Does Feynman's Work on Gravitons Clarify Quantum Gravity?

[TensorAndTensor]

Back in the 1960s, Richard Feynman worked on quantum gravity for a few years, and most of his notes are collected in the 'Feynman Lectures on Gravitation'. His approach was that of a particle physicist applying the principles of QED to GR, notably the concept of gravitons mediating the force of gravity the way photons are electromagnetic exchange particles. He soon became frustrated with the sea of algebra when he attempted to renormalize the theory, leading to conclude that quantum GR was probably not renormalizable, something that has been generally accepted by the community over the years. The difficulty seems to lie in the non-linearities resulting from gravitational interactions between the gravitons themselves.

What I do find fascinating with these lectures is a chapter in which he starts with the idea of a spin 2 boson - the graviton - and ends up deriving from that a gravitational potential, gauge transformations analogous to those applied in QED, and comes up with the equations relevant to gravity in the weak-field approximation in which the gravitational effects are applied to a flat-space background.

To my knowledge, this language is applicable to the study of gravitational waves as we know them here in 2017, and with the LIGO experiments of the last two years, we have gotten confirmation of the existence of gravitational waves consistent with the weak-field approximation, which Feynman had shown can be derived from the assumption that a spin 2 graviton exists.

So, some questions:

1) Does all of this reasonably settle the question of the existence of gravitons? (independent of the fact that gravity's extreme weakness relevant to other forces makes it unlikely to actually detect a graviton). In other words, here in our relatively low energy world (compared to the big bang or black hole event horizons), the concept of a graviton seems to be a valid one , despite that fact that it is said (at some higher energies), that " gravity is not really a force mediated by a boson in the way the electromagnetic force is. Instead, it's a warping of spacetime masquerading as a force such as electromagnetism".

2) What of non-renormalizability? It is said that this is a sign of a higher theory of undetermined from lurking behind the curtain of high energies.

3) extending 2). What of renormalizability? Does it imply that a theory such as QED is valid, as is, at very high energies? Or do we likely have something still unknown behind that high energy curtain? If the latter, then it would seem that QED is a low-energy approximation to something more involved. If so, are photons really just cousins of the graviton, force-mediating particles that emerge in our low energy world?

--Tensor

[mentors' note: This post has been lightly edited as part of moving it into a thread of its own]

 

[PeterDonis]

Does all of this reasonably settle the question of the existence of gravitons?

Not really. The fact that the GR equations can be derived starting from the field theory of a massless spin-2 field on a flat spacetime background does not mean that the GR equations being experimentally verified in this regime confirms the field theory of a massless spin-2 field on a flat spacetime background. That's because there are other ways of deriving the GR equations that don't require the spin-2 field assumption.

Basically, the only way we'll be able to experimentally test the spin-2 field theory, assuming we consider it as one possible candidate for a quantum theory of gravity (which it probably isn't--see below) is to find a way to probe for quantum effects of gravity.

What of non-renormalizability? It is said that this is a sign of a higher theory of undetermined from lurking behind the curtain of high energies.

Yes. And yes, this applies to the spin-2 field theory of gravity. The modern conception is to view it (and indeed to view GR as a whole) as an "effective field theory", which describes the low energy degrees of freedom of gravity but which is expected to fail at some appropriately high energy scale (which might be the Planck scale, although we have no way to test this at present).

Actually, this modern conception even applies to renormalizable theories like QED; nobody expects QED to be valid at arbitrarily high energy scales, even though it is renormalizable.

What of renormalizability? Does it imply that a theory such as QED is valid, as is, at very high energies?

No. See above.