Influence of Gravitational Shielding on Time Dilation

Round 1

Reviewer 1 Report

The authors of this paper speculate on a “old” idea of Ettore Majorana
about a possible “gravitational shielding” effect.
If in principle the original idea of Majorana is interesting
even if particularly “exotic”,
it is practically impossible to follow the logic of this paper.
Indeed the paper is written in a very confused and imprecise way;
full of strong claims that do not look fully justified
by convincing arguments and rigorous scientific method.
Even the pagination of equations, a lack of precision in editing
and the poorness of language level give the general
impression that this paper is far to be in publishable form.
Therefore I cannot take the responsibility to accept this paper.

Reviewer 2 Report

he paper discuss actual and interesting questions of Relativity and I recommend it for publication. However, some moderate changes should be done to it.
1.In the section "Introduction" should be adde some notes about negative masses as it can play the role of gravitational shield, too. Kazimir effect should be described in more detailed and clear way.
I advice to include the following citations concerning the negative mass problem:
Bondi, H. (1957). "Negative Mass in General Relativity". Reviews of Modern Physics. 29 (3): 423–428. Bibcode:1957RvMP...29..423B.
Petit, J. P.; d'Agostini, G. (2014). "Negative mass hypothesis in cosmology and the nature of dark energy". Astrophysics and Space Science. 354 (2): 611. doi:10.1007/s10509-014-2106-5.
Petit, J. P.; d'Agostini, G. (2014). "Cosmological bimetric model with interacting positive and negative masses and two different speeds of light, in agreement with the observed acceleration of the Universe". Modern Physics Letters A. 29 (34): 1450182.

2. Equations (1) and (22) - integrating limemts should be added.

3. The equations (15)-(21): it's enough to leave in the main text the first (15) and the last one (21) only. The rest can be placed in an Appendix.
The same for the set of equations (23) to (28).

4. Two sections - "Gravitational Shielding and time dilation" and "Discusiion" have the same number 6.

5. There are also some misprints, namely:
31-32: "gravitational effect" - it looks like here the word "shielding" is missed ("gravitational shielding effect").
40: be4.3 - space between be and 4.3. is needed
41: as0.6 - the same
71-72: ...EM. Theory but... -> ...EM theory. But...
136: Higgsfield -> Higgs field
151: "magnetic field dust" is not understandable.

Reviewer 3 Report

Gravitational shielding has been considered for a long time as a phenomenon that is beyond General Relativity. The new idea in this paper is considering its effect on time dilation. I do not recommend it to be published due to the following concerns:

In the main result, equation (29), the meaning of the time t_f is not clear. The author do not specify where the time t_f should be measured if it is to be tested in experiments or observations. Equation (29) is wrong in the sense that the reduced mass of the sun and the earth is finally used, but the distance of shield is taken as the distance from the earth. As we know, the center of mass for the earth-sun system is inside the sun. Equation (29) is also wrong because it is derived from equation (1), which applies to a point mass placed at the center of a spherical shell. The solar eclipse model described by the authors treats the moon as the shielding material. However the moon is not a spherical shell enclosing the earth-sun system. The sections on Casimir effect, negative energy and gravitational shielding by scalar field try to give motivations or theoretical explanations to gravitational shielding phenomena. But they do not explain equation (1) in a more fundamental level. These sections seem irrelevant to the purpose of the article.