Quantum mechanics is our best physical theory of the constitution of matter, but infamously it only gives probabilistic predictions. Instead of telling us exactly where an electron is, quantum mechanics can only say, for example, that the electron will be located here with probability one half. In this class, we’ll ask how one should interpret the probabilistic statements of quantum mechanics. Could our probabilistic predictions about the electron signify a mere lack of knowledge about where the electron is? Could we find a better theory of the electron with more information, or hidden variables, that allows us to predict where the electron is with certainty? We’ll discuss a number of famous mathematical results, including Bell’s theorem and the Kochen-Specker theorem, that are sometimes interpreted as showing that the answer is “no”—quantum mechanics is inherently indeterministic. This course will use mathematical methods: students will be asked to write mathematical proofs using the theory of probability. However, no background in mathematics or physics is assumed or required.
TEXT: No Textbook Required – course materials will be available on Canvas.