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The following is strictly a thought experiment, so please forgive the implausability of the scenario. I've read that if an object in space is moving in a relatively straight line, it will begin to follow a curved path around a nearby planet due to the curvature of space around said planet. But now imagine a rock floating motionless in space, far away from any celestial body. Suddenly, the Earth appears a few hundred miles away, causing a local curvature of space and thus causing the rock to begin moving towards the Earth. Since the rock wasn't initially moving, isn't this new movement an indication of the necessary existence of gravitons? Therefore, am I correct in saying that in order for gravity and its effects to exist, one must have three things: matter, curvature of space, AND gravitons, and that an object doesn't have to be initially moving for it to be affected by said gravity? If this is so, then why do most books on gravity refer to gravitons as only a "theoretical possibility"? And shouldn't they also say that any object, regardless of its momentum, will be affected because the resulting gravitons will instantaneously begin to act on it in a way similar to the way bosons act between particles?

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    $\begingroup$ You seem to be lacking a lot of knowledge of particle physics (gravitons are particles that mediate gravity). Why do you think that a movement of an object necessarily implies the existence of gravitons? $\endgroup$ Commented Nov 9, 2021 at 19:41

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I've read that if an object in space is moving in a relatively straight line, it will begin to follow a curved path around a nearby planet

This is true in Newtonian Mechanics also, as seen by the orbits of the planets, and no need to involve "curvature of space", where time is just a parameter. In General Relativity the Newtonian orbits can be mathematically modeled with four vectors where time is also a specific coordinate, and there is a specific four vector algebra. In this algebra the solutions of the orbits are seen as a curvature is space, induced by the existence of the masses and energies in the system.

due to the curvature of space around said planet.

The GR mathematical frame.

But now imagine a rock floating motionless in space, far away from any celestial body. Suddenly, the Earth appears a few hundred miles away,

In four vector algebra there is no"suddenly". The process has to be modeled, of how the four momentum appears, as energy and momentum are conserved quantities within an inertial frame

causing a local curvature of space and thus causing the rock to begin moving towards the Earth.

This is a "no-go" thought experiment.

Since the rock wasn't initially moving, isn't this new movement an indication of the necessary existence of gravitons?

Up to now we are discussing classical General Relativity gravitation. Gravitons belong to the possible quantization of gravitation, hypothetical because only effective quantization models of general relativity exist, not definite correct theories. Your thought experiment should be talking about gravitational waves . Still, there should be energy/momentum conservation for the thought experiment to work, and "suddenly" does not have this.

Gravitons are the quantum mechanical analogue particles to what photons are for electromagnetism.

Therefore, am I correct in saying that in order for gravity and its effects to exist, one must have three things: matter, curvature of space, AND gravitons,

No, it only needs mass and energy/momentum tensor and the Einstein tensor .

and that an object doesn't have to be initially moving for it to be affected by said gravity?

Objects either at rest to each other or moving are affected by the gravitational field , in classical formulation, by the curvature of space in the general relativity formulation.

If this is so, then why do most books on gravity refer to gravitons as only a "theoretical possibility"?

Because gravity has not been definitively quantized.

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You are thinking only in 3 dimensions. Remember that physicists all say that we are dealing in spacetime. So you have to start thinking in 4 dimensions by adding time to the equation. While your object is not moving in space, it is moving in time. In fact we travel through time at the speed of light. There are lots of science videos that show this. By traveling forward through time, we have the "motion" necessary for gravity to function.

I like to think that gravity works exactly like a low pressure system in the weather. The sheets on your clothes line are sucked in towards the centre of the low. So, with regards to your question, the clothes line is not moving in space, but the wind passes in time, so the sheets are sucked in with the wind.

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