On the Inaccessibility of Time Machines

Round 1

Reviewer 1 Report

The article describes how trips to the past are made unfeasible when effects of a specific proposal for gravity quantization are introduced.  The article in general is well written, but some obscure points deserve attention.

 

 1. In my opinion, the reference to the first solution of Einstein's equations with CTC was missing, the 1949 Gödel solution.

 2. It is not clear how the average energy-momentum tensor is computed in equations (3.4) and (3.21).

 3. What kind of matter does (3.19) represent?

 4. These supposed quantum gravity effects appear to be semi-classical approaches.  Thus, it is debatable to state that time travel is prevented by quantum effects, as there is not only one approach to the quantization of gravity.

Author Response

Thank you for your report. Please let me know if the points outlined below do not address your questions properly or if there is a need for further clarification.

1) Bottom of page 3: added a sentence: “The first solution of Einstein's equations with CTCs has been found by G\"{o}del in 1949” and the relevant reference;

2) Both expressions are obtained by taking 3.3 and 3.20 (expressed in x^\pm and r coordinates, respectively) and replacing the coordinates through the aforementioned coordinate changes. For instance, in 3.20, if we put r^2 = 1 - \tau^2, and we change space <-> time, we obtain 3.21; similarly, for 3.4 where we use the definition of x^\pm in terms of \tau and \phi (around 3.2 equation);

3) The expression given in 3.19 is the definition of a Brown-York stress tensor with the relevant counterterm. This procedure has been outlined in Ref. [31, 32]. This stress tensor is quasi-local and associated with a gravitating spacetime region, and we compute it on the boundary of the said region (the original paper can be found here: gr-qc/9209012);

4) Indeed, these are semiclassical effects in the sense that we are using the formalism of quantum field theory in curved spacetimes---this is why in the abstract, we say that we need not invoke quantum gravity (whatever it is) in order to resolve these issues. Note that the use of holography here is similarly regarded as QFT on curved spacetimes since we are always working with a fixed metric.

Reviewer 2 Report

The author studies the problem of time machines (characterized by closed time-like curves)  in General Relativity and explains why they cannot  be accessed by observers once quantum effects are included. The author also discusses the relation between traversable wormholes and time machines in the presence of quantum effects.

The paper is well-written, interesting, sufficiently well documented  and worth being published by Universe. I have no basic objection to its  publication in its present form.  However, a couple of comments may be useful for the author to consider optional improvements:

- It is mentioned the following:  "...even though traversable wormholes of the XX century used exotic matter and advanced civilizations, nowadays their construction is regarded as a physical possibility [3–11]".  My comment is: why several of the cited papers (despite being written by well-known experts) remain nevertheless unpublished after years of having appeared in the arXiv?  Is it not surprising that a typical paper in this list, starting with "We present a wormhole solution in four dimensions..."  and ending with "The solution can be embedded in the Standard Model by making its overall size small compared to the electroweak scale", has not been published in a good journal yet?  What went wrong?  Maybe something is not quite right and maybe the statement should be softened in the meantime.   While a paper is not published,  the ideas disputed  in it  cannot be considered fully  accepted by the general community of scientists.  This is especially so for papers making big claims.  A hint on what happened may come from noting  that in subsequent papers, such as [9] for example (which by the way  became recently published -- despite the current author does not seem to be aware),  one can see after a lot of discussions that there is a small (sub)section of the paper  mentioning:  "Some practical problems",  in which the authors intend to show that perhaps this story is not  a fully rosy picture  after all.  So the statement by the present author "nowadays their construction is regarded as a physical possibility"  looks at best a sheer exaggeration.  No less exaggeration is the abstract of the mentioned paper, which starts saying "We point out that there can be humanly traversable wormhole solutions ..."   This is not what anybody reading (sub)section 2.4 of that paper would conclude.  Now if we are ready to admit  that this is "possible"  after fine tuning a lot of parameters, then we are back to a science ready to admit fine tuned reality as real (like e.g. the cosmological constant problem, as a supreme example) . But such a "reality" is not reality at all. Again, it is, at best, "science fiction".

