I’m giving a presentation next Wednesday for Learning Unlimited, an organization that presents educational talks to seniors in Woodstock, Ontario. The talk introduces the fundamental forces and talks about Yang and Mills before moving on to introduce my work.
While practicing the talk today, someone from Perimeter’s outreach department pointed out a rather surprising missing element: I never mention gravity!
Most people know that there are four fundamental forces of nature. There’s Electromagnetism, there’s Gravity, there’s the Weak Nuclear Force, and there’s the Strong Nuclear Force.
What ties these things together, though? What makes them all “fundamental forces”?
Mathematically, gravity is the odd one out here. Electromagnetism, the Weak Force, and the Strong Force all share a common description: they’re Yang-Mills forces. Gravity isn’t. While you can sort of think of it as a Yang-Mills force “squared”, it’s quite a bit more complicated than the Yang-Mills forces.
You might be objecting that the common trait of the fundamental forces is obvious: they’re forces! And indeed, you can write down a force law for gravity, and a force law for E&M, and umm…Ok, it’s not quite as bad as xkcd would have us believe. You can actually write down a force law for the weak force, if you really want to, and it’s at least sort of possible to talk about the force exerted by the strong interaction.
All that said, though, why are we thinking about this in terms of forces? Forces are a concept from classical mechanics. For a beginning physics student, they come up again and again, in free-body diagram after free-body diagram. But by the time a student learns quantum mechanics, and quantum field theory, they’ve already learned other ways of framing things where forces aren’t mentioned at all. So while forces are kind of familiar to people starting out, they don’t really match onto anything that most quantum field theorists work with, and it’s a bit weird to classify things that only really appear in quantum field theory (the Weak Nuclear Force, the Strong Nuclear Force) based on whether or not they’re forces.
Isn’t there some connection, though? After all, gravity, electromagnetism, the strong force, and the weak force may be different mathematically, but at least they all involve bosons.
Well, yes. And so does the Higgs.
The Higgs is usually left out of listings of the fundamental forces, because it’s not really a “force”. It doesn’t have a direction, instead it works equally at every point in space. But if you include spin 2 gravity and spin 1 Yang-Mills forces, why not also include the spin 0 Higgs?
Well, if you’re doing that, why not include fermions as well? People often think of fermions as “matter” and bosons as “energy”, but in fact both have energy, and neither is made of it. Electrons and quarks are just as fundamental as photons and gluons and gravitons, just as central a part of how the universe works.
I’m still trying to decide whether my presentation about Yang-Mills forces should also include gravity. On the one hand, it would make everything more familiar. On the other…pretty much this entire post.