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PHYSICS AND REALITY 317
semble of systems" in the sense of statistical mechanics. If,
except for certain special cases, the 1jJ function furnishes only
statistical data concerning measurable magnitudes, the reason
lies not only in the fact that the operation of measuring introduces
unknown elements, which can be grasped only statistically,
but because of the very fact that the 1jJ function does not,
in any sense, describe the state of one single system. The
Schriidinger equation determines the time variations which are
experienced by the ensemble of systems which may exist with
or without external action on the single system.
Such an interpretation eliminates also the paradox recently
demonstrated by myself and two collaborators, and which relates
to the following problem.
Consider a mechanical system consisting of two partial systems
A and B which interact with each other only during a
limited time. Let the 1jJ function before their interaction be
given. Then the Schriidinger equation will furnish the 'ljl function
after the interaction has taken place. Let us now determine
the physical state of the partial system A as completely as
possible by measurements. Then quantum mechanics allows
us to determine the 'ljl function of the partial system B from
the measurements made, and from the 'ljl function of the total
system. This determination, however, gives a result which depends
upon which of the physical quantities (observables) of A
have been measured (for instance, coordinates or momenta).
Since there can be only one physical state of B after the interaction
which cannot reasonably be considered to depend on the
particular measurement we perform on the system A separated
from B it may be concluded that the 1jJ function is not unambiguously
coordinated to the physical state. This coordination
of several 1jJ functions to the same physical state of system B
shows again that the 1jJ function cannot be interpreted as a
(complete) description of a physical state of a single system.
Here also the coordination of the 1jJ function to an ensemble of
systems eliminates every difficulty.·
,.. A measurement on A, for example. thus involves a transition to a narrower
ensemble of systems. The latter (hence also its '11 function) depends upon the
point of view according to which this reduction of the ensemble of systems is
carried ou t.