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Philosophy of Science

The Trouble with Superselection Accounts of Measurement

Mariam Thalos

Published Sep 1, 1998• 2 citations
Publisher

Abstract

A superselection rule advanced in the course of a quantum-mechanical treatment of some phenomenon is an assertion to the effect that the superposition principle of quantum mechanics is to be restricted in the application at hand. Superselection accounts of measurement all have in common a decision to represent the indicator states of detectors by eigenspaces of superselection operators named in a superselection rule, on the grounds that the states in question are states of a so-called classical quantity and therefore not subject to quantum interference effects. By this strategy superselectionists of measurement expect to dispense with use of projection postulates in treatments of measurement. I shall argue that superselection accounts of measurement are self-contradictory, and that treatments of infinite systems, if they can avoid the contradiction, are not true superselection accounts.

DOI
10.1086/392659

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A superselection rule advanced in the course of a quantum-mechanical treatment of some phenomenon is an assertion to the effect that the superposition principle of quantum mechanics is to be restricted in the application at hand. Superselection accounts of measurement all have in common a decision to represent the indicator states of detectors by eigenspaces of superselection operators named in a superselection rule, on the grounds that the states in question are states of a so-called classical quantity and therefore not subject to quantum interference effects. By this strategy superselectionists of measurement expect to dispense with use of projection postulates in treatments of measurement. I shall argue that superselection accounts of measurement are self-contradictory, and that treatments of infinite systems, if they can avoid the contradiction, are not true superselection accounts.
In quantum theory, physically measurable quantities of a microscopic system are represented by self-adjoint operators. However, not all of the self-adjoint operators correspond to measurable quantities. The superselection rule is a criterion to distinguish measurable quantities. Any measurable quantity must obey the superselection rules. By contraposition, any quantity which does not obey the superselection rules cannot be measured. Although some of superselection rules were proved, the raizon d'être of the superselection rules has been still obscure. In this paper we deduce the superselection rules from an assumption on symmetry property of measurement process. We introduce the notion of covariant indicator, which is a macroscopic observable whose value indicates the value of a microscopic object observable. We prove that if an object system has a quantity that is conserved during the measurement process, other quantities that do not commute with the conserved quantity are non-measurable by the covariant indicator. Our derivation of superselection rules is compared with the uncertainty relation under the restriction by a conservation law. An implication of the color superselection rule for the color confinement is discussed. It is also argued that spontaneous symmetry breaking enables a measurement that the superselection rule prohibits.
The superposition principle is a very basic ingredient of quantum theory. What may come as a surprise to many students, and even to many practitioners of the quantum craft, is tha superposition has limitations imposed by certain requirements of the theory. The discussion of such limitations arising from the so-called superselection rules is the main purpose of this paper. Some of their principal consequences are also discussed. The univalence, mass and particle number superselection rules of non-relativistic quantum mechanics are also derived using rather simple methods.
In quantum mechanics it is well known that, if any two states are superposed, they interfere with each other. It is true, we should not deny such interference in principle, but we may assert what follows. When two states different from each other in a great many degrees of freedom are superposed, the interference effect becomes obscure. If they are different in an infinitely many degrees of freedom, they do not interfere at all, and their superposition is nothing but a mere probability function. This assertion enables us to understand how the probability amplitude for a micro-system is converted into a probability function for a measuring apparatus in the cource of measurement.
With the exception of superselection rules, there are no known explicit violations of the Principle of quantum Superposition. However, quantum measurement and the emergence of classicality seem to imply that the Principle of Superposition is not universal, so perhaps new superselection rules or something similar wait to be found. This invites us to search for explicit violations of superposition, even in places where we expect it to hold. Given that many quantum measurement devices rely on atoms absorbing photons, these processes are natural places for a first search for such violations. We propose experiments designed to test whether the emission and absorption of photons by atoms may suppress the interference in certain conditions. If the atom is found, in certain situations, to absorb completely the photon, this would mean that in those situations the atom cannot exist or at least it cannot be stable as a superposition of states in which it absorbed the photon and it did not absorb it. Then we will have a new possibility to resolve the problem of measurement, and that of the emergence of classicality. A negative result would mean an additional confirmation of the Principle of Superposition in these particular cases.