The gravitational constant as a quantum mechanical expression

Abstract

A quantitatively verifiable expression for the Gravitational Constant is derived in terms of quantum mechanical quantities. This derivation appears to be possible by selecting a suitable physical process in which the transformation of the equation of motion into a quantum mechanical wave equation can be obtained by Einstein's geodesic approach. The selected process is the pi-meson, modeled as the one-body equivalent of a two-body quantum mechanical oscillator in which the vibrating mass is modeled as the result of the two energy fluxes from the quark and the antiquark. The quantum mechanical formula for the Gravitational Constant appears to show a quantitatively verifiable relationship with the Higgs boson as conceived in the Standard Model. keywords: gravitational constant; Higgs boson; quark model; pion; geodesic equation 1.IntroductionThe basic concept in quantum physics is the particle wave duality, which implies that a particle can dually be described by a mechanical equation of motion and by a quantum mechanical wave function. This wave function is the solution of a wave equation. The wave equation is obtained by a transformation of the particle's equation of motion in a way as conceived by Dirac [1]. Although Einstein's geodesic equation of motion [2] is the most generic of all, it is, so far, not adopted as the axiomatic base for the particle wave duality description. This is probably due to the mathematical complexity of 4D space-time. It is also the reason for the failure to unify quantum physics with gravity. Instead, Dirac derived his wave equation from the Einsteinean energy relationship of a particle in motion. Therefore, the equation is relativistic, but only special relativistic and not general relativistic. In this article I wish to develop the particle wave duality on the basis of Einstein's geodesic equation in 2D space-time and to compare it with Dirac's result. Next to that, I wish to motivate that the 2D space-time approximation is a justified modeling of a realistic physical process. This enables to relate gravity and quantum physics to the extent that the Gravitational Constant can be formulated as a quantitatively verifiable expression of quantum physical quantities. The concepts as will be outlined in this article, are invoked from previous work by the author [3]. Section 4 is devoted to a comparison of the 2D quantum mechanical wave equations as derived respectively by the geodesic approach (section 2) and Dirac's approach (section 3). This will result into an expression for the Gravitational Constant (section 5). In section 6 a physical process is selected that will deliver the quantity values. The result is subject to a relativistic correction (section 7). The final result is discussed in sections 8 and 9.The equations in this article will be formulated in scientific notation and the quantities will be expressed in SI units. Space-time will be described on the basis of the "Hawking" metric (+,+,+,+).

The Granularity of Gravity

“…In this respect, I would like to point to an intriguing observation. In a previous work, I have expressed the gravitational constant G in quantum mechanical quantities [17], which probably so far is just considered as a curiosity, because of an unconventional view on the binding force between quarks. The expression contains a factor α of order 1, which had to be set as = α 0.69, to obtain a perfect fit between the derived expression and the numerical value of G .…”

Dark Matter and Its Relationship with Gravity, Electromagnetism and the Two Nuclear Forces

“…To this end, the Lagrangian density of the cosmological gravity field will be derived from the generic expression, Generically, it represents a field with a format that corresponds with the potential as proposed by Yukawa to explain the short range of the nuclear force. It has been used by the author of this article for the purpose to express the Gravitational Constant in quantum mechanical quantities [3].…”

“…These reasons have to do with the relationship between mass, gravity, electromagnetism and the two basic nuclear forces. It all starts with the concept of quarks as described in previous work [3,4]. In this concept, a quark is a mass less pointlike source of an energetic flux.…”

Dark Matter and Its Relationship with Gravity, Electromagnetism and the Two Nuclear Forces

“…Generically, it represents a field with a format that corresponds with the potential as proposed by Yukawa to explain the short range of the nuclear force. It has been used by the author of this article for the purpose to express the Gravitational Constant in quantum mechanical quantities [3].…”

“…These reasons have to do with the relationship between mass, gravity, electromagnetism and the two basic nuclear forces. It all starts with the concept of quarks as described in previous work [3,4]. In this concept, a bare quark is a massless pointlike source of an energetic flux.…”