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Bullet-hole "paradox"
This is a variant of the so-called "bullet-hole paradox" (the guns can be lasers and the train a spaceship):
Two guns are mounted a distance of 40 ns apart (SR unit system) on the embankment beside a railroad track. The barrels of the guns project toward the track so that they almost touch a speeding train as it passes by. The train moves at 3/5 the speed of light with respect to the ground. Suppose the two guns fire simultaneously (in the ground frame) as the train passes leaving two bullet holes in the train.
The Lorentz transformations show that in the train frame, the space-time coordinate separation between the events of the guns firing is 50 ns apart spatially and 30 ns in time (with the forward gun firing before the rear gun). In this frame the distance between the guns is seen as 32 ns.
My questions are these: (1) In the train frame how far apart do the bullet holes apear to be?; (2) If the train is stopped after the firing of the guns, how far apart are the holes measured to be?
As the train is a physical object I expect the answer in both cases to 40 ns. Can anyone justify this or contradict it?
This is a variant of the so-called "bullet-hole paradox" (the guns can be lasers and the train a spaceship):
Two guns are mounted a distance of 40 ns apart (SR unit system) on the embankment beside a railroad track. The barrels of the guns project toward the track so that they almost touch a speeding train as it passes by. The train moves at 3/5 the speed of light with respect to the ground. Suppose the two guns fire simultaneously (in the ground frame) as the train passes leaving two bullet holes in the train.
The Lorentz transformations show that in the train frame, the space-time coordinate separation between the events of the guns firing is 50 ns apart spatially and 30 ns in time (with the forward gun firing before the rear gun). In this frame the distance between the guns is seen as 32 ns.
My questions are these: (1) In the train frame how far apart do the bullet holes apear to be?; (2) If the train is stopped after the firing of the guns, how far apart are the holes measured to be?
As the train is a physical object I expect the answer in both cases to 40 ns. Can anyone justify this or contradict it?