Equivalence principle and gravitons

Question

If gravitons exist, are they always detectible in any frame? I'm asking because if I'm in a freely falling frame in a uniform gravitational field, and I detect gravitons, I will no longer be able to say that my frame is equivalent to another inertial frame in which there are no gravitons. Is this line of reasoning accurate?

Answer 1

Before diving into answer this question, first let's acknowledge as discussed in the comments that the notion of "gravitons" is not needed to describe any gravitational observation to date. There are good theoretical reasons to hypothesize that gravitons are a good way to describe quantum gravity when the gravitational field is not too strong, but there is no direct experimental evidence the world works this way.

Any physical effect is detectable in any frame. However, the notion of an exchange of "virtual particles" is not physical (because virtual particles are a mathematical artifact of one way of thinking about approximate calculations in quantum field theory), and the right way to think about what is happening depends on the situation.

First, let's start with the case of uniform acceleration. Would a graviton be involved in this situation? Well, the geodesic equation is $$ \frac{d^2 x^\mu}{d\tau^2} + \Gamma^\mu_{\rho\sigma} x^\rho x^\sigma = 0 $$ If you aren't familiar with GR, you can roughly read this as saying that the acceleration (second time derivative of $x$) is related to the gravitational field $\Gamma$. However, $\Gamma$ depends on you choice of coordinates. For uniform acceleration, it will be possible to select coordinates where $\Gamma=0$. In graviton language, you should be able to describe the process of a uniformly accelerating particle with virtual gravitons in some frame, but you will get an equivalent answer to a different frame where no virtual gravitons where created. In the lingo, any apparent effect from virtual gravitons in this case is "pure gauge", or fictitious.

If you had a legitimate scattering process due to exchange of gravitons (for example, this might describe bending of light by the sun), then you would see non-zero gravitational scattering in any frame. The gravitons in this process are virtual, not real, gravitons, which means they are properly interpreted as a mathematical artifact of perturbation theory and not a real physical particle. However, the gravitational effect is there.

To detect a real graviton, you would need to look at a process like a gravitational wave, except one with a very small amplitude. (Similar to how we detect photons by looking at very low intensity light). In particular, if the gravitational wave had frequency $\omega$, we would want the total energy contained the wave to be of order $\hbar \omega$. This is much smaller than gravitational waves that have been detected to date. However, in principle you could build a sensitive enough detector to see individual real gravitons.

Now, to make the story a little more complicated, actually if you dig into the statement "in principle you could detect a gravitation with a sensitive enough detector," it is not clear that it is true. For example, if you try to build a LIGO type interferometric detector to look for gravitons, the detector will collapse into a black hole before it becomes sensitive enough to detect gravitons. This question is explored in detail in Freeman Dyson's essay Is a graviton detectable. (See also https://arxiv.org/abs/gr-qc/0601043).