Constructivism and Operationalism in the Foundations of Quantum Mechanics

Abstract

The debate about constructivism in physics (and in quantum mechanics, in particular) has led to different kinds of questions that can be conventionally framed in two classes. One concerns the mathematics that is considered for the theoretical development of physics. The other is concerned with the experimental parts of physical theories. It is unnecessary to observe that the intersection between our two classes of problems is far from being empty. In this paper we will mainly deal with topics belonging to the second class. However, let us briefly mention some important problems that have been debated in the framework of our first class. For instance, the following:

• 1) to what extent do the undecidability and incompleteness results of classical mathematics affect fragments of physical theories, in such way as to have a “real physical meaning”?

• 2) are the mathematical arguments that seem to be essential for physics justifiable in the framework of traditional mathematical constructivism?

The first question has recently been investigated by Pitowski, Penrose, da Costa, Doria, Mundici, Svozil and others. As expected by most logicians, one can construct undecidable sentences whose physical meaning seems to be hardly questionable. This happens both in classical and in quantum mechanics.