Time delocalization and causality across temporal quantum reference frames

• URL: http://arxiv.org/abs/2603.08845v1
• Date: Mon, 09 Mar 2026 19:00:08 GMT
• Title: Time delocalization and causality across temporal quantum reference frames
• Abstract summary: In relational quantum dynamics, evolution emerges via the correlations between some system of interest and a clock system.<n>We investigate the interplay of two aspects, namely temporal localization and causal relations, when comparing emergent dynamics with respect to different choices of clock.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In relational quantum dynamics, evolution emerges via the correlations between some system of interest and a clock system, which plays the role of a temporal reference frame. Their combined state satisfies a Wheeler-de Witt-like constraint equation, and therefore does not evolve, leading to a ``block universe'' picture. Here we investigate the interplay of two aspects, namely temporal localization and causal relations, when comparing emergent dynamics with respect to different choices of clock. We first explore the extent to which two clocks can agree on the temporal localization of events. Then, focussing on the operational notion of causality, we require a clearly defined notion of interventions, i.e. quantum operations, and consider two different approaches to modeling these operations within relational dynamics. The first considers their application via the choice of solutions to the constraint equation, i.e.~the choice of which ``history'' is considered. The second approach incorporates the operations into the constraint equation itself and thereby into its solutions, giving a dynamical picture of the interventions. From the perspective of a single clock, both approaches allow for a notion of operational causality in relational dynamics. However, for multiple clocks, only the second approach gives a consistent picture regarding causal relations, while necessarily manifesting some degree of temporal delocalization between frames. Moreover, this second approach, when considering certain cases of temporal delocalization, naturally describes scenarios with indefinite causal order, a well-known quantum feature of operational causality.

Related papers

• Beyond Directed Acyclic Graphs: Causal Zeros and Causal Differential Equations [0.02648566468224904]
  Pearl's structural causal model is the dominant formal language for causal reasoning.<n>This paper examines two classes of phenomena that strain these restrictions.<n>We give the extended do-calculus, identifiability conditions, counterfactual semantics, and open problems.
  arXiv  Detail & Related papers  (2026-07-24T20:54:42Z)
• Temporal-Causal Unity as an Operational Framework for Collective Dynamics: Causal-Progress Clocks, Synchronization, and Polarization [5.995482369040288]
  This paper develops a framework connecting a process-philosophical thesis time is the ordered unfolding of causal change.<n>The framework deliberately separates three claims: an interpretive thesis about becoming, a measurable causal-progress coordinate, and a network model.<n>The paper derives falsifiable hypotheses and an out-of-sample protocol for comparing causal-progress and chronological-time models.
  arXiv  Detail & Related papers  (2026-07-21T01:39:53Z)
• The time of arrival problem in the Page-Wootters formalism [0.0]
  The time-of-arrival problem asks for the probability distribution for when a quantum particle reaches a specified location.<n>It has been the subject of decades of debate, exemplifying the lack of a self-adjoint time observable in quantum theory.<n>We construct a time-of-arrival distribution by inverting the Page-Wootters approach, asking what time a clock reads given that the particle arrives at some fixed position.
  arXiv  Detail & Related papers  (2026-03-31T18:10:55Z)
• A magnetic clock for a harmonic oscillator [89.99666725996975]
  We study how the quantum dynamics transforms into a classical-like behaviour when conditions related with macroscopicity are met by the clock alone. In the description of this emerging behaviour finds its place the classical notion of time, as well as that of phase-space and trajectories on it.
  arXiv  Detail & Related papers  (2023-10-20T09:55:51Z)
• Measurement events relative to temporal quantum reference frames [44.99833362998488]
  We compare two consistent approaches to the Page-Wootters formalism to clarify the operational meaning of evolution and measurements.<n>We show that for non-ideal clocks, the purified measurement approach yields a time non-local evolution equation.<n>We argue that these approaches describe operationally distinct situations.
  arXiv  Detail & Related papers  (2023-08-21T18:26:12Z)
• Initial Correlations in Open Quantum Systems: Constructing Linear Dynamical Maps and Master Equations [62.997667081978825]
  We show that, for any predetermined initial correlations, one can introduce a linear dynamical map on the space of operators of the open system. We demonstrate that this construction leads to a linear, time-local quantum master equation with generalized Lindblad structure.
  arXiv  Detail & Related papers  (2022-10-24T13:43:04Z)
• Robustness of the Page-Wootters construction across different pictures, states of the universe and system-clock interactions [0.0]
  I study the robustness of the Page-Wootters construction across different pictures, states of the universe and clock interactions. I consider both pure and mixed states of the universe and extend the analysis to include interactions between the clock and the other subsystem of the universe.
  arXiv  Detail & Related papers  (2022-04-25T15:55:48Z)
• Non-linear equation of motion for Page-Wootters mechanism with interaction and quasi-ideal clocks [0.0]
  We propose an equation of motion for a mixed state system that evolves according to its gravitationally induced interaction with a non-ideal quantum clock. As a result of our considerations, we obtained an equation of motion that is non-linear in nature, dependent on the system's initial conditions.
  arXiv  Detail & Related papers  (2021-07-23T20:34:04Z)
• Equivalence of approaches to relational quantum dynamics in relativistic settings [68.8204255655161]
  We show that the trinity' of relational quantum dynamics holds in relativistic settings per frequency superselection sector. We ascribe the time according to the clock subsystem to a POVM which is covariant with respect to its (quadratic) Hamiltonian.
  arXiv  Detail & Related papers  (2020-07-01T16:12:24Z)
• There is only one time [110.83289076967895]
  We draw a picture of physical systems that allows us to recognize what is this thing called "time" We derive the Schr"odinger equation in the first case, and the Hamilton equations of motion in the second one.
  arXiv  Detail & Related papers  (2020-06-22T09:54:46Z)
• Einselection from incompatible decoherence channels [62.997667081978825]
  We analyze an open quantum dynamics inspired by CQED experiments with two non-commuting Lindblad operators. We show that Fock states remain the most robust states to decoherence up to a critical coupling.
  arXiv  Detail & Related papers  (2020-01-29T14:15:19Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.