Why doesn't Gravitons have charge?

I have been reading about the Bentley's Paradox the other day and I had an idea where Gravitons should have charge.

With Issac Newton's equation of gravitational attraction $$F=\frac{GMm}{r^2}$$

We theoretically can show that all 'stuff' in the universe should be attracted to each other, however it is not the case. The universe does not collapse into one giant black hole. Since this relates to gravity, this should relate to the unproved particle: Gravitons.

However, when I search up in Wiki, or on this Why doesn't gravity have charges? question, it doesn't really answer my question exactly. They all show that gravitons have 0 charge. However, if gravitons do not repel each other, how can the universe maintain the state where nothing collapse into one giant black hole?

• Even in Newtonian gravity paradigm, the paradox can be solved if stars are moving, therefore all the objects will just orbit the rest of them. However a most convincing explanation is given by general relativty. While trying to quantize general relativity, the graviton field just happens to lack charge – Alejandro Menaya Jul 14 '18 at 6:31
• Interestingly, the rate of expansion of the universe is increasing. One would actually expect the rate to decrease because of the attraction between matter... en.wikipedia.org/wiki/Dark_energy Hence the "... attracted to each other, however, this is not the case" is a confusing simplification of a much more elaborate scenario. Also try reading about the 'critical density'. – user191954 Jul 14 '18 at 6:42

The reason that the universe didn't become a giant blackhole has nothing to do with the charge of the graviton or self-repulsion. Even in Newtonian gravity, the universe would be fairly wide instead of a giant bulk of matter. This is because things attract each other but they can orbit if they have a transverse velocity component to the direction of attraction.

On the other hand, if you consider the term, charge, as a generalized concept of simplectic geometry and analitic mechanics, then gravity involves a charge, namely, the energy and momentum.

Let me back up a little.

Electric charge is the conserved quantity of the electromagnetic interactions which originate from the local phase symmetry. This is called $U(1)$ gauge symmetry since it has only 1 phase parameter. In a similar way, we have other gauge symmetries in the universe. For instance, there is color charge which is the conserved quantity of the strong nuclear force because of another phase symmetry, $SU(3)$ gauge symmetry. There is also $SU(2)$ symmetry for the weak interaction but it is broken at lower energies than ~200 times the proton mass. These are quantum mechanical gauge symmetries.

Here, a gauge freedom exist because of these symmetries, meaning that an extra field would show up because of the symmetry. For electromagnetism this field is called photon, for strong nuclear interaction it is called gluon, and for weak interaction they are W and Z bosons.

Gravity is also a gauge symmetry but a classical one, just like the Maxwell theory. The symmetry of the gravity is called local translation symmetry, or diffeomorphism symmetry, which means the local shifts on space and time. The conserved quantities (charges) of this symmetry are energy and momentum because energy and momentum would remain the same after shifting in time and position, respectively. The gauge field of this symmetry is called gravitational potential, $\phi(x)$, but since it is classical it is not a particle.

However, it is believed that one day physicist will find a quantum theory of gravity, so the hypothetical gauge particle of this symmetry would be a spin-2 particle, called graviton. It would have no electrical charge, no color charge, or no weak charge. But it would have energy and momentum. So, it may carry a gravitational charge but if it is massless it would follow the null geodesics just like light, and it wouldn't interact with itself.

I think you are approaching your problem from the wrong side : go Big not Small.

General relativity resolves your question (Bently's paradox) by providing a mechanism for the expansion of the universe, and this is shown using the FLRW metric.

So you don't need to think about gravitons at all for this paradox, but you do need to forget Newtonian physics and use General Relativity.

We theoretically can show that all 'stuff' in the universe should be attracted to each other, however it is not the case.

In terms of gravitational attraction, it most certainly is the case that everything is attracted to everything else. There's absolutely no evidence that gravity doesn't work that way.

The universe does not collapse into one giant black hole.

Small point : you're mixing and matching Newtonian physics and General Relativity. Newtonian physics doesn't have any concept of a black hole - it's purely a concept from GR.

Don't mix and match - you are guaranteed to have problems if you do that in physics.

Since this relates to gravity, this should relate to the unproved particle: Gravitons.

However, if gravitons do not repel each other, how can the universe maintain the state where nothing collapse into one giant black hole?

The FLRW metric predicts that in addition to the normal gravitational attraction between objects we should also see spacetime (on the scale of the entire universe) expanding. This is another idea which Newtonian physics can't describe and which explains, without any reference to (unproven) particles like gravitons, why the universe can expand and doesn't just collapse.

The non-collapse of the Universe is not related to the small scale repulsion of gravitons (which we don't know to exist anyway), but to the large scale behavior of space-time as described by the FLRW metric.

Apart from all theoretical considerations, they would have been seen in bubble chambers.

• Please add some more details to this answer. I don't have any citation for this, but from my understanding, a charged particle moving at an extremely high speed won't show up too clearly in a bubble chamber because the radius of the curve would be huge. And we theoretically believe that gravitons move at the speed of light. If that's correct, your argument in this answer doesn't say anything conclusive. – user191954 Jul 14 '18 at 9:08
• But there would still be bubbles. – my2cts Jul 14 '18 at 12:26