A Proposed Test for the Gravitational Tunnel Effect

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors analyze, from a theoretical perspective, the tunnel effect, which they call the "gravitational tunnel effect" due to the potential energy configuration considered. Furthermore, the authors provide the possibility of analyzing this effect experimentally, which makes the analysis more interesting due to the possibility of comparing the results obtained with the experiment. I believe the results are interesting and should be published in this journal, but only after some necessary responses and suggestions are accepted or refuted after a good argument.

1) The results are found in the table, but the analytical or approximate result used to define the tebala results is not found in the manuscript, such as the transmission coefficient. It would be helpful to have these analytical results present, so that readers could compare or reproduce the results.

2) The nomenclature for the potential considered would be more general and correct as "Coulomb potential", since it does not fit both the gravitational and electromagnetic cases, the context to be evaluated would be a mere adjustment in the parameter of the numerator of the same.

3) I have a question about the experimental apparatus used for this analysis. Why do the spheres have to be tungsten? It would be interesting to have a motivation in the manuscript for this.

4) Do the authors have any justification for why the last five measurements of the transmission coefficient seem to stabilize at a constant value? Does it have to do with some upper or lower limit of some parameter? Hence the relevance of the mathematical expressions of the results.

Once my questions have been answered and/or my suggestions have been accepted, the manuscript is suitable for publication in this journal.

Author Response

Comments 1:

1) The results are found in the table, but the analytical or approximate result used to define the tebala results is not found in the manuscript, such as the transmission coefficient. It would be helpful to have these analytical results present, so that readers could compare or reproduce the results.

Response 1:  

A clarification has been provided regarding the different data shown in the table. Regarding your comment about the transmission coefficient, I have considered these values. They could be any other, just as in the electromagnetic case, where a transmission coefficient x can be considered if we play with the potential width or the initial value of E. This can be done since there is a relationship for the transmission coefficient; in our specific case, it is equation (9). I'm putting it into the new version, lines 174 and 208.

 

Comments 2:

2) The nomenclature for the potential considered would be more general and correct as "Coulomb potential", since it does not fit both the gravitational and electromagnetic cases, the context to be evaluated would be a mere adjustment in the parameter of the numerator of the same.

Response 2:

You're right about this. In fact, I've taken this into account in my calculations, although I haven't explicitly stated it in the paper. I'm putting it into the new version, line 174.

 

Comments 3:

3) I have a question about the experimental apparatus used for this analysis. Why do the spheres have to be tungsten? It would be interesting to have a motivation in the manuscript for this.

Response 3:

The greater the density of the material creating the gravitational potential, the larger and more abrupt the barrier produced will be. For this reason, we use a very dense material such as tungsten. I'm putting it into the new version, line 174.

 

Comments 4:

4) Do the authors have any justification for why the last five measurements of the transmission coefficient seem to stabilize at a constant value? Does it have to do with some upper or lower limit of some parameter? Hence the relevance of the mathematical expressions of the results.

Response 4:

The values do not stabilize and have nothing to do with any upper or lower limit. In the last five configurations, I simply considered values for which the same theoretical transmission coefficient value (0.3) is obtained. I considered this on purpose to see how the problem varies for this fixed value when changing the mass and/or the percentage of V for the value of E. This allows us to see the trends that each configuration follows when varying one of the parameters, having fixed another—in these last cases, the transmission coefficient—and see that it agrees with what is expected. Any other value could be used and a different result would be obtained.

I have chosen values that may be experimentally feasible, but as I mention in the conclusion, these parameters can be played with depending on the needs or experimental limitations.

Reviewer 2 Report

Comments and Suggestions for Authors

Referee Report on universe-3822654 “A proposed test for the gravitational tunnel effect” by Alfonso Gonzalez Jimenez, Enderson Falcon Gomez, Isabel Carnoto Amat, and Luis Enrique Garcia Munoz

This paper investigates the gravitational tunnel effect using the WKB approximation and proposes a potential lab test instead of relying on astrophysical confirmation of this effect via Hawking or Unruh radiation, both of which are generally weak for stellar mass objects. I have my doubts about whether this is actually feasible, but I can find nothing obviously incorrect about the proposal and if true this would be a step toward validating effects like Hawking and Unruh radiation. Thus, I think the paper should be published. However, I have one suggestion and then some optional comments about missing references.

