# How can particles account for the curvature of spacetime?

Classical General Relativity rests on the idea that what we call gravity actually is one property of spacetime itself. The matter distribution determines the metric by means of the Einstein field equations and hence the associated Levi-Civita connection which tells how particles move on such a background.

Now, classical electrodynamics is different. We picture spacetime as already there, and then we picture the electromagnetic field as something "on top" of the background spacetime.

Thus the transition to QED, where electromagnetic interaction ends up becoming exchange of photons, is not that strange. Instead of having a field value on each event, we have exchange of photons all the time on that spacetime background.

Now, it seems quite well accepted that a quantum theory of gravity will have one corresponding graviton, which I believe will mediate the gravitational force by means of exchange of such particles.

But things are different in gravity. Gravity is not a force, it is a property of spacetime.

1. How can gravity be described by exchange of particles if it is a property of spacetime and not a force?

2. How can this exchange of particles even take place, if there is no background in this case? I believe that gravity and spacetime are somehow inseparable, i.e., if there is no classical gravity, no spacetime.

3. How can the geometry of spacetime (the manifold with the metric and connection) be accounted for with exchange of particles?

Since the graviton idea seems quite well accepted (I've seem people say that theoretically it is fine, it just hasn't been detected), I believe these questions have plausible answers at least.

• To quote one of my favorite people (John Duffield): "The map is not the territory." Curved spacetime is a model. You can't actually believe that spacetime is a smooth manifold. (What does that even mean?) "Gravity is spacetime curvature" is just a slogan for GR, it is not reality. Aug 28, 2017 at 0:24
• Well, I know that representing spacetime as a smooth manifold is a model, but if we are to talk about particles propagating and exchanging particles that mediate forces, I believe that there must be a background. If spacetime isn't represented mathematically as a smooth manifold, then what is done? Because to do the most basic things like talking about smooth tensor fields require this structure and QFT is built on top of it.
– Gold
Aug 28, 2017 at 0:29
• Duplicate of physics.stackexchange.com/q/427/37364 Aug 28, 2017 at 1:58
• Gravitons are believed to describe quantized gravitational interaction approximately, in the regime where the mean geometry is Minkowski. The full nonperturbative theory of gravity is not known yet, and it is not at all clear whether gravitons would play a fundamental role in it. Aug 28, 2017 at 3:42
• If spacetime isn't represented mathematically as a smooth manifold, then what is done? Find a better model/theory. This is more of s chatroom / philosophical (glib) remark, but although we all do want bedrock, something will have to give to get it. I mean no offence, but to me it makes no sense to accept the standard model to be, well a model, but then try to impose it on a spacetime with any aspect of absoluteness about it. It is very difficult to get away from the notion of spacetime as a continuous 4 D container, but this is a model just as much as any other.
– user167453
Aug 28, 2017 at 6:05

Gravitons are a result of direct application of perturbative quantization to General Relativity. Because both perturbative QFT and GR are concise and renowned physical theories which have been checked in numerous experiments, there's little doubt that gravitons show up when we do high-energy (compared to the LHC, but low-energy compared to Planck scale) experiments with gravity.

In perturbation theory, one is always interested in small perturbations of the field around the mean value given by the classical solution. GR is no exception; in the approximation of perturbative theory we model the spacetime metric as

$$g_{\mu \nu} (x) = \eta_{\mu \nu} + h_{\mu \nu} (x)$$

for small $h$, and work in powers of $h$. Note that this breaks background independence and the geometrical interpretation of GR, but we shouldn't expect an approximation to preserve it.

We know that perturbative quantum General Relativity is nonrenormalizable. From the Wilsonian point of view, this pretty much means that there's a domain of applicability beyond which it can no longer be trusted. This domain has always been identified with the Planck scale.

To summarize: perturbative quantum General Relativity is widely believed to be a valid description of the gravitational force in the low-energy regime, and it models the gravity field with particles called gravitons. Classical General Relativity is another approximation, which models the same field in a slightly different regime (strong but classical gravitational fields).

If any, gravitons play an interesting role in most of the quantum gravity models that we have today: they serve as a kind of sanity check. A sensible quantum gravity theory should give General Relativity in the classical limit and perturbative GR with gravitons in the limit of small geometry fluctuations. Both String Theory and Loop Quantum Gravity give gravitons in some limit.