Physical foundations of quantum theory: Stochastic formulation and proposed experimental test

V. J. LeO

The time-dependent Schrddinger equation has been derived from three assumptions within the domain o f classical and stochastic mechanics. The continuity equation is not used in deriving the basic equations o f the stochastic theory as in the literature. They are obtained by representing Newton's second law in a time-inversion consistent equation. Integrating the latter, we obtain the stoehastie Hamilton-Jacobi equation. The Schr6dinger equation is a result o f a transformation o f the Hamihon-Jacobi equation and linearization by assigning the arbitrary constant h : 2mD. An experiment is proposed to determine h and to test a hypothesis o f the theory directly. A mathematical apparatus is formulated from the Jacobian formalism to derive physical parameters from ¢(x, t) and to obtain operators for the boundary eases o f the theory. The operator formalisms are compared by means o f a well-known solution in the quantum theory.

Luigi Accardi

M. D. Srinivas

Statistical physical theories are frequently formulated in terms of probabilistic structures founded on a ’’logic of experimentally verifiable propositions.’’ It is argued that to each experimentally verifiable proposition there corresponds an experimental procedure which, in general, alters the state of the system, and is completely characterized by a ’’measurement transformation’’ or ’’operation.’’ An analysis of the relations among these experimental procedures leads us to a ’’logic of operations’’ which is quite different from the ’’lattice theoretic logics’’ that are often considered (albeit inadequate empirical justification), as models for the calculus of experimentally verifiable propositions of quantum theory. It is seen that the quantum probability theory based on the logic of operations provides the proper mathematical framework for discussing the statistics of successive observations in quantum theory. We also indicate how a theory of quantum stochastic processes can be formulated in a way similar to the Kolmogorov formulation of the classical theory.

Anastasios Kyprianidis

David Deutsch

Claims that the standard procedure for testing scientific theories is inapplicable to Everettian quantum theory, and hence that the theory is untestable, are due to misconceptions about probability and about the logic of experimental testing. Refuting those claims by correcting those misconceptions leads to an improved theory of scientific methodology (based on Popper׳s) and testing, which allows various simplifications, notably the elimination of everything probabilistic from the methodology (‘Bayesian’ credences) and from fundamental physics (stochastic processes). • Everettian quantum theory is testable. • Stochastic theories suffer from a flaw in the logic of their testability. • Popper׳s methodology is needed to understand the testability of quantum theory.

Junichiro Fukai