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Going off from what others have told me on here, and based on the Wikipedia page for Quantum Gravity, General Relativity can be described mathematically in a way different than the geometrical curved spacetime interpretation.

The Wikipedia article specifically states:

In particular, contrary to the popular claim that quantum mechanics and general relativity are fundamentally incompatible, one can demonstrate that the structure of general relativity essentially follows inevitably from the quantum mechanics of interacting theoretical spin-2 massless particles (called gravitons).

So if the quantum mechanics of spin-2 massless particles (gravitons) can apparently reproduce the results of general relativity, wouldn’t that in some way be preferable to the idea of spacetime curving for unclear reasons? I guess the geometric interpretation could be talked about more because it is mathematically simpler than the graviton idea, but i am curious as to whether or not this could be because of limitations to the graviton idea. Does it not reproduce the results that the geometric interpretation does exactly?

Qmechanic
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Thatpotatoisaspy
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    The quote from the Wikipedia article is misleading, see https://physics.stackexchange.com/q/387/50583. – ACuriousMind Apr 06 '19 at 12:16
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    Physics only gives us tools to figure out what happens. It doesn't tell us what really happens. Often you will have many completely equivalent formalisms with totally different notions of what "really" happens. The graviton picture is one possible idea. It's generally regarded an incomplete one because it takes spacetime as a fixed background structure on which things propagate, while some would argue the core lesson of general relativity is that spacetime isn't like that. At this level, it's all pure speculation anyway. – knzhou Apr 06 '19 at 12:25
  • @knzhou Thanks. So is the graviton picture severely limited or is it for the most part an equivalent formalism? – Thatpotatoisaspy Apr 06 '19 at 12:44
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    It's good enough for all the GR effects we've actually observed. I expect this debate will be finished sometime around the year $2500$, at the earliest. – knzhou Apr 06 '19 at 12:57
  • I guess it might be possible to detect gravitons by then, if they exist. And we have the finances & technology to build such a detector. ;) – PM 2Ring Apr 06 '19 at 13:48
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    I believe that massless spin-2 gravitons naturally correspond to gravitational wave propagation as described by the linearized Einstein equation, but not to the full Einstein equation. Gravitons correspond to small perturbations about a fixed (typically flat) metric, and are not expected to give a good description of situations with strong and highly dynamic spacetime curvature. – tparker Apr 06 '19 at 13:59
  • @tparker Are you sure? Because i seem to have found a paper describing the derivation of the full einstein field equations from a spin 2 field with the energy-momentum tensor as the source. It’s beyond my mathematical abilities though so i don’t really understand it. Here it is:https://arxiv.org/pdf/1702.00319.pdf – Thatpotatoisaspy Apr 07 '19 at 00:20
  • @Thatpotatoisaspy No, I'm not sure. – tparker Apr 07 '19 at 04:14
  • @Thatpotatoisaspy that article is in the realm of Effective Field Theory, which assumes that gravity is weak and necessary uses perturbation theory. It does not quantise the background – thedoctar Apr 08 '19 at 14:48
  • @thedoctar Yeah, but it seems that they derived the full einstein field equations in it. Wouldn’t that make it an equivalent formalism to the classical geometric formalism of general relativity? Like just a weak field approximation to a true theory of quantum gravity that breaks down around the planck scale? – Thatpotatoisaspy Apr 10 '19 at 16:26

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I think your question is good because it asks about the fundamental nature of gravity seen from both the conventionally geometric approach and QFT approach.

First, the quoted text from Wikipedia is not entirely accurate. You must be careful with the words people use to describe physics. Every physical theory is an effective field theory (EFT), as explained in another answer here. There is nothing problematic in combining general relativity and quantum mechanics as long as you don't probe very high energies. By 'very high', I mean Planck scale. GR as a QFT is a useful example of an EFT. The paper you point out in one of your comments is a good reference for it.

In physics, the ultimate task is to compute physical observables and then compare them with experimental data. How one computes the physical observables depends on the theory, approximations, etc. And this is up to you. You can choose GR or QFT. People have worked way more on GR methods and have sharpened them to the point that it is now the standard way of calculating observables in gravity/cosmology. GR's geometric approach which is classical from the get-go is more developed and easier to use than the QFT approach.

