Is the Copenhagen Interpretation Inapplicable to Quantum Cosmology?

Round 1

Reviewer 1 Report

The  paper consisits of two parts.

The first part is a revew of different interpretations of quantum physics concerning  application to quantum gravity with remarks by the author.

The second part is devoted to some special model with finite number of degrees of freedom imitating some features of the quantum gravity.A new idea

is presented to consider measurement in quantum gravity as breaking of gauge invarince taking different gauges for different mesurements.

Comparison of Copenhagen and Everett interpretations is made.

I consider this idea interesting and recommend this paper for publication in the Unuverse.

Author Response

Thank you for your report.

Reviewer 2 Report

The refereed paper is devoted to the comparison between the Copenhagen interpretation of quantum theory and of the many-worlds interpretation and their applications to quantum gravity and cosmology. The paper is clearly written and can be published. I would only advise to cite some papers, where related questions were analyzed in many detail, namely:

1. A.O.Barvinsky and A.Y. Kamenshchik,Preferred basis, decoherence and a quantum state of the Universe, arXiv:2006.16812 [gr-qc].
2. M.B. Mensky, Quantum measurements, the phenomenon of life, and time arrow: Three great problems of physics (in Ginzburg's terminology) and their interrelation,Phys. Usp. 50, 397 (2007).

Author Response

Dear Reviewer,

I have included references to the papers you recommended, see the references [26] and [19] of the revised version of my paper. They are mentioned in the end of Sec. 4 (page 8) and in the end of Sec. 3 (page 6), respectively.

Sincerely yours,
Tatyana Shestakova.

Reviewer 3 Report

See attached file.

Comments for author File: Comments.pdf

Author Response

Dear Reviewer,

Please find below my answers to your comments.

1. Perhaps should try to present a more clear definition of some concepts as the "principle of integrity", "principle of complementarity", "relative states", "extended phase spaces". I had the impression that the definitions of these concepts were somehow diluted in the text.

I believed that these concepts are generally accepted. However, I have tried to give a more clear explanation of them.

a. the principle of integrity. I replaced the word "integrity" by the word "wholeness" which was used in the original papers by Bohr. I changed the text on p.4 as following:

"In my opinion, the Bohr's passage refers to two fundamental principles of the Copenhagen interpretation, namely, the principle of wholeness (indivisibility) of quantum phenomena and the principle of complementarity. The principle of wholeness states the impossibility to separate any quantum object from a measuring device, the object and the device must be studied together as a holistic quantum phenomenon. In his other paper [12] Bohr also emphasized the feature of wholeness of a quantum phenomenon expressed in the circumstance that any attempt of its subdivision requires a modification in the experimental conditions incompatible with the definition of the phenomena under investigation."

b. the principle of complementarity. I continued on p.4:

"On the other hand, physical properties of the quantum object, manifested by its interaction with measuring instruments of some type, should be supplemented by those of its properties that can be detected in experiments of another type. Understanding of the behaviour of the quantum object in various experimental conditions will give us a complete knowledge about the object as far as possible in quantum theory. Physical pictures one can observe in different experimental condition complement each other. This is an essence of the principle of complementarity. Complementarity is understood here in a broader sense then just complementarity between particles and waves.

The statements emphasized by other authors can be considered as consequences of these two principles…"

c. relative states. The concept of relative states was introduced by Everett in his paper (ref. [14] of the revised version). In the beginning of Sec. 3 (p.5) I added the explanation of this concept following the paper [14].

d. extended phase space. I have rewritten the beginning of Sec. 6. On p.11 I wrote:

"The Dirac approach was the first attempt to construct a quantum theory of constrained systems. Dirac believed that it would be important to put any theory in the Hamiltonian form before quantizing it. He divided all variables into physical and nonphysical (gauge) ones, and only physical variables were included into phase space."

