Quantum Mechanics

15 Oct 2014 12:50

I am not going to try to explain quantum mechanics here.

Interpetations --- Copenhagen (pure logical positivism, of course), quantum logic, many worlds. Is there any reason to take the Bohmian (non-local hidden variables) interpretation seriously?

Entanglement (= spooky, non-classical correlations) and coherent states. Decoherence --- the process by which coherent, entangled states lose their coherence due to interaction with other things, particularly very large, complicated, effectively-random things (such as people and measuring devices). There's a growing body of work saying that the rate of decoherence depends on the Lyapunov exponents, which are classical measures of sensitivity to initial conditions and information production. This is very suggestive, and I need to look into it.

Quantum computing; i.e., computing with entangled quantum bits ("qubits"). Problems for which quantum computing is more powerful than classical computing. (To check: nothing classically uncomputable is quantum-computable, is it?) Avoiding decoherence of the quantum computer. Can we test different interpretations by experiments on quantum computers? Quantum information theory.

Quantum general relativity, a.k.a. loop quantum gravity, is really interesting. But reading the introductory surveys (especially Thiemann's, below) reminds me of the reason I got out of fundamental theoretical physics in the first place (viz., I'm not smart enough).

The many-worlds interpretation should probably be called something more like "many histories". I like it, because it completely avoids the awful notion of the wave function collapsing, and denies any role whatsoever to measurement, consciousness, etc. And it makes the success of quantum computers remarkably sensible, which I don't think we can say for any of the other interpretations. The only exception I can think of is the Ithaca interpretation, which merges very nicely with many-worlds. This is, roughly, the idea that the wave-function is a real, objective thing, as are correlations between systems, and that "measurement" is just a particular case of decoherence. While on the subject of measurement, I need to learn about algebras of observables.

Things to think about: Quantum computational mechanics. Can entanglement be treated as a thermodynamic resource? What does the quantum version of large deviations theory look like?

Things far beyond my ken: Where does that weird complex-valued not-quite-a-probability measure come from anyway?

See also Field Theory.