Abstract

Review of "The Collected Works of Eugene Paul Wigner", Volume I, III, and VI. Excerpt from the Conclusions: Many of Wigner’s papers on mathematical physics are great classics. Most famous is his work on group representations which is of lasting value for a proper mathematical foundation of quantum theory. The modern development of quantum theory (which is not reflected in Wigner’s work) is in an essential way a representation theory (e.g. representations of kinematical groups, or representations of C*-algebras). This view owes very much to Wigner’s seminal papers on the unitary representations of compact and noncompact groups. Wigner showed much courage in relating the then unresolved questions of the measurement problem to the much deeper problem of consciousness. In view of this very unorthodox proposal it is astonishing that Wigner was very reactionary with respect of the dogmas of orthodox quantum mechanics. In contrast to von Neumann himself, he took the old von-Neumann codification of quantum mechanics as authoritative and not to be questioned. Much of the efforts to interpret the meaning of this codification and to prove no-go theorems, such as the insolubility of the measurement problem or the impossibility of a quantum theory of individual objects, are physically irrelevant since they are based on a codification of quantum mechanics that is valid only for strictly closed systems with finitely many degrees of freedom. However, in nature there are no such systems. Every material system is coupled to the gravitational and to the electromagnetic field – systems which require in a Hamiltonian description infinitely many degrees of freedom. A deeper insight into the conceptual problems of quantum theory is possible only if the modern development of a quantum theory of infinite systems is taken into account.