And further on p.12,

"...However, the phase space can be extended by including into it gauge degrees of freedom on an equal footing with physical ones. At first, the idea of extended phase space was put forward by Batalin, Fradkin and Vilkovisky (BFV) [50–52] in the framework of path integral quantization. In the case of gauge fields one should use an effective action which includes gauge-fixing and ghost terms. The missing velocities corresponding to gauge variables can be introduced into the Lagrangian by means of special (differential) gauge conditions. It actually extends the phase space of physical degrees of freedom."

Also, on p.13 I emphasized the point where the extended phase space approach differs from the BFV approach.

2. Concerning the question of gauge invariance and the Wheeler-DeWitt equation, it came to my mind that the lapse function is related to the time coordinate by the canonical conjugation relations, and different choices may be connected by canonical transformations. Could the author comment this point?

The lapse function cannot be related to the time coordinate by the canonical conjugation relations since the lapse function is one of the coordinates of extended phase space while time is one of the coordinates in spacetime which the lapse function depends on.

However, one can use different parametrizations of gauge variables (for example, components of metric tensor or the ADM variables), and transformations from some variables to other can be proved to be canonical transformations in extended phase space (see the text above and below Eq.(5)).

3. At page 10, the author says: "The only theoretical result, which has been obtained using the Dirac approach, is the Wheeler - DeWitt quantum geometrodynamics, but it has never been verified experimentally." I am not sure I have understood this statement. What about Quantum electrodynamics? It is also a constrained system to which the Dirac approach can be applied.

In the beginning of Sec. 6 (p.11) I gave the following explanation:

"Dirac illustrated his approach taking electrodynamics as an example. But quantum electrodynamics as a very successful and experimentally verified theory was created fully independently from the Hamiltonian formulation proposed by Dirac and was based mainly on the Lagrangian formalism and perturbation theory. Successful gauge theories of modern physics are also grounded on other theoretical and mathematical methods but not the Dirac conjecture. The predictions of these theories by no means depend on imposing constraints in an operator form as conditions on the state vector. In this sense, I would say that the Dirac approach has not been verified directly. The only theoretical result, which follows uniquely from the Dirac approach, is the Wheeler - DeWitt quantum geometrodynamics,  but it has never been verified experimentally."

4. I am not sure I have understood what would be the measuring apparatus for the universe. The author is invoking some kind of anthropic principle?

I have not invoked any kind of the anthropic principle. The anthropic principle states that we can see the Universe in this way, because we as observers can exist only in such a universe. I did not discussed this principle in my paper. In Introduction (p.2) I wrote that the conditions, in which we, as human beings, exist, determine that we have to use macroscopic instruments. On p.14 I pointed out that in general relativity the reference frame plays the role of a measuring device. In the extended phase space approach observers in different reference frames will see different physical pictures. I touched upon the question what could be a physical realization of the reference frame. Mathematically the reference frame can be described as a medium with some equation of state (p.15). On p.16 I added a citation to Landau and Lifshitz who also had described the reference frame as some sort of "medium". I hypothesized that this medium phenomenologically reflects some properties of vacuum in a given reference frame. At present, the properties of physical vacuum is a subject of study and have not understood enough.

Sincerely yours,
Tatyana Shestakova.

Round 2

Reviewer 3 Report

The author has addressed satisfactorily to my previous remarks and I am happy to recommend the publication of the
article in its present form. There are some minors editing corrections to be made (Planck instead of Plank, etc.) but the text is essentially in its final form in my opinion.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

REPORT

"Is the Copenhagen interpretation inapplicable to Quantum Cosmology?"

Modern science is in crisis. It faces a number of fundamental problems that it cannot solve. Physics is no exception. It provides us with two different descriptions of reality—quantum and classical. Our basic intuition shared by both scientists and lay audience rebels against the idea that reality in which we live represents two separate and largely irreconcilable domains—quantum and classical. Yet our physicists tell us otherwise. All attempts to solve this problem have so far failed.

