Is quantum gravity research implying that gravity is actually a force and not spacetime curvature according to GR?

Question

I am all the time reading that gravity is actually the curvature of spacetime according to general relativity (GR) established theory and not a force, like the known three fundamental forces of nature, electromagnetism, and the strong and weak nuclear quantum forces.

However, my intuition says, that the whole concept of quantum gravity (QG) research and present not-yet-established theories is to fundamentally interpret gravity's origin as a force and not geometry(?).

If the above QG research enterprise finally succeeds and we find an established QG theory experimentally verified, will it then be proven that at the most fundamental quantum level gravity is actually another quantum force?

Answer 1

First, the concept of "force" is not as easy as it might seems. It is inherited from Newtonian mechanics in which it is defined as a vector sourcing the motion of the particles. In a sense, this concept completely disappeared from modern physics. Besides their names, electromagnetism and the nuclear forces are better understood today as "interactions", and they can be represented (under certain conditions) as the exchange of fundamental particles.

Only certain attempts at building a quantum theory of gravity could lead to such an interpretation of gravity as an interaction. The canonical case being "string theory" in which one of the vibrating modes of the strings, called the graviton behaves somewhat like a particle that can be exchanged to mediate gravity.

Some other approaches, as loop quantum gravity, give a description of gravity much closer to GR, but in which space-time itself is a quantum entity (roughly, space-time becomes "fuzzy" and "granular"). In that framework however, space-time is itself a quantum field interacting with other quantum fields, so the border between what is an interaction or not is quite blurred.

To further blur the line, it is possible to give geometrical interpretations of electromagnetism and the nuclear forces, such that they appear to be very similar to general relativity in their structure (using differential geometry). As such the distinction you are making between force and geometry is far from being so sharp.

Answer 2

Disclaimer: I am mainly a relativist, and I think science has benefitted much more by thinking of gravity as a geometrical entity than as a "force". It is impossible to answer this question without some personal views, so you should know my bias in advance.

That being said, something that no one mentioned yet is: we know how to quantize gravity (with some caveats) and any description of quantum gravity should recover this description at low energies.

We Know How to Quantize Gravity

This is nothing new. The original works, to my knowledge, are due to John Donoghue in the 1990s. One simply quantized general relativity as we would quantize any other theory. This is possible, and has been done. It is highly misleading (and even wrong) when people say "gravity and quantum mechanics are fundamentally incompatible" or anything like this. If you want a discussion about this, I like Percacci's An Introduction to Covariant Quantum Gravity and Asymptotic Safety (this is a book in Asymptotic Safety, which is a specific programme in quantum gravity).

So why does everybody say that we don't know how to quantize gravity? Or why is it an open problem? Because the approach I just mentioned, known as the effective field theory (EFT) approach, only works so far. It is marvelous for simpler calculations such as quantum corrections to the Sun's gravity, or even to black hole gravitational fields. However, it becomes useless at very high energies—namely, at the Planck scale (about $10^{-35} \mathrm{m}$). Now, the Planck scale is precisely when quantum gravity becomes interesting, so the question must go on. We want a theory that describes Physics at the Planck scale.

All Theories Must Recover Gravity as an EFT

So we know gravity as an EFT, but it doesn't describe the Planck scale. Hence, we must figure out that ultimate theory. It has, however, constraints.

For example, any theory of quantum gravity should recover classical general relativity in some limit. That is because we know experimentally that GR works amazingly well, and the theory of quantum gravity should thus make the same predictions (with perhaps negligible corrections) in the situations we tested GR.

However, if gravity is quantum, then it means that gravity as an EFT is correct, because this is just the same theory of classical gravity in a quantum language. Therefore, if gravity is quantum, any quantum theory of gravity should agree (in some limit) with gravity as an EFT.

All Theories of Quantum Gravity Predict the Graviton

Here's the interesting bit: gravity as an EFT predicts a graviton, so since all other theories of quantum gravity must reduce to it, all other theories of quantum gravity must predict a graviton as well. Thus, any theory of quantum gravity can be roughly thought of as being related to some interaction.

So How Can Gravity Be Geometrical?

The fact the theory predicts a graviton doesn't mean the most useful interpretation of the theory is that gravity is a force, or an interaction. For example, one way of thinking about GR is that it is just a field theory like any other field theory. In my experience, however, most interesting developments in GR happened because people treated it as a geometrical theory, not as a field theory. The point of view you take can make it simpler or more difficult to think about the theory, and in GR the geometric point of view surely makes things simpler, at least if you're interested in anything that happened in GR over the last sixty years or so.

Quantum gravity is likely the same. You may prefer to take the point of view that, e.g., string theorists do and view gravity as an interaction, which will lead you some way. It is expected that at least in some limit you need to recover a geometric interpretation, but that geometric interpretation might not be fundamental (just like the force interpretation of Newtonian gravity wasn't fundamental). Other approaches, such as loop quantum gravity, take an inherently geometrical point of view in their descriptions, but this approach need to recover the interaction point of view of gravity as an EFT.

