Part One of a Series on N=8 supergravity
This blog is called four gravitons, so I ought to explain what a graviton actually is. Starting from that, I can begin to explain N=8 supergravity, gravity’s highly supersymmetric cousin.
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:
Where d is the full distance. If space is bent, the formula changes:
Here and 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 because physicists are overly enamored of Greek letters. If is its momentum (physicists also really love subscripts), then its total momentum can be calculated using the Pythagorean Theorem as well:
Or with gravity:
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 and represent the graviton, then this formula says that one graviton can interact with two particles, like so:
Saying that gravitons can interact with particles ends up meaning the same thing as saying that gravity changes the way we measure the 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. I’ll say more about that later in this series.