The author explains that she tries to show in her article that the Copenhagen interpretation is compatible with quantum gravity. Indeed, the article shows this compatibility and, to this extent, the article is successful. However, the author also indicates that she sees her effort as part of a larger agenda. She writes: “We hope that quantum gravity will be a verifiable theory. But what could we observe to verify it? It must be macroscopic consequences of quantum gravitational phenomena fixed by our macroscopic instruments. Then, the main ideas of the Copenhagen interpretation may be relevant, though their generalization and future development may be required.” It is the fact that the author sees her effort as part of a broader agenda that raises questions. For one thing, quantum gravity is still largely a hypothesis, rather than a theory. Also, since quantum gravity deals with quanta, its compatibility with the Copenhagen interpretation is largely a purely academic issue.

The Copenhagen interpretation draws a clear line between the classical and quantum domain. On one hand, it recognizes the fact that the quantum domain underlies classical reality. On the other hand, it also recognizes that the classical domain, to which the observer and instruments belong, are an essential condition for observing quantum reality. The Copenhagen interpretation is implicitly dualistic and the existence of both domains is essential for it; it relies on both.

The goal that the author ultimately pursues will eliminate the duality implicit in the Copenhagen interpretation, which creates a contradiction in her overall perspective. She intends to use the Copenhagen interpretation to bolster quantum gravity but in the process she will undermine the very interpretation that she uses to achieve her goal.

There is no outside in quantum gravity. Therefore, the observer in quantum gravity will be located in the quantum domain. The conclusion that follows is that the state of the observer can only be a quantum, not classical state. Consequently, the state of the observer, just like the state of any other quantum object, will be defined by the wave function with all its characteristic features, including superposition. Such superposition must include all possible states of the observer. In other words, like the proverbial Schrodinger’s cat, the observer must be dead and alive at the same time. One can see from this observation that the approach proposed by the author will add to the conundrum that the Copenhageners wanted to avoid.

The reason why Bohr and other Copenhageners imposed a classical constraint on the observer was not idle. They recognized that the conundrum of quantum mechanical description of the observer might render the theory completely intractable and unusable. They were pragmatic and wanted their theory to be relevant. They did not want their theory to be a mere intellectual curiosity. They wanted it to have practical significance.

Another concern that I have relates to author’s suggestion that quantum gravity allows for the observer to have a specific frame of reference. If I understand the author correctly, in quantum gravity the observer is located inside, rather than outside the quantum domain—there is no outside in quantum gravity. The theory of relativity allows the observer to chose a particular frame of reference. This frame critically affects observations conducted in this frame, which is one of the main points of the theory of relativity.

However, the theory of relativity recognizes at the same time that all frames are equal; and no one observer’s frame is preferential to frames chosen by other observers. In accordance with this principle, the universe should look the same regardless of the frame of observation. That is why the theory of relativity recognizes the speed of light as constant in all frames. The speed of light constant is what all possible observers’ frames have in common. The speed of light provides the frame for the entire universe.

Similar to light, quantum gravity also relates to the entire universe and serves as a frame for it. In the light of this consideration, I do not quite understand the meaning that the author attributes to the specific frame of the observer in the domain of quantum gravity.

The author understands well that the demonstration of the relevance of some principles and mathematical gymnastics are at this point merely an intellectual curiosity. She says that the unification that she seeks will require more efforts. However, does the path she chooses lead to such unification? This question remains unanswered and even unaddressed.

There is one consideration that raises serious doubts as to whether the author’s approach will ever lead to success in resolving the fundamental problem that looms behind her limited argument. Gravity represents a non-radiant form of energy. The Copenhagen interpretation deals with radiant energy. It is not clear how the two can be reconciled since they ultimately relate to two very different forms of energy. Perhaps a more productive approach would be to use Dirac’s relativistic wave equation that allows for two possible solutions: one for familiar radiant energy and another for non-radiant one.

