Rethinking Electron Statistics Rules

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper presents a novel interpretation of spin-statistics correlations constructed from first principles.  The arguments are well formulated and clearly presented.  This work should be of interest to researchers in foundations of quantum mechanics and may potentially lead to new applications.

Three small language issues:

1.  Line 30:  consider "directions" instead of "direction"

2.  Lines 63 and 79:  consider "In principle" instead of "Principally"

3.  Line 137:  "phenomonelogically" should be "phenomenologically"

I strongly recommend publication of this manuscript.  

Author Response

Thank you for the review comments and grammar corrections. We made the recommended grammar corrections for the revised article.

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript provides a discussion on the nature of spin statistics from a Lamor spin-precession perspective. Although the representation of Bose-Einstein statistics for coherent states (superfluids) have been previously established, the present work is an interesting communication and overview:

1. The authors conclude that the actual particle spin value plays no role and the claim that the classification of fermion vs boson is not always applicable. Perhaps the authors mean the applicable classification should be: fermion, boson and the coherent states of both?

2. In Jacak, (2024), it has been theoretically shown that gravitational singularity may cause a local departure from the Pauli Exclusion Principle affecting the quantum statistics. What is the authors view of this phenomenon from the proposed quantum statistical framework?

3. A minor comment: the authors should reconsider using the theorem-proof format in the text. If the theorem is proposed then the proof  segment should also be provided as well.

 

Reference:

Jacak, J.E., 2024. Topology-induced quantum transition in multiparticle systems in vicinity of a black hole. Classical and Quantum Gravity, 41(3), p.035006. 

Author Response

1. The authors conclude that the actual particle spin value plays no role and the claim that the classification of fermion vs boson is not always applicable. Perhaps the authors mean the applicable classification should be: fermion, boson and the coherent states of both?
   
   Response to 1: The scope of our article is to investigate the quantum statistics of the electron (mainly) and proton. There can be follow-up implications to more exotic particles, and we leave it to particle scientists to investigate those.
   
   
2. In Jacak, (2024), it has been theoretically shown that gravitational singularity may cause a local departure from the Pauli Exclusion Principle affecting the quantum statistics. What is the authors view of this phenomenon from the proposed quantum statistical framework?
   
   Response to 2: We think that Mr Jacak is on the right track with the idea that a strong gravitational field may impact the quantum statistics of electrons, and that is relevant for some astrophysical phenomena. A more simple example is to consider that in those stars where gravity creates extreme large pressure, there is a strong thermodynamic drive towards electron coherence, which mitigates the pressure by multi-electron state occupancy.  We added a paragraph on this astrophysical implication to the Discussion section.
   
   
3. A minor comment: the authors should reconsider using the theorem-proof format in the text. If the theorem is proposed then the proof  segment should also be provided as well.
   
   Response to 3: It is a good point, we have taken the proof segment into use for the revised article.

Reviewer 3 Report

Comments and Suggestions for Authors

In the work by Kovacs and coauthors, they investigate the physical origin of the two statistics termed Fermi-Dirac statistic and Bose-Einstein statistic. Their major finding is that whether an individual electron spin is measurable or not serves as the crucial factor to distinguish the two. In particular, the spin-precession in electron-electron interactions plays a key role.  The authors make many discussions to advocate their claims and they take superconductivity as an example to take about the coherent electron states.

Overall, this paper seems to address an important topic which has a long history. The paper is nicely organized and well written. Therefore, it merits publication in this journal after consideration of the following point.

The authors discuss the superconductivity in Sec. 6. As we know, the core idea of the BCS theory is the occurrence of the Cooper pairs in the low temperature. The Cooper pairs are identified as the Bosons and thus obey the Bose-Einstein statics. The author are suggested to explain it by using their theory.

Author Response

Thank you for your review and comments.

Comment 1: The authors discuss the superconductivity in Sec. 6. As we know, the core idea of the BCS theory is the occurrence of the Cooper pairs in the low temperature. The Cooper pairs are identified as the Bosons and thus obey the Bose-Einstein statics. The author are suggested to explain it by using their theory.

Response to 1: It is a good point that our theory and BCS theory both consider superconducting electrons being in a coherent bosonic state. The reader may then wonder what the differences between the two theories are. We believe that the differences between our theory vs BCS theory are best demonstrated in the context of the Meissner effect. As suggested, we expanded section 6 by an investigation of the Meissner effect and the London equation. We describe a mathematically complete derivation of the London equation, and  show how our model leads to simple thermodynamic considerations that explain the microscopic mechanism of Meissner flows. It is an interesting application of our theory.