# How do gravitons and photons interact?

First of all, I am a noob in physics (I‘m a computer scientist) and started reading Hawking‘s „A brief history of time“. In Chapter 6 he says that “electromagnetic force [...] interacts with electrically charged particles like electrons and quarks, but not with uncharged particles such as gravitons.”

My question now: how come that extremely massiv object are able to bend light (e.g. we are able to see distant stars that are behind the sun)? I mean, how can gravitation (actually gravitons) affect photons if gravitons are not charged?

I know that there are some questions here that go in the same direction but as I‘m a noob in physics, I don‘t quite get the answers.

I‘d appreciate if someone had a laymen‘s explanation for this that not necessarily covers all different aspects (I might pose some follow-up questions) but explains the essence.

Thanks to y‘all!

• Possible duplicate of "How do I derive the Feynman rules for graviton-photon coupling?".
– user87745
May 5, 2020 at 12:48
• That might be the same question but as I only read Hawking‘s book, I don‘t understand these formulas.. May 5, 2020 at 12:56
• Ok, good point. I am not sure what is the official PSE policy on marking duplicates if the questions are asked at different levels of proficiency but I am going to unmark this as a possible duplicate because it sounds reasonable to do so. If someone aware of a concrete policy regarding this comes across this comment, kindly enlighten me :P
– user87745
May 5, 2020 at 13:06
– rob
May 5, 2020 at 15:30

Gravity couples to energy, not just mass as in Newtonian theory (really it couples to energy density, momentum, and stress). Since photons have energy, they feel gravity.

As a classical phenomenon, lensing is generally thought about as light interacting with the curvature of space rather than gravitons. A physical process involving the interaction of gravitons with photons would be the electromagnetic scattering of gravitational waves, as hypothetically happened in the early universe when primordial gravitational waves scattered off the cosmic microwave background.

• Also, at the loop level, two gravitons can scatter each other off by exchanging photons. So, the statement by Hawking is only classically true. Quantum mechanically, you can have uncharged particles interacting via the electromagnetic force.
– user87745
May 5, 2020 at 12:43
• Thanks for the answer! I think I have had the misconception that all forces between particles add up to a single „attraction“ between these particles. Is it okay to say that in the classical case, light is bent by massive objects because gravitons act on all particles (no matter what particles are influenced by photons through electromagnetic force)? EDIT: actually, if electromagnetic force between photons and gravitons was repulsive it WOULD influence the attraction between both but as the electromagnetic force is not existent (in the classical case) the attraction only stems from gravity? May 5, 2020 at 13:48
• Second EDIT: „I think I have had the misconception that all forces between particles add up to a single „attraction“ between these particles.„ This is not clearly written, sorry. I mean that I had the misconception that since Hawking states that no electromagnetic force acts between photons and gravitons, I thought there was no force at all while in fact this statement says nothing about gravitational force. May 5, 2020 at 13:56
• Follow-up question: Hawking also writes that “A cannonball fired upward from the earth will be slowed down by gravity and will eventually stop and fall back; a photon, however, must continue upward at a constant speed.” How is this consistent with gravity coupling to energy and photons therefore feeling gravity? May 5, 2020 at 15:16
• @frederik. There are couple points here. First: Classically, since gravitons carry no charge, they do not interact electromagnetically. But, as Dvij points out above, at the quantum level gravitons do in fact exchange virtual photons. Second: Since photons carry energy, they interact gravitationally (both through virtual exchange of gravitons, which is better understood as coupling to curvature, and by scattering off real gravitons in the form of gravitational waves). May 5, 2020 at 16:05

Gravitational lensing (light being "bent" by stars for instance) relates to general relativity, the graviton is a theorised particle in quantum field theory. There is currently no complete and accepted theory of quantum gravity which connects the two.

In general relativity the curvature of spacetime alters the path of particles and causes what we call gravity. This means even massless particles like photons have their paths changed since they still travel through spacetime.

• There is a quantum field theory of gravity, it is just not renormalizable. That doesn't stop us from doing quantum mechanical calculations about gravity at low enough energies. So, for example, you can derive Feynman rules for the interaction of photons and gravitons without any problem at all. See, for example, physics.stackexchange.com/questions/335917/….
– user87745
May 5, 2020 at 12:46
• Building on the previous comment, only the quantum part of higher loop terms suffer from not being renormalizable. The classical limit of these terms is fine and can be used to calculate the bending of light in the weak field limit. May 5, 2020 at 12:50
• @mmeent Thanks for that clarification. In addition, you can also calculate quantum effects on gravity because of the fact that divergences only show up at and beyond two-loop diagrams in the QFT of gravity. And at low enough energies, you can also calculate higher-order loops because you can always work with a hard cutoff.
– user87745
May 5, 2020 at 13:01
• @DvijD.C. Have edited now to reflect this, I do not know QFT so my answer is not intended to be comprehensive, thanks for the correction though. May 5, 2020 at 13:09

Gravitons should couple to almost every particle. It is just a matter of how much it couples with the particle. However in the particle world gravitons are pretty weak compared to the other forces. However on the largest of scales gravitons and gravity wins over. To answer the question gravitons do couple to photons.

• -1: There is no "how much" and "almost every particle" is misleading. Graviton couples to all particles with the exact same strength. In classical physics, this corresponds to the equivalence principle. In QFT, this follows directly from the Weinberg soft graviton theorem.
– user87745
May 5, 2020 at 15:23
• Well the coupling of how gravitons interact with different particles, depends on that particles energy. The more massive and hence the more energetic the object the more gravity couples to it, right. May 6, 2020 at 14:11