Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
5.2
2.0
Journals
Entropy
Special Issues
Time in Quantum Mechanics
entropy-logo
Submit to Special Issue Submit Abstract to Special Issue Review for Entropy Propose a Special Issue

Journal Menu

► Journal Menu

Journal Browser

► Journal Browser
share announcement

Time in Quantum Mechanics

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Time".

Deadline for manuscript submissions: 31 July 2026 | Viewed by 4792

Special Issue Editor

Dr. Michael Ridley

E-Mail Website
Guest Editor
Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan 5290002, Israel
Interests: quantum foundations; molecular electronics; nonequilibrium statistical mechanics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

At the foundations of quantum theory, many unresolved puzzles concerning the basic nature of time exist. In particular, the 'problem of time’ refers to the apparent impossibility of reconciling time as a background parameter of the quantum state with the dynamical concept of time used in relativity theory. The arrow of time in quantum processes does not always appear to be directed towards the future, or in any unique direction whatsoever. These puzzles bear upon many fast-moving fields in physics, including the race for a theory of  quantum gravity, temporal correlations and the theory of measurement.

This Special Issue aims to bring together physicists and philosophers of physics to address all aspects of time in quantum mechanics, including, but not limited to, the following areas: The existence of a time operator in quantum theory, energy–time uncertainty relations, retrocausality, the quantum arrow of time, tunneling times, traversal times in quantum transport, quantum stochastic processes, quantum events, time in quantum gravity, multiple-time quantum mechanics, the two-state vector formalism, the transactional interpretation, timeless quantum theory and the Page–Wootters approach, quantum clocks, quantum reference frames, the persistence of quantum objects through time, presentism vs. eternalism in quantum mechanics, and determinism vs. objective chance.

Dr. Michael Ridley
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • quantum time
  • quantum gravity
  • time operator
  • retrocausality
  • quantum clocks

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (5 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

Jump to: Review

35 pages, 580 KB  
Article
From Quantum Time to Manifestly Covariant QFT: On the Need for a Quantum-Action-Based Quantization
by Nahuel L. Diaz
Entropy 2026, 28(4), 425; https://doi.org/10.3390/e28040425 - 10 Apr 2026
Viewed by 357
Abstract
In quantum time (QT) schemes, time is promoted to a degree of freedom, allowing Lorentz covariance to be made explicit for single particles. We ask whether this can be lifted to QFT so that Lorentz covariance becomes manifest at the Hilbert-space level, rather [...] Read more.
In quantum time (QT) schemes, time is promoted to a degree of freedom, allowing Lorentz covariance to be made explicit for single particles. We ask whether this can be lifted to QFT so that Lorentz covariance becomes manifest at the Hilbert-space level, rather than being hidden as in the standard canonical formulation. We address this question by proposing a second-quantized approach in which the elementary particle is the QT particle itself, leading naturally to the notion of spacetime field algebras and of quantum action. We show, however, that a naive many-body construction runs into inconsistencies. To pinpoint their origin we introduce a classical counterpart of the second-quantized formalism, spacetime classical mechanics (SCM), and prove a no-go theorem: Dirac quantization of SCM collapses back to standard QFT and therefore hides covariance. We circumvent this problem by presenting a quantum-action-based quantization that yields a spacetime version of quantum mechanics (SQM), making covariance manifest for (interacting) QFTs. Finally, we show that this resolution is tied to a genuine spacetime generalization of the notion of a quantum state, required by causality and closely connected to recent “states over time” proposals and, in dS/CFT–motivated settings, to microscopic notions of timelike entanglement and emergent time. Full article
(This article belongs to the Special Issue Time in Quantum Mechanics)
►▼ Show Figures

Figure 1

9 pages, 941 KB  
Article
A Time-Symmetric and Retrocausal Resolution of the EPR Paradox
by Michael B. Heaney
Entropy 2026, 28(3), 319; https://doi.org/10.3390/e28030319 - 12 Mar 2026
Viewed by 908
Abstract
The Copenhagen Interpretation of quantum mechanics explains the Einstein, Podolsky, and Rosen (EPR) experiments with “spooky action at a distance” and nonlocal wavefunction collapse. A time-symmetric and retrocausal interpretation of quantum mechanics explains the same experiments without spooky action at a distance or [...] Read more.
The Copenhagen Interpretation of quantum mechanics explains the Einstein, Podolsky, and Rosen (EPR) experiments with “spooky action at a distance” and nonlocal wavefunction collapse. A time-symmetric and retrocausal interpretation of quantum mechanics explains the same experiments without spooky action at a distance or nonlocal wavefunction collapse. An experiment that can distinguish between the Copenhagen and Time-Symmetric Interpretations is described. Full article
(This article belongs to the Special Issue Time in Quantum Mechanics)
►▼ Show Figures

