Crítica, Revista Hispanoamericana de Filosofía, Volumen 20, número 60, Diciembre 1988
Mediciones ideales en la mecánica
Instituto de Investigaciones Filosóficas
Universidad Nacional Autónoma de México
Resumen: 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
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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".