# What’s A Graviton? Or: How I Learned to Stop Worrying and Love Quantum Gravity

I’m four gravitons and a grad student. And despite this, I haven’t bothered to explain what a graviton is. It’s time to change that.

Let’s start like we often do, with a quick answer that will take some unpacking:

Gravitons are the force-carrying bosons of gravity.

I mentioned force-carrying bosons briefly here. Basically, a force can either be thought of as a field, or as particles called bosons that carry the effect of that field. Thinking about the force in terms of particles helps, because it allows you to visualize Feynman diagrams. While most forces come from Yang-Mills fields with spin 1, gravity has spin 2.

Now you may well ask, how exactly does this relate to the idea that gravity, unlike other forces, is a result of bending space and time?

First, let’s talk about what it means for space itself to be bent. If space is bent, distances are different than they otherwise would be.

Suppose we’ve got some coordinates: x and y. How do we find a distance? We use the Pythagorean Theorem: $d^2=x^2+y^2$

Where d is the full distance. If space is bent, the formula changes: $d^2=g_{x}x^2+g_{y}y^2$

Here $g_{x}$ and $g_{y}$ come from gravity. Normally, they would depend on x and y, modifying the formula and thus “bending” space.

Let’s suppose instead of measuring a distance, we want to measure the momentum of some other particle, which we call $\phi$ because physicists are overly enamored of Greek letters. If $p_{x,\phi}$ is its momentum (physicists also really love subscripts), then its total momentum can be calculated using the Pythagorean Theorem as well: $p_\phi^2= p_{x,\phi}^2+ p_{y,\phi}^2$

Or with gravity: $p_\phi^2= g_{x}p_{x,\phi}^2+ g_{y} p_{y,\phi}^2$

At the moment, this looks just like the distance formula with a bunch of extra stuff in it. Interpreted another way, though, it becomes instructions for the interactions of the graviton. If $g_{x}$ and $g_{y}$ represent the graviton, then this formula says that one graviton can interact with two $\phi$ particles, like so: Saying that gravitons can interact with $\phi$ particles ends up meaning the same thing as saying that gravity changes the way we measure the $\phi$ particle’s total momentum. This is one of the more important things to understand about quantum gravity: the idea that when people talk about exotic things like “gravitons”, they’re really talking about the same theory that Einstein proposed in 1916. There’s nothing scary about describing gravity in terms of particles just like the other forces. The scary bit comes later, as a result of the particular way that quantum calculations with gravity end up. But that’s a tale for another day.

## 5 thoughts on “What’s A Graviton? Or: How I Learned to Stop Worrying and Love Quantum Gravity”

1. G.

Apologies for the off-topic post, but: I just read your piece in ArsTechnica. Truly excellent, it’s exactly the kind of science reporting that we need, the more the better. I’m a layperson who keeps abreast of science news and I’d never heard of N=4 super Yang-Mllls before, but you spelled it out clearly enough to make sense to me, along with a few other ideas I’d encountered before but hadn’t understood. I’m going to put your blog on my regular reading list (and probably show up from time to time, to pester you with stoopid questions;-).

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2. Wyrd Smythe

So the interaction with (virtual?) gravitons is what bends a light ray around the sun? How does the apparent equivalence of gravity and acceleration fit into the picture?

As I understand it, the other three forces are seen as fields where ripples in these fields are the bosons representing (the application of?) the forces. Is there, then, a gravity field in which gravitons are ripples?

One of your other posts talks about how physicists “do the math” and don’t worry too much about the ontology. But I am interested in the ontology… what gravity really is! My (unscientific) hope is that it’s nothing like the other forces, that there’s no gravity “field” and no (real) gravitons. Just that mass affects the geometry of space.

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1. 4gravitonsandagradstudent Post author

Yes and no. Basically, if you think of electromagnetism as working based on interaction with (virtual?) photons, then you should think about gravity in a similar way. Both statements aren’t completely rigorous (hence why I left the question mark in after virtual), but both are equally good ways of visualizing what’s going on.

There is indeed a gravity field of which gravitons are ripples. This was present all the way back in Einstein’s formulation: you get gravitational waves out of Einstein gravity in the same way you get light out of Maxwell’s E&M.

This may seem to be inconsistent with the idea that gravity is equivalent to acceleration, but it really all ties back to the way that gravity modifies how we measure. If gravity modifies how we measure, it sits in a particular place in the formulas for kinetic energy and the like. And since gravity can vary from place to place, that makes it a field. (I talk a bit about this idea here: http://4gravitonsandagradstudent.wordpress.com/2013/03/15/nature-abhors-a-constant/)

I like ontology, but one has to be careful to avoid insisting on ontological distinctions that aren’t meaningful. Being a field and being the geometry of space aren’t mutually inconsistent, they’re deeply connected concepts.

If you like, one way to think about it is that there “really” isn’t any space at all, just interactions with the gravity field. It’s very hard to do practical calculations that way, which is one of the big problems quantum gravity theories struggle with. But it’s certainly something that has some ontological appeal, and it seems to be Nima Arkani-Hamed’s favored perspective.

Finally, you might want to google the Unruh Effect, if you’re interested in the more mind-bending sorts of consequences that the equivalence between acceleration and gravity has in quantum contexts.

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1. Wyrd Smythe

Thank you, that both clarifies some things and gives me food for thought. Does this mean that, one some level, gravity is indeed just the fourth force and not significantly different? (For example, would it be possible to unify all four forces?)

I went to school with Jessie Unruh’s daughter…. oh, wait, different Unruh! 😀

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1. 4gravitonsandagradstudent Post author

Gravity does have a different format than the other three forces, just because it’s the other ones “squared”, so you can’t combine them in the “Grand Unified Theory” sense. But there are broader ways to unify things, and one of the big advantages of string theory is that you get unification of gravity and Yang-Mills forces “for free”.

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