The clock hypothesis of relativity theory equates the proper time experienced by a point particle along a timelike curve with the length of that curve as determined by the metric. Is it possible to prove that particular types of clocks satisfy the clock hypothesis, thus genuinely measure proper time, at least approximately? Because most real clocks would be enormously complicated to study in this connection, focusing attention on an idealized light clock is attractive. The present paper extends and generalized partial results along these lines with a theorem showing that, for any timelike curve in any spacetime, there is a light clock that measures the curve's length as accurately and regularly as one wishes.
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Acknowledgements Thanks to Erik Curiel for bringing the work of Gautreau and Anderson to my attention, and to David Malament similarly for the work of Synge and for suggestions leading to the formulation of the lemma involved in the proof of the central theorem. This work was supported by a National Science Foundation Graduate Research Fellowship.
- Born rigid
- Clock hypothesis
- General relativity
- Light clock