The quantum within - Mustafa Amin

Hilbert space, superposition, uncertainty relations, and Wigner negativity, are terms usually associated with quantum phenomena and formalism. In this talk, I present recent work where we show that all of these have analogues in classical mechanics using the Koopman-von Neumann formulation. I will attempt to explain their (in hindsight, unsurprising) meaning in a classical context. This is in an effort to characterize and identify the root of the differences between classical and quantum mechanics, and investigate the possibility of combining both theories into a single framework.