Arithmetic Relations Connected with Planck Scale

Abstract

We show that Schwarzschild radius of Planck mass plays a vital role in electroweak and strong interactions. With reference to the observed large proportionality ratios, it seems appropriate to consider two large gravitational constants assumed to be associated with nuclear and electromagnetic interactions. Qualitatively, this idea is similar to “Strong gravity” concept proposed by Abdus Salam and C.Sivaram [Mod. Phys. Lett., A8(4), 321- 326. (1993)]. Among the wide range of applications (i.e., Planck scale, elementary particles, atomic nuclei, planets and neutron stars), we generated a set of arithmetic relations and developed arithmetic methods for estimating the Newtonian gravitational constant from the known microscopic physical constants. As the current unification paradigm is failing in developing a ‘practical unification procedure’,  the point that we wish to emphasize here is that, by considering ‘only two’ assumptions, 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 in microscopic physics. We appeal the mainstream physicists to see the possibility of considering the proposed relations for further investigation with respect to strong, electroweak and gravitational interactions collectively.