Gravity is an Important Force

Brad DeLong, in re Quantum Hyperion, wonders whether photons are really responsible for the decoherence of Saturn’s moon:

But gravity works–presumably, at some level–by massive objects constantly bombarding each other with gravitons, so we are also averaging over all the possible states of gravitons that we are not keeping track of, aren’t we? That should cause decoherence too, shouldn’t it?

This is an annoyingly good question. In fact, I’m probably not giving anything away if I reveal that my esteemed co-blogger Daniel and I once tried to figure out whether or not dark matter, if it truly interacts with ordinary matter only through gravity, would be in a coherent quantum state. Still don’t know the answer (although I strongly suspect it is “no,” I’m just not sure how to prove it).

The force due to gravity on Hyperion is much larger than the force due to electromagnetism on Hyperion. All else being equal, gravity is a much weaker force, but it has the helpful quality of adding up rather than canceling out, which is why it tends to dominate over astrophysical distances.

However — it’s not always useful to think of the gravitational force on a planet as due to the exchange of gravitons. You can think of the static force between two objects as arising from the exchange of virtual particles, whether you are talking about gravity or electromagnetism. But it is also true that, in the limit where the bodies giving rise to the gravitational force are perfectly static, those gravitons add up to define a unique quantum state. (The Sun, Saturn, and Titan are not static, but probably good enough for these purposes.) So the state of Hyperion becomes entangled with the quantum states of the individual gravitational fields of those celestial bodies, not with a jillion separate gravitons from each source. When we ignore the quantum states of all the gravitons reflected off of Hyperion, we are ignoring a lot more than when we ignore the quantum states of the gravitational fields of the Sun, Saturn, and Titan.

So I think it’s the photons, not the gravitons, that are primarily responsible for the decoherence, by a wide margin. But I wouldn’t bet my reputation on it. Maybe Daniel’s reputation.