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In the classical view of General Relativity, time moves slower near massive objects where the gravitational field (spacetime curvature) is stronger. In the quantum view however, the gravitational force is produced by the quantum field represented by gravitons as its gauge bosons.

It appears, the more virtual gravitons are there (stronger quantum field), the slower time moves, but why? The concept of the gravitational attraction can be explained by the math of the exchange of gravitons, but how can the gravitational time dilation be explained at the quantum level?

I understand that we don't yet have a full theory of quantum gravity to explain what happens at the Plank scale in singularities. However, my question is far from such extremes and should have a logical answer without the full theory of quantum gravity.

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    $\begingroup$ I was interested in this once, and found that there's an explanation in Feynman's lectures on gravitation bit.ly/2xZO1fi but I never quite got to the bottom of it. Hopefully someone else can spell out the argument for us. $\endgroup$ – Mitchell Porter Sep 23 '17 at 10:12
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    $\begingroup$ In what model of not-full quantum gravity do you want this question to be answered? They don't even all have gravitons! This question, like so many about "gravitons", seems underspecified since there is no "Standard Model with gravitons" that would be what we always go to. $\endgroup$ – ACuriousMind Sep 23 '17 at 11:02
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    $\begingroup$ @ACuriousMind: In any model that has gravitons and accounts for the gravitational time dilation. If different models provide different explanations and you could highlight the differences, it would be fascinating to compare! $\endgroup$ – safesphere Sep 23 '17 at 18:10
  • $\begingroup$ @CosmasZachos Well, in GR, gravity is defined by a spatial gradient of the time dilation. So time goes slower even in the linear Newtonian limit. $\endgroup$ – safesphere Dec 9 '20 at 2:21
  • $\begingroup$ Right. You may have time slowdown in flat space. $\endgroup$ – Cosmas Zachos Dec 9 '20 at 2:35
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I believe a possible answer to this problem relies on understanding the ingredients involved and the scales involved. Let us speak first about the ingredients and the definitions.

We can speak about time dilation only when we have at least two frames of reference, $A. B$. That way we can say "time flows slower for reference system $B$ w.r.t. $A$". How do we do it mathematically? We compare time intervals among the two systems to find $\Delta t_A$ and $\Delta t_B$ are either equal or not.

How does gravity come in? Well we know general relativity (GR) tell us how the metric, $g$ evolves given a energy-momentum tensor (a energy, mass distribution). The metric is the object that describes the time intervals. So, so far no quantum field theory. This is indeed enough to describe gravitational time dilation because it is a phenomena that pertains large masses and large length scales, since we are speaking about distances of order speed of light (allow me the theoretical units speech).

Since GR (which describes gravity) is the one responsible for this time interval differences, we say that gravity causes time dilation.

Now you must understand that the graviton is the name give to a quanta of the gravitational field and at larger scales, the field description is more appropriate and allows us to compute things.

Mixing both worlds, we arrive for example at quantum field theory in curved spacetimes, where one usually uses an Ansatz for the metric, which will be a background (sometimes dynamical, sometimes fixed) to explore its impact on particle physics phenomena, such as scattering processes. Therefore in this cases since we are interested in smaller length scales it is more useful to speak about single particles instead of fields (at least before you actually have to compute the amplitudes associated to Feynman diagrams). Here the graviton appears again (understood always as some asymptotic state), however most computations occur within a fixed reference frame given by the background chosen. So time dilation effects are not important. At the end of the day it is like trying to describe how the discrete levels of the harmonic oscillator are related to a basketball bouncing. My final message is then "Physics at greatly different (energy) scales decouple".

I hope the discussion above clarifies some of your questions.

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I hope that you are aware of the fact that gravity can bend space time. If the gravity of a planet (p1) is huge compared to another planet (p2) the time on p1 will be SLOWER compared to the time on p2, this is because the larger the curvature caused by gravity, the larger the time difference. However the gravitons are a medium through which gravity can travel and can't make time go slower unless they are present in huge concentrations.

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    $\begingroup$ This seems to be a restatement of the problem. What is the quantum formulation for how gravitons exert such a spacetime-bending effect? $\endgroup$ – Guy Inchbald Nov 2 '20 at 9:26

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