The theory of gravitons for the mechanism of gravity can be proven by deriving a test that will allow us to observe gravitons. Dropping a ball and observing that it is accelerated to the earth at the rate graviton theory predicts is not a proof of graviton theory. A true test of the mechanism is required.
In principle, it is impossible to observe individual gravitons directly, we can only measure their effects. The way that you would "observe" gravitons is essentially the equivalent of dropping a ball. It's as if the universe won't let you observe the mechanism, but that's okay. You don't need to know what the mechanism is in the sense that you don't need to be able to envision in your head
how gravitons function, just that they do. You can have a vision of an imaginary gravity fairy if it helps you think about gravity, but know that that's only an aid to understanding. If the mechanism is truly unobservable, then any discussion on the matter is inherently not scientific.
Gravity predicted that galaxies should spin faster at the middle than the edges, yet they spin as solid disks.
Gravity predicted that the universe should be decelerating due to the the gravitational attraction of matter in the universe, yet it is accelerating.
Gravity predicted that the planet Neptune should have been far larger and in a far different place than where it was discovered.
I don't really want to go down this rabbit hole, but as we've seen from countless recently discovered exoplanets, we don't know nearly as much about how planets form as we thought we do.
I think we are getting too far from the original question.
There are multiple mechanisms for gravity in the Round Earth model. Don't you think that's a problem? Talk to one scientist and he says that gravity is a "puller particle," talk to another one and he says that it's "bendy space." Why all of these wacky theories? Where is the Grand Unified Theory?
But I don't want to seem like I'm dodging questions. Science refers to this phenomena as dark matter / energy. It's simply an unknown. It may be a force all its own, it's probably a type of non-linearity correction for gravity. This doesn't mean that gravity is fundamentally wrong, it just means that our model isn't accurate at larger scales, as we probably would have expected anyways, since we've only very recently been able to observe these large structures where gravity is non-linear. We didn't have any data to go on before, so essentially what we've done is extrapolate the trend we observed on the small scale to the universe at large. Now that we have the data and can see these inconsistencies, we're now able to work towards understanding and accounting for them in our model. It just takes a little time. Again, this doesn't mean that gravity is fundamentally wrong. After all, it works so well on the small scale. We've used it for nearly half a millennia, and only recently have had any sort of inkling that anything was amiss. Any correction will likely be a small detail in the math.
Anyways, my point was that having multiple theories for the same thing isn't necessarily conflicting. We also had 5 different String Theories until someone finally realized that they were all the same thing. And then when someone did realize that they were all the same thing, that strengthened the case for String Theory. Scientists are able to talk about gravity in different ways because the mechanism is unobservable. At least we think it is. If so, it makes no difference if its a particle or if gravity is just an intrinsic property of matter to bend spacetime. They give the same exact predictions. If they didn't, that is when we'd have a problem with our theory. But since they do and since we can't observe the mechanism, that's good enough for everyone else.
Your understanding of "a priori" is misguided. It is a term popularized by Immanuel Kant, a German philosopher who synthesized early modern rationalism and empiricism.
https://en.wikipedia.org/wiki/A_priori_and_a_posteriori
A priori and a posteriori
These terms are used with respect to reasoning (epistemology) to distinguish "necessary conclusions from first premises" (i.e., what must come before sense observation) from "conclusions based on sense observation" (which must follow it).
I don't use words without knowing their meanings. Allow me to clarify. My use of a priori highlights the fact that you
can't "prove" gravity in any epistemic sense. You can't write a proof on gravity. That's not how physics works, but that doesn't make it any less true.
There is no direct evidence that there is something small and invisible pulling things to the the ground, and no experiment has observed such a thing. If we go by pure priori reasoning, in fact, then we must conclude that the earth is rising upwards to cause this phenomenon.
See the above. We're not going by pure priori reasoning, because that's not physics. I've already said that, but it didn't seem to compute. If you limit yourself to priori reasoning, you will never be able to understand the universe in any great detail, and that prospect is personally upsetting.
If we step onto a chair and walk off of the edge and become inert while observing the surface of the earth carefully we see that the earth accelerates upwards to us. This is a direct observation of a mechanical action for gravity. We do not see anything pulling us down to the earth. The only observation from an inert position is that the earth is moving upwards. This is a strong empirical example for the mechanism of gravity.
In your frame of reference, the Earth is rises up to meet you, but in the Earth's frame, you fall down to meet it. What's so special about your frame of reference?
When standing upright we feel the earth pushing up upwards against our feet. If we pay attention we will feel that we are being pushed upwards by something. If we were take a baseball and and put it into an inert position by extending out our hand and releasing it into the air, we would see that we rise up with the earth to the level of the inert ball to meet it.
I've never observed that actually.