Quantum Reference Frames and Quantum Transformations

TL;DR

This paper explores the concept of quantum reference frames, examining their mathematical structure and highlighting the importance of internal degrees of freedom, which differ from classical frames and require new approaches.

Contribution

It introduces a framework for understanding quantum reference frames, showing they cannot be fully described by classical groups and necessitate new mathematical structures.

Findings

Quantum frames involve internal degrees of freedom.

Classical Poincare' group is insufficient for quantum frames.

Quantum group structures are considered but found inadequate.

Abstract

A quantum frame is defined by a material object subject to the laws of quantum mechanics. The present paper studies the relations between quantum frames, which in the classical case are described by elements of the Poincare' group. The possibility of using a suitable quantum group is examined, but some arguments are given which show that a different mathematical structure is necessary. Some simple examples in lower dimensional spacetimes are treated. They indicate the necessity of taking into account some "internal" degrees of freedom of the quantum frames, that can be disregarded in a classical treatment.