Yet Another Form of the Relation Between Quantum and Classical Physics

Abstract

I met Larry Biedenham in the Fall of 1965 when I began graduate school at Duke University. One of our early conversations dealt with the relationship of classical physics to quantum mechanics. He argued that quantum mechanics is really a subset of classical physics because all our observations of the world are inherently classical and it is exactly this web of relationships among classical observations that quantum mechanics describes. I was impressed by Ehrenfest’s theorem and disagreed, but the cogency of his position made a lasting impression on me and I’ve understood Bohr’s positions better as a result. About the same time he encouraged me to read Weyl on quantum kinematics and some then current stuff by Schwinger with the remark that quantum dynamics is the unitary group, U(n), for n→∞. This was heady stuff for a new graduate student and carried an air of excitement that I appreciated. I’m very happy to contribute the following observations to this celebration of his 70th birthday.