Towards Relational Foundations for Spacetime Quantum Physicsâ€
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis is a remarkable paper, presenting and discussing a novel and brilliant observation. It addresses an open problem in the relational interpretation of quantum mechanics. This was formulated in the context of systems with finitely many degrees of freedom, in a form that was manifestly inconsistent with field theory. This was a weakness of the interpretation, which called for more than a technical adjustment. The paper proposes a conceptual solution to the problem by relating it to the Wilsonian idea that qft must be understood a meaningful at some scale. The proposed solution is brilliant, and certainly deserves to be known.
Author Response
Comments: This is a remarkable paper, presenting and discussing a novel and brilliant observation. It addresses an open problem in the relational interpretation of quantum mechanics. This was formulated in the context of systems with finitely many degrees of freedom, in a form that was manifestly inconsistent with field theory. This was a weakness of the interpretation, which called for more than a technical adjustment. The paper proposes a conceptual solution to the problem by relating it to the Wilsonian idea that qft must be understood a meaningful at some scale. The proposed solution is brilliant, and certainly deserves to be known.
Response: Thank you for the positive review.
Reviewer 2 Report
Comments and Suggestions for AuthorsI think this paper is suitable for publication. Its most original idea is the link between the renormalization group and the "relational" interpretation of the quantum measurement process.
Here are some suggestions for improving the writing:
Lines 58-67: This paragraph starts by emphasizing that it is about quantum theory. It is then very confusing to say that "the space of states of the system is finite dimensional." Surely the Hilbert space of quantum states is infinite-dimensional, except for certain simple spin systems. What is finite-dimensional is the classical configuration space.
L. 156-158: How can a "restriction" be "considered as subsystems"? This sentence needs to be recast.
L. 276-294: What are the "two basic ingredients"? Regularization maps and what else?
L. 321: containS
L. 427-435: I found this paragraph obscure.
L. 459: hypotHetical
L. 460: casted -> cast
L. 466: "non gauge invariant level" is awkward and arguably nongrammatical (see next point). This sentence should be improved.
L. 469-470: non confined -> nonconfined. "Non" is never a word by itself.
L. 507 and 512: Refs. 16 and 21 are identical.
Comments on the Quality of English Language
See the report.
Author Response
Thank you for the positive review and your very valuable feedback.
The writing was polished throughout the paper. Below we address each specific comment.
Comment 1: Lines 58-67: This paragraph starts by emphasizing that it is about quantum theory. It is then very confusing to say that "the space of states of the system is finite dimensional." Surely the Hilbert space of quantum states is infinite-dimensional, except for certain simple spin systems. What is finite-dimensional is the classical configuration space.
Response 1: Lines 58-67: We completely agree with your remark. We have clarified this paragraph. The new version of this paragraph is located in L.59-L.73 and marked in red.
Comment 2: L. 156-158: How can a "restriction" be "considered as subsystems"? This sentence needs to be recast.
Response 2: L. 156-158: We fixed the issue. The new version of this paragraph is located in L.164-L. 166 and marked in red.
Comment 3: L. 276-294: What are the "two basic ingredients"? Regularization maps and what else?
Response 3: L. 276-294: The second ingredient is a set of coarse graining maps. We edited accordingly. The new version of this paragraph is located in L.284-L. 309 and marked in red.
Comment 4: L. 321: containS
Response 4: Corrected. Thank you.
Comment 5: L. 427-435: I found this paragraph obscure.
Response 5: The paragraph has been amended. The new version of this paragraph is located in L.457-L.463 and marked in red.
Comment 6: L. 459: hypotHetical
Response 6: Corrected. Thank you.
Comment 7: L. 460: casted -> cast
Response 7: Corrected. Thank you.
Comment 8: L. 466: "non gauge invariant level" is awkward and arguably nongrammatical (see next point). This sentence should be improved.
Response 8: Corrected. Thank you.
Comment 9: L. 469-470: non confined -> nonconfined. "Non" is never a word by itself.
Response 9: Corrected. Thank you.
Comment 10: L. 507 and 512: Refs. 16 and 21 are identical.
Response 10: Corrected. Thank you.
