Science communication is a gradual process. Anything we say is incomplete, prone to cause misunderstanding. Luckily, we can keep talking, give a new explanation that corrects those misunderstandings. This of course will lead to new misunderstandings. We then explain again, and so on. It sounds fruitless, but in practice our audience nevertheless gets closer and closer to the truth.
Last week, I tried to explain physicists’ notion of a fundamental particle. In particular, I wanted to explain what these particles aren’t: tiny, indestructible spheres, like Democritus imagined. Instead, I emphasized the idea of fields, interacting and exchanging energy, with particles as just the tip of the field iceberg.
I’ve given this kind of explanation before. And when I do, there are two things people often misunderstand. These correspond to two topics which use very similar language, but talk about different things. So this week, I thought I’d get ahead of the game and correct those misunderstandings.
The first misunderstanding: None of that post was quantum.
If you’ve heard physicists explain quantum mechanics, you’ve probably heard about wave-particle duality. Things we thought were waves, like light, also behave like particles, things we thought were particles, like electrons, also behave like waves.
If that’s on your mind, and you see me say particles don’t exist, maybe you think I mean waves exist instead. Maybe when I say “fields”, you think I’m talking about waves. Maybe you think I’m choosing one side of the duality, saying that waves exist and particles don’t.
To be 100% clear: I am not saying that.
Particles and waves, in quantum physics, are both manifestations of fields. Is your field just at one specific point? Then it’s a particle. Is it spread out, with a fixed wavelength and frequency? Then it’s a wave. These are the two concepts connected by wave-particle duality, where the same object can behave differently depending on what you measure. And both of them, to be clear, come from fields. Neither is the kind of thing Democritus imagined.
The second misunderstanding: This isn’t about on-shell vs. off-shell.
Some of you have seen some more “advanced” science popularization. In particular, you might have listened to Nima Arkani-Hamed, of amplituhedron fame, talk about his perspective on particle physics. Nima thinks we need to reformulate particle physics, as much as possible, “on-shell”. “On-shell” means that particles obey their equations of motion, normally quantum calculations involve “off-shell” particles that violate those equations.
To again be clear: I’m not arguing with Nima here.
Nima (and other people in our field) will sometimes talk about on-shell vs off-shell as if it was about particles vs. fields. Normal physicists will write down a general field, and let it be off-shell, we try to do calculations with particles that are on-shell. But once again, on-shell doesn’t mean Democritus-style. We still don’t know what a fully on-shell picture of physics will look like. Chances are it won’t look like the picture of sloshing, omnipresent fields we started with, at least not exactly. But it won’t bring back indivisible, unchangeable atoms. Those are gone, and we have no reason to bring them back.
4 gravitons 
Think of a particle as a dirac delta function, and a wave as a sine function. Fields are arbitrary real distributions (generalised functions).
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For those with the background for it, that is indeed a good way to think about it. (Mostly because it’s almost literally true. 😉 )
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Great post Matt. I find the on-shell off-shell dichotomy confusing. If Feynman diagrams with off-shell internal lines give the right answer to 11 sig. figures, how can an on-shell calculation also give the right answer? The physics seems to be completely different in each case.
I will thank you in advance for any assistance you can provide.
JR
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The key thing to keep in mind here is that, when we calculate something with on-shell methods, it’s not just a matter of plugging on-shell lines instead of off-shell lines and doing the same thing. The calculation method is different. There are a couple of different things people refer to as on-shell methods. Sometimes, as in generalized unitarity, we make an ansatz that includes arbitrary off-shell integrals, then use on-shell calculations to constrain it. Sometimes it’s a kind of recursion method, building up something off-shell from on-shell building blocks. And sometimes it’s something like the amplituhedron, where the on-shell information is a sort of “box” containing the answer. Either way, you still have to do integrals over something like off-shell lines, but you don’t need to think about off-shell fields: the actual physics you use is all on-shell.
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Thanks for some interesting posts. The issue with some of these notions is that they try to provide a physical interpretation to things that are in the end not observable. In other words, it assumes to provide knowledge that cannot be tested. In that sense such interpretations are essentially non-scientific. Now I’m not saying one should not try to understand these things physically. Humans will always try to that. That is fine, as long as we are honest with ourselves about how much of it we can trust.
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