Handshake on a Fast Train: Understanding Relativity

[BenHGuitar]

I have just started reading "The Elegant Universe" by Brian Greene. In chapter 2, on pages 34-37 he uses an analogy to help explain relativity, and it made me think about the following scenario, I'm wondering if I'm missing something:

2 people face each other on a train moving at a very high, constant velocity. Person A faces the train's direction of motion, person B faces the opposite direction. A lightbulb is placed in the middle of them and they agree to shakes hands when they see the lightbulb flash on.
In Brian Greene's book the 2 people were signing something simultaneously when the light flashed, but to observers on a platform, Person A sees the light first, as he is traveling towards the light, so signs first.
In my scenario of shaking hands, would the platform-observers see person A go to shake hands first, as he has seen the light first from their perspective? This would mean he would be shaking hands with thin air until person B sees the flash and leans forward to start shaking. I'm wondering if I'm missing something here. Perhaps the actual scenario would play out so that the platform-observers just see person B lean forward and shaking hands at the same time as person A, but person B appears to do so before actually seeing the light?

 

[ghwellsjr]

I have just started reading "The Elegant Universe" by Brian Greene. In chapter 2, on pages 34-37 he uses an analogy to help explain relativity, and it made me think about the following scenario, I'm wondering if I'm missing something:

2 people face each other on a train moving at a very high, constant velocity. Person A faces the train's direction of motion, person B faces the opposite direction. A lightbulb is placed in the middle of them and they agree to shakes hands when they see the lightbulb flash on.
In Brian Greene's book the 2 people were signing something simultaneously when the light flashed, but to observers on a platform, Person A sees the light first, as he is traveling towards the light, so signs first.
In my scenario of shaking hands, would the platform-observers see person A go to shake hands first, as he has seen the light first from their perspective? This would mean he would be shaking hands with thin air until person B sees the flash and leans forward to start shaking. I'm wondering if I'm missing something here. Perhaps the actual scenario would play out so that the platform-observers just see person B lean forward and shaking hands at the same time as person A, but person B appears to do so before actually seeing the light?

Different frames may disagree on when the two people see the light and start to reach out their hand to the other person but that will take additional time and by the time their hands meet, all frames will agree that they meet at the same time, at the location of the light, presumably. It's no different than having two mirrors at the locations of the two people and reflecting the light flashes back to the light bulb, the two flashes arrive simultaneously in all frames, even though the light may take a longer time to go in one direction than in the other. The point is that what ever time it takes for the flash to go from the light bulb to A and back to the bulb is the same as for B. In both cases, there are two round trips, slow in one direction, fast in the other but it's the same total trip time for both flashes, just in a different order.