The Space Communication Paradox

(based on a problem in Taylor and Wheeler's Spacetime Physics)

Two rockets are approaching each other (5a). The captain of the top rocket wants to send a message to the bottom rocket by flashing a light as they pass. His communications officer decides to send the message when the nose of the top rocket is even with the tail of the bottom rocket. Because of the Lorentz contraction, the flash should miss the bottom rocket, according to the calculations of the ship's engineer (5b).

But the communications officer claims that the message will be received because the top rocket is Lorentz contracted (5c). This results in a dispute that must be resolved by the captain. Who is right? How can the flash of light miss from one point of view and not from another?

Think about this question in terms of the relativity of simultaneity. Carefully examine the statement of the problem for ambiguities.

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