Constructive Mathematics and Quantum Physics

Antonino Drago

M. Esfahanian

The objective of this paper is to show that non-constructive mathematics is incapable as a framework for research on consciousness. Indeed, we shall discuss how non-constructive mathematics is inconsistent with the physics of consciousness which deals with quantumness. This inconsistency implies the incapability of non-constructive mathematics to represent the free will of a conscious agent. Furthermore, we shall suggest Constructive mathematics (and topos theory which is one of its models) as an alternative framework to study consciousness. The pivotal role of the excluded middle law in our discussion will be addressed in detail.

Cécile de Witt-Morette

Bengy Tsz Tsun Wong

Dualism is a metaphysical, philosophical concept which refers to two irreducible, heterogeneous principles. This idea is known to appear in a lot of places in the universe, however a rigorous mathematical definition and is not yet established in a formal way. In this paper, we develop a novel to represent philosophical dualism in a formal mathematical construction with the context of quantum physics, known as the theory of duality. We will use traditional Chinese philosophical concepts in duality as the foundation as it greatly resembles to the mathematical and physical construction for our purpose. This paper will demonstrate how to convolve metaphysical idea into mathematics and physics.

Wesley E. Brittin, A.Y. Sakakura

A systematic account of projection operators (projectors) and orthogonalization techniques together with applications to selected areas of physics is presented. This unified approach is shown to have advantages over other approaches in that the mathematical statements are more precise. The mathematical level, however, is aimed at the practicing physicist and lies between rigorous mathematics and current use in physics. Further, the techniques presented have practical applications as is demonstrated by examples in the quantum theory of measurement, in the relationship between second quantization and configuration space techniques, and in an account of generalized Wannier and Bloch functions. Attention is paid to the problem of construction of orthogonal projection operators (orthogonal projectors). The construction of orthogonal projectors even in approximate form would allow the solution of many practical problems ranging from the eigenvalue spectrum problem to the construction of states for many-body systems. One can almost say that any problem in quantum mechanics can be formulated as a problem involving the construction of projectors.

Manahel Thabet