The Statistical Interpretation of Quantum Mechanics

The topic of the present inquiry is the foundation of the statistical interpretation of quantum mechanics, the
interpretation used, explicitly or implicitly, in all practical applications of quantum theory. Although it was
the first coherent interpretation of the complete quantum formalism and had eminent supporters as Born,
Einstein, or Schrödinger, there was, from the outset, a deeply rooted dissatisfaction with the probabilistic
character of its predictions inciting the search for alternatives. The most prominent among these is the so-
called Copenhagen interpretation developed by Bohr, Heisenberg, Pauli, and others asserting that a pure
quantum state does not describe an ensemble of physical systems as does the statistical interpretation, but
provides a complete description of an individual system and that a quantum system can be only grasped in
complementary classical pictures. At present, the statistical interpretation is considered as one of several
different, but more or less equally founded interpretations. This is clearly no satisfactory state of affairs
all the more than Copenhagen type of interpretations are plagued by all kinds of ’fundamental problems’
completely absent in the statistical interpretation. Moreover, the interpretation of the quantum mechanical
formalism should be based on better foundations than just on mere convenience or on the matter of taste.
Such a better foundation is provided by the fact that physical laws do not relate directly to individual physical
systems but to experimental arrangements, whole classes of similar physical systems, and to an individual
system only insofar as it is a member of such a class. The most general physical statement is, therefore,
a probability prediction for the outcome of single experiments revealing the statistical interpretation of
quantum mechanics as the correct and fundamental one.
The statistical interpretation of quantum mechanics considers the experimental fact that physical processes
are causal but basically indeterministic in contrast to the causal and determinstic classical theories. The sta-
tistical prognoses of quantum theories are objective properties of the experimental arrangement considered,
and observable values are definite, objective properties of concrete, individual systems. These properties of
of an individual physical system always have definite values which may be determined by suitable measure-
ments, but it is not possible to prepare the system in such a way that all observable values can be sharply
predicted because of the noncommutativity of the quantum mechanical observable algebra. This indicates
a limitation on principle of human command on nature. The concepts of objectivity and realism accord
with the status of physics as the base science of engineering and technology. It is shown that these con-
cepts do not entail paradoxes or contradictions in the statistical interpretation of quantum mechanics. It is
shown that classical hidden variables theories, supposed to underly quantum theories, do not exist if the
quantum mechanical Hilbert space has dimension bigger than two. Quantum indeterminism is intrinsic,
not reducible to mere subjective ignorance. In particular, there is no hidden variables model for Bohm’s
setting of the Einstein-Podolsky-Rosen thought experiment, be the model local or nonlocal, or whether it
should reproduce quantum mechanical predictions or not. As a consequence, ’nonlocality proofs’ for quan-
tum mechanics based on Bell’s inequality are not conclusive. In the statistical interpretation, the quantum
mechanical description of isolated, free systems is, fortunately, strictly local.