Earman, John
(2022)
A Guide to the Bargmann Mass Superselection Rule: Why There Is--and Isn't--Mass Superselection in Non-Relativistic Quantum Mechanics.
[Preprint]
Abstract
What became known as the Bargmann mass superselection rule for non-relativistic quantum mechanics arose from a exercise, set by Arthur Wightman in 1959, to demonstrate that "superposition of two states with different mass gives a state whose existence in Nature would contradict Galilean invariance (Bargmann's Superselection Rule)." A solution to the exercise in the form of a heuristic argument first appeared in journal articles and was then repeated in textbooks. Subsequently, however, attacks on the rule were launched from various directions, and perusing the literature, old and new, leaves one with the impression that the rule enjoys an uncertain status. The goal here is to explain the sense in which there most certainly is a mass superselection rule for ordinary quantum mechanics, as well as a sense in which there isn't a superselection rule for mass. Reaching this goal requires a careful look at the nature of superselection rules and the meaning of Galilean invariance in ordinary quantum mechanics.
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