# A handshake on a very fast train

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 travelling 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?

Related Special and General Relativity News on Phys.org
ghwellsjr