly absurd.

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