Emergent Time and Time Travel in Quantum Physics

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper provides a quantum mechanical framework to manifest time travel. The introduction contains a comprehensive overview of the literature, then the paper details the PW formalism in section 2. In section 3 the authors construct a POVM for the measurements, based on harmonic oscillator Hamiltonians. In section 4 the time travel idea is reported, giving a "boring" model, where no observable time evolution occurs.

The construction of the paper is, despite its simplicity, intriguing. It seems to be a first, but promising step, and further works is needed (which is also discussed in section 5).

My question that may be clarified further concerns the commensurability condition of eq. (21). I think it would be useful to explain its role in the construction in more detail.  What happens, if it breaks "weakly". Does it leads to an approximate time travel?

Please fix reference issue in page 2 , line 49.

I think the paper is suitable for publication, after considering the minor issues listed above.

Author Response

We thank the referee for their review. Text changes have been marked in red in the current version. The broken reference label in line 49 and footnote 1 has been repaired. Some additional references which have been brought to our attention since submission have been added. We added a footnote after equation (21) to answer the question about a weak violation of the commensurability condition.

Reviewer 2 Report

Comments and Suggestions for Authors

Please check the references in lines 18 and 49. After carefully reading the manuscript I found that it is original and has sufficient novelty. 

The introduction is written in detail and the results and discussion parts are done nicely. 

I recommend the manuscript to be considered for publication. 

Author Response

We thank the referee for their review. Text changes have been marked in red in the current version. The broken reference label in line 49 and footnote 1 has been repaired. Some additional references which have been brought to our attention since submission have been added. We carefully double-checked the references in line 18, but could find no issues. To our knowledge, all printings of reference [3] should have identical page numbers, so the specific referencing should be unambiguous. We changed the comma between "[1,2]" and "[3, p.212ff]" to an ampersand for better readability.

Reviewer 3 Report

Comments and Suggestions for Authors

In this manuscript authors discuss the possibility of time travel that invariably will challenge dearly the concepts of fundamental physics. For thus authors apply the toy models implementing the Hamiltonian constraint in quantum theory, with an aim towards understanding what an emergent notion of time can tell us about the (im)possibility of time travel. Before acceptance authors should add some details for the readers:

1- On page 2 line 35, authors use canonical gravity? They should add a very short review of it.

2- Page 2 line 49, refrence is showing question mark [?] , please cite this reference.

3- Authors many times use  quantum field theory under refrence [20], a short review should be added.

4- Page 8 line 318, what is cosmological 318 singularity? please elaborate briefly.

5- Page 9 line 337, reference is unclear [25, §9] ? please cite properly.

6-  What specific information can be found from Figure 1?.

7- what are future applications of this research?

 

Author Response

We thank the referee for their review. Text changes have been marked in red in the current version. Some additional references which have been brought to our attention since submission have been added.
Concerning the specific concerns listed:
(1) We deem the term "canonical gravity" for the Hamiltonian formulation of general relativity to be sufficiently standard terminology, that reviewing it in the introductory overview of related questions would distract too much from the aims of the introduction. Also, while inspired by canonical (quantum) gravity, the model of the paper is not employing it. A more in-depth explanation would make misunderstanding this more likely.  We added a sentence to and mildly changed the phrasing in the end of the introduction to emphasize this once more.
(2) The broken reference label in line 49 and footnote 1 has been repaired. 
(3) Similarly to item (1), quantum-field-theoretic points raised in the introduction are background material (not employed in the computations themselves). As the main text is concerned with purely quantum mechanical issues, this would again distract and needlessly lengthen the introduction. 
(4) The term "cosmological singularity" for a singular scale factor is, again, fairly standard terminology in general relativity and cosmology. As we use the term primarily to make readers from a (quantum) cosmological background aware of important differences of our toy model to the setting more familiar to them, we believe that elaborating on its definition would increase the likelihood of this misunderstanding of our model as cosmological rather than reduce it. Readers unfamiliar with the term can easily understand the main part of the article, and will only encounter it if they would want to contrast the present model with the related, quantum-cosmological models. The work of the paper itself does not make use of cosmological singularities, as the work intentionally is not derived from a gravitational Hamiltonian model.
(5) We specifically added the section "§9" to be more precise than a simple [25]. Given the length of reference [25] (now [26], with the fix of item (2)) and the amount of material covered in it, we think it important to be more precise. This is similar to the earlier use of page numbers for the first appearance of reference [3]. The symbol "§" in English refers to sections and hence is called "section sign"; we are aware that this differs from other languages, where it refers often to paragraphs and is named accordingly and differently. We consider its usage in the present context proper, correct, and helpful to the reader.
(6) We have added wording in this version in its caption to emphasize that figure 1 serves primarily illustrative purposes. This relates to item (4) above, as in quantum cosmology only half of this wave function would have been encountered. The figure and its caption should serve to highlight this difference once more.
(7) We hope that the current bullet list of section 5, "Interpretation, Discussion and Outlook", adequately covers this. Here we give a partial list of future applications to a phenomenological study program of emergent time and its relation to time travel. As the current paper is a matter of fundamental research, no immediate technological application is foreseeable, and we would deem it unwise or even scientifically dishonest to make predictions regarding these.