FOUNDATIONS OF QUANTUM MECHANICS

VIII
THE MEASUREMENT PROBLEM
[. . . ] if one has to stick to these darn quantum jumps then I regret that I ever have taken
part in the whole thing.
— Erwin Schrödinger
In this final chapter we will elaborate on the most important interpretation problem, the measurement
problem, which has the subject of an ever-continuing series of publications. We will give
an introduction to Von Neumann’s quantum mechanical measurement theory and formulate the
measurement problem, we will go through a number of attempts to solve it, and finally we will
discuss some criticism of the theory.
VIII. 1
INTRODUCTION
The term ‘measurement’ plays a very special role in quantum mechanics, and we suggest a short
rereading of the first paragraphs of chapter V. It is remarkable that the term arises in the Von Neumann
postulates as described in chapter III, p. 41, ff. Both in the measurement postulate, specifying the
possible outcomes of measurement and giving a physical meaning to the probability measure which
is determined by the state vector, or the state operator, in terms of outcomes of measurement, and
in the projection postulate, establishing the evolution in time of the state at measurement, the term
‘measurement’ comes forward.
That special role also becomes apparent in the debates concerning the interpretation of the theory,
where it is frequently remarked that measurement ‘creates’ the value for a quantity, or that it causes a
sudden state change, as expressed by Dirac (1958, p. 36),
In this way we see that a measurement always causes the system to jump into an eigenstate
of the dynamical variable that is being measured, the eigenvalue this eigenstate
belongs to being equal to the result of the measurement.
From the perspective of classical physics, this is extremely unusual. In Newton’s theory of gravitation,
or the electrodynamics of Faraday and Maxwell, measurements are sometimes mentioned, as
suppliers of experimental facts, but never as specific types of operation on physical systems, needing
a separate treatment in the theory.
The point here is not only that measurements in classical physics, as is frequently stated, always
bring about a negligible or compensable disturbance of the system and therefore can remain outside
consideration, much more important is, that in in classical physics there is no distinction in principle