Prof. Ariel Caticha (SUNY Albany, USA): The Entropic Dynamics approach to Quantum Mechanics
Channel: Centrum Fizyki Teoretycznej PAN
Date: 2023-12-20

Prof. Ariel Caticha (Department of Physics, University at Albany — SUNY Albany, USA).
The Entropic Dynamics approach to Quantum Mechanics.

Entropic Dynamics (ED) is a framework for reconstructing Quantum Mechanics as an application of entropic methods of inference. The starting point is to establish a clear distinction between ontic and epistemic variables. In this talk we shall take the positions of particles to be the only ontic variables and probabilities are epistemic.

In ED the dynamics of the probability distribution is driven by entropy subject to constraints that are codified in terms of a quantity later related to the phase of the wave function. The challenge is to specify how those constraints are themselves updated. The important ingredients are two: the cotangent bundle associated to the probability simplex inherits (1) a natural symplectic structure from ED, and (2) a natural metric structure from information geometry. The requirement that the dynamics preserves both the symplectic structure (a Hamilton flow) and the metric structure (a Killing flow) leads to a Hamiltonian dynamics of probabilities in which the linearity of the Schrödinger equation, the emergence of a complex structure, Hilbert spaces, and the Born rule, are derived rather than postulated.

ED is a conservative theory in that it attributes a definite ontic status to things such as particles (or fields) and a definite epistemic status to probabilities and wave functions without invoking exotic probabilities; it is radically non-classical in that it denies the ontic status of dynamics and of all observables except position (or fields).
‍Wednesday colloquium at CTP PAS – 2023-12-13