Intuitionistic interpretation of quantum mechanics

TL;DR

This paper proposes an intuitionistic interpretation of quantum mechanics by linking the law of excluded middle to the decidability of the Schrödinger equation, allowing for a non-classical logical framework that abandons quantum fundamentalism.

Contribution

It introduces a novel logical interpretation of quantum mechanics based on intuitionism, connecting the undecidability of the Schrödinger equation to the rejection of classical logic principles.

Findings

The decision problem of the Schrödinger equation is generally undecidable.

The law of excluded middle applies only if quantum fundamentalism holds.

An intuitionistic framework allows for statements without definite truth values.

Abstract

In the present paper, the decision problem of the Schr\"odinger equation (asking whether or not a given Hamiltonian operator has the nonempty solution set) is represented as a logical statement. As it is shown in the paper, the law of excluded middle would be applicable to the introduced statement if and only if quantum fundamentalism (asserting that everything in the universe is ultimately describable in quantum-mechanical terms) held. But, since the decision problem of the Schr\"odinger equation is in general undecidable, such a statement is allowed to be other than true or false, explicitly, it may fail to have truth values at all. This makes possible to abandon the law of excluded middle together with quantum fundamentalism in the proposed intuitionistic interpretation of quantum mechanics.