On my “Who Am I?” page, I open with my background, calling myself a string theorist, then clarify: “in practice I’m more of a Particle Theorist, describing the world not in terms of short lengths of string but rather with particles that each occupy a single point in space”.
When I wrote that I didn’t think it would confuse people. Now that I’m older and wiser, I know people can be confused in a variety of ways. And since I recently saw someone confused about this particular phrase (yes I’m vagueblogging, but I suspect you’re reading this and know who you are 😉 ), I figured I’d explain it.
If you’ve learned a few things about quantum mechanics, maybe you have this slogan in mind:
“What we used to think of as particles are really waves. They spread out over an area, with peaks and troughs that interfere, and you never know exactly where you will measure them.”
With that in mind, my talk of “particles that each occupy a single point” doesn’t make sense. Doesn’t the slogan mean that particles don’t exist?
Here’s the thing: that’s the wrong slogan. The right slogan is just a bit different:
“What we used to think of as particles are ALSO waves. They spread out over an area, with peaks and troughs that interfere, and you never know exactly where you will measure them.”
The principle you were remembering is often called “wave-particle duality“. That doesn’t mean “particles don’t exist”. It means “waves and particles are the same thing”.
This matters, because just as wave-like properties are important, particle-like properties are important. And while it’s true that you can never know exactly where you will measure a particle, it’s also true that it’s useful, and even necessary, to think of it as occupying a single point.
That’s because particles can only affect each other when they’re at the same point. Physicists call this the principle of locality, the idea that there is no real “action at a distance”, everything happens because of something traveling from point A to point B. Wave-particle duality doesn’t change that, it just makes the specific point uncertain. It means you have to add up over every specific point where the particles could have interacted, but each term in your sum has to still involve a specific point: quantum mechanics doesn’t let particles affect each other non-locally.
Strings, in turn, are a little bit different. Strings have length, particles don’t. Particles interact at a point, strings can interact anywhere along the string. Strings introduce a teeny bit of non-locality.
When you compare particles and waves, you’re thinking pre-quantum mechanics, two classical things neither of which is the full picture. When you compare particles and strings, both are quantum, both are also waves. But in a meaningful sense one occupies a single point, and the other doesn’t.