- The author states that one does not need quantum gravity for the resolution of time machines since  semiclassical back reaction must be sufficient enough.  However, the language maybe a bit confusing here since  the author is supposed to  study the problem of time machines in General Relativity. But GR is not amenable to quantization, as it is well-known, and therefore one would like to see some more care in using the denomination "semiclassical". In fact, semiclassical gravity is not the same as GR since the former admits some cures for renormalization which do not hold for the latter.  Apart from that, QG, of course, does not exist yet, no matter how many times we use this couple of words in the literature.

- There is no discussion about the role played by the vacuum energy and the cosmological constant problem insofar as the possibility of  time machines.  It is surprising that one may consider feasible  to reach some realistic conclusion without taking into account the difficulties inherent to that problem.  It is only mentioned in passing in Sec. 3.2  below eq. (3.19), where it is stated that ℓ is associated to the three-dimensional cosmological constant ( the author must mean the inverse of  ℓ, I suppose, see however next point). But the subject is not mentioned anymore.

- Units are a bit peculiar all along the exposition, since G is maintained everywhere, but the metrics being used in different places do not seem to  have dimension of distance and then all the remaining quantities are deprived from a definite dimension as well, take e.g. equation (3.19)  and following.  A clarification on these "niceties" would be welcomed by (some) readers.

Author Response

Thank you very much for your report. I have fixed the references by adding the publisher where applicable.

1) Indeed, it is a bit peculiar that the papers were not published, so I reached out to one of the authors, who confirmed that they simply forgot to submit it to a journal. The paper on "Traversable wormholes in 4d" is currently under consideration in a reputable journal, while the "humanly traversable one", as noted, has been published now;

2) The use of the word "semiclassical" indicates we are dealing with a quantum field theory in curved spacetime; we are not making claims beyond this regime, including the existence and the form of a model of quantum gravity;

3) It is not clear to me that there is a relation between the problem of time machines and that of the cosmological constant;

4) The units can always be restored. Namely, in most of the calculations, we are simply setting the cosmological constant to one. 

Reviewer 3 Report

This work is an interesting study and a good contribution to the literature. The paper is well written and consists new results. I only suggest that the author improve the abstract of the manuscript, it should be understandable to the reader. After a minor revision, I can recommend it for publication in the Universe.

Author Response

Thank you for your report. May I ask what part of the abstract needs to be improved? For instance, if I add after the first sentence: "Using holography, we will show that observers cannot cross the chronological horizon since they would require infinite energy.", would that be beneficial and sufficient?

Reviewer 4 Report

The manuscript addresses the topic of accessibility of time machines, defined as causality-violating regions of the spacetime generated by the presence of a closed causal curve. A claim is made that, while such kinds of time machines are generally permitted by General Relativity (GR), the subsequent inclusion of quantum effects prevents them from being accessed by an observer. Furthermore, it is highlighted how time machines can be "built as" traversable wormholes only when quantum effects are included.

Sections 2 and 3 of the manuscript review results previously obtained by the Authors (see Refs. [20] and [21]), while the core findings are shown in section 4 and discussed in the last section.

The study contains novel and interesting results, and it is clearly written. The research design is appropriate and the methodology employed is adequately described. It meets the standards of quality, originality, and robustness for this journal.

Before recommending it for publication in Universe, I propose that the Author takes care of two minor and simple aspects:

1.   On page 5, third line below Eq. (2.9): "BTZ black hole"  --->  "Bañados-Teitelboim-Zanelli (BTZ) black hole". A reference should also be added here.

2.   At the beginning of section 4, on page 11: I would rephrase the sentence "Traversable wormholes have been shown to exist" since, although being formally allowed by GR, from an experimental viewpoint they still remain hypotetical objects.

