Superposition of states in quantum theory

TL;DR

This paper proposes applying a general composition law, similar to that in special relativity, to quantum theory, potentially offering a new interpretation of quantum probabilities and expanding the mathematical framework.

Contribution

It introduces a novel composition law for quantum states, inspired by relativistic velocity addition, and explores its implications for quantum probability interpretation.

Findings

The composition law can be applied to quantum states.

It offers a new perspective on quantum probability.

Potential for a new interpretation of quantum mechanics.

Abstract

The most general mathematical law for summing bounded quantities is not the arithmetic law, but a composition law of which the summation law for velocities in special relativity is only one particular example. We believe that this composition law, should also be used in quantum theory. We present it with a few examples, we discuss its physical meaning and we show how it can be useful in quantum theory. We show in particular that its use may open the way for a new interpretation of the use of probabilities in quantum theory.