The conclusion that follows from the above is that the author succeeds in showing the relevance of some principles and mathematical formalism to the current emerging state of quantum gravity. On this count, the article merits publication. However, she should show critical awareness and closely circumscribe her attempt. She should clearly indicate that what she does in this piece does not necessarily lead to the solution of the larger problem that looms behind her attempt—a theory that purports to reconcile the current division in our representation of physical reality.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

The manuscript presents a profound discussion comparing applicability of Everett interpretation of quantum mechanics (QM) to Copenhagen interpretation of QM with regard to quantum gravity. Relevance of the differing approaches are evaluated with regard to gauge invariance (or lack thereof), and transformation from time-independent fundamental quantum gravity state to time-dependent classical solution through quantum jump. The relationship between and the prioritization of the Wheeler-DeWitt equation and the Schroedinger equation is evaluated. The historical context of the discussion is nicely done, with ample references. I highly promote this manuscript for publication.

Author Response

I an grateful to the Reviewer for his/her assessment of my paper.

Reviewer 3 Report

This is an interesting paper. Making very strong claims but defending them in a plausible way. As it stands however, there is far too little engagement with relevant work. In particular, the deep and sustained engagement with these issues by philosophers of physics is simply ignored (the citation to relevant physicists is also patchy). Moreover, many of the key steps in the argument are not made with the necessary level of care and precision. So I suggest a round of revisions focused on making the argument clearer and links with existent relevant work stronger.

Major Comments

Claims about the "Copenhagen interpretation"

First, it would make sense to engage more clearly with historical and philosophical discussion of the Copenhagen interpretation -- which is extensive. A good starting point would be the discussion and references listed here:

https://plato.stanford.edu/entries/qm-copenhagen/

The work of Camilleri (in particular “Bohr, Heisenberg and the Divergent Views of Complementarity”, in Studies in History and Philosophy of Modern Physics, 38: 514–528.) should be particularly useful.

Then, I'm not convinced by the claim that relative states and Copenhagen can be fitted together unproblematic. At the least, I think the view which the author ends up defending is more like a hybrid between Copenhagen and relative states than a Copenhagen view proper. Surely if the reduction of wave function is only relative to an observer the view ends up having more in common with many worlds (without a definite splitting) then it does with the standard way of thinking about Copenhagen in terms of collapse on measurement. So I think a little more needs to be said in defence of this not really a "many worlds in disguise" view.

Presentation of the Interpretations

The way the paper is set up in at the start of the introduction it appears that the choice in interpretation is between Copenhagen and Many Worlds. This is obviously a big misrepresentation (and is corrected later) but I think it would be appropriate to mentioning a wider range of discussions regarding application of different interpretations of quantum mechanics to quantum cosmology a bit earlier. Things it might be worth mentioning:

For example:

- Bell `Quantum Mechanics for Cosmologists’
- Rovelli's relational interpretation.
- Dowker's quantum measure theory approach
- No mention all of dynamical collapse -- which presumably won't work very well in quantum cosmology.

Then, I think it is too strong a statement (or at least overly vague) to say that (with regard to de Broglie-Bohm and decoherent histories) "[the] mathematical content of these theories is not equivalent to the generally accepted Schrödinger – Heisenberg formulation" -- surely, at least in the case of de Broglie-Bohm, the point is that formally they ARE equivalent in that the equations can all be derived from the standard formalism. Moreover, decoherence is surely now part of "standard" quantum mechanics. A little more needs to be said here. So it would be good to be a bit clearer with regard to what the inequivlence is supposed to mean. (Also, it would probably make more sense to refer to the standard formalism as the Dirac-von Neumann formalism, in the Schrödinger – Heisenberg pictures. Since of course there is also the contrast between Schrödinger's wave mechanics and Heisenberg's matrix mechanics, which strictly speaking are not equivalent.)

