Abstract
THE answer to the question posed by Professor Dingle1 is quite simply that the Lorentz transformation formula does not imply what he claims it does. In the situation he describes, the interval dt′ that B's clocks would show is related to the interval dt shown by A's clock by the usual formula where β and γ have their usual significance, and D is the coordinate difference between the two events as measured in A's frame. This formula involves only the relative velocity β of A and B, and it is clearly impossible to deduce from it anything about the relative sizes of dt and dt′. The common result, described too succinctly by the phrase “the moving clock appears to be slow”, refers only to the very special case where the coordinate difference D is zero. Even in this case, the corresponding difference measured by B will not be zero, the situation is clearly asymmetric and no paradox arises.
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Dingle, H., Nature, 242, 423 (1973).
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WHIPPMAN, M. Whippman's Answer. Nature 244, 27 (1973). https://doi.org/10.1038/244027c0
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DOI: https://doi.org/10.1038/244027c0
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Dingle's Question
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