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"In a gravitational field clocks slow down" - this is an effect of gravitational redshift.

Are the following statements correct? If I take a "clock" from the surface of the Earth up to a certain distance in space

  1. an atomic clock will run faster (have shorter periods) than an atomic clock on Earth because this difference is measured by emitted light pulses subjected to gravitational redshift.
  2. the oscillation period of a physical pendulum will increase because the gravitational acceleration of the Earth g is less.
  3. a wristwatch or a mechanical tabletop clock will sense no difference.
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  • $\begingroup$ Related: physics.stackexchange.com/q/277995/123208 $\endgroup$
    – PM 2Ring
    Commented Dec 21, 2021 at 21:40
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    $\begingroup$ BTW, you can calculate gravitational time dilation in the Schwarzschild metric using $\tau=t_\infty\sqrt{1-\frac{r_s}r}$, where $\tau$ is the proper time measured by a clock at distance $r$ from the centre of a body of Schwarzschild radius $r_s$, and $t_\infty$ is the time measured on a clock outside the gravitational field. For the Earth, $r_s\approx8.870056$ mm. $\endgroup$
    – PM 2Ring
    Commented Dec 21, 2021 at 21:47
  • $\begingroup$ Notice that the gravitational time dilation occurs in General Relativity, not in Special Relativity. While there is a time dilation effect in Special Relativity, it is not the same thing that happens in the presence of gravitational fields. I've updated the question tags due to this. $\endgroup$
    – Níckolas Alves
    Commented Dec 21, 2021 at 22:28

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Gravitational time dilation is about time, not about clock mechanisms. Wristwatches, atomic clocks, and biological processes like aging all proceed "faster" (relative to the ground) when they are higher up, and this has been verified experimentally e.g. in the Global Positioning System.

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  • $\begingroup$ "Gravitational time dilation is about time, not about clock mechanisms." But is this actually true? If we provide an operational definition of time, then there is no difference between the two. Please note that I don't disagree with you. If atomic processes are slowed down (as GR predicts) then it follows that wristwatches, atomic clocks, and biological processes also slow down. I agree. My point is that GR can be interpreted in a fully operational manner such that your first sentence simply makes no sense (unless you have some ill-defined philosophical notion of time). $\endgroup$
    – MaximusIdeal
    Commented Dec 22, 2021 at 5:54
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    $\begingroup$ @MaximalIdeal : fair enough, I probably should have said "not about any particular clock mechanism". The OP seemed to think that different kinds of clocks would be affected differently, and that's what I was trying to correct. $\endgroup$
    – Eric Smith
    Commented Dec 23, 2021 at 12:21

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