Wednesday, October 24, 2007

Conversations with a Mathematical Physicist, OR: How Does a Mortal Learn Quantum?

A few days ago, I was riding the train across the bay area, and I found myself sitting next to a mathematical physicist, with a former physics student across the aisle. Naturally (being me) I asked him to explain why Quine said, in "Two Dogmas of Empiricism," that quantum physics might require dumping the law of excluded middle. A lot of talk ensued about about electron positions and hidden variables and the Copenhagen interpretation, some of which I sort of understood, but it came down to this: either the law of excluded middle croaks, or locality croaks. And if locality croaks, all of physics (or perhaps all of science!) croaks, because we'd have to study every point in the universe simultaneously.*

(Allow me to just point out the coolness of that. Every point in the universe. Simultaneously. Sure, it's impossible. But isn't it just awesome nonetheless?)

Quantum physics seems to come up a lot in my life lately. (Paul Gowder: this is your life!) I'm taking a philosophy of science course right now, on theories of explanation. The professor, amusingly, does most of his work in philosophy of physics. Consequently, every example features electrons spinning higgledy-piggledy to and fro, lagrangians asymptoting off into singularities**, and light being wave and particle and sausage and indeterminate and a hyperintelligent shade of vaguely pinkish in a yellow-black kind of way, all at the same time. Needless to say, they're mostly totally incomprehensible to anyone without a strong undergraduate major in physics at the very least. Fortunately, the papers we're reading have more mundane examples!

For these and other reasons, I'd like to learn me some quantum physics. And therein the problem arises. I get the impression that there's really no intuitive presentation in words that's also correct. One has a choice between reading math and reading something that's a misrepresentation.

So is this true? Is there a physicist in the house? Is it in principle possible to get a basic grasp of the debates in quantum physics without knowing, say, topology? Comments?

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* Yeah, but, but, but... uh... what happens to science if we drop the law of excluded middle? Do we have to start from the beginning again? Is there a logician in the house who can explain that one to me? (And, while we're at it, you can try and make me comfortable with the old ugly business with material conditionals being true whenever they have a false antecedent. Actually, if we iced the law of excluded middle, could we get rid of that rule too and say that material conditionals are neither true nor false when they have a false antecedent? Pleeeaaassseeee? I'll bet it would make it a lot easier to make sense of counterfactuals! Or, uh, even harder.)

** I have no idea if the five words preceding this footnote marker mean anything at all in the order I put them in, but it sounds cool.