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In General Relativity, time moves slower near massive objects where spacetime is curved stronger. In quantum gravity, the gravitational force is represented by the quantum field that refers to the probability of interactions, which can be in a simplified way described as exchanges of virtual gravitons. Such interactions usually involve a transfer of energy, momentum, spin, and other quantum numbers, but how is the gravitational time dilation explained at the quantum level?

Does the answer depend on a specific approach to quantum gravity? If so, what are the different explanations? I understand that we don't yet have a full theory of quantum gravity yet. I am just interested in the conceptual approach to the time dilation in the quantum theory.

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  • $\begingroup$ Duplicate of physics.stackexchange.com/q/358734 ? $\endgroup$ – Mitchell Porter Oct 4 '17 at 2:35
  • $\begingroup$ @MitchellPorter No, the earlier question was specifically about gravitons. This one is about the quantum field in general. Similar, but not the same. Can you answer? Thanks! $\endgroup$ – safesphere Oct 4 '17 at 3:33
  • $\begingroup$ Follow the link I posted there, that's the best I can give you right now. $\endgroup$ – Mitchell Porter Oct 4 '17 at 11:39
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Third link on google here. Free publication and quite interesting. (First link was not accurate for my search.. I blame me. Second link was Wikipedia.. General time dilation explained.)

I think any good answer here on this topic would raise more detailed questions, so my suggestion is that you Google and/or read books to get a comprehensive insight on this subject. But that's just my opinion...

(Edit: but I did favorize your question since it would be interesting to see how a simple comprehensive answer from other users would look like)

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Your question is requiring a whole theory of quantum gravity, but such thing has not been confirmed yet. Nevertheless, here are some hints for the solution regarding the compatibility of QM with the Schwarzschild metric:

  1. "time moves slower near massive objects": time and proper time are defined by SR and the Schwarzschild solution mainly for mass particles and for lightlike phenomena. Beside, they are defined also for other energetic phenomena, but SR and Schwarzschild solution do not treat the vacuum between mass particles, because they are referring to worldlines only.

  2. That implies for QM the rule of timelessness of QM: QM is timeless, except the above-mentioned phenomena for which time is defined.

  3. By consequence, gravitational time dilation of these phenomena may be taken into account within QM. It may be used to derive the proper time of the concerned particle/ phenomena from the measured coordinate time.

  4. For this purpose it is good to know that gravity of Schwarzschild metric may be expressed not only in terms of curved spacetime, but also in terms of gravitational time dilation in uncurved space, as you can check easily.

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  • $\begingroup$ What is your reasoning for that my "question is requiring a whole theory of quantum gravity"? The Hawking radiation is a quantum solution in the gravity field without "a whole theory of quantum gravity". Why do you think my simple question is so much different? $\endgroup$ – safesphere Nov 1 '17 at 0:05
  • $\begingroup$ Your question about time dilation is related to the problem of time which is a key issue of quantum gravity. $\endgroup$ – Moonraker Nov 1 '17 at 6:42

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