Can Quantum Field Theory be Recovered from Time-Symmetric Stochastic Mechanics?

by Prof. Simon Friederich (University of Groningen)

Wednesday 22 Apr 2026, 16:15 → 18:15 Europe/Berlin

Abbeanum/1-HS2 - Straubel-HS (TPI, FSU Jena)

I explore whether quantum field theory can be understood as the statistical mechanics of a time-reversal-invariant stochastic generalization of Hamiltonian dynamics, in conformity with how Einstein envisioned a future, mature, understanding of quantum theory. The motivation for this project is to assign sharp values to all observables and thereby avoid the quantum measurement problem while understanding the quantum state as an expression of our knowledge, not as an objective physical quantity, in analogy to the probability density in classical statistical mechanics. There, the phase space probability density evolves according to Liouville's equation. I derive a time-symmetric generalization of the Liouville equation, subject to natural constraints, which is a Fokker-Planck equation with a generalized diffusion matrix that is symmetric, traceless, and constructed from the Hessian of the Hamiltonian. I then show that the Schrödinger equation in the coherent-state phase-space formulation of certain bosonic QFTs has precisely this form, with the Husimi function playing the role of the phase space probability density. I then discuss to what extent this equation can be interpreted in terms of objective stochastic field trajectories and which obstacles remain for realizing the Einsteinian vision for the future of quantum theory.

Jena_Dresden.pdf