To fit Fermi’s weak coupling constant with three gravitational constants

By considering three virtual gravitational constants assumed to be associated with gravitational, electromagnetic and strong interactions, Fermi’s weak coupling constant can be shown to be a natural manifestation of microscopic quantum gravity. As our approach is heuristic and completely different from the current methods of estimating the Newtonian gravitational constant, concerning the call of ‘Ideas lab 2016’ organized by NSF, we appeal for inclusion of this theoretical work as a project under the unification scheme. Estimated magnitudes of Fermi’s weak coupling constant and Newtonian gravitational constant are 1.44021X10(-62) J.m3 and 6.679856X10(-11) m3/kg/sec2 respectively.


Introduction
The most desirable cases of any unified description are: a) To implement gravity in microscopic physics and to estimate the magnitude of Newtonian gravitational constant. b) To develop a model of microscopic quantum gravity. c) To simplify the complicated issues of known physics. d) To predict new effects, arising from a combination of the fields inherent in the unified description. In this context, in our earlier publication [1] and references therein, we suggested the role of two new gravitational constants associated with strong and electromagnetic interactions. In this paper, we make a bold attempt to interrelate the Fermi's weak coupling constant [2,3] and Newtonian gravitational constant [4,5,6] via the two proposed electromagnetic and nuclear gravitational constants. We would like to appeal that, with respect to String theory models, Quantum gravity models [7] and proposed assumptions, it is possible to show that, weak interaction is a natural manifestation of microscopic quantum gravity [3].

Two basic assumptions of final unification
In our earlier publication, we proposed the following two assumptions [1].

Important and interesting relations
A) Ratio of rest mass of proton to electron: B) Nuclear charge radius: Note: Considering  as a probability of finding electron in any orbit labeled with 1, 2,3,.. n = further research can be carried out.

E) Characteristic atomic radius of
Note: By considering , 2  mass of neutron star can be estimated to be 1.5875M  .This is just greater than the famous Chandrasekhar mass limit of 1.4M  .

Fitting Fermi's weak coupling constant and electron rest mass
Fitting the gravitational constant with elementary physical constants is a very challenging issue. According to G. Rosi et al [3]: "There is no definitive relationship between N G and the other fundamental constants, and there is no theoretical prediction for its value, against which to test experimental results. Improving the precision with which we know N G has not only a pure metrological interest, but is also important because of the key role that N G has in theories of gravitation, cosmology, particle physics and astrophysics and in geophysical models".
In this context, we would like to stress that, by considering the Fermi's weak coupling constant, in a verifiable approach, it is certainly possible to explore the back ground physics of the role of the Newtonian gravitational constant in microscopic physics. It may be noted that, according to Roberto Onofrio [3] With reference to the proposed assumptions and based on the above points, quantitatively, we noticed that, Based on this relation, 3 12 If, recommended Based on relations (11) and (14) Based on relations (15, 16 and 17),

To understand proton's melting point
With reference to Hawking black hole temperature formula [12], melting point of proton [13,14] can be understood with: 3 12 0.15 10 K 8 Based on this relation and with reference to up quark, other quark melting points can be expressed with the following kind of relation.

To fit neutron's life time
Neutron life time [15] can be fitted with: This value can be compared with the recommended value [2] and results of bottle experiments [16].
Using this ratio, proton-neutron stability relation can be fitted directly in the following way [17].

b) Nuclear binding energy:
s α being the strong coupling constant [2], characteristic nuclear binding energy potential can be expressed with the following relation [19,20].

Discussion and conclusion
We appeal that, a) We presented a number of applications connecting micro-macro physical systems and finally developed arithmetic relations for understanding the role of the Newtonian gravitational constant [22] in microscopic physics. Following this kind of computational approach, it is certainly possible to reproduce another set of arithmetic relations by using which, in near future; in a verifiable approach, it may be possible to find a set of absolute relations and N G can be estimated. relative uncertainties approaching or surpassing one part in 100,000. In this context, we humbly and sincerely request NSF to consider and encourage our proposed method of estimating the Newtonian gravitational constant with possible support. c) As it is inevitable to unite gravity and other three atomic interactions, if one is willing to explore the possibility of incorporating the proposed assumptions either in String theory models or in Quantum gravity models, certainly, background physics assumed to be connected with proposed semi empirical relations can be understood and in near future, a 'workable' or 'practical' model of "everything" can be developed. Based on relations (11) to (14), Fermi's weak coupling constant and the three gravitational constants can be fitted in a unified approach and finally, in a verifiable approach, Newtonian gravitational constant can be estimated accurately with microscopic physical constants.