New Interpretations of Quantum Mechanics and the Theory of Knowledge

Roland L. Omnes

Frederico Rodrigues Pfrimer

What is the nature of reality? How should be an answer to this question? At this level, we are so deep that all our concepts are obscure. Quantum theory (QT) is at this level. The quest for interpreting it fails because the clarity of our actual fundamental concepts in ordinary language cannot match the precision of the theory's mathematical formalism. The interpretation of quantum mechanics should define and bring clarity to fundamental concepts; not simply rely over them. Quantum theory requires a new worldview, the one that will make it understandable. We discuss on the formulation and interpretation of closed, and final theories, in other words, completely axiomatic theories that define their own conceptual framework, and closed theories that cannot be made simpler. We claim that everything we can properly say about a theory follows from its interpretation, and that interpreting is saying the meaning of each of its mathematical statements. We argue that quantum mechanics is a closed theory; and, therefore, that part of it is part of the final or fundamental theory of physics (FTP). We propose a new entirely axiomatic formulation of part of quantum theory (including all its mathematical framework) in which new powerful and useful elements are added to the existing formalism. Our interpretation is straightforward: it allows us reading or saying the meaning of each of the theory's axiom, theorem or element. We state that the proposed theory is the FTP. Its interpretation may dissolve most of the existing paradoxes around QT. The principle of excluded middle is not valid in general. Both epistemic and ontic elements are present in the theory since it is a theory of knowledge and truth. This and other fundamental concepts are defined by the theory, which can represent both reality and our knowledge about it. Aesthetics is one of its key features.

Roland L. Omnes

Germano Resconi, Blagovest A. Nikolov

We propose a new interpretation of Dempster-Shafer theory of evidence based on a stochastic model for a quantum system developed in terms of amplitude on entities. An entity provides an axiomatic description for the set of tests and states of a physical system and an amplitude density gives a mean for computing probability and pseudo-probability within this framework. The interference and independence of tests relative to an amplitude density are formulated. Various ways of combining entities and amplitudes are presented as superpositions of amplitude. We propose to extend the theory of evidence also to the physical observable experiment in quantum mechanics. So we can use, for quantum mechanics, all the knowledge in the evidence theory. On the contrary the knowledge in the evidence theory can give new insight in the quantum mechanics uncertainty. We give a modal logic interpretation of evidence theory and entity and tests definitions. We establish a bridge between mental approach to uncertainty by evidence theory and the physical phenomena represented by quantum mechanics. When one use the amplitude density in the evidence theory one can generate a new interpretation of joint and conditional definition of the basic probability assignment ( pseudo-probability).

Eugene Paul Wigner

John Hemp

Abstract In the 1950s and 1960s it was causing interest among physicists that in the formalism of quantum mechanics (complex-valued) ‘probability amplitudes’ obeyed laws similar to the laws obeyed by probabilities in the ordinary probability calculus. But this did not then lead decisively to the claim that probabilities should be represented by complex numbers. It became fashionable instead to regard probability amplitudes as an abstract concept from which actual probabilities could be derived by taking the squared moduli of the amplitudes. In this monograph, however, we make another attempt to show how probability amplitudes might after all be identified with actual probabilities. To do this, probability itself is interpreted in a rational Bayesian manner (i.e. as an extension of logic) and a new (complex-valued) probability theory is formulated that incorporates the uncertainty principle (i.e. that takes account of the fact that acquisition of knowledge of a quantum mechanical process generally interferes with it). Taking this probability theory as the new logic of science, and assuming certain physical laws and properties of matter, an interpretation of non-relativistic quantum mechanics is built up. It is consistent with the usual quantum mechanical formalism but allows a clear distinction to be made between the physical world and our knowledge of it.