Figure 1

16 pages, 626 KB  
Article
When Does a Spin Flip? Arrival Time Distributions and Information Propagation in Discrete Quantum Systems
by Lionel Martellini
Entropy 2026, 28(3), 315; https://doi.org/10.3390/e28030315 - 11 Mar 2026
Viewed by 463
Abstract
We analyze three distinct approaches to time of arrival (TOA) distributions for discrete quantum systems using a spin-12 particle in a constant magnetic field as a paradigmatic example. We argue that these distributions should not be regarded as competing predictions for [...] Read more.
We analyze three distinct approaches to time of arrival (TOA) distributions for discrete quantum systems using a spin-12 particle in a constant magnetic field as a paradigmatic example. We argue that these distributions should not be regarded as competing predictions for the same notion of arrival time, but rather relate to fundamentally different notions whose relevance depends on the physical context. These results are used to analyze information propagation arrival time distributions in XX spin chain systems, and discuss potential applications in quantum information science. Full article
(This article belongs to the Special Issue Time in Quantum Mechanics)
►▼ Show Figures

Figure 1

11 pages, 275 KB  
Article
Relativistic Limits on the Discretization and Temporal Resolution of a Quantum Clock
by Tommaso Favalli
Entropy 2025, 27(10), 1068; https://doi.org/10.3390/e27101068 - 14 Oct 2025
Cited by 2 | Viewed by 759
Abstract
We provide a brief discussion regarding relativistic limits on the discretization and temporal resolution of time values in a quantum clock. Our clock is characterized by a time observable chosen to be the complement of a bounded and discrete Hamiltonian that can have [...] Read more.
We provide a brief discussion regarding relativistic limits on the discretization and temporal resolution of time values in a quantum clock. Our clock is characterized by a time observable chosen to be the complement of a bounded and discrete Hamiltonian that can have an equally spaced or a generic spectrum. In the first case, the time observable can be described by a Hermitian operator, and we find a limit in the discretization for the time eigenvalues. Nevertheless, in both cases, the time observable can be described by a POVM, and, by increasing the number of time states, we show how the bound on the minimum time quantum can be reduced and identify the conditions under which the clock values can be treated as continuous. Finally, we find a limit for the temporal resolution of our time observable when the clock is used (together with light signals) in a relativistic framework for the measurement of spacetime distances. Full article
(This article belongs to the Special Issue Time in Quantum Mechanics)

Review

Jump to: Research

43 pages, 548 KB  
Review
Minimum Spacetime Length and the Thermodynamics of Spacetime
by Valeria Rossi, Sergio L. Cacciatori and Alessandro Pesci
Entropy 2026, 28(1), 97; https://doi.org/10.3390/e28010097 - 13 Jan 2026
Viewed by 736
Abstract
Theories of emergent gravity have established a deep connection between entropy and the geometry of spacetime by looking at the latter through a thermodynamic lens. In this framework, the macroscopic properties of gravity arise in a statistical way from an effective small-scale discrete [...] Read more.
Theories of emergent gravity have established a deep connection between entropy and the geometry of spacetime by looking at the latter through a thermodynamic lens. In this framework, the macroscopic properties of gravity arise in a statistical way from an effective small-scale discrete structure of spacetime and its information content. In this review, we begin by outlining how theories of quantum gravity imply the existence of a minimum length of spacetime as a general feature. We then describe how such a structure can be implemented in a way that is independent from the details of the quantum fluctuations of spacetime via a bi-tensorial quantum metric qαβ(x,x′) that yields a finite geodesic distance in the coincidence limit x→x′. Finally, we discuss how the entropy encoded by these microscopic degrees of freedom can give rise to the field equations for gravity through a thermodynamic variational principle. Full article
(This article belongs to the Special Issue Time in Quantum Mechanics)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-5
Back to TopTop