The Spinor-Tensor Gravity of the Classical Dirac Field

Round 1

Reviewer 1 Report

The author intend to construct a version of the Dirac equation including gravitational effects with some specific purposes. Although the paper might be interesting, I suggests significant improvements. If the author follows my suggestions, I am willing to verify the content of the paper again. My comments are as follows:    1). The abstract is too long and it contains equations. It is inappropriate to use equations inside the abstract. Please write a short paragraph with the main statement of the paper as an Abstract. 2). The introduction must be improved and please explain the whole content of the paper, section by section at the end of the introduction. Avoid equations inside the introduction up to some small expressions. 3). If the idea of the paper is to find the gravitational version of the Dirac equation, why to spend so many pages of calculations in at least 19 pages before going to the main subject of the paper? Please avoid to write all the calculations step by step and just keep the main results.  4). The Dirac equation including gravitational effects has been derived before by several authors, what is the new contribution of this paper?  5). The author has mentioned a couple of times Modified Gravity. Beyond Brans-Dicke theory, which is introduced with the possibility of being reproduced naturally by the version of the Dirac equation including Gravity. Does the author observe some possibility of reproducing other modifications of gravity within the same formulation? This point is relevant because the author has mentioned several times the Cosmological Constant on the paper. The author also mentioned a "Cosmological effect on the motion of galaxies". such Cosmological effect on Galaxies, related to the Cosmological Constant sound to me like Modified Newtonian Dynamics (MOND), see for example  Int.J.Mod.Phys.D 23 (2014) 1450008; Astrophys. J. 270 (1983) 371; Astrophys. J. 270 (1983) 365; Living Rev.Rel. 15 (2012) 10; Astrophys.J. 270 (1983) 384; Nucl.Phys. A827 (2009) 555C. 6). Finally, please verify typos. There are some typos mistakes. See for example eq. (2.0.4), which has a typos mistake.    After the author arrange the paper in agreement with these suggestions, then I will happily verify again its content. 

Author Response

The response is highlighted in yellow in the attached file.

Author Response File: Author Response.doc

Reviewer 2 Report

This paper describes a theoretical study of the role of gravity in quantum mechanical models. It builds on the author’s prior work. The paper provides a detailed description of the approach with most of the accompanying equations. The work seems to be correct but it is difficult to check all of the equations in the time given for review.

 

There are some issues to address.

 

The abstract is far too long and should be much shorter and one paragraph. Much of this could be in the conclusions.

 

Lagrangian, not Lagrangean.

 

Line 954 and elsewhere. Explain what is meant by a branched polymer phase.

 

Please check and make sure all references are correct.

 

Author Response

The response is highlighted in yellow inn the attached file.

Author Response File: Author Response.doc

Reviewer 3 Report

This ms tries to link the quantum fluctuations of a fermionic field to the right-hand side of Einstein's equations by proposing an effective hydrodynamic description of fermionic densities.

Sadly, in spite of a concerted effort by the author this ms does not provide anything new and even is technically and conceptually misleading (already l. 15 in the abstract does not make sense, the consideration of a fermionic density associated with a single-particle solution of Dirac's equation in whatever background is not what effectively generates hydrodynamics that could possibly contribute to the right-hand side of Einstein's equations: here a nonlinear Gross-Pitaevskii-equation for the condensate of such single-particle states in whatever background must be considered; the CC did NOT yield a stable cosmological solution but solely an instabile, static one), contains confused and incorrect statements (see above), and it does not comply with minimum requirements on a scientific presentation (l. 124 is simply wrong, introduced variables that are not defined: dot(q) was never introduced, the actions S_pm were not introduced, etc.).     

Therefore, I cannot recommend this ms for publication in SYMMETRY. 

 

Author Response

The response is highlighted in yellow inn the attached file.

Author Response File: Author Response.doc

Round 2

Reviewer 1 Report

The author has addressed my comments. I only want to remark something about the paragraph added by the author in Section 6. (Discussion) when he talks about MOND. It is true that MOND happens at low accelerations, which come out when the body under analysis is far from the gravitational source such that Newtonian gravity regime operates and is small. Even if the body generating the gravitational field is a Black-Hole or a very massive object, if we are very far from it, MOND effects might appear. On the other hand, if we are  very far from the object, the cosmological constant will eventually dominates the gravitational interactions. This happens at the scale of MegaParsecs. MOND regime happens however at the scale of KiloParsecs. Then let's say that MOND happens when the Newtonian gravitational attraction and the cosmological constant effect, have comparable effects. Please read the references 33-34. I would suggest the author to correct or improve the sentence on page 24, section 6.2 and saying

"Moreover, as shown in section 4.1, the cosmological constant term is a second order gravitational
613 contribution to the weak (Newtonian) gravity. This output owns a similarity with the modified
614 Newtonian dynamics (MOND) theories [33-34] that assume that the Newtonian gravity, for very low
615 accelerations, is slightly in order to fit the experimental data of motion of galaxies (instead of
616 hypothesizing the presence of dark matter). In the present model the correction to the Newtonian
617 gravity comes from the energy of the quantum potential that is originated by huge concentration of
618 matter in highly massive body, while the modification to the Newtonian gravity postulated in the
619 MOND is a consequence of the body accelerations in the very low regime. Nevertheless, the force
620 generated by the cosmological constant, on very far bodies, subject to very small Newtonian force,
621 can lead to the change of the gravitational interaction in a relevant percentage to produce the same
622 effect as foreseen by the MOND models." 

Please improve this sentence based on my previous comments. Probably the author is trying to say the same thing which I am saying but the way how he said it might be confusing. Please also revise the typos mistakes. I found a few. Please read the whole paper again and then correct the typos in addition. After this minor arrangement, the paper can be published.

 

 

 

Author Response

Thank you for your professional suggestions. We have revised our manuscript according to your comments.