# Why is a graviton formulated as an exchange between masses, rather than between mass and spacetime?

In Sean Carroll's Lecture Notes on General Relativity he states:

The gravitational interaction, meanwhile, can be thought of as due to exchange of a virtual graviton (a quantized perturbation of the metric). The nonlinearity manifests itself as the fact that both electrons and gravitons (and anything else) can exchange virtual gravitons, and therefore exert a gravitational force:

Why would gravitons exchange information directly between particles? Doesn't general relativity show that gravity is a secondary result of mass affecting the curvature of spacetime, not a direct interaction between masses?

I.e, why is it (mass)->{graviton}->(mass), and not (mass)->{graviton}->[spacetime]?

[Note: This question is not whether gravity is a force or not, but why a quantization of gravity would be formulated as an exchange between particles instead of between masses and spacetime itself (as general relativity seems to indicate).]

• Is any graviton ever observed? How can any formulation of something never observed happen?
– Atif
Commented Jan 17, 2023 at 10:45
• Is spacetime ever observed? Not asking about space or time, mind you. Other terms can be combined together to make meaningless terms such as MomentumEnergy, ChargeMass etc. Are such questions on topic here? If something is never observed how can science deal with it? What would any formulation or theory based upon in absence of data?
– Atif
Commented Jan 17, 2023 at 10:51
• I mean, the very quote you post as part of your question literally says "virtual graviton (a quantized perturbation of the metric)". That's what a quantum is - a particular "pattern" in the underlying field - with virtual "particles" being a less particular pattern; indeed, you might outright think of them as "the whole field except for actual quanta". You already have spacetime in that diagram - it's the (virtual) "graviton" in the middle". It's the same with a photon, for example - quanta (and virtual "particles") aren't something separate from their fields. Commented Jan 17, 2023 at 15:20
• @Atif I think you have a valid case to make about gravitons (of course none have ever been observed and according to Freeman Dyson it may not even be possible to detect one in principle), but not about spacetime. For example, time dilation for muon decay is a clear demonstration of why relativity involves spacetime, not absolute space and absolute time separately. Commented Jan 17, 2023 at 19:24
• Does it answer the question if you assume that spacetime and gravity are one and the same? Commented Jan 17, 2023 at 19:55

One could equally well ask "why is QED formulated as $$\text{charge} \to \text{photon} \to \text{charge}$$, and not $$\text{charge} \to \text{photon} \to \text{EM field}$$?" The answer is that photons are the quantum-mechanical excitations of the EM field; trying to draw a distinction between "photons" and "the EM field" is not terribly fruitful, since they are really two ways of looking at the same thing.

Similarly gravitons are the quantum-mechanical excitations of the metric on spacetime (or they would be if we had a self-consistent theory of quantum gravity.) Trying to draw a distinction between "gravitons" and "the metric" is not really fruitful for the same reason.

• A "GR-graviton" seems like it should be an exchange between a mass and spacetime, as curving space is all mass is "doing" (not exchanging energy/charge with another mass). Photons travel through an EM field at a reduced propagation speed, yet don't increase the field, so they are indeed separate from the field (if they are not a part of the virtual photons that make up the field itself). It seems that a mass in a gravitational field behaves more like a photon in an EM field than an electron in an EM field. Perhaps mass is it's own boson? :) Commented Jan 16, 2023 at 15:29
• @JDUdall Photons are the EM field. The existence of a photon in the EM field does cause changes in the $E$ and $B$ field strength observables. Conversely a photon is nothing more than a certain "pattern" in the $E$ and $B$ fields. In some contexts it might be possible to approximate the EM field as a constant classical background + few enough quantum photons that don't disturb the macroscopic field, but that is just an approximation. All of this should remain true for gravitons and the metric.
– HTNW
Commented Jan 16, 2023 at 17:16
• This is basically the correct answer - although I guess there is the added complication of (per somewhere in MTW iirc) the concept of the metric being "the" gravitational field doesn't quite work Commented Jan 18, 2023 at 4:40

The gravitons are excitations on spacetime itself. In this sense, matter particles exchanging gravitons means exactly they are moving closer together due to spacetime effects. Furthermore, notice that gravitons interact with other gravitons, and hence you can also have matter particles exchanging gravitons with other gravitons, which is an exchange between mass and spacetime.

By the way, do notice the graviton is not formulated like that. What you actually do is to pick a spacetime, add perturbations, compute how these perturbations behave using your favorite theory (typically General Relativity) and then quantize that. This interaction is derived from other principles, not proposed in an ad hoc manner.

• As if the "other principles" were not an ad hoc abstraction of the phenomena. Commented Jan 16, 2023 at 15:04
• Gravitational waves, for example, are then understood as just loads of gravitons with similar properties. Hence, if you prefer, another way of interpreting the math is that the influence of one mass upon another is communicated by means of gravitational waves. Commented Jan 16, 2023 at 15:44
• @TrixieWolf LQG will not describe gravity using gravitons as a fundamental point of view, but gravitons would need to be an approximation to LQG when one is considering small deviations of a classical field. Any quantum theory of gravity will get to a graviton-like description in sufficiently weak fields. Commented Jan 17, 2023 at 21:47
• More specifically, gravitons are indeed just what you get when you quantize General Relativity perturbatively. This is a non-renormalizable QFT (which is a way of saying that it is inconsistent if you insist on very small scales, such as the Planck scale), but it is well-understood nowadays. Furthermore, any theory of quantum gravity needs to recover GR in some limit, which means that they need to recover this graviton description (it is, after all, the quantum version of GR) Commented Jan 17, 2023 at 21:49
• If you'd like to read more detailed accounts of this treatment of GR, I suggest starting here: scholarpedia.org/article/… Commented Jan 17, 2023 at 21:50

Part of the Deus ex machina here that supposedly resolves the circular definition is that mass, for purposes of many theories of gravity, can be of various kinds. Many theories argue that inertial mass for example is different from gravitational mass--therefore they can be measured separately or can be present independently.

The spacetime-curvature model or analogy you are referring to provides an example, in which mass is a quantity that is tied without a known mechanism to a conceptual curvature property, and is not necessarily identical to an inertial mass.

Doesn't general relativity show that gravity is a secondary result of mass affecting the curvature of spacetime, not a direct interaction between masses?

No, that was a descriptive analogy, not a mechanistic interpretation of how things really work--in some respects similar to Maxwell's equations, which model relationships between quantities but form no opinion as to the mechanisms. Note that so long as mechanism is in question, causality is up in the air, and in general it could not be inferred that a phenomenon is a "secondary result" of a model, equation, or analogy, since the precedence and "order of operations" in a physical sense is unknown.