Quantum reference frames, time and measurements

Sergey Nikolaevich Mayburov

S.N. Maiburov

Pierre Martin-Dussaud

Luca Apadula, Esteban Castro-Ruiz, Časlav Brukner

Since their first introduction, Quantum Reference Frame (QRF) transformations have been extensively discussed, generalising the covariance of physical laws to the quantum domain. Despite important progress, a formulation of QRF transformations for Lorentz symmetry is still lacking. The present work aims to fill this gap. We first introduce a reformulation of relativistic quantum mechanics independent of any notion of preferred temporal slicing. Based on this, we define transformations that switch between the perspectives of different relativistic QRFs. We introduce a notion of ''quantum Lorentz transformations'' and ''superposition of Lorentz boosts'', acting on the external degrees of freedom of a quantum particle. We analyse two effects, superposition of time dilations and superposition of length contractions, that arise only if the reference frames exhibit both relativistic and quantum-mechanical features. Finally, we discuss how the effects could be observed by measuring the wave-packet extensions from relativistic QRFs.

Ahmed Albezawi

The quantum reference frame (QRF) programme has demonstrated that the distinction between superposition and entanglement is observer-dependent: what appears as entanglement from an external perspective may appear as a definite relational state from within a quantum frame. However, QRF has operated primarily in the kinematic and spatial domain, leaving the temporal structure of observation unaddressed and providing no account of why each internal frame experiences definiteness. We propose a synthesis with Relational Retrocausal Quantum Mechanics (RRQM), in which measurement is the retroactive rewriting of an observer’s accessible history. The central result is the entanglement/measurement duality theorem: the temporal frame-change transformation from an external observer to an internal observer maps an entangled description onto a measurement-with-definite-outcome description, and this map is precisely the RRQM rewriting operator acting on history space. We formalize this through the introduction of temporal quantum reference frames (tQRFs), extending QRF from instantaneous Hilbert space into the space of observer-relative histories. The framework resolves Wigner’s friend, Bell correlations, and Schr¨odinger’s cat through a single mechanism: observer-relative temporal frames, each retroactively consistent.

R. Edward Nather