Reader Request: Quantum Complexity

There's some good stuff in yesterday's post asking what physics you'd like to read more about. I'm nursing a sore neck and shoulder, so I'll only do one or two quick ones today, starting with James D. Miller in the first comment:

1) Is it true that our understanding of quantum physics comes from studying systems with only a small number of particles and there is a good chance our theories won't hold in more complex systems.

It all depends on how you define your terms-- what counts as a "small number" of particles, and what counts as not holding?

It's certainly true that most of the experiments to date on quantum foundations have used small numbers of particles-- usually single-digit numbers of particles. The best tests of things like Bell's theorem and the best examples of Schrödinger cat states come from experiments on trapped ions that generally deal with only a couple of particles, and most of the theoretical effort has also focused on these simple systems.

It's not hard, though, to come up with examples of quantum fundamentals using much larger numbers of particles. To pick two that I cite in millions of electrons in superconducting loops (free registration required), and there are some beautiful experiments on diffraction of fullerene molecules.

If 60 or 10,000,000 particles aren't enough for you, there's the entire field of condensed matter physics.

Condensed matter physics is fundamentally about what happens when you put together a really gigantic number of particles that obey quantum rules-- the billions of billions of atoms and electrons inside a solid crystal. When you do that, you need different language to describe the material-- it's all about band structure and Fermi surfaces and that stuff-- but fundamentally all that's going on is the application of quantum mechanics to mind-bogglingly big numbers of particles.

And condensed matter physics is generally pretty successful. There are some phenomena that emerge from it that you wouldn't necessarily expect from a simple quantum picture-- topological insulators, say-- and other phenomena that we don't yet have a good explanation for-- high temperature superconductivity is a good example-- but the theory works really well.

So, it really comes down to what you mean by "our theories won't hold for more complex systems." If you mean that there are likely to be phenomena that emerge from having macroscopic numbers of particles that we couldn't easily predict from looking at the behavior of single-digit numbers of particles, then that's absolutely true. Topological insulators, after all, are only a few years old, and while high-temperature superconductors have been around for twenty-odd years, we still don't really understand those.

If you mean that the behavior of complex systems will call into question the rules we have for the behavior of microscopic systems, though, I'd say that's false. The rules for small numbers of particles have been tested to exquisite precision, and work extremely well. There's not a lot of wiggle room there.

The unexpected and so far unexplained phenomena observed in condensed matter systems are a result of the complex interactions of simple rules. At this point, I think I'm contractually obligated to mention Conway's gmae of Life and other such systems. The fact that you see complex behavior in the game does not suggest that there's anything missing from the simple description of the rules. It just means that large numbers of particles following simple rules can give you surprisingly complex patterns. See also the Emergent Universe web site put together by ICAM, which has more examples of emergent complexity.


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One thing I like about condensed matter is that lots of things work with fairly simple approximations. For example if you describe a metal with the free (or nearly-free) electron approximation you get lots of stuff right, up to using an "effective" mass and stuff. It's all magic. And cool.