Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.9
2.1
Journals
Entropy
Special Issues
Quantum Foundations: 100 Years of Born’s Rule
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

Quantum Foundations: 100 Years of Born’s Rule

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

Deadline for manuscript submissions: 25 August 2025 | Viewed by 1760

Special Issue Editor

Dr. Dustin Lazarovici

E-Mail Website
Guest Editor
Humanities and Arts Department, Technion–Israel Institute of Technology, Haifa 3200003, Israel
Interests: foundations of quantum mechanics; foundations of statistical mechanics; the arrow of time; the ontology of physics; the metaphysics of natural laws

Special Issue Information

Dear Colleagues,

In his seminal 1926 paper, nearly 100 years ago, Max Born introduced the statistical interpretation of the quantum wave function. Since then, the Born rule has become central to quantum mechanics, providing the main link between the mathematical formalism of the theory and its extraordinarily successful empirical predictions. Despite this undeniable success, there are ongoing debates about the status of the Born rule, the interpretation of quantum mechanical probabilities, the nature of the wave function, and many other related topics.

This Special Issue aims to explore these foundational questions from physical, mathematical, and philosophical perspectives. We invite original papers and comprehensive reviews that provide an appraisal of the Born rule and its place in modern quantum physics, or that highlight new research directions in the foundations of quantum mechanics. Suitable topics include (but are not limited to) the following:

  • Derivations of the Born rule;
  • Interpretations of probability in quantum mechanics and its relationship to classical probability;
  • Interpretations of the wave function;
  • The Born rule in relativistic quantum theory;
  • Quantum equilibrium versus thermodynamic non-equilibrium;
  • The scope and status of the quantum measurement formalism;
  • Epistemic limits and empirical (in)equivalence;
  • Possibility of new experimental tests of quantum statistics.

Dr. Dustin Lazarovici
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 100 words) can be sent to the Editorial Office for announcement on this website.

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 foundations
  • Born rule, probability in quantum mechanics
  • quantum measurement theory
  • quantum statistical mechanics
  • interpretations of the wave function

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.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

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

Published Papers (4 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

13 pages, 232 KiB  
Article
Probability of Self-Location in the Framework of the Many-Worlds Interpretation
by Lev Vaidman
Entropy 2025, 27(4), 416; https://doi.org/10.3390/e27040416 - 11 Apr 2025
Viewed by 349
Abstract
The growing interest in the concept of probability of self-location of a conscious agent has created multiple controversies. Considering David Albert’s setup in which he described his worries about consistency of the concept, I identify the sources of these controversies and argue that [...] Read more.
The growing interest in the concept of probability of self-location of a conscious agent has created multiple controversies. Considering David Albert’s setup in which he described his worries about consistency of the concept, I identify the sources of these controversies and argue that defining “self” in an operational way provides a satisfactory meaning for the probability of self-location of an agent in a quantum world. It keeps the nontrivial feature of having subjective ignorance of self-location without ignorance about the state of the universe. It also allows defining the Born rule in the many-worlds interpretation of quantum mechanics and proving it from some natural assumptions. Full article
(This article belongs to the Special Issue Quantum Foundations: 100 Years of Born’s Rule)
29 pages, 363 KiB  
Article
The Born Rule—100 Years Ago and Today
by Arnold Neumaier
Entropy 2025, 27(4), 415; https://doi.org/10.3390/e27040415 - 11 Apr 2025
Viewed by 385
Abstract
The details of the contents and formulations of the Born rule have changed considerably from its inception by Born in 1926 to the present day. This paper traces the early history of the Born rule 100 years ago, its generalization (essential for today’s [...] Read more.
The details of the contents and formulations of the Born rule have changed considerably from its inception by Born in 1926 to the present day. This paper traces the early history of the Born rule 100 years ago, its generalization (essential for today’s quantum optics and quantum information theory) to POVMs around 50 years ago, and a modern derivation from an intuitive definition of the notion of a quantum detector. Also discussed is the extent to which the various forms of the Born rule have, like any other statement in physics, a restricted domain of validity, which leads to problems when applied outside this domain. Full article
(This article belongs to the Special Issue Quantum Foundations: 100 Years of Born’s Rule)
18 pages, 314 KiB  
Article
The POVM Theorem in Bohmian Mechanics
by Christian Beck and Dustin Lazarovici
Entropy 2025, 27(4), 391; https://doi.org/10.3390/e27040391 - 7 Apr 2025
Viewed by 260
Abstract
The POVM theorem is a central result in Bohmian mechanics, grounding the measurement formalism of standard quantum mechanics in a statistical analysis based on the quantum equilibrium hypothesis (the Born rule for Bohmian particle positions). It states that the outcome statistics of an [...] Read more.
The POVM theorem is a central result in Bohmian mechanics, grounding the measurement formalism of standard quantum mechanics in a statistical analysis based on the quantum equilibrium hypothesis (the Born rule for Bohmian particle positions). It states that the outcome statistics of an experiment are described by a positive operator-valued measure (POVM) acting on the Hilbert space of the measured system. In light of recent debates about the scope and status of this result, we provide a systematic presentation of the POVM theorem and its underlying assumptions with a focus on their conceptual foundations and physical justifications. We conclude with a brief discussion of the scope of the POVM theorem—especially the sense in which it does (and does not) place limits on what is “measurable” in Bohmian mechanics. Full article
(This article belongs to the Special Issue Quantum Foundations: 100 Years of Born’s Rule)

Review

Jump to: Research

36 pages, 908 KiB  
Review
Can de Broglie–Bohm Mechanics Be Considered Complete?
by Aurélien Drezet and Arnaud Amblard
Entropy 2025, 27(4), 399; https://doi.org/10.3390/e27040399 - 8 Apr 2025
Viewed by 228
Abstract
In this work celebrating the centenary of quantum mechanics, we review the principles of the de Broglie–Bohm theory (dBB), also known as pilot-wave theory. We assess the most common reading of it (the Nomological interpretation based on the notion of primitive ontology in [...] Read more.
In this work celebrating the centenary of quantum mechanics, we review the principles of the de Broglie–Bohm theory (dBB), also known as pilot-wave theory. We assess the most common reading of it (the Nomological interpretation based on the notion of primitive ontology in tridimensional space) and defend instead a more causal and pluralistic approach, drawing on classical analogies with optics and hydrodynamics. Within this framework, we review some of the approaches exploiting mechanical analogies to overcome the limitations of the current dBB theory and perhaps quantum mechanics itself. Full article
(This article belongs to the Special Issue Quantum Foundations: 100 Years of Born’s Rule)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-4
Back to TopTop