Discussion of Measurement

I completely failed to follow the following crucial passage (p3-4 l126-134):

"It follows from the principle of superposition that if we consider the superposition of two states, A and B, such that some observation which is certain to lead to the results a and b when made on the system in the states A and B, correspondingly, the result of the observation made on the system in the superposed state will never be different from a and b [12]. In other words, the superposition principle, being one of the axioms which quantum mechanics as a mathematically consistent theory is grounded on, implies the notorious “quantum jump” from the superposed state to one of states (A or B) in the superposition, independently on an interpretation."

It seems simply false to me to assert that the superposition principle *implies* quantum jumps. Rather, I think what is meant is that the superposition principle *together with the observation of definite outcomes* implies that there must be some reduction of the superposed state. However, this reduction can be effective in the sense it relates to a change in knowledge (e.g. de Brogile-Bohm) or an actual "jump" (e.g. dynamical collapse).

Then, the representation of Everett is inaccurate -- clearly if world splitting happens upon "measurement" then the view ends up making measurement even more mysterious than it is in Copenhagen. But very few modern Everettians actually hold that view. See for example Wallace's Emergent Multiverse and also and Vaidman's discussion in https://plato.stanford.edu/entries/qm-manyworlds/.

I think the difference between relative states and many worlds is a good idea: however again engagement with the historical and philosophical literature on this would be a good idea -- in particular see https://plato.stanford.edu/entries/qm-everett/ and references therein.

Finally, what I think is the absolutely key reference on measurement -- in particular its relation to decoherence is https://arxiv.org/abs/quant-ph/0312059 -- it would be well worth the author reading this paper carefully as it touches on many issues relevant to the discussion of section 4. Further papers by the same author in fact gives an extremely detailed discussion of a Copenhagen style interpretation consistent with decoherence. These are

https://arxiv.org/abs/1009.4072
https://arxiv.org/abs/0804.1609

Discussion of the Constraints

I found the the following statement rather problematic:

"In the Dirac approach the central part is given to a postulate, according to which each constraint after quantization becomes a condition on a state vector. Let us emphasize that it is indeed a postulate, since it cannot be justified by the reference to the correspondence principle. The role prescribed to the constraints could be explained by the fact that at the classical level the constraints express gauge invariance of the theory. It was initially believed that imposing constraints at the quantum level would also ensure gauge invariance of wave functional. However, this issue has not been thoroughly investigated and gauge invariance of the theory has not been proved."

This significantly understates the formal basis behind constraint quantization. Whilst it is certainly true that as regards the Hamiltonian constraints there is room for debate, the general relationship between classical constrained theories and the quantum Dirac prescription is far from a "postulate" -- and is nothing to do with the correspondence principle. In eleccronmanentism for example the constraint condition is well justified. Moreover, I think with regard the momentum constraints, it is pretty formally clear that the quantum condition is equivalent to the classical diffeomorphism invariance of three geometries. (Thiemann's book argues for this in detail).

Then, with regard to the Hamiltonian constraint, this is surely more than a simple conjecture. In particular, the semi-classical analysis does appear to indicate that the WDW equation has some formal relationship with the classical equations. E.g. Gerlach, Ulrich H. (1969, Jan). Derivation of the ten Einstein field equations from the semiclassical approximation to quantum geometrodynamics. Phys. Rev., 177(5), 1929–1941. So I think a little more should be said here.

I also found it rather odd that the major review papers on the problem of time were not mentioned. Clearly these, rather than Wheeler or DeWitt, would be the best first stop for a reader interested to know more. So I would certainly cite the Isham, Kuchar and Anderson review papers.

Minor Comments

p.2 37-8 Sentence "I believe that it is the idea about the role of the observer with his instruments in quantum theory. " Doesn't make sense and should be re-written.

p.2 54 "The interpretation comes at the last stage helping to judge about the obtained results." Not idiomatic -- remove "about".

