Is Quantum Field Theory Necessarily “Quantum”?

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The presented manuscript by A. Shojaei-Fard presents a compilation of previous works of the author, on basis of which he proves that quantum field theory can be considered as “neo-realist” theory. Indeed, quantum field theory is inherently not “realist,” due to challenges like the underdetermination of theories, the need for renormalization that introduces "bare" vs. "physical" particles, and the difficulty in specifying exactly what the theory describes in reality. Some non-realist implications of quantum theory are like those highlighted by the Kochen-Specker theorem that excludes the description of quantum mechanics by a “hidden variable” theory where the properties of a particle are predetermined and have definite values, regardless of how they are measured.

     This work seeks to address the non-realist problem of quantum theory with the aid of non-perturbative topos. Thus, the author has applied the universal non-perturbative topos formalism to describe quantum field theory in a special way, so that it attains the features of the “neo-realist” theory. The main question addressed by the research can be considered to be original and relevant in the field of theoretical physics, because a non-realist problem in quantum field theory is a long-standing philosophical issue challenging the mathematical models of quantum field theory to correspond to a physical reality in a sense.

The manuscript is well written and systematically structured, reminding some sort of an excerpt from learning books on quantum field theory. There are no queries to the work itself, but there are to its representation. First of all, the introduction starts from phrases involving specific terminology familiar to a very narrow circle of readers, such as “orthomodular lattice structure,” “non-boolean topos,” “Heyting algebra,” etc. The terminology is not explained at its first appearance and leaves readers embarrassed. The introduction, in general, represents vague and barely understandable text that does not address the main problem raised by the author, i.e. the problem of non-realist feature of quantum field theory. There was no analysis of the previously published material on the topic of non-realist problem presented either. In the end of introduction, one can find only a mentioning that the presented article aims to answer a series of questions addressed by A. Doring, in “Some remarks on the logic of quantum gravity, arXiv:1306.3076, 2013”, on the nature of physical theories beyond quantum theory. What are those questions? Why the author did not describe them in introduction? To my mind, the introduction must be overwritten to clarify the following issues:

1. What is the main problem addressed by this research work?
2. What are the consequences of the described problem?
3. What were the attempts to resolve the problem (a brief discussion of previously published material)?
4. What is the essential difference of presented approach to the previous ones?
5. Explain all terminology at its first appearance in the text.

 

The manuscript ends up with corollary “The universal non-perturbative topos describes quantum field theory as a “neo-realist theory.” This must be the main result of this work. As proof, the author suggests that it is a consequence of Theorems 3, 4 and Corollaries 6, 6 and [51]. This is not sufficient. In my opinion, the proof should be given in full detail, without referring any external links.

 

Conclusions are not given in a separate section. I think that it is a flaw for any scientific work. The author should clearly state what exactly he has achieved.

 

For wide readership, it would be also very desirable to describe what may be the use of the presented theory?

 

After the author makes his manuscript more understandable and reader-friendly, I will consider the possibility to recommend the publication for publishing in Quantum Reports.

Author Response

Dear Reviewer, 

I would like to thank because of your important comments. In response, I have prepared the revised version of the work. Here I address a short list of revisions in terms of your report. Please note that all page numbers, line numbers and reference numbers in this letter are on the basis of this revised version of the article. 

1- In reply to adding terminologies: Definitions of all important mathematical concepts are presented as some footnotes to the text. Please check Nine footnotes in Pages 4 – 6. 

2- In reply to challenges in Introduction: The whole Introduction section is rewritten. New paragraphs and subsections are added to the text to address motivation, main problem, previous efforts, and new progresses. Please check

- Page 2, Lines 43 – 79: the text addresses motivation and the main problem

- Pages 4 – 6, Lines 134 – 242: the text addresses previous efforts

- Pages 6 – 8: Lines 243 – 335: the text addresses the essential progresses performed by this article and differences with past efforts.

3- In reply to adding Doring—Isham’ questions and the author’s answers: These cases are added. Please check

- Page 8, Lines 309 – 321: the text addresses the questions.

- Page 30, Lines 981 – 1008: the text addresses author’s answers in terms of the achievements of this article.

4- In reply to adding Conclusion: The Conclusion section is added. Please check

 -  Pages 29 – 31, Lines 953 – 1037.

5- In reply to the use of results of this article: Please check

 -  Page 31, Lines 1009 – 1037: the text addresses two applications.

6- In reply to the presentation of the proof of the last corollary: Section four is reorganized to clarify better the proof structure. Please check

  - Pages 27 – 29, Lines 876 – 952.

7- New references [1],[2],[3],[4],[6],[13],[31],[34],[35],[65],[66] are added in the support of new paragraphs.

Thank you for your consideration.

Reviewer 2 Report

Comments and Suggestions for Authors

The author attempts to construct a new framework of quantum field theory. This research direction holds potential theoretical value. However, despite the mathematical depth of the paper, there are several significant issues regarding the physical motivation, clarity of presentation, and rigor of argumentation, which affect the acceptability of the paper.

