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According to General relativity the clocks in our satellites in the atmosphere tick faster than those on Earth, as they are farther from the gravitational well of Earth and are free falling.

According to Newtonian mechanics and Gauss theorem, a hollow massive spherical shell has no net gravitational field at any point inside the shell as the geometry cancels out the pull from each extrema.

I would imagine that this does not change in GR (am I wrong?), an object inside should be free falling. But does time behave different inside the shell and outside very far from the shell?

Qmechanic
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Mauricio
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    Possible duplicate: https://physics.stackexchange.com/q/43626/2451 – Qmechanic Nov 27 '17 at 13:39
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    FWIW, gravitational time dilation is a function of the gravitational potential, not the field strength. – PM 2Ring Dec 30 '19 at 12:11
  • Just some more precise wording: clocks in satellites don't "tick faster": they tick exactly at the standard rate. Rather, the ticks an observer on Earth receives from them arrive at a faster rate than those of the observer's own clock. For the same reason time doesn't "behave" differently inside a shell. Maybe this is obvious to the OP who just used an approximate wording, but there are people who really think that "time flows faster" in space – whatever that might mean. – pglpm Sep 02 '23 at 17:07

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Yes, time will go differently.

Imagine a single photon, emitted from inside the shell and absorbed far outside. The energy outside should be lower than the energy inside because some energy was 'spent' to get out from gravitational well.

Now imagine two persons, one inside, the other outside. The 'inside' one sends radio waves at some frequency. Let's say the frequency of radio waves he transmits is $N$, the transmission time is $t$ so that the transmission has $N*t$ full periods.

His colleague will receive a transmission having $N*t$ full periods as well.

But the wave he receives is red-shifted (see the experiment with photons). So, the frequency of the wave is lower and the time of transmission is longer for him. Time goes slower for the person inside the shell, even though the space-time is flat around him.

lesnik
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