 

The authors are very clear about the masses and radii of the masses, M, which will form the potential through which the particle must tunnel – see figure 4 and table 1. They are much less clear about the mass of the particles, m, which will do the tunneling. They do mention the electron so I suppose this is the particle they have in mind, however since the electron is charged, this may then lead to non-gravitational interactions (i.e. electromagnetic interactions) which could swamp the gravitational influence. Is it possible to do this experiment with a neutral hydrogen atom or neutron? I know neutrons decay, but they may live long enough to tunnel. From equation (5) and the defined k below I understand more massive particles would tunnel less, but this (i.e. tunneling of a neutral particle) should at least be mentioned. And neutrons where in fact used in the famous COW experiment (Collela R, Overhauser A W and Werner S A, “Experimental Test of Gravitationally Induced Quantum Interference”, Phys. Rev. Lett. 34, 1472 (1975)) which demonstrated interference of neutrons in a gravitational field.

 

In the introduction the authors mention the temporal contribution to the tunneling effect. There are two additional papers aside form [8] which made note of this temporal contribution. They are B. D. Chowdhury, Pramana 70, 593(2008) and E. T. Akhmedov et al., Int.J.Mod.Phys.D 17, 2453 (2008). Also, in terms of the WKB method and gravitational tunneling there is the paper Andrea de Gill et al., “A WKB-Like Approach to Unruh Radiation”, Am.J.Phys. 78 (2010) 685-691.

A minor error: On page 2 line 46 the authors have repeated “So far,” twice. They should correct this typo.

These references are optional suggestions. Aside from the request to include more detail about the tunneling particle, the paper is of interest and should be published.

 

Author Response

Comments 1:

This paper investigates the gravitational tunnel effect using the WKB approximation and proposes a potential lab test instead of relying on astrophysical confirmation of this effect via Hawking or Unruh radiation, both of which are generally weak for stellar mass objects. I have my doubts about whether this is actually feasible, but I can find nothing obviously incorrect about the proposal and if true this would be a step toward validating effects like Hawking and Unruh radiation. Thus, I think the paper should be published. However, I have one suggestion and then some optional comments about missing references.

 

The authors are very clear about the masses and radii of the masses, M, which will form the potential through which the particle must tunnel – see figure 4 and table 1. They are much less clear about the mass of the particles, m, which will do the tunneling. They do mention the electron so I suppose this is the particle they have in mind, however since the electron is charged, this may then lead to non-gravitational interactions (i.e. electromagnetic interactions) which could swamp the gravitational influence. Is it possible to do this experiment with a neutral hydrogen atom or neutron? I know neutrons decay, but they may live long enough to tunnel. From equation (5) and the defined k below I understand more massive particles would tunnel less, but this (i.e. tunneling of a neutral particle) should at least be mentioned. And neutrons where in fact used in the famous COW experiment (Collela R, Overhauser A W and Werner S A, “Experimental Test of Gravitationally Induced Quantum Interference”, Phys. Rev. Lett. 34, 1472 (1975)) which demonstrated interference of neutrons in a gravitational field.

 

In the introduction the authors mention the temporal contribution to the tunneling effect. There are two additional papers aside form [8] which made note of this temporal contribution. They are B. D. Chowdhury, Pramana 70, 593(2008) and E. T. Akhmedov et al., Int.J.Mod.Phys.D 17, 2453 (2008). Also, in terms of the WKB method and gravitational tunneling there is the paper Andrea de Gill et al., “A WKB-Like Approach to Unruh Radiation”, Am.J.Phys. 78 (2010) 685-691.

A minor error: On page 2 line 46 the authors have repeated “So far,” twice. They should correct this typo.

These references are optional suggestions. Aside from the request to include more detail about the tunneling particle, the paper is of interest and should be published.

 

Response 1:

In response to your question, yes, the particle used for the calculations was the electron, without taking electromagnetic interactions into account.

A priori, the experiment could be replicated with another neutral particle, such as the neutron or the hydrogen atom, as you mention, without any theoretical inconvenience. The main reason the electron was used, as you also mentioned, is that it is a less massive particle. The greater the mass of the particle, the lower its tunneling capacity, as indicated by equation (5). I'm introducing this in the new version, line 133.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have answered my questions coherently and accurately. Furthermore, they have accepted some of my suggestions. Therefore, I consider the manuscript suitable for acceptance by this journal.