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International Journal of Theoretical Physics

Minimal-disturbance measurement as a specification in von Neumann's quantal theory of measurement

Fedor Herbut

Published Nov 1, 1974• 18 citations
Publisher
DOI
10.1007/bf01809569

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As a series of investigations have shown, the interpretation of the change upon measurement in quantum mechanics described by the "projection pastulate", as a purely statistical formula, is clear. This formula, here denoted by VNL, is a version of the conditional expectation in Hilbert spaces, and this mathematical result can be given a salid physical interpretation in terlDl of quantum statistics. The problem of interpretation arises when the formula comes in for interpretation, as a description of what happens to (states of) individual systems in measurement. Usual interpretations see the formula VNL as a description of a class of measurement transformations which are "minimally disturbing". However, a series of arguments show that such an interpretation is seriouslf flawed. (See Teller (1983), Martínez (1988) and references therein.] In Martínez (1987) I have derived the formula VNL from simple physical assumptions in a lattice theoretical framework. The formula so derived describes individual state transformations of a certain type. The states involved are states that describe the properties a system has relative to magnitudes (measuring situations). In this paper I propase that the change of state on measurement deseribed by the formula VNL, as derived in (1987), can be understood as a change on individual states along the lines of Von Neumann's initial proposal for interpreting non-maximal measurements. I discuss the objections raised by Lüders and others to Von Neumann's idea and show that they do not apply to the interpretation proposed here. This proposal has the advantage, among others, that it does not need to reify a controversial class of "minimally disturbing measurement transformations".

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As a series of investigations have shown, the interpretation of the change upon measurement in quantum mechanics described by the "projection pastulate", as a purely statistical formula, is clear. This formula, here denoted by VNL, is a version of the conditional expectation in Hilbert spaces, and this mathematical result can be given a salid physical interpretation in terlDl of quantum statistics. The problem of interpretation arises when the formula comes in for interpretation, as a description of what happens to (states of) individual systems in measurement. Usual interpretations see the formula VNL as a description of a class of measurement transformations which are "minimally disturbing". However, a series of arguments show that such an interpretation is seriouslf flawed. (See Teller (1983), Martínez (1988) and references therein.] In Martínez (1987) I have derived the formula VNL from simple physical assumptions in a lattice theoretical framework. The formula so derived describes individual state transformations of a certain type. The states involved are states that describe the properties a system has relative to magnitudes (measuring situations). In this paper I propase that the change of state on measurement deseribed by the formula VNL, as derived in (1987), can be understood as a change on individual states along the lines of Von Neumann's initial proposal for interpreting non-maximal measurements. I discuss the objections raised by Lüders and others to Von Neumann's idea and show that they do not apply to the interpretation proposed here. This proposal has the advantage, among others, that it does not need to reify a controversial class of "minimally disturbing measurement transformations".