A Second Foundation for Quantum Theory

Abstract

As shown in a previous paper ², the combination of complementarity logic and probability calculus is sufficient to establish the essential features of the general formalism of quantum theory, known as statistical transformation theory. The advantages of this way of founding quantum theory as compared to other procedures lie in the following:

• (1) The complex-valuedness of the state vectors (unitary metric) is seen to be a direct consequence of complementarity logic.³

• (2) The concept of physical quantity is reduced to the more general concept of physical property. Hence it can be proved that the operators representing physical quantities must be hypermaximal.

• (3) The existence of a Hamiltonian is not required.

Translated from ‘Eine zweite Begruendung der Quantentheorie’, Monatsber. Dtsch. Akad. Wiss. Berlin 3 (1961), 532–534.

The basic idea underlying the new foundation outlined in this paper has first been presented to the Internationales Symposium anlaesslich der 550-Jahr Feier der Karl-Marx- Universitiit Leipzig in October 1959; cf. M. Strauss, ‘Quantentheorie und Philosophie’ in Naturwissenschaft und Philosophie (ed. by G. Harig and 1. Schleifstein), Berlin 1960 [Chapter XX this volume]. The first presentation in extenso was given to an ad-hoc Colloquium in the Max-Planck-Institutfur Physik und Astrophysik in Munich, May 1961. The author is indebted to Professor W. Heisenberg [and his co-workers] for the hospitality extended to him.