The Statistical Interpretation of Quantum Mechanics

The topic of this inquiry is the foundation of the statistical interpretation of quantum mechanics, the inter-pretation used, explicitly or implicitly, in all practical applications of quantum theory. Although it was thefirst consistent interpretation of the quantum formalism and had eminent supporters as Born, Einstein, orSchrödinger, there was, from the outset, a deeply rooted dissatisfaction with the probabilistic character ofthe quantum mechanical predictions inciting the search for alternatives. The most prominent among theseis the so-called Copenhagen interpretation developed by Bohr, Heisenberg, Pauli, and others asserting thata pure quantum state does not describe an ensemble of physical systems as it is stated by the statisticalinterpretation, but provides a complete description of an individual system, and that a quantum system canbe grasped only in complementary classical pictures. At present, the statistical interpretation is consideredone of several different but more or less equally founded interpretations. This is clearly no satisfactorystate of affairs all the more as Copenhagen type of interpretations are plagued by all kinds of ’fundamentalproblems’ completely absent in the statistical interpretation. Moreover, the interpretation of the quantummechanical formalism should be based on better foundations than just on mere convenience or on the matterof taste. Such a better foundation is provided by the fact that physical statements are universal i.e. thatphysical laws do not relate directly to individual physical systems but to experimental arrangements, wholeclasses of similar physical systems, and to an individual system only insofar as it is a member of such aclass. The most general physical statement is, therefore, a probability prediction for the outcome of a singleexperiment, which is the point of view of the statistical interpretation of quantum mechanics. In contrast to classical theories, the statistical interpretation of quantum mechanics can cope with the exper-imental fact that certain physical processes, e.g. radioactive decays, are causal but basically indeterministic.In accordance with classical theories, the statistical interpretation of quantum mechanics is compatible witha realistic and objective view of the physical world. Realism and objectivity mean in physics that the valuesof all observables of an individual, material system are always definitely given and objective properties ofthat system and that these values can be determined with appropriate measurements. Classical and quan-tum theories rest on the same epistemological foundations and are devised for the same purpose namelyto provide predictions of the properties of material physical systems. They are similar in this respect. Itis, however, important to be aware of the structural peculiarities of these two classes of physical theories.The decisive difference is that the observables form a commutative algebra in classical theories, whereasthe algebra of quantum mechanical observables is not commutative. As a consequence, the values of non-commuting quantum mechanical observables cannot be simultaneously definitely predicted (Heisenberg’suncertainty relations). The structural difference between classical and quantum theories cannot be bridged:there are no classical hidden variables models of quantum theories if the dimension of their Hilbert spaceis greater than two. A related, even more important consequence is that there exist physical systems, whichpossess a quantum mechanical but no classical description, e.g. all spin systems of total spin greater or equalthan one.