Probabilistic Interpretation of Quantum Mechanics

Slavnov D. A

It is shown that probabilistic treatment of quantum mechanics can be coordinated with causality of all physical processes. The physical interpretation of quantum-mechanical phenomena such as process of measurement and collapse of quantum state is given.

Bryce de Witt

Shiro Ishikawa

Recently we proposed "quantum language" (or, "the linguistic Copenhagen interpretation of quantum mechanics", "measurement theory") as the language of science.This theory asserts the probabilistic interpretation of science (=the linguistic quantum mechanical worldview), which is a kind of mathematical generalization of Born's probabilistic interpretation of quantum mechanics.In this paper, we consider the most fundamental problems in philosophy of science such as Hempel's raven paradox, Hume's problem of induction, Goodman's grue paradox, Peirce's abduction, flagpole problem, which are closely related to measurement.We believe that these problems can never be solved without the basic theory of science with axioms.Since our worldview (=quantum language) has the axiom concerning measurement, these problems can be solved easily.Thus we believe that quantum language is the central theory in philosophy of science.Hence there is a reason to assert that quantum language gives the mathematical foundations to science.

Mário J. de Oliveira

Leon W. Cohen

Алессандро Струмиа

The Born postulate can be reduced to its deterministic content that only applies to eigenvectors of observables: The standard probabilistic interpretation of generic states then follows from algebraic properties of repeated measurements and states. Extending this reasoning suggests an interpretation of quantum mechanics generalized with indefinite quantum norm.