Particles vs Waves, Particles vs Strings

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.

8 thoughts on “Particles vs Waves, Particles vs Strings

  1. dr universe

    Hey! So I’m 14 and I was reading a bit about quantum mechanics and string theory and stuff before I wrote some blog posts about them. I had a small question – I read that quantum mechanics and the theory of relativity have an antagonistic relation buuuut the laws of quantum mechanics can also apply on the larger scale. So do the laws of quantum mechanics give the same result as those of newtonian physics but in a longer way and obviously excluding gravity.
    Thanks

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    1. 4gravitons Post author

      Good question! When people say that quantum mechanics and relativity don’t agree, they mean general relativity (and thus gravity), not special relativity. Quantum mechanics and special relativity work fine together (or to be precise, quantum field theory and special relativity work fine together, quantum mechanics came before quantum field theory). If you use quantum field theory and go to large scales it does indeed follow the normal rules of special relativity (and when the speed is slow, Newtonian physics).

      There’s one caveat and that’s the measurement problem. It’s still controversial whether we really understand how quantum things on small scales become classical things on large scales. That’s not because the math doesn’t work: you can follow known math to go from one theory to the other. People just argue about whether that’s the correct way to interpret the theories and whether it’s fully understood, or whether there’s some principle we’re missing in how it works.

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      1. dr universe

        Thanks so much for the reply-I knew it was quantum mechanics and general relativity-sorry for the unclear question. But this is super helpful. I really appreciate it.
        Would you mind if I ask some random physics questions to you when I think of them?

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  2. Marees

    I find it easy to visualise a swimming pool example.

    Electron: When there are many swimmers in a pool swimming furiously they generate waves that interfere with each other

    Photon: when there are many high energy/high frequency waves, then they can interfere to produce point like behaviours due to resonance effects

    Above example is probably more like the pilot wave theory but it helps me to visualise a (classical) picture in my mind

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  3. ohwilleke

    Are the point particle properties of particle that matter in quantum mechanics indistinguishable from the limit of the properties of an arbitrarily small particle of finite volume, or is this a case like that of the difference between a massive particle of arbitrarily small mass which behaves differently in a gravitational field than a particle of exactly zero mass?

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    1. 4gravitons Post author

      It’s more like the former: the smaller a finite-size particle is the more it looks like a point particle, so while in practice we think of, say, the electron as a point particle, what we have experimentally is an upper limit for its size. (If this wasn’t the case, string theory would already be ruled out!)

      With that said, I’m not 100% sure your analogy with masslessness is correct: a very low-mass particle will behave approximately like a massless particle until you have the experimental resolution to tell the difference. (Recall that neutrinos were thought to be massless for quite some time, for example.)

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