Nonlocal Quantum Field Theory and Stochastic Quantum Mechanics

W. Garczyński

Millard Baublitz

Electron field-emission experiments conclusively eliminate a family of classical stochastic theories that have been proposed as alternatives to quantum mechanics. Modified stochastic theories with certain nonlocal interactions may be postulated and may agree with the experimental data, but these revised theories should not be described as classical stochastic theories.

Sheldon Goldstein

Matthias Lienert

Pilot wave theory (PWT), also called de Broglie-Bohm theory or Bohmian Mechanics, is a deterministic nonlocal `hidden variables' quantum theory without fundamental uncertainty. It is in agreement with all experimental facts about nonrelativistic quantum mechanics (QM) and furthermore explains its mathematical structure. But in general, PWT describes a nonequilibrium state, admitting new physics beyond standard QM. This essay is concerned with the problem how to generalise the PWT approach to quantum field theories (QFTs). First, we briefy state the formulation of nonrelativistic PWT and review its major results. We work out the parts of its structure that it shares with the QFT case. Next, we come to the main part: We show how PW QFTs can be constructed both for field and particle ontologies. In this context, we discuss some of the existing models as well as general issues: most importantly the status of Lorentz invariance in the context of quantum nonlocality. The essay concludes with a more speculative outlook in which the potential of PWT for open QFT questions as well as quantum nonequilibrium physics are considered.

Luis de la Peña, Ana Marı́a Cetto

Luis de la Peña, Ana Marı́a Cetto, Andrea Valdés-Hernández

We study the behavior of the atomic matter immersed in a zero-point radiation field, which is taken as the source of the endless stochastic motion of electrons. The starting point is a statistical phase-space equation for a particle in interaction with the field. Under certain natural approximations, the system reaches a stationary condition; the corresponding reduced description obtained in configuration space is just the Schrodinger quantum mechanics. Quantum nonlocality is revisited from this point of view and is shown to appear as an artifact of the reduced description. The theory presented also serves to explain why usual quantum mechanics is not amenable to a phase-space formulation.