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Sometimes, the form of an equation for a phenomenon that relates to an elementary particle is identical to the form of an equation for a different phenomenon of the same symmetry that relates to another elementary particle.
In particular, two different force equations of the same spatial symmetry should possess the same form, yet their historical representations are different and do not consider the quantum nature of the phenomena involved. These are Coulomb's electromagnetic- and Newton's gravitational-force equations, which, in their historic form, are, respectively:
Fem = q1 q2 (ε0 4 π r2)-1 (64
and
Fgm = G m1 m2 r-2 (65
We have already studied Coulomb's electromagnetic-force equation and found that, by using the SE of unit measures, it takes the following form:
Fee = 2 q1 q2 (4 π r2)-1 (66
In this and the following two chapters, we put Newton's gravitational-force equation into the same form, which is, as follows:
Fgg = 2 m1 m2 (4 π r2)-1 (67
and Newton's gravitational constant, G, reverts to a dimensionless value of one and no longer exists in the equation. We do this in three steps:
1) In this chapter, we determine the Fge equation.
2) In Chapter 9, we determine the quantum attributes of the masson, which is the name that we use in this book--for lack of an existing one--to the elementary particle of matter, which is acted upon by the graviton. We use the quantum attributes of this, so-called, masson to create a Système Gravitatif (SG) of unit measures
3) In Chapter 10, we determine the Fgg equation.
Let us convert Newton's gravitational-force equation from using the SI units of measure into one that uses SE units (we will convert it to using SG units in Chapter 10).
The historical SI equation is:
Fgm = G m1 m2 r-2 (68
where: G = 6.7 × 10-11 m3·kg-1·s-2.
In the constant, G, replacing the SI units with SE units gives:
G = (6.7 × 10-11) (4.1 × 1011 λe)3 ×
(1.1 × 1030 me)-1 (1.2 × 1020 te)-2 (69
G = 2.8 × 10-46 λe3·me-1·te-2 (70
Converting G into a form that is similar to the one for ε0 in Coulomb's SE electromagnetic-force equation gives G in terms of the SE of unit measures, as follows:
G = 2 (β θ2 4 π)-1 λe3·me-1·te-2 (71
where θ2 is the constant of proportionality, which value we calculate to make the equation work. Notice that the fine-structure constant, β, is placed into the gravitational constant. This is because the same unit of inertial force, the newton, was used in the historical definition of the gravitational constant, G.
Equating Equations 70 and 71 to each other, excluding the SE units of measure, gives:
|G|e = 2 (β θ2 4 π)-1 = 2.8 × 10-46 (72
Solving for the value of θ2 gives:
θ2 = 2 (β 4 π)-1 (2.8 × 10-46)-1 = 4.2 × 1042 (73
which is the empirically-established electromagnetic- to gravitational-force strength ratio. It exists in the SE formulation of the gravitational constant, G, because, for G to be fully rationalized, it should use the SG rather than the SE of unit measures. We establish the rationalized (no θ2 factor) value of G in SG units in Chapter 10.
The square root of θ2, θ, is the massonic-to-electronic, quantum-attribute conversion ratio, which is:
and the only factor that we use to establish the quantum attributes of the masson. See Chapter 9.
Inserting the SE value of the gravitational constant, G, from Equation 71 into Newton's gravitational-force equation gives:
Fge = [2 (β θ2 4 π)-1 λe3·me-1·te-2] [m1 m2 r-2] (75
which is the same form as that of Coulomb's electromagnetic-force equation except for the occurrence of the factor θ2 and of (m1 m2), which replaces (q1 q2). In Chapter 10, we see that by using the quantum attributes of the masson as units of measure rather than those of the electron, the factor θ2 vanishes.
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