On statements of experimental results expressed in the mathematical language of quantum theory

TL;DR

This paper explores the dual nature of quantum experimental descriptions, highlighting the multiplicity of explanations and results, and discusses how this ambiguity influences the understanding of invariance and control parameters in quantum physics.

Contribution

It introduces the concept that quantum descriptions form a family of related explanations and results, emphasizing the implications for invariance and the role of control parameters.

Findings

Quantum descriptions are part of a family of related explanations.

Statements of results induce topologies on control parameters.

Ambiguity in descriptions is fundamental to invariance in physics.

Abstract

We note the separation of a quantum description of an experiment into a statement of results (as probabilities) and an explanation of these results (in terms of linear operators). The inverse problem of choosing an explanation to fit given results is analyzed, leading to the conclusion that any quantum description comes as an element of a family of related descriptions, entailing multiple statements of results and multiple explanations. Facing this multiplicity opens avenues for exploration and consequences that are only beginning to be explored. Among the consequences are these: (1) statements of results impose topologies on control parameters, without resort to any quantum explanation; (2) an endless source of distinct explanations forces an open cycle of exploration and description bringing more and more control parameters into play, and (3) ambiguity of description is essential to the concept of invariance in physics.