Chapter 11. Fine-Structure Constant

In this chapter, we investigate the fine-structure constant, α, or, if you will, β, the form that we use in this book.

We show that its historical definition was derived from other FUPCONs, which were considered to be more basic than it, yet, are not.

A. Historical Definition

The historical definition of the fine-structure constant contains the following FUPCONs:

1) Circumference-to-diameter ratio, π

2) Charge of the electron, q_e

3) Permittivity, ε₀

4) Planck, h

5) Speed of light, c

The historical equation that defined the fine-structure constant is, as follows:

α = e² (h_bar c)^-1 (104

where: e² = q_e² (4 π ε₀)^-1

and: h_bar = h (2 π)^-1.

Historically, α appeared to contain electric charge, the speed of light, and Planck's constant, as we can see in Equation 104. This combination of factors prompts some people to believe that the fine-structure constant pulls the disciplines of electromagnetics, relativity, and quantum physics together into one constant. This chapter shows that this is not true.

All of the units of measure of these factors cancel each other to give a dimensionless value of (137.036...)^-1, which, of course, remains the same in any system of unit measures.

Conflicting questions arise: How can α be a FUPCON when, supposedly, it is composed of up-to-five other FUPCONs? Then, again, how can it not be a FUPCON when its value is a fixed, dimensionless number in any system of unit measures? The answer is that α is not composed of those five FUPCONs, which, when separated into their electronic-attribute factors, cancel each other. In essence, the historical definition of α is recursive, in which it was defined in terms of itself.

Let us go through this cancelling process, as follows:

α = e² (h_bar c)^-1 (105

where:

e² = q_e² (4 π ε₀)^-1,

h_bar = h (2 π)^-1 = E_e·t_e (2 π)^-1

ε₀ = q_e² (2 α E_e·λ_e)^-1,

E_e = m_e·λ_e²·t_e^-2,

c = λ_e·t_e^-1.

Substituting, gives:

α = q_e² {4 π [q_e² (2 α E_e·λ_e)^-1]}^-1 ×

{[E_e·t_e (2 π)^-1] [λ_e·t_e^-1]}^-1 (106

Collecting factors into one numerator and one denominator, gives:

α = (q_e² 2 α E_e·λ_e 2 π t_e) (4 π q_e²·E_e·t_e·λ_e)^-1 (107

Canceling factors, gives:

α = α (108

All of the numerator factors cancel the denominator ones except for α. Therefore, the fine-structure constant is more basic than the FUPCONs that, historically, have been used to define it.

B. Significance

One definition of the fine-structure constant, α, is that it is the ratio between the magnitudes of the SE units of electromagnetic and inertial force. Another, is that it is the ratio between the magnitudes of the SG units of gravitational and inertial force.

In general, the fine-structure constant, α, appears in an equation that pertains to a phenomenon affected by both inertial force and either electromagnetic or gravitational force, such as in the hydrogen atom or a Black Hole.

In the case of either the purely electromagnetic- or gravitational-force equation, inertial force is absent; however, we use a force unit that is based upon inertial force to measure both electromagnetic and gravitational forces. This introduces the fine-structure constant, β, into these force equations by way of the permittivity, ε₀, permeability, µ₀, and gravitational, G, constants. This opens a whole new area of speculation as to the significance of the fine-structure constant, which I pursue in the subjective, metaphysical contents of Chapter 21 in Part Two.