| Gravitational Coupling Constant |
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Assume SI units. Let:
Then the following algebra yields a Dimensionless Quantity : :. This equation is (5.8) in Barrow and Tipler (1986) except that they, following Eddington, replace ''m''e with the mass of the Proton , in which case αG = 1.752x10-45xβ2 ≈ 10-39. Barrow and Tipler invoke αG freely, but never give it a name. αG is calculated to only four significant digits, because ''G'' is known to only about one part in 7000. (Meanwhile, the Meter and Second are defined so as to make ''c'' exact, and ''e'', ''m''e, and ''h'' are known to better than one part in 5,000,000.) αG is to Gravitation what the dimensionless Fine Structure Constant (defined assuming Cgs Units for ''e'', ''c'', and ) :, is to Electromagnetism and Quantum Electrodynamics . αG may be defined in terms of any two masses whatsoever. However, if the two masses are those of the Proton or the Electron , the two stable Elementary Particles with charge ''e'' and nonzero mass, then the ratio α/αG measures the relative strengths of Gravitation and Electromagnetism . Assuming Planck Units (so that ) and defining αG in terms of a pair of electrons, αG = ''m''e2, α = ''e''2, and α/αG = (''e''/''m''e)2. Thus the ratio of the electron's mass to its charge, when both are measured in Planck units, grounds the relative strengths of Gravitation and Electromagnetism . The third and final possible definition of αG involves the mass of one proton and one electron, in which case αG = βx1.752x10-45 = 3.217x10-42, and α/αG ≈ 1039. α/αG defined in this manner is (C) in Eddington (1935: 232) (except that he employs Planck's Constant in place of Dirac's) and (4.5) in Barrow and Tipler (1986). Because α is 39 Orders Of Magnitude greater than αG, the Electrostatic attraction between the Proton and the electron is vastly stronger than the corresponding gravitational attraction. In fact, the gravitational attraction among Subatomic Particle s can be ignored. That gravitation is relevant for macroscopic objects proves that they are electrostatically neutral to a very high degree. These three sensible definitions of αG differ merely by a factor of β or its square. The arbitrariness of any choice made among the three definitions of αG proposed here, and the relatively low precision with which it can be measured, may explain why the physics literature seldom mentions αG. SEE ALSO REFERENCES
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