If light changes wavelength in the presence of a gravitational field, how can this be described by the quantum theory of gravity?
Light changes wavelength in the presence of gravity
I'm sorry Alex, but actually, it doesn't. You know how if you're moving away from a light source you see a redshift? The photon energy appears to reduce and the wavelength appears to increase? Well the photons coming from that light source haven't changed one iota. Instead you've changed. You also change if I lift you up to some high elevation above an upward-pointing light source. I do work on you. I add energy to you. Because of this, the photon energy appears to reduce and the wavelength appears to increase. But the photons coming from that light source haven't changed one iota. Instead you've changed. You can find Einstein talking about red-shift in the digital papers hosted at Princeton. Note that he doesn't say light changes frequency (or wavelength) as it climbs out of the gravitational field. He says it's emitted at a lower frequency.
can the quantum theory of gravity explain this?
No. And whilst some might say there's a consensus that gravity will one day be understood as the exchange of gravitons, it just isn't true. Because a virtual particle isn't a real particle. See ACM's answer here: "a virtual particle is not a particle in the usual (or any other rigorous) sense". Also see Professor Matt Strassler's article: "The best way to approach this concept, I believe, is to forget you ever saw the word “particle” in the term. A virtual particle is not a particle at all". A virtual particle isn't some short-lived real particle that pops into and out of existence like magic. Instead it's a field quantum. It's like you divide an electromagnetic field up into little squares and say each is a virtual photon. The electron and the proton "exchange field" when they move together, such that the hydrogen atom doesn't have much in the way of an electromagnetic field left. That's why it's OK to say they exchange virtual photons. Because they exchange field. What they don't do is magic up real photons and throw them back and forth at one another. Hydrogen atoms don't twinkle. Then when two hydrogen atoms attract each other gravitationally, they don't "exchange field". The resultant field is doubled up, not weakened by a field exchange. So the idea of gravity working via an exchange mechanism doesn't get very far. Especially since a real photon has an "active gravitational mass". In a way, it isn't just some E=hf or E=hc/λ electromagnetic wave, it's a gravitational wave too.