Equivalence Principle in Classical and Quantum Gravity
Round 1
Reviewer 1 Report
Paunković and Vojinović discuss several formulations of the equivalence principle (EP) and its interpretation in the contexts of general relativity, mechanics and field theory. Particular emphasis is given to the weak equivalence principle (WEP), and it is argued that it must be violated under, both, very general real physical conditions and extreme quantum regimes such as superpositions of space-time geometries.
Although the article is interesting, particularly the overview of the various
formulations of the EP, I find the paper somewhat disappointing overall. There are three reasons for this.
First, the conclusion that the WEP must be violated is quite trivial, because it is a statement about idealized point-like particles, as the authors have rightly explained. By assumption, classical effects such as tidal forces or the coupling of curvature to angular momentum (or spin, if one includes quantum mechanics of fermions) are neglected. Therefore, one should not be surprised to find a violation of the WEP, if such effects are taken into account.
Second, the paper contains a number of vague, dubious or incorrect statements. Take the generalization of the EP to electromagnetic fields. It is not really clear to me what that means exactly. The coupling of electromagnetic fields to matter is dictated by the gauge principle, i.e., the promotion of a global to a local symmetry. Now, also gravity can be formulated as a gauge theory (using either torsion or curvature), but a consequence of the EP is the WEP: a point-like inertial observer will not feel any force. In contrast, electromagnetic forces are real. One cannot gauge them away.
Another vague discussion concerns what the authors call a "trajectory". It is again trivial that a system of two particles whose trajectories diverge from each other cannot be idealized as a system of small or even negligible size.
Third, the discussion of particles in field theory has the level of a introductory school book, with all its shortcomings. For example, the distinction into free and bound particles is not only superficial, but also wrong. Even a real electron in quantum electrodynamics is not a fundamental free particle, but a bound state of a "fundamental" electron with a cloud of photons. Moreover, in quantum mechanics, a plane wave state is not a particle, but a normalized wave packet is used to describe a particle. Despite the uncertainty principle, the expectation value of the position operator has a well-defined meaning. Going to relativistic field theory, there is no relativistically invariant particle number operator. And so on.
As for the discussion of quantum gravity effects such as superpositions of geometries, what is missing is a discussion of the very meaning of an idealized local test particle in such a setting. It may well be that localized (point-like) test particles have no meaning in quantum gravity, which would invalidate all conclusions reached by using them.
In conclusion, the paper is in need of a thorough rewriting or else it should not be published.
Author Response
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Author Response File: 
Author Response.pdf
Reviewer 2 Report
I have revised this manuscript giving a general overview of the equivalence principle in GR and discussing its various formulations, including its possible generalization in QG. They discuss in particular their own work [20] where it is shown that if superpositions of states of gravity and matter are allowed, WEP can be violated. The authors also mention other recent studies [19,21–24] suggesting that the QG is not violated, which is at odds with their own result. However, I find positive that the two points of view are presentled honestly. In my opinion the review is fine and can be of interest. I have no objection for its publication in the special issue of Universe.
Author Response
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Author Response File: Author Response.pdf
Reviewer 3 Report
Thi paper is a review of the equivalence principle with great enphasis on the weak equivalence principle. The authors present an interesting and complete overview of the different formulations of the principle in classical and quantum physics, distinguishing between the formulation of the weak and the strong versions of the principle. The main and most interesting result presented is about the necessity of a violation of the weak EP in the context of quantum physics, hence in the context of quantum gravity. This point is stated in the form of a theorem. The paper is suited for publication, there are only few suggestions about the possibility to improve the presentation.
In the sentence at line 50 the EP is defined with the purpose to describe the interaction of gravity with other fields, that is matter. Perhaps it would be better to explain that matter stands for matter and all the matter interactions except gravity.
On the same hand, at line 53 it is not clear the sentence: the purpose of EP is to prescribe the interaction of any gauge fields and all the other fields in nature. It could be better to specify that the other fields include matter and gravity.
At line 202 and the following the exmple of the dipole is well conceived?Obviously the center of mass of the system is well defined, but if two particles are separated for a long distance, are they again a dipole?
The conclusions could be improved including a discussion about some theories or models that provide some predictions in the context of quantum gravity perturbations induced by non-universal QG corrections, such as:
arXiv:hep-ph/9809521 [hep-ph]arXiv:0801.0287 [hep-ph] arXiv:1111.5643 [hep-ph] arXiv:1910.05997 [gr-qc] arXiv:1906.05595 [hep-th] As a final comment I suggest the publication of the paper as it stands,
but I suggest to the authors to take into consideration the suggestions
in order to improve the presentation.
Sincerly,
the Reviewer
Author Response
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Round 2
Reviewer 1 Report
The authors have made a significant effort to improve the manuscript. I appreciate this.
As a comment, what the authors describe in App. A.2 is known as the gauge principle: An interaction is introduced by first making a global symmetry local and then demanding that the action be invariant under the local symmetry, which requires the gauge field. So, the logic should be how the gauge principle can be generalized to gravity (it can be done using either the rotations or the translations of the Poincaré group, there is a lot of literature on this), not how the strong equivalence principle can be generalized to gauge fields.
