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What happens to quantum states if Planck’s constant changes?

The variability of physical “constants” is a possibility that cannot be ruled out and which is an active area of research in cosmology and astrophysics. In fact, since Dirac in his “Large Numbers Hypothesis” suggested that some constants of Nature could vary in space and time, the topic has fascinated not only physicists but also philosophers of science and has motivated numerous theoretical and experimental findings. In this talk, we focus on the quantum mechanical consequences of possible changes in Planck’s constant and show that the purity of a quantum state is extremely sensitive to such changes, but that quantum states can evolve into classical states, and vice versa. A complete classification of such transitions is however not possible for the moment because of yet unsolved mathematical difficulties related to the study of positivity properties of trace class operators. Reference: M. de Gosson, Phys. Lett. A 381 (2017).