FOUNDATIONS OF QUANTUM MECHANICS

I. 1. INTRODUCTION 9
of affairs. [. . . ] Its acceptance would lead to an attempt to obtain a complete description
of the real state of affairs as well as the incomplete one, and to discover physical laws
for such a description. The theoretical framework of quantum mechanics would then be
exploded.
(b) In reality the particle has neither a definite momentum nor a definite position; the description
by [the] ψ - function is, in principle, a complete description. The strictly defined
position of the particle, obtained by measuring the position, cannot be interpreted as the
position of the particle prior to the measurement. The sharp localization which appears as
a result of the measurement is brought about only as a result of the unavoidable (but not
unimportant) operation of measurement. The result of the measurement depends not only
on the real particle situation but also on the nature of the measuring mechanism, which
in principle is incompletely known. An analogous situation arises when the momentum
or any other observable quantity relating to the particle is measured.
Interpretation (b) is accepted by the majority of the physicists and Einstein admits
[. . . ] it alone does justice in a natural way to the empirical state of affairs expressed in
Heisenberg’s principle within the framework of quantum mechanics.
Nevertheless, he emphasizes his preference for interpretation (a). His argument is that it is basic
to physics that physical concepts refer to entities, such as particles, fields, etc., that exist independently
of the observer, and are situated in space and time. Interpretation (b) renders this kind of
description impossible. A second argument has to do with composite systems and will be discussed
in section I. 2.
(iii) The next example, also originating from the correspondence between Einstein and Born
(Born 1971, pp. 188, 208 - 209), concerns a freely moving macroscopic object, for instance a star.
A simple Schrödinger equation applies to the center of mass of such a body, namely that of a free
particle. Since all wave functions which are solutions of the Schrödinger equation are admissible,
one may consider as a solution a wave function with two peaks of equal size, located far from each
other.
Upon measurement of the position of the center of mass of such a body, the outcome is found at
one peak in about half of the measurements, in the other half the outcome is found at the other peak.
In this case it is tempting to say that for half of these measurements the center of mass was at that
one position, that the object was at that position, while at the other half the center of mass was at the
other position. But according to the standard interpretation this is incorrect: prior to the measurement
no position can be assigned to the center of mass. Quantum mechanics applies just as well to the
center of mass of a macroscopic body as to an electron. It is, however, difficult to imagine how a
measurement ‘creates’ the position of the center of mass of a star as a result of a disturbance in the
order of the size of one single quantum .
According to Pauli, one of the representatives of the Copenhagen interpretation, this is a creation
outside the laws of nature (ibid., p. 223). The laws of nature only say something about the statistics
of the outcomes. The quantum mechanical probability description does not express our ignorance
concerning the position of the center of mass of the body; the probability description corresponds