Furthermore, it is important to notice the comparison with electromagnetism and the nuclear forces that Léo Vacher mentioned. These three interactions can be understood geometrically in the language of principal fiber bundles. There is a very clear vision of how their quantized versions recover the geometrical picture in the classical limit, and you can picture their quantization as quantization of geometry, but that ends up giving room to an interaction.

Answer 3

I don't understand the statement that ``gravity is geometry and not a force". It is a force, but it isn't some magical phenomena where things are just attracted to each other. That is, gravity isn't just $R_{\alpha \beta \gamma \delta }$ but the fact that this description of geodesics and equations of motion is equivalent to the "more physical" stress tensor $T_{\mu \nu }$. This is precisely why quantum gravity even makes sense: we want a quantum field theory describing gravity. Semiclassical gravity achieves this effect a little conveniently because we allow ourselves the abuse of perturbation theory by fixing a background metric and adding backreactions to it. In string theory, the notion of a graviton becomes much more interesting but as such is what we naturally expect -- it is a spin-2 boson that in the classical limit reduces to GR, since the source is just $T_{\mu \nu }$. What a quantum force that you mention is not clear to me as well.

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Edit-1: In case this helps, we know what a quantum gravity theory looks like. If you don't like the more fancy descriptions like string theory (although in my opinion, string theory is the only theory I would consider to be true for reasons that are too lengthy and formal to explain here), there is canonical quantum gravity due to Wheeler and DeWitt, which should not be considered naive, since this formalism is turning out to relate to a lot of what we make of quantum gravity in spacetimes with a string theoretic description. For instance, $T\overline{T}$-deformations and canonical QG are very active topics for works (see Wall, Regado, Shyam, etc.) and relate very precisely to what we expect from holography arising due to string theory in AdS. Quantum gravity is very well-understood, but there are subtleties that become important, like UV-completion.

Answer 4

There is no conflict between being a manifestation of spacetime geometry and being a quantum force. Fields, classical or quantum, are spacetime geometry. The gauge fields of the Standard Model can be understood geometrically as a certain kind of curvature/twisting of extra dimensions beyond the big four, as I described in this answer. If you quantize that classical picture, you get bosons. Bosons are "particles", but they aren't particles in the ordinary English sense of the word, like dust motes. They are more like vibrational modes of spacetime (extended with extra gauge dimensions).

Gravity is another manifestation of spacetime curvature, involving only the big four spacetime dimensions, and although quantizing it has been surprisingly nightmarish, there is no reason to think that it's fundamentally different from the Standard Model forces.

Answer 5

In short, no. Or, read on for curious intrigues in the quest for (QG)...

Quantum Mechanics (QM) shares a set of physical axioms with General Relativity (GR). These are foundational (sine qua non) principles justified in that they make useful predictions and have never been observed to be incorrect or logically incompatible. The chances they are incorrect are now extremely low, given the history of empirical observation in physics.

Both physical theories are instantiated as mathematical models before they can be used to compare hypothesis to experiment. Each model requires mathematical axioms additional to the physical ones. Quantum Field Theory (QFT) is a (QM) model from differential calculus; broadly, a set of algebraic functions of the flat Minkowski geometry of Special Relativity (SR). (GR) is a model from tensor calculus; broadly, a set of algebraic functions that bend the dimensions of (SR) to make a curved transform of Minkowski geometry.

It is these mathematical models, not the physical axioms, that direct how we interpret a result either as "force" or "curvature". It is also these models, not the axioms, that (mostly) bring about the current difficulty reconciling a theory of (QG). Nobody has yet found a way to express (GR) as a (QFT) model of the flat (SR) geometry, nor has anyone found a way to apply (QFT) to a (GR) curved geometric transform of (SR).

A breakthrough extending either approach might still happen, but given many incomplete attempts, it is now more likely to come from a third approach to Quantum Relativity (QR) involving the same physical axioms, but a different mathematical basis to either: I call this third approach Gödel Plan A. It also remains possible that (QFT) and (GR) are forever mathematically irreconcilable but both compatible with physical axioms: I call this the Gödel plan B outcome; no further progress is possible!

Regardless, any workable new approach (plan A) will express the known foundational physical axioms on a different mathematical basis and the result will be something other than "force", or "curvature". Perhaps it will be both, making a beautiful adjunct to "wave-particle" duality.

Which modelling approaches justifies more valuable research time? Given the history of physics as a Bayesian prior I would argue for (10% QFT extension,10% GR extension,60% Gödel plan A, 20% Gödel plan B).

references: "Quantum theory from five reasonable axioms" Lucien Hardy. "Energy: The subtle concept" Jennifer Coopersmith.