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based on the paradox resolved at A relativistic meter stick and a thin disk

if in the place of a relativistic stick, was a relativistic man whose length is the same as that of a stick, and instead of an end of a hole, was a bullet. In the man's frame, would he die(Does the bullet effectively hit the man?)? and in the reference of the hole?

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By construction in that problem, the center of mass of the man and the bullet coincide at some time. Two objects being at the same place at some time is Lorentz invariant: if two objects are at the same place as one another in one frame at time $t_1$, they are guaranteed to be at the same place as one another in any other frame at some (possibly different) time $t_2$.

So, yes, they collide in both reference frames. Since the man is being hit at relativistic velocities by a meter wide bullet, it's pretty safe to assume he doesn't survive.

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  • $\begingroup$ the problem is that, in this matter, the end of the hole does not reach the end of the stick in the frame of the stick when the end of the hole reaches the x-axis. However, the end of the hole hits the end of the stick in frame L.that comes to my doubt. In this case ,one end of the hole reaches the x-axis in γ/2, not in 1/2 (required to reach the end of the stick) , γu/2c². my doubt is resolved if the stick measures, in the reference frame L, lγ $\endgroup$ – Bruno Queiroz Nov 26 '17 at 3:37
  • $\begingroup$ @BrunoQueiroz It's hard to understand what you're trying to say, but you are mistaken. There is no collision in either reference frame in the other problem. Naturally, since you've replaced the hole with an object, that means that in your problem there will be a collision in every reference frame. $\endgroup$ – Chris Nov 26 '17 at 5:18

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