Reviewer 3 Report
Comments and Suggestions for AuthorsThis is an interesting paper which, for a large part, reviews existing approaches to demystifying the measurement process in quantum mechanics in terms of relational variables introduced and valued by the interaction of the system and the probe (Rovelli) and how this idea is purported to quantum field theories keeping the amount of information attainable by a measurement finite through the finite resolution associated with the process. This necessarily makes contact with the Wilsonian Renormalisation Group and its application to deduce concrete effective quantum field theories (Polchinski). The authors alos describe how an alternative description by Fewster and Verch, where interactions are confined to a compact region of the supporting spacetime manifold, can be generalised by certain glueing conditions of interaction cells.
I do like the emphasis on a coupling between gauge systems being described by non-gauge invariant terms in the interaction Lagrangian and how this fundamental observation relates to relational variables for two given gauge systems. "Then work on the relational interpretation of quantum physics should address gauge systems." To my mind a "quantum event" (say, a photon) is triggered by a gauge relation between a given gauge system (the finite part of a 4D euclidean gauge theory living on spatially infinitely extended R³xS¹ say, the central part of a caloron in deconfining SU(2) YM thermodynamics) and its gauge-system surroundings (the complement of this finite region), the gauge relation being a propagating excitation (a plane wave, supported by caloron peripheries but eventually - depending on its wave length and off-shellness - probing a caloron center). The authors provide such an example in Sec. 3. For future research on how quantum measurement relates to the idea of relational quantum systems I would thus welcome definite identifications of systems and subsystems, starting from a thermal, gauge-theory based setting and subsequently deforming this adabiatically (temperature as a functions of emergent Minkowskian spacetime) into much more general situations. Such work could be based on https://www.worldscientific.com/worldscibooks/10.1142/8015#t=aboutBook and also on the remarkable result in https://www.sciencedirect.com/science/article/pii/S0550321324000713 where a photonlike solution to the classical Minkowskian 4D SU(2) Yang-Mills equations was constructed.
On the whole, this is an interesting contribution on a deep subject that, if pursued properly, could mature into significant and useful insights into the nature of quantum systems under measurements. My (and the authors') bet is that this progress will be made on the basis of gauge theory. The authors should spell-check the paper, I have also found a couple of mistakes in the construction of sentences.
I recommend this article for publication in Universe.
Author Response
Comment 1: ... I do like the emphasis on a coupling between gauge systems being described by non-gauge invariant terms in the interaction Lagrangian and how this fundamental observation relates to relational variables for two given gauge systems. "Then work on the relational interpretation of quantum physics should address gauge systems." To my mind a "quantum event" (say, a photon) is triggered by a gauge relation between a given gauge system (the finite part of a 4D euclidean gauge theory living on spatially infinitely extended R³xS¹ say, the central part of a caloron in deconfining SU(2) YM thermodynamics) and its gauge-system surroundings (the complement of this finite region), the gauge relation being a propagating excitation (a plane wave, supported by caloron peripheries but eventually - depending on its wave length and off-shellness - probing a caloron center). The authors provide such an example in Sec. 3. For future research on how quantum measurement relates to the idea of relational quantum systems I would thus welcome definite identifications of systems and subsystems, starting from a thermal, gauge-theory based setting and subsequently deforming this adabiatically (temperature as a functions of emergent Minkowskian spacetime) into much more general situations. Such work could be based on https://www.worldscientific.com/worldscibooks/10.1142/8015#t=aboutBook and also on the remarkable result in https://www.sciencedirect.com/science/article/pii/S0550321324000713 where a photonlike solution to the classical Minkowskian 4D SU(2) Yang-Mills equations was constructed.
Response 1: Thank you for the input.
We agree that in the modeling of real life laboratory situations and non-ideal general situations, the essential tool is statistical quantum field theory, and that this fact, together with the mentioned ubiquitous appearance of gauge systems, says that in order to extend the considerations of this paper to non-idealized situations a framework for quantum field theory of gauge systems at finite temperature should be considered. We added a paragraph addressing it, and we gave as a reference one of your suggestions.
The mentioned paragraph is located in L. 499-503 and marked in red.
Comment 2: The authors should spell-check the paper, I have also found a couple of mistakes in the construction of sentences.
Response 2: We did spell check the document and polished its writing throughout.
