“Insights into Quantum Time Reversal from the Classical Schrödinger Equation”

Craig Callender (University of California, San Diego)

Abstract: The need to implement time reversal via complex conjugation in quantum theory has always been a bit of a puzzle. Why should i go to -i under temporal reflection when it has no spatiotemporal dimensions? In the talk I’ll provide a new explanation. I begin with the little-appreciated fact that classical statistical mechanics has exactly the same issue when it is represented in the “quantum-looking” classical Schrodinger equation of Schiller and Rosen. Since we know what is going on classically, it is possible to extricate ourselves from this puzzle. I then take the classical solution’s counterpart in the quantum context. No doubt this last step will be controversial because it involves invoking an interpretation of quantum theory. If I’m right, the puzzle over time reversal in quantum theory arises because standard quantum mechanics gives us only “half” a theory.