I believe that there are no "gravitons". A mass warps SpaceTime. Anything moving past the mass has it's direction changed by that warping not by the mass. "Freeze" SpaceTime & remove the mass & it's "gravity" and things will still follow the same warped path. Therefore, there is no "force of gravity."
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1No, you are wrong, the warped path is due to the existence of the mass if you remove the mass you have flat space time. Beliefs do not have a place in mathematical formulae. – anna v Aug 21 '18 at 16:02
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2In order to have a question that will not be closed because it is not mainstream physics, focus on the issue of how the gravitons do whatever they are supposed to do (a real question) rather than stating your own beliefs about gravity. – Anders Sandberg Aug 21 '18 at 16:28
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1Hi, welcome to Physics SE! Unfortunately, non--mainstream questions are considered off-topic here, so there's no point in pitching for theories. – Aug 21 '18 at 16:28
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1Gravitons are predicted by the Quantum Field Theory. This theory requires all fields to be quantum. Gravity is not a standard quantum field, the standard QFT does not work for gravity. To unite both theories with "Quantum Gravity", the QFT must be modified. We don't know how. It may be that gravity is quantum in a non-standard way. Or it may be that the QFT must be changed to allow the interaction with non-quantum fields. It sure is hard to explain the gravitational time dilation (the source of gravity) as an exchange of virtual gravitons, but the quantum world is weird enough, so who knows. – safesphere Aug 21 '18 at 20:52
1 Answers
We do not know if there are gravitons. There is no experiment that would prove their existence.
Theoretically, it is a good idea to learn about EM forces, and their carriers, the photons. The mediator of EM forces is the photon. Two particles can have EM interaction by exchanging photons.
Photons do not have rest mass, just like gravitons. That explains the long range of both EM and gravitational forces. The same way the mediator of gravitational effects is the graviton. Two particles can have gravitational interaction by exchanging gravitons.
It is not mass but stress-energy that causes gravity. This way, even particles, like the photon, that have no rest mass, can have gravitational effects.
When stress-energy bends spacetime, that is an effect of gravity. You are right that when a photon travels past the Sun, it travels in bent spacetime (because of the Sun's stress-energy).
Even the Earth orbits the Sun in bent spacetime, because of the Sun's stress-energy.
Gravitons, just like photons, travel with speed c in vacuum, when measured locally. Both EM waves and gravitational waves travel at this speed. If you remove the Sun, the Earth would still move along the bent spacetime orbiting the Sun (even if the Sun is not there anymore) for another 8 minutes. After 8 minutes, the effects of gravity from the Sun's stress-energy disappear, and the Earth starts to move out of the solar system.

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There is very much an experiment that would prove their existence (for a certain meaning of "prove"), just not any currently feasible experiment. – Javier Aug 21 '18 at 17:19
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A number of ambiguities in your answer. (1) The electromagnetic interactions are mediated by exchanging virtual photons, not real photons. (2) Photons are massless and cannot decay by emitting gravitons. The gravitational field of a photon is created by the gravitons emitted at the photon emission and absorption events, but not by the photon in flight. (3) The Earth is attracted to the instantaneous position of the Sun, but not to its retarded position. If you tow the Sun away (slower than light), the attraction force will always point to the actual position of the Sun with no 8-minute delay. – safesphere Aug 21 '18 at 20:43
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@safesphere (1) Correct. Though, I would like to know if you call it an EM interaction if an atom emits a real photon and another atom absorbs it. Do you call that EM interaction? (2) Correct, photons cannot decay by emitting gravitons. Correct that the gravitational field of the photon is created at the emission. I believe that the gravitational field of the photon travels with the photon at speed c. (3) I think I disagree. If you tow the Sun, the Earth will feel that position change of the Sun only 8 minutes delayed. – Árpád Szendrei Aug 22 '18 at 00:21
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(1) Yes, I do. This is why I said "ambiguous" instead of "incorrect". I was referring to, "Two particles can have EM interaction by exchanging photons." These photons are usually virtual, because a single massive particle cannot emit or absorb a real massless photon without violating either energy or momentum conservation. On (3) I also could not believe it, but it is true for both gravity and electromagnetism. Not my idea. I'll try to find a link. – safesphere Aug 22 '18 at 04:06
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This is the link I was thinking about: "The attraction toward an object moving with a steady velocity is towards its instantaneous position with no delay, for both gravity and electric charge." See the answer by hawkeye among others here: https://physics.stackexchange.com/questions/5456/how-fast-does-gravity-propagate - Also another one: https://physics.stackexchange.com/questions/338456/do-we-feel-a-gravitational-pull-towards-where-a-mass-will-be-in-the-future – safesphere Aug 22 '18 at 04:38
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@safesphere You seem to be correct here. The reason is that it is made analogous to the electric field lines. Those are modeled in math by virtual photons, and virtual photons do not obey the speed limit of c. So with the electric field lines virtual photons really make EM interactions seem instantaneous around a charge. If we take gravity around a mass like the Sun analogously then these gravitational field lines could be mediated by virtual gravitons that do not obey the speed limit c. Then really these gravitational effects of the Sun would be instantaneous. – Árpád Szendrei Aug 23 '18 at 17:31
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I see what you are saying. I actually have asked a specific question here related to the "speed of virtual photons", but did not get a good answer: https://physics.stackexchange.com/questions/364427/speed-of-electromagnetic-interactions – safesphere Aug 23 '18 at 17:35
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Electric charges also warp SpaceTime. Stretch an elastic membrane over a frame. Near the center, stick one finger (electron A) up to distort it. While still poking it, a small distance away, poke it again with another finger (electron B). The membrane’s “surface tension” between the fingers is small but on the other side of the fingers, it is large and tends to pull the fingers (electrons) away. Next, poke one finger (electron) up and poke another finger (positron) down. Now the “surface tension” between the fingers is large and pulls the two fingers (particles) together. – John Majka Sep 05 '18 at 22:16
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@safesphere I think I have an answer for that question of yours, I think the answer has to do with the fact that EM charges curve spacetime just like stress-energy, and therefore, the gravitational effects that you mentioned are said to be instantaneous, when we are inside (or interact with) the gravitational field, and analogously, when we are inside (or interact with) the EM field, it feels to be instantaneous too. The reason is that both stress-energy and EM charges alter the fabric of spacetime. – Árpád Szendrei Sep 06 '18 at 00:29
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@safesphere For gravity, since everything we experiment with interacts with gravity, all kinds of particles will be affected by the gravitational field, we say that "spacetime is bent where the gravitational field is". That is how we explain that instantaneous interaction. But with EM, for some reason we do not say that "spacetime is bent where the EM field is", but we could say that, and that would the same way explain the instantaneous interactions of the EM charges. – Árpád Szendrei Sep 06 '18 at 00:32
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I hear you. In fact the Kaluza–Klein theory views electromagnetism as spacetime bent in the 5th dimension: https://en.m.wikipedia.org/wiki/Kaluza–Klein_theory - This theory is currently ruled out, because it predicts a wrong spin for the graviton (and consequently a different behavior of gravity in some ways). I am not sure though if this theory has been disproven by experimental observations. So who knows. – safesphere Sep 06 '18 at 03:17