On the Observables Describing a Quantum Reference Frame

Abstract

A reference frame F is described by the element g of the Poincare' group P which connects F with a given fixed frame F_0. If F is a quantum frame, defined by a physical object following the laws of quantum physics, the parameters of g have to be considered as quantum observables. However, these observables are not compatible and some of them, namely the coordinates of the origin of F, cannot be represented by self-adjoint operators. Both these difficulties can be overcome by considering a positive-operator-valued measure (POVM) on P, covariant with respect to the left translations of the group, namely a covariance system. We develop a construction procedure for this kind of mathematical structure. The formalism is also used to discuss the quantum observables measured with respect to a quantum reference frame.

23 pages, no figures

References in corpus (2)

• Localization of Events in Space-Time
• Variance of the Quantum Coordinates of an Event

Cited by in corpus (6)

• Toy Model for a Relational Formulation of Quantum Theory
• The Time-Energy Uncertainty Relation
• Operational Quantum Reference Frame Transformations
• Events in a Non-Commutative Space-Time
• Another derivation of Weinberg's formula
• The Limits of Quantum Mechanics in the Light of the Genuine Fortuitousness Principle