Two Approaches to Measurability Concept and Quantum Theory

TL;DR

This paper explores two approaches to the measurability concept in quantum theory, constructing measurable analogs of key quantum frameworks and proposing a more general, principle-independent definition applicable to both non-relativistic and relativistic cases.

Contribution

It introduces a new approach to quantum measurability, constructing measurable analogs of Fourier and Heisenberg pictures, and proposes a broader definition not reliant on the Uncertainty Principle.

Findings

Constructed measurable analogs of Fourier transformations.

Developed a measurable analog of the Heisenberg picture.

Proposed a generalized measurability concept applicable to various quantum regimes.

Abstract

In the present paper, in terms of the measurability concept introduced in the previous works of the author, a quantum theory is studied. Within the framework of this concept, several examples are considered using the Schrodinger picture; analogs of Fourier transformations from the momentum representation to the coordinate one and vice versa are constructed. It is shown how to produce a measurable analog of the Heisenberg picture. At the end of this paper the obtained results are used to substantiate another (more general) definition of the measurability concept that is not based on the Heisenberg Uncertainty Principle and its generalization, as it has been in the previous works of the author, and may be equally suitable for both non-relativistic and relativistic cases.