 (1)  The title of the paper raises a fundamental question: "Is quantum field theory necessarily 'quantum'?" However, I believe the author's discussion of this question is not very clear. Specifically, what is meant by "quantum" in this context? Does it refer to the superposition principle, non-commutativity, or the Hilbert space formalism itself? To clarify the paper's argument, I suggest the author further elaborate on the meaning of "quantum" in the title, and specify which aspect(s) of quantum theory are being challenged in the text, or if all of them are being addressed.
    
   (2) I do not believe the author has strictly proven from a physical perspective that quantum field theory is not necessarily "quantum." Rather, the author proposes a highly complex alternative mathematical framework based on combinatorics and topology to describe quantum field theory (especially in the non-perturbative regime). If this is indeed the case, the author should clarify this point in the paper and explicitly distinguish the constructed mathematical framework from traditional quantum field theory.

(3)The abstract is overly brief and should be expanded to explain the physical motivation for the research, the processes used, and so on. Specifically, the author should more clearly state the objectives, key issues, and the primary theoretical tools employed in the abstract.

(4)There are several issues with the references in the paper. First, the citation order is rather disorganized; secondly, the author cites a significant number of their own works (a total of 10 papers), but it remains unclear whether these references are crucial to the current study. I recommend that the author review and streamline the references, ensuring that only those directly supporting the paper's themes are included.

(5)The paper contains many long sentences, which make it difficult to read. I suggest the author break down some of the more complex sentences to improve readability and help the reader better understand the arguments being made.

Author Response

Dear Reviewer,

I would like to thank because of your important comments. In response, I have prepared the revised version of the work. Here I address a short list of revisions in terms of your report. Please note that all page numbers, line numbers and reference numbers in this letter are on the basis of this revised version of the article. 

1- In reply to concerning about the concept of “quantum” : Please check

- Pages 5 – 6, Lines 168 – 242: the texts provides an overview about quantum nature from standard and topose perspectives.

- Pages 7 – 8, Lines 247–301: the texts provide more details about quantum nature in quantum field theory from the perspective non-perturbative topos.

2- In reply to clarifying the answer to the question of the title: Please check

- Pages 7 – 8, Lines 274 – 335: the text explains how formal objectivity of non-perturbative topos support the “quantum” nature of quantum field theory.

- Pages 29 – 30, Lines 954—1008: the text provides more explanation about the “quantum” nature of quantum field theory.

3- In reply to short abstract: The Abstract is revised. Please check

-   Page 1, Lines 2 – 18.

4- In response to References Issues: Required revisions are performed. Please check

- The references are ordered in terms of their appearance in the text.

- Some of author’s articles are deleted from the list to reduce self-citation rate.

5- In response to Language case: The whole text has been checked to replace long sentences with modified versions to improve the Language.

6- New references [1],[2],[3],[4],[6],[13],[31],[34],[35],[65],[66] are added in the support of new paragraphs.

Thank you for your consideration.

 

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

All issues are addressed properly. I recommend the manuscript for publication in QR.

Author Response

Dear Reviewer,

Thank you for your comments to the original version of the work.

Reviewer 2 Report

Comments and Suggestions for Authors

I am pleased to see that the author has made meaningful revisions, and addressed most of my concerns. However, I still believe that the paper does not meet the publication standard. The reasons are as follows:

Although I mentioned the issue of excessive self-citation in the previous version, the author has only removed some of the references, while still retaining five of their own works. Moreover, the author’s first paper has already cited all of their previous works, so there is no need to reference so many of them again.

In addition, these citations form a "self-citation loop," making the acceptability and verifiability of the proposed framework largely dependent on whether the reader accepts the author's ideas. To strengthen the academic rigor and persuasiveness of the paper, the author must clearly and thoroughly compare and position the concepts introduced with existing, well-established areas of research.

Author Response

Dear Reviewer,

• I deleted some other of my works from the Reference List to follow your comments.
• However, in general, I disagree with your opinion in this case. Because a research article can have several results and some of them could be applied in one research and the other results could be applied in other research. In this present work I deleted around seven or more of my works from the Reference List and I think those references were essential to readers to better follow the mathematical strategies of the work. For example, the geometry of the Banach manifold of stretched graphons is only explained in my 2021 article in Nuclear Phys B, and I was forced to remove it to respect to your comments. The analytic evolution of large Feynman graphs is only explained in my 2021 article in Math Phys Anal Geom, and I was forced to remove it to respect to your comments. The computability of renormalized stretched Feynman graphons is only explained in one of 2023 works and I was forced to remove it to respect to your comments. My purpose is not increasing my citation number, there are only few people who work in this particular research field and I always try in my works to provide all more details with direct access to it. In my opinion all those deleted articles from the Reference List are essential to the present article, and if Academic Editor agrees, I can return all those deleted Reference to the article. 
• I have double checked Conclusion and it seems to me it presents carefully the results and compares concepts introduced concepts with existing ones.   
• I did improve English of the text. It is not clear to me why you address its improvement twice. I think English of the paper is fine and there is no need for any modification. 

Thank you for your consideration