Stochastic Approach to Determining the Mass Standard Based on the Fixed Values of Fundamental Physical Constants

Round 1

Reviewer 1 Report (Previous Reviewer 2)

The reference [7] is not cited anywhere in the paper.  Either it should be removed or cited appropriately in the paper.

The appendix has no relevance to the paper and should be removed.

Author Response

Thanks for the comments.

Reference [7] has been removed, all other references have been brought into line with the article's test.

Appendix 1 has been removed. Also, the mention of this Appendix has been removed from the text of the article.

Author Response File: Author Response.docx

Reviewer 2 Report (New Reviewer)

This paper gives a novel proposal for a mass standard, based on the defined Planck constant.

The idea seems to be rather interesting, but I cannot be confident that this proposal really gives a mass standard with low uncertainty.

Some parameters are included which are questionable about their uncertainties. For example, the gravitational acceleration depends on the position, and it can be determined with the uncertainty of 10^-9 with atomic interferometer. 

Also the velocities, and temperature have uncertainties. Considering these uncertainties, is it advantageous mass standard in comparison with Si ball?

If the comparison of uncertainties is discussed, it would be publishable

Author Response

Thanks for the comments.

The article proposes to combine two projects for the creation of thermoelectric semiconductor ampere-balances and a quasi-ideal silicon-28 ball into one project (see Fig. 7).

This can lead to the solution of a number of problems in creating a stable and easily reproducible mass standard.

In connection with this remark, changes have been made in lines 18-21 and 425-434.  

Indeed, gravitational acceleration is included in Expression (56) for thermoelectric semiconductor ampere-balances, but it is also included in expression (1) for the Kibble balance. Therefore, in this parameter, the proposed project is not inferior to the previous one.

The article proposes to combine two projects for the creation of Si ball and thermoelectric semiconductor ampere-balances. Therefore, these projects can complement each other and increase the accuracy of measurements due to mutual balancing.

In connection with this remark, changes have been made in lines 425-434.

Unfortunately, at this stage of research it is impossible to calculate the uncertainty of the proposed method, for this it is necessary to conduct a series of experiments. In addition, the uncertainty will depend on the parameters of the climate chamber.

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report (Previous Reviewer 2)

The author has made improvements to the manuscript and removed the redundant appendix and reference. It may now be accepted for publication.

Reviewer 2 Report (New Reviewer)

I think the fundamental of proposal became clear after the revision.

I think it is publishable now

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

1.     The author claims that “These projects are related to each other, because without quasi-ideal 28Si balls having 47 a mass of 1 kg with a relative error of about 10–8, it is impossible to compare the readings 48 of "Kibble balances" located in various laboratories around the world. On the other hand, 49 without the "Kibble balance" it is impossible to verify the equivalence of the inert mass of 50 a quasi-ideal 28Si ball to its gravitational mass [4].” I don’t agree with this statement, as the Kibble balance and the XRCD method are independent mass realization approaches. Either of the two experiments can be employed for mass realization or precision measurement.

 

2.     I don’t doubt the author's idea that links the mass to a thermal average. The shortcoming is that in the present state of the art, any real energy measurement can not go high accuracy. The thermal noise method has been applied in the Kelvin realization. Even under the help of the Josephson voltage standard, the best measurement accuracy is several ppm. While the Kibble balance and XRCD methods are focusing on measurement accuracy at the 10-8 level. I don’t see the merit of the method.

 

3.     As an experimental instrument, the author needs to give a clear technical route to reach the idea. The related major limitations must be clarified.

 

 

Reviewer 2 Report

The author has shown that stationary random processes involve Planck constant h as a proportionality factor and that h.tau_x/2D_x has the dimension of mass.  He also points out the deficiencies of the current method of determining the mass using the Kibble balance and determining h using XRCD method.  He suggests that his method is potentially better than other methods, but does not show how it could achieve, let alone exceed the accuracy of the Kibble balance and XRCD method.  The paper is thus speculation rather than research that could provide advancement of science.

The appendix in the paper has not been referred to anywhere in the body of the main paper and so is the reference [7].  Also, the appendix has no relevance to the main paper.