The Algebra of the Pseudo-Observables III: Transformations and Time Evolution

TL;DR

This paper extends the algebra of pseudo-observables to include transformations and time evolution, offering a new formalism that parallels and enhances traditional quantum mechanics approaches, with insights into time reversal and measurement.

Contribution

It introduces a novel algebraic framework for quantum transformations and time evolution, providing deeper insights and minor modifications to existing Dirac-Jordan theory.

Findings

Time evolution treated with minor modifications to Dirac-Jordan theory

Introduction of time reversal offers new insights into Hermitian transposition

Discussion on the relationship between time evolution and measurement

Abstract

This paper is the third part concluding the introduction of the powerful algebra of the pseudo-observables. In this article will be dealt how to treat the time evolution, and, more in general, the transformations, in the framework of the new theory. It will be shown that this requires only minor changes with respect to the Dirac-Jordan transformation theory that can be found in almost any textbook, with some more care about the treatment of the continuous limit. A remarkable difference is also in the introduction of the time reversal, which gives the opportunity to a deeper insight about the Hermitian transposition. In the conclusions, we will examine better the relationship between time evolution and measurement, a very problematic aspect in the framework of the Copenhagen interpretation (and in many others ones). Finally we will present a list of compelling reasons for which the physics community would seriously have to evaluate a switching to the new formalism.