A spacetime-covariant approach to inertial and accelerated quantum clocks in first-quantization

• URL: http://arxiv.org/abs/2508.05897v2
• Date: Wed, 03 Sep 2025 19:16:50 GMT
• Title: A spacetime-covariant approach to inertial and accelerated quantum clocks in first-quantization
• Authors: Eduardo A. B. Oliveira, Andre G. S. Landulfo,
• Abstract summary: We propose a spacetime-covariant formalism to describe clocks in first quantization.<n>We compute the joint time evolution of a pair of quantum clocks in two cases.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: It is expected that a quantum theory of gravity will radically alter our current notion of spacetime geometry. However, contrary to what was commonly assumed for many decades, quantum gravity effects could manifest in scales much larger than the Planck Scale, provided that there is enough coherence in the superposition of geometries. Quantum Clocks, i.e. quantum mechanical systems whose internal dynamics can keep track of proper-time lapses, are a very promising tool for probing such low-energy quantum gravity effects. In this work, we contribute to this subject by proposing a spacetime-covariant formalism to describe clocks in first quantization. In particular, we account for the possibility of dynamically accelerated clocks via suitable couplings with external fields. We find that a particular decomposition of the (quadratic) clock Hamiltonian into positive- and negative-mass sectors, when attainable, enables one to compute the evolution of the system directly in terms of the clock's proper-time while maintaining explicit covariance. When this decomposition is possible, the evolution obtained is always unitary, even with couplings with external fields used to, e.g., accelerate the clocks. We then apply this formulation to compute the joint time evolution of a pair of quantum clocks in two cases: (i) inertial clocks with relative motion and (ii) charged clocks accelerated by a uniform magnetic field. In both cases, when our clocks are prepared in coherent states, we find that the density matrix $\rho_{\tau_2|\tau_1}$ describing time-measurements of the two clocks yields not only conditional probabilities whose peaks match exactly the classical expected values for time dilation, but also yields coherent quantum fluctuations around that peak with a Gaussian profile.

Related papers

• Time Symmetry, Retrocausality, and Emergent Collapse: The Tlalpan Interpretation of Quantum Mechanics [51.56484100374058]
  The Tlalpan Interpretation (QTI) proposes that the wavefunction collapse is not a primitive, axiomatic rule but an emergent phenomenon.<n>The novelty of QTI lies in its embedding of collapse within the conceptual language of critical phenomena in statistical physics.
  arXiv  Detail & Related papers  (2025-08-25T20:30:56Z)
• Conditions for Unitarity in Timeless Quantum Theory [0.0]
  This work derives necessary and sufficient conditions for the relative dynamics to be unitary.<n>A physical interpretation of these conditions is given in terms of the clock's rate.
  arXiv  Detail & Related papers  (2025-04-02T10:31:25Z)
• Geometry and proper time of a relativistic quantum clock [0.0]
  A new framework is demonstrated for perturbing the classical path-length functional to include quantum degrees of freedom. In this framework, a quantum clock travels on geodesics of a family of spacetimes deformed by parameters specifying the clock's quantum state.
  arXiv  Detail & Related papers  (2024-10-10T17:39:29Z)
• Looking for Carroll particles in two time spacetime [55.2480439325792]
  Carroll particles with a non-vanishing value of energy are described in the framework of two time physics. We construct the quantum theory of such a particle using an unexpected correspondence between our parametrization and that obtained by Bars for the hydrogen atom in 1999.
  arXiv  Detail & Related papers  (2023-10-29T15:51:41Z)
• Quantum operations with the time axis in a superposed direction [0.0]
  We introduce an expanded concept of matrix transposition, that takes into account general bipartite unitary transformations of a quantum operation's future and past Hilbert spaces. This framework may have applications in approaches that treat time and space equally like quantum gravity.
  arXiv  Detail & Related papers  (2023-06-05T10:20:59Z)
• Universality of quantum time dilation [0.0]
  We show that kinematic quantum time dilation is universal for any clock mechanism, while gravitational quantum time dilation is not. We also show that although both of these effects reduce to incoherent averaging of different classical time dilation contributions, there exists an additional quantum time dilation effect that has no classical analog and can be extracted from higher-order corrections to the system's Hamiltonian.
  arXiv  Detail & Related papers  (2022-11-04T12:59:00Z)
• Quantum time dilation in a gravitational field [39.58317527488534]
  We investigate how the superposition principle affects the gravitational time dilation observed by a simple clock. We show that the emission rate of an atom prepared in a coherent superposition of separated wave packets in a gravitational field is different from the emission rate of an atom in a classical mixture of these packets.
  arXiv  Detail & Related papers  (2022-04-22T10:02:21Z)
• Non-inertial quantum clock frames lead to non-Hermitian dynamics [0.0]
  We study an accelerating massive quantum particle with an internal clock system. We show that the evolution from the perspective of the particle's internal clock is non-Hermitian.
  arXiv  Detail & Related papers  (2022-04-08T16:52:24Z)
• Universality-of-clock-rates test using atom interferometry with $T^{3}$ scaling [63.08516384181491]
  Atomic clocks generate delocalized quantum clocks. Tests of universality of clock rates (one facet of LPI) to atom interferometry generating delocalized quantum clocks proposed. Results extend our notion of time, detached from classical and localized philosophies.
  arXiv  Detail & Related papers  (2022-04-05T12:26:56Z)
• 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)
• Projection evolution and quantum spacetime [68.8204255655161]
  We discuss the problem of time in quantum mechanics. An idea of construction of a quantum spacetime as a special set of the allowed states is presented. An example of a structureless quantum Minkowski-like spacetime is also considered.
  arXiv  Detail & Related papers  (2019-10-24T14:54:11Z)

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.