If gravitons are proven to exist, would that mean space is not curved?
No. What made you suspect that it might mean that?
If light rays passing near the sun were deflected by gravitions and not following a straight line that merely seems to be curved to us.
There are at least 4 different ways to look at it:
1. It is the presence of gravitons that makes space-time curved.
2. Curvature is fundamental, while gravitons are only an emergent effective description of certain phenomena.
3. Gravitons are fundamental, while curvature is only an emergent effective description of certain phenomena.
4. Neither curvature nor gravitons are fundamental. Both are only emergent effective descriptions of certain phenomena.
Your way of thinking corresponds to 3. but as you see there are other interpretations too. We don't know which one is the best or the "correct one".
Photons are known to exist. Does that mean that electric and magnetic fields don't exist?
I thought there might be a difference when considering gravity because of the 1st Law of Motion (something like: if gravity is a field there's no change in inertia when a light beam passes near a star, but if it is a particle there is a change in inertia).
wait.... I thought gravitons DON'T exist, and that it's all waves
each object belongs to a theory : gravitons are the quanta of the gravitationnal field of a presumed quantum theory and curvature is an RG theory concept similar to a field.
You cannot mix the 2 theories. The quantum theory may include a kind of dictionnary to translate the concepts of previous theories but it would be just for pedagogic or historical purposes
Wait... could we reset please? The original question was brief to the point of being almost meaningless, and so the answers have been a bit flippant and dismissive. But it's a question that has been on my mind recently. So with respect to the original poster in case this is not what they intended to ask, could I paraphrase the question and hope to receive a more meaningful set of responses.
GR demonstrates that gravity is an apparent acceleration observed as particles travel through curved space-time. Einstein proposes that an observer inside an accelerating box would observe an acceleration indistinguishable from gravity. My minor extension of this thought-experiment is that the occupant of the accelerating box might conclude that the observed acceleration is due to a field, and begin looking for a particle that mediates the observed field. But there is no field, and therefore any attempt to discover the particle that mediates this non-existent field will thus fail. If gravity is an observed acceleration due to the curvature of space-time, then it cannot be a field, and therefore will have no corresponding particle to mediate it. I suspect this might have been the thought being the original poster's question: if somebody were to discover the graviton and prove that's what it was, then surely it would show that space-time cannot be curved because geometry isn't mediated by particles.
Given then GR has proven to be so successful at predicting the behaviour of gravity and the structure of the universe, while remaining mathematically elegant, would this not constitute strong evidence that quantum gravity is a sterile line of investigation based on a misapprehension that gravity is a field? Would it not make more sense for quantum physics to account for gravity in terms of geometry rather than a particle?
The word "field", as used in quantum field theory, means something different than the classical notion of a field so we can't settle the question so easily. Gravity can be a curvature effect and gravitons could appear in a theory of quantum gravity without any irresolvable contradiction between the two models.
Demystifier's post #4 above is worth reading again.
This is just one aspect of gravity according to GR, and not the most important one. The most important one is curved spacetime itself. The "apparent acceleration", as you note, can be mimicked (but only locally--see below) in an accelerating rocket in flat spacetime. But the curvature of spacetime itself--i.e., tidal gravity--cannot. So the proper way to think of a "field" corresponding to gravity is a field that produces tidal gravity, since that's what GR models as spacetime curvature--not "apparent acceleration".
To see the difference, consider the key qualifier I gave above: "only locally". Suppose I have two rockets, one "hovering" above the Earth and one accelerating in flat spacetime. Each rocket is 3 meters tall and about 2 meters wide (about 10 feet tall and 6 feet wide--just enough for an observer to stand inside and run the experiment I'm about to describe). An observer inside each rocket drops a rock and observes it to have an "apparent acceleration" of 1 g. So there is no way to distinguish the two cases in a small enough rocket, and hence there is no way for there to be a physical "field" that produces "apparent acceleration".
Now consider a second pair of rockets, one "hovering" above the Earth and one accelerating in flat spacetime, but this time each rocket is 1000 kilometers tall and 1000 kilometers wide. Station observers at the top and bottom of each rocket, and at each side, and have them all drop rocks. The observers in the rocket hovering above the Earth will observe "apparent accelerations" that differ in magnitude (for the top vs. bottom) or direction (for the left vs. the right side), because of the presence of tidal gravity. The observers in the rocket accelerating in flat spacetime will see a tiny difference in magnitude (for the top vs. the bottom--this is because their proper acceleration has to vary with height in order for them to remain at rest relative to each other) and no difference in direction. So with a large enough rocket it is easy to distinguish the two cases--i.e., to distinguish the presence vs. absence of a "field" that produces tidal gravity.
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