As you pointed out in your comments, it is correct that one can model GR using QFT. I think the first paper that discussed this on a firm footing was Quantization of Einstein's gravitational field: general treatment by S.N. Gupta. It has been worked on by many authors since. Deser showed in Self-Interaction and Gauge Invariance how one can derive non-linear GR starting from the action for a free, massless, spin-2 field.

It's about ease-of-usage. Just like for some problems you would use Newton's laws instead of Hamiltonian mechanics, GR is used instead of QFT. That being said, using the method of scattering amplitudes to compute physical observables in GR is an active field of research and I expect many new, exciting things to come forth in future. An example is the recent paper General Relativity from Scattering Amplitudes.

Avantgarde
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My opinion has always been the idea that spacetime is just a spin-2 particle is crap. (EDIT: However, there are different lines of though. See https://en.wikipedia.org/wiki/Anatoly_Logunov#Relativistic_theory_of_gravitation where gravity is developed as a theory within special relativity. This goes against Einsteins conception of gravity, and indeed is a different theory from the theory of General Relativity.)

The statement assumes that gravity is analogous to electromagnetism. In QED, interactions between charges occur to virtual photon exchange. Shouldn't gravity just be the same?

No, because of the equivalence principle. Gravity is an intertial phenomenon, which led Einstein to the idea that we should describe it as curved spacetime, i.e. as a geometric effect.

When one wants to measure the mass of a black hole, one does not exchange a virtual graviton with it. Rather, one can merely orbit around it for a very large radius, so that we can use the formulas from Newtonian gravity, and then measure the time it takes to complete a circular orbit. Kepler's third law would then provide a formula for the mass. In real life, we measure geodesic deviation, via gravitational lensing, say.

There is no virtual exchange here as there is no force. One merely measures things like lengths and durations, which are purely local processes. The effect of gravity is a global one (ignoring extended systems where tidal effects play a role). By the equivalence principle, we can always find a coordinate system where the Christoffel symbols vanish (these tell you about geodesic deviation, i.e. how fast two inertial paths starting with parallel velocities close together deviate after a small period of time).

That gravity is fundamentally different to all other forces was first realised by Matvei Bronstein. Google his name for more details.

One can, however, quantise perturbations above some fixed background of spacetime. We need to assume the perturbations are weak, otherwise how could one separate background from perturbation? One can also formulate quantum field theory on top of a classical spacetime.

One cannot, however, quantise the background. I.e. we have no idea what gravity is on a microscopic level.

On the other hand, we know an electron is a combination of left and right Weyl quantum fields, which interact via the Higgs condensate.

thedoctar
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  • Thank you for your answer. As i said in another comment somewhere here, the article i found which you mentioned seemed to derive the full Einstein Field Equations. I understand it uses perturbations, but someone else here also said that general relativity itself is an EFT. That would make sense to me as even the geomtric version breaks down at high energies (singularities, etc). If the article can prove that the EFE can be derived as a weak field limit of some true quantum theory, wouldn’t that make the spin-2 idea an equivalent formalism to classical general relativity? – Thatpotatoisaspy Apr 10 '19 at 16:35
  • @Thatpotatoisaspy You need to be clear on what you want. The EFT does give you corrections to GR, but you need a specific background, which does not behave quantum-mechanically. This is not self-consistent, because there's no good way to separate background from perturbation. If you make the perturbation large, it becomes part of the background. But we said the background was classical and the perturbation was quantum, so we're mixing up two qualitatively different things. This is why people say GR & QM is inconsistent. (Also the EFT is non-renormalisable). – thedoctar Apr 11 '19 at 16:35
  • @Thatpotatoisaspy Since I detect you are still unsatisfied, I have edited my answer to include an alternative theory of gravity, which conforms to you desire that gravity is just gravitons rather than geometry. I can't give you more references on Logunov's work as I'm not familiar, but I'm sure you can do that yourself. – thedoctar Apr 12 '19 at 13:20
  • I’m aware of the problems with the EFT presented in the paper, but what i was trying to ask about was if this EFT is mathematically equivalent to classical geometric GR (minus some extra corrections). As i said the maths is beyond me right now so apologies if i sound quite confused. My question is more about formalisms and not about finding a true self-consistent quantum theory. The stuff with Lognuov is interesting though, i’ll check it out. – Thatpotatoisaspy Apr 12 '19 at 18:40