Author Response

Thank you very much for your report. I have made the following changes:

1) Top of page 5: instead of BTZ, the full Banados-Teitelboim-Zanelli has been written, and a reference to the original paper has been added;

2) Beginning of Sec. 4 (p.11): Instead of “Traversable wormholes have been shown to exist,” we write, “We know how to construct solutions for traversable wormholes, so we can proceed to the next step\footnote{We emphasize that the experimental confirmation of their existence is still lacking.}”;

 

Would you agree with these changes?

 

Thank you once again.

Round 2

Reviewer 1 Report

The author have properly answered my previous points.

Author Response

Thank you very much for your report.

Reviewer 2 Report

I have no serious  objections against this manuscript, except the answer to the point 4):

4) The units can always be restored. Namely, in most of the calculations, we are simply setting the cosmological constant to one.

If they can be restored why not to restore them? Or at least to warn the reader what conventions are used.   I think this must be fixed in one way or another.  Also, setting the cosmological constant to 1 can be misleading. Not surprising to find then the author's answer to my question 3:

3) It is not clear to me that there is a relation between the problem of time machines and that of the cosmological constant;

The author may be missing a possible relation simply because of this unappropriate convention.   As I said, units should be fixed and the CC too.  It is not such a big effort.

Author Response

Thank you very much for your reply. I will put in the text around eqn. 3.11 that the cosmological constant is set to one. 

 

To answer the question of why I think the cosmological constant won't make a difference, let me explain an example that involves a Cauchy horizon inside a charged black hole, namely the inner horizon. It was shown by Hollands et al. in 1912.06047 that the Cauchy horizon of a Reissner-Nordstrom (RN) black hole in de Sitter in 4D will diverge due to quantum effects. The reason why this example was interesting is that classical matter fields were not enough to render this inner horizon unstable---one could always find some geodesics that could cross the horizon. Nevertheless, once quantum effects have been included, the divergence of the stress tensor at the inner horizon was such that a proper curvature singularity would be made, and no observers could ever cross to the other side. For RN black holes in flat and Anti-de Sitter spacetimes, even classical matter was enough in most cases. Still, the quantum calculation of the stress tensor leads to the same result as in de Sitter. The reason is due to the emergent symmetry next to the inner horizon, which puts the stress tensor in a particular form, and the divergence is then fixed by this symmetry. Therefore, one can claim with confidence that the inner horizons of RN black holes will be divergent whenever quantum matter is present.

 

Now, the RN black hole does not have closed timeline curves behind its inner horizon, like Kerr black holes. Nevertheless, there is nothing qualitatively different about the calculation of the quantum stress tensor between the RN and Kerr cases; indeed, the authors themselves expect that the calculation should go through in a similar manner since there should also be this emergent symmetry. Furthermore, there are arguments from many other directions that enforce the strong cosmic censorship (a singular Cauchy horizon)---one can argue through holography that it would make no sense to connect two completely disconnected CFTs by passing to the other asymptotic region through the inner horizon: such a possibility would render AdS/CFT wrong. There are other arguments one can make regarding the entanglement of quantum fields across these horizons, or simply arguing for the predictive power of General Relativity, so it is with great confidence that we believe inner horizons of black holes should be singular.

 

Having said that, the Kerr inner horizon is a chronological horizon, and the Kerr-dS black hole would undergo the same calculation as Hollands et al. which would make the inner horizon singular due to quantum effects. This is the same statement as the one made in this manuscript: quantum effects definitively make chronology horizons singular, and building on the results of Hollands et al., this statement should hold regardless of the cosmological constant.

Reviewer 3 Report

I can recommend the paper for the publication in the journal.

Author Response

Thank you very much for your report.

Reviewer 4 Report

All the points raised have been addressed. I recommend the manuscript for publication.

Author Response

Thank you very much for your report.