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Canadian Journal of Physics

Superselection rules, quantum measurement, and the Schrödinger's cat

Kay-Kong Wan

Published Jul 1, 1980• 20 citations
Publisher

Abstract

A precise formulation of superselection rules in quantum mechanics is presented. An explicit measurement model is then constructed using the idea of superselection rules so formulated. The model is free from the usual difficulties associated with the projection postulate and it also allows a measurement to be completed within finite time interval.

DOI
10.1139/p80-135

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•Jul 9, 2019•0 citations
A precise formulation of superselection rules in quantum mechanics is presented. An explicit measurement model is then constructed using the idea of superselection rules so formulated. The model is free from the usual difficulties associated with the projection postulate and it also allows a measurement to be completed within finite time interval.
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.
Some physicists believe that superselection rules should be implemented to get rid of inconsistencies when a theory is framed in terms of a new mathematical formulation, whilst others think that this new formulation should be modified instead of implementing those rules, at the expense of introducing additional mathematical structure. The outcome, however, is that we are still uncertain whether these rules should be implemented and how they should be interpreted and assessed from the philosophical point of view. Based on a detailed examination of the group-theoretic reformulation of (relativistic and non-relativistic) quantum mechanics that prompts physicists to impose superselection rules, I shall argue that the implementation of these rules involves serious heuristic and epistemological concerns. Considering this argument, I shall conclude that there are suitable philosophical reasons to claim that the implementation of superselection rules should be rejected and that there are certain circumstances when the formulation of a theory should be modified.
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.
For orthodox quantum systems, pure states correspond one-to-one to all one-dimensional subspaces and observables correspond one-to-one to all selfadjoint operators in the state space. A relaxation of this one-to-one correspondence will bring about superselection rules. A general formulation of superselection rules is technically complicated. 1 We shall adopt an intuitive approach here and limit our discussion to some special cases to see how superselection rules can be incorporated in a Hilbert space structure of quantum theory.