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Papers by Alexander Santman
Foundations of Physics, 1979
Foundations of Physics, 1979
The problem of simultaneous measurement of incompatible obseruables in quantum mechanics is studi... more The problem of simultaneous measurement of incompatible obseruables in quantum mechanics is studied on the one hand from the uiewpoint ofan e:;illrt, i,treet*lenl of quanlum mechanic-c and on !h: ttlter 4snd :;tc.t!it:. i,.:,.: .. theory of measurement. It is argued that it is preciseiy sucit c iheory of measurement thct should prouide a meaning to the axiomatically introduced c'oncepts, especially to the concept of obseruable. Defining an obseruable as a class of measurement procedures yielding a certain prescribed result for the probability distribution of the set of talues of some quantity (to be desuibed by the set of eigenualues of some Hermitian operator), this notion is extended to joint probability distributions of incompatible obseruables. It is shown that such an extension is possible on the basis of a theory of measurement, under the profiso that in simultaneously measuring such obseruables there is a disturbance of the measurement results of the one obseroable, caused b,,-the presence of the measuring instrument of the other obseruable. This has as a consequence that the joint probability distribution cannot obey the marginal distribution laws usually imposed. This result is of great importance in exposing quantum mechanics as an axiomatized theory, since ouerlooking it seems to prohibit an axiomatic description of simultaneous measurement of inconpatible obsert:ables by quantum mechanics.
Foundations of Physics, 1979
Foundations of Physics, 1979
The problem of simultaneous measurement of incompatible obseruables in quantum mechanics is studi... more The problem of simultaneous measurement of incompatible obseruables in quantum mechanics is studied on the one hand from the uiewpoint ofan e:;illrt, i,treet*lenl of quanlum mechanic-c and on !h: ttlter 4snd :;tc.t!it:. i,.:,.: .. theory of measurement. It is argued that it is preciseiy sucit c iheory of measurement thct should prouide a meaning to the axiomatically introduced c'oncepts, especially to the concept of obseruable. Defining an obseruable as a class of measurement procedures yielding a certain prescribed result for the probability distribution of the set of talues of some quantity (to be desuibed by the set of eigenualues of some Hermitian operator), this notion is extended to joint probability distributions of incompatible obseruables. It is shown that such an extension is possible on the basis of a theory of measurement, under the profiso that in simultaneously measuring such obseruables there is a disturbance of the measurement results of the one obseroable, caused b,,-the presence of the measuring instrument of the other obseruable. This has as a consequence that the joint probability distribution cannot obey the marginal distribution laws usually imposed. This result is of great importance in exposing quantum mechanics as an axiomatized theory, since ouerlooking it seems to prohibit an axiomatic description of simultaneous measurement of inconpatible obsert:ables by quantum mechanics.