I'd be very interested to know the extent to which the model discussed here is related to a similarly "Schrodinger-type equation" derived by Unruh and Wald (https://journals.aps.org/prd/abstract/10.1103/PhysRevD.40.2598) and recently studied in more detail by Gryb and Thebault (https://www.sciencedirect.com/science/article/pii/S0370269318306178?via%3Dihub)

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

COMMENTS ON THE AUTHOR’S RESPONSE TO MY REVIEW OF HER ARTICLE

I do not intend to engage in the second round of reviewing the same article. Nobody has time for this.

Here is what the author writes in response to my criticism:

“The Reviewer writes that my goal is more than just to demonstrate that the Copenhagen interpretation is compatible with quantum gravity. Well, my actual goal is to present some aspects of the extended phase space approach to quantum gravity which I have been developing for many years. The approach does not pretend to be a final quantum theory of gravity, but it proposes an alternative view on problems which one faces in searching for a consistent theory.”

I do not want to parse her every word and I do not require her explanation of what she actually meant by what she wrote. I am responding strictly to what she wrote in her article, not what she might think about what she wrote. I simply write how what she writes appears to an average reader.

Here is what she wrote, for example, in her original paper:

“We hope that quantum gravity will be a verifiable theory. But what could we observe to verify it? It must be macroscopic consequences of quantum gravitational phenomena fixed by our macroscopic instruments. Then, the main ideas of the Copenhagen interpretation may be relevant, though their generalization and future development may be required.”

I do not want to sit and speculate what she means by this paragraph. If this does not sound ambiguous to her, it does to me. She must write it in a way that would preclude any ambivalence and ambiguity. I specifically cited this paragraph in my review. The author chose to ignore it and left it unchanged in the new version.

The author chooses a bad strategy in her response. She tries to turn the table on me and asks me to explain what I mean by this or that. She may be well advised to remember that I am not writing an article and I am not required to explain myself as I would have in an exhaustive piece that she submits. So, my writing is not in question here. But hers is. She creates ambiguity and ambivalence, not I. Frankly, I do not see how what the author does in her article will lead to a quantum theory of gravity, which is at this point a very tentative enterprise anyway. I think the author should clearly state this point and clearly delineate the boundaries of what she tries to do. There should be no ambivalence, no ambiguity, and no maybes.

I understand that the author has spent a great deal of time on developing her ideas, and I appreciate this fact. I have not disputed her formalism and in many places indicated that I understand the limited nature of her enterprise. The author does not have to beat into my head that her task is limited. I say so myself in several places of my review. I write:

“The author explains that she tries to show in her article that the Copenhagen interpretation is compatible with quantum gravity. Indeed, the article shows this compatibility and, to this extent, the article is successful. However, the author also indicates that she sees her effort as part of a larger agenda.”

But the passages, as the one I cited above, point beyond this limited nature to something bigger. And that’s what troubles me.

Finally, I made a passing suggestion about Dirac’s equation. But this is merely a suggestion for the author in her future work. It is not to be taken as a requirement for this article. If she disregards my suggestion, I will not hold it against her in any way and certainly not against her limited article.

To conclude, if the author fixes the issue of ambivalence and ambiguity that she creates, the article, as I indicated in my review, can be published. If she refuses to do so, I am afraid I will have to withdraw my tentative endorsement and recommend against its publication.

Reviewer 3 Report

I do not find the response to my comments at all satisfactory: I don't see how the author can maintain a refusal to properly engage with relevant literature on the interpretation of quantum mechanics whilst writing a paper on the interpretation of quantum cosmology. It is simply irrelevant whether I or the author is a philosopher of physicists, and, moreover, whether this paper is for philosophy journal or a scientific journal. There are basic standards of intellectual scholarship that are simply not met in the paper as it stands. As such, I don't think it is worthwhile for me to engage further with the author regarding this paper.

(Let me just point out, however, that the author is simply incorrect (or at least very unclear) about the Dirac prescription in electromagnetism and more generally: see Henneaux and Teitelboim's textbook chapter 19)