20pRC-1 Separable states with a definite relative phase of macroscopic systems subject to the charge supereselection rule

G. C. Wick, Arthur S. Wightman, Eugene Paul Wigner

The customary notion of superselection rule stipulates the vanishing of those matrix elements of the density matrix that connect states separated by the superselection rule, i.e., the relative phases of which are, according to the superselection rule, meaningless. It is shown that, if any two states for which an additive conserved quantity has different values are separated for all physical systems by a superselection rule at one time, the separation will persist for all times. It is concluded that the states with different electric (or baryonic) charges are so separated. The reason for the difference between electric charge and other additive conserved quantities, such as momentum, is brought out.

Jean-Pierre Provost, F. Rocca, Gérard Vallée

Edwin C. Kemble

Von Neumann's macroscopic entropy definition is not wholly satisfactory because ($a$) it rests on an unsatisfactory characterization of macroscopic variables, ($b$) it fails to make satisfactory connection with the Nernst heat theorem, ($c$) it is based on an unsatisfactory definition of thermal equilibrium, ($d$) it is not applicable to microscopic systems. It is proved that if two systems initially in independent states are placed in thermal contact and isolated, the sum of their microscopic entropies cannot decrease, but will in general increase. This theorem is a substitute for the usual rule regarding the increase in entropy of a single isolated system. Appreciable departures from the canonical state are shown to have a vanishingly small probability in the case of a system subjected to the thermostat experimental procedure described in a preceding paper.

Paul Tappenden

Objective probability in quantum mechanics is often thought to involve a stochastic process whereby an actual future is selected from a range of possibilities. Everett's seminal idea is that all possible definite futures on the pointer basis exist as components of a macroscopic linear superposition. I demonstrate that these two conceptions of what is involved in quantum processes are linked by two alternative interpretation of the mind-body relation. This leads to a fission, rather than divergence, interpretation of Everettian theory and to a novel explanation of why a principle of indifference does not apply to self-location uncertainty for a post-measurement, pre-observation subject, just as Sebens and Carroll claim. Their Epistemic Separability Principle is shown to arise out of this explanation and the derivation of the Born rule for Everettian theory is thereby put on a firmer footing.

L.W.J. den Ouden, Hans W. Capel, Jacques H. H. Perk +1 more