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Suppose to be in an arbitrary gravitational field and you are moving in it arbitrarily with a clock in your hand. In this general situation I ask: if I read the positions of the hands of the clock, what am I really measuring the proper time or a simple coordinate?

Qmechanic
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Yildiz
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1 Answers1

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You are reading the proper time (which is, of course, the value of one of many possible coordinates).

  • @Yildiz Indeed they will: given the curve you follow in spacetime, all observers agree on its length. –  May 31 '16 at 20:52
  • Suppose there is a strong gravitational field between you and your clock and that it varies in such a way that the light that arrives from the hands of the clock changes so you see the hands going in an irregular, non periodic way, as a normal clock shouldn't do: how is it possible that everyone will agree on this measure of "time" if this is a proper time and so a scalar? – Yildiz May 31 '16 at 21:08
  • @Yildiz: Periodicity is not a necessary requirement for a clock, only monotonicity is. – CuriousOne May 31 '16 at 21:19
  • I want to be precise about this: suppose to be in an arbitrary gravitational field, what is your operative definition of "time"? – Yildiz May 31 '16 at 21:26
  • @Yildiz The proper time along a (suitably smooth) timelike curve is simply its length, which, if you know the metric, is $\int\sqrt{\pm g(\vec{\lambda}(t), \vec{\lambda}(t))},dt$ where $t$ parameterises the curve, and$\vec{\lambda}(t)$ is the tangent vector to the curve at $t$. –  May 31 '16 at 21:32
  • I asked how to measure, in a real and concrete way, time in general relativity using a clock: I want an operative definition that take in consideration also the presence of strong gravitational fields between me and clock, able to deviate the light that i see coming from the hands. If is not possible to give this definition how is it possible to say that the proper time is the one "measured" if i don' t have a standard definition on how to compute this measure? – Yildiz Jun 01 '16 at 13:16
  • @Yildiz you read what the hands on the clock say: it's as simple as that. –  Jun 01 '16 at 14:13