Measurements and Time Reversal in Objective Quantum Theory

Frederik Jozef Belinfante

J. L. Martin

F J Belinfante Oxford: Pergamon 1975 pp xix + 142 price £4.75 The author writes: ‘The purpose of this book was primarily to give a reply to … a large number of authors, about fundamental questions … ’ This is fair enough, and describes the book well. But it is inevitable, therefore, that the book should become a series of comments of varying character and depth – almost a commentary on the writings of other authors.

Chon-Fai Kam, Kai-Wen Wong

Time reversal $Θ$ squares to $-1$ on a half-integer spin, so every state is orthogonal to its time reverse. This sign has been read only from quantum objects. The equilibrium state loses it, but the classical record keeps it. For a detector that resolves handedness, the probabilities that one stretch of record is followed by the time reverse of another measure the cohomology class of time reversal, $Θ^2=\pm1$. Their matrix carries this sign in its signature, a topological integer that survives equal emission and absorption losses. A programmed emitter on quantum processors reads it in about $10^3$ shots.

P. M. Harrington, Andrew N. Jordan, Kater W. Murch

Simon Friederich, Mritunjay Tyagi

We explore whether quantum field theory can be understood as the statistical mechanics of a time-reversal-invariant stochastic generalization of Hamiltonian dynamics. The motivation for this project, started with this paper, is to assign sharp values to all observables and thereby avoid the quantum measurement problem. In classical mechanics, motion is deterministic and corresponds to an evolution of the phase space probability density according to Liouville's equation that is governed by first derivatives of the Hamiltonian in phase space. We derive a generalization of the Liouville equation with natural constraints -- namely, reduction to classical Hamiltonian dynamics as the stochasticity parameter $\hbar\mapsto0$, Fokker-Planck form for the probability density evolution, local Hamiltonian dependence, time-reversal invariance, energy conservation, and minimality -- which turns out to be a Fokker-Planck equation with a generalized diffusion matrix that is symmetric, traceless, and constructed from the Hessian of the Hamiltonian. We 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. The question to what extent this equation can be interpreted in terms of objective stochastic field theories is discussed in a companion paper.

Andrew Knight

In a recent paper, Żukowski and Markiewicz showed that Wigner's Friend (and, by extension, Schrödinger's Cat) can be eliminated as physical possibilities on purely logical grounds. I validate this result and demonstrate the source of the contradiction in a simple experiment in which a scientist S attempts to measure the position of object $|O\rangle = |A\rangle_S + |B\rangle_S$ by using measuring device M chosen so that $|A\rangle_M \approx |A\rangle_S$ and $|B\rangle_M \approx |B\rangle_S$. I assume that the measurement occurs by quantum amplification without collapse, in which M can entangle with O in a way that remains reversible by S for some nonzero time period. This assumption implies that during this "reversible" time period, $|A\rangle_M \neq |A\rangle_S$ and $|B\rangle_M \neq |B\rangle_S$ -- i.e., the macroscopic pointer state to which M evolves is uncorrelated to the position of O relative to S. When the scientist finally observes the measuring device, its macroscopic pointer state is uncorrelated to the object in position $|A\rangle_S$ or $|B\rangle_S$, rendering the notion of "reversible measurement" a logical contradiction.