The lure of blogging is strong. Having guest-posted about problems with eternal inflation, Tom Banks couldn’t resist coming back for more punishment. Here he tackles a venerable problem: the interpretation of quantum mechanics. Tom argues that the measurement problem in QM becomes a lot easier to understand once we appreciate that even classical mechanics allows for non-commuting observables. In that sense, quantum mechanics is “inevitable”; it’s actually classical physics that is somewhat unusual. If we just take QM seriously as a theory that predicts the probability of different measurement outcomes, all is well.
Tom’s last post was “technical” in the sense that it dug deeply into speculative ideas at the cutting edge of research. This one is technical in a different sense: the concepts are presented at a level that second-year undergraduate physics majors should have no trouble following, but there are explicit equations that might make it rough going for anyone without at least that much background. The translation from LaTeX to WordPress is a bit kludgy; here is a more elegant-looking pdf version if you’d prefer to read that.
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Rabbi Eliezer ben Yaakov of Nahariya said in the 6th century, “He who has not said three things to his students, has not conveyed the true essence of quantum mechanics. And these are Probability, Intrinsic Probability, and Peculiar Probability”.
Probability first entered the teachings of men through the work of that dissolute gambler Pascal, who was willing to make a bet on his salvation. It was a way of quantifying our risk of uncertainty. Implicit in Pascal’s thinking, and all who came after him was the idea that there was a certainty, even a predictability, but that we fallible humans may not always have enough data to make the correct predictions. This implicit assumption is completely unnecessary and the mathematical theory of probability makes use of it only through one crucial assumption, which turns out to be wrong in principle but right in practice for many actual events in the real world.
