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Before we pursue the meaning of the FUPCONs that pertain to force equations, we must understand the nature of the inertial, Fi, electromagnetic, Fe, and gravitational, Fg, force equations.
In our discussion of these forces, we expand the subscript of the force code to include two characters, Fxy, to specify the following characteristics of the force equations:
The first character, x, specifies the type of force that the equation determines and can assume a value of either i for inertial, e for electromagnetic, or g for gravitational.
The second character, y, specifies the system of unit measures that is used in creating the force equation and can assume a value of either m for metric, SI, e for electromagnetic, SE, or g for gravitational, SG.
Each type of force relates to a particular elementary particle and, using the SI of unit measures, to particular FUPCONs, as follows:
Force Constant
Electronic Permittivity, ε0
Magnetic Permeability, µ0
Gravitational Gravitational, G
The term magnitude refers to the absolute physical size of an entity or phenomenon without regard to units of measure. For example, the magnitude of a person's height remains the same; however, the value of the magnitude is a function of the unit of length that is applied--feet, meters, inches, light years, or angstrom units.
A FUPCON can possess a magnitude. For example, the magnitude of Planck's constant, h, is the combination of magnitudes of its constituent factors, which consist of some of the quantum attributes of the electron. Each attribute possesses only one magnitude, but it can be expressed by one of a multitude of values, depending upon the system of unit measures being used. By using SE, SP, or SG units of measure, the value of Planck's constant is equal to the number one. These units are based upon the magnitudes of the quantum attributes of the electron, proton, and masson, respectively, all of which are discrete entities that exist in nature.
Various forms of phenomena create various types of force, but they all either "push" or "pull" something. Pushing a mass creates inertial force. Groups of electrons create electromagnetic force between themselves. In like manner, groups of masses create gravitational force.
To study a phenomenon, we apply a known action to a system and record the resulting reaction. By repeating this procedure, we eventually discover the mathematical relationship between the action and the reaction such that they are proportional to each other. In other words, varying the magnitude of the action changes the magnitude of the reaction by the same factor value. For example, if the action triples, so does the reaction; if the action is halved, so is the reaction, et cetera. These proportions show us, quantitatively, what the actions do to the system.
However, because we continue to use the metric system of units for studying quantized phenomena, the value of a quantized action is not necessarily equal to the value of its reaction so as to form an equation, which is easier to manipulate mathematically than is a proportion. To make these values equal to each other, a constant of proportionality is inserted into the proportion such that both the numerical and dimensional values of the action and reaction equal each other. Otherwise, a valid equation is impossible. For detailed information about proportions and equations, see Appendix C.
The constants of proportionality that our use of the metric system created were, at some point, renamed fundamental, universal physical constants of nature (FUPCONs). This was unfortunate because just the term, itself, seems to indicate that these constants are inherent everywhere in nature and each one cannot be composed of a collection of more-basic factors. This, of course, is not true.
A force applied to a mass creates an equal opposing inertial force and causes the mass to accelerate. This inertial-force proportion possesses an action of force and a reaction of mass times acceleration. The dimensions of this (inertial) reaction are MLT-2.
Similarly, two groups of electrons create an electronic force between themselves. This electronic-force proportion possesses an action of charge squared per length squared and a reaction of force. The dimensions of this (electronic) action are Q2L-2.
Also, two parallel conductors with electrons flowing through them create a magnetic force between themselves. This magnetic-force proportion possesses an action of charge squared per time squared and a reaction of force. The dimensions of this (magnetic) action are Q2T-2.
With regard to gravitational force, two masses create a gravitational force between themselves. This gravitational-force proportion possesses an action of mass squared per length squared and a reaction of force. The dimensions of this (gravitational) action are M2L-2.
We now return to inertial force because the SI unit of force, which is based upon inertial force, is used to measure not only inertial force but all of the above-mentioned forces, as well. This practice affects the values of the permittivity, permeability, and gravitational constants because, as we see in succeeding chapters, each one of them contains the fine-structure constant, α, as one of its factors.
The most-often-used unit of force is the SI's newton, N. When a newton of force is applied for one second to a one-kilogram mass, the mass's velocity changes by one meter per second. Of course, if it were applied to half that mass, the acceleration would be double, et cetera; therefore, an inertial force is proportional to a mass times an acceleration. Because the newton is a defined unit of inertial force, no constant of proportionality need be inserted into the proportion to convert it into an equation. This, unfortunately, gives the impression that a newton is equal to a (kilogram-meter per second squared). This is not true. A newton is an action (or cause), and a (kilogram-meter per second squared) is the reaction (or effect).
For measuring quantized force, the newton is inappropriate. We should use a unit of force based upon the magnitudes of the natural dimensional attributes of the elementary particle being examined.
The SE unit of inertial force, fie (see Table XI in Appendix E), can accelerate me at a rate of λe per te squared. In like manner, the SG unit of inertial force, fig (see Table XII in Appendix E), can accelerate mg at a rate of λg per tg squared.
We define two SE units of electromagnetic force. The first one, fee(λ), is based upon length, (λ), and pertains to the permittivity constant, ε0, in Coulomb's electronic-force equation (see Chapter 6). The second one, fee(t), is based upon time, (t), and pertains to the permeability constant, µ0, in Ampère's magnetic-force equation (see Chapter 7).
The smallest possible magnitude of electronic force, fee(λ), appears to be caused by one electron separated from another electron by the SE unit of length, λe, such that fee(λ) is proportional to, but not equal to, qe2·λe-2. The action is qe2·λe-2, the reaction, fee(λ). All other magnitudes of this type of force are positive, integral multiples of this basic unit, fee(λ), of electronic force (fractions are not allowed in a system of quantized elementary particles).
The smallest possible magnitude of magnetic force, fee(t), between two parallel conductors of indefinite length appears to be caused by the flow of one electron, qe, per one SE unit of time, te, through each conductor, where the force is applied over the same length of each conductor as is the distance between the two, such that fee(t) is proportional to, but not equal to, qe2·te-2. The action is qe2·te-2, the reaction, fee(t). All other possible magnitudes of this type of force are positive, