Related papers: Non-inertial quantum clock frames lead to non-Hermitian dynamics

Non-inertial quantum clock frames lead to non-Hermitian dynamics

URL: http://arxiv.org/abs/2204.04177v2
Date: Wed, 23 Nov 2022 17:46:22 GMT
Title: Non-inertial quantum clock frames lead to non-Hermitian dynamics
Authors: Ismael L. Paiva, Amit Te'eni, Bar Y. Peled, Eliahu Cohen, Yakir Aharonov
Abstract summary: 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.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: The operational approach to time is a cornerstone of relativistic theories, as evidenced by the notion of proper time. In standard quantum mechanics, however, time is an external parameter. Recently, many attempts have been made to extend the notion of proper time to quantum mechanics within a relational framework. Here, we use similar ideas combined with the relativistic mass-energy equivalence to study an accelerating massive quantum particle with an internal clock system. We show that the ensuing evolution from the perspective of the particle's internal clock is non-Hermitian. This result does not rely on specific implementations of the clock. As a particular consequence, we prove that the effective Hamiltonian of two gravitationally interacting particles is non-Hermitian from the perspective of the clock of either particle.

Related papers

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)
Time-System Entanglement and Special Relativity [0.0]
Page-Wootters mechanism of quantum time is a promising starting point. We study how this time-system entanglement depends on the rapidity of the Lorentz boost.
arXiv Detail & Related papers (2022-12-27T03:09:58Z)
The solution to the problem of time in quantum gravity also solves the time of arrival problem in quantum mechanics [0.0]
We introduce a solution to the problem of time in quantum gravity which consists in formulating the quantum theory in terms of real clocks. We show here that this construction provides a natural solution to the time of arrival problem in quantum mechanics and leads to a well defined time-energy uncertainty relation for the clocks.
arXiv Detail & Related papers (2022-04-18T15:30:24Z)
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)
Time and Evolution in Quantum and Classical Cosmology [68.8204255655161]
We show that it is neither necessary nor sufficient for the Poisson bracket between the time variable and the super-Hamiltonian to be equal to unity in all of the phase space. We also discuss the question of switching between different internal times as well as the Montevideo interpretation of quantum theory.
arXiv Detail & Related papers (2021-07-02T09:17:55Z)
Flow of time during energy measurements and the resulting time-energy uncertainty relations [0.0]
We investigate whether quantum mechanics inherently imposes a fundamental minimum duration for energy measurements with a certain precision. We show that the duration of an energy measurement carried out by an external system cannot be performed arbitrarily fast from the perspective of the internal clock.
arXiv Detail & Related papers (2021-06-01T14:37:45Z)
On the Problem of Time(s) in Quantum Mechanics and Quantum Gravity: recent integrating developments and outlook [0.0]
How to restore time is the Problem of Time(s) It introduces an intrinsic time property tau associated with the mass of the system. It invalidates Pauli's objection to the existence of a time operator.
arXiv Detail & Related papers (2021-04-20T17:51:05Z)
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)
Quantum time dilation: A new test of relativistic quantum theory [91.3755431537592]
A novel quantum time dilation effect is shown to arise when a clock moves in a quantum superposition of two relativistic velocities. This effect is argued to be measurable using existing atomic interferometry techniques, potentially offering a new test of relativistic quantum theory.
arXiv Detail & Related papers (2020-04-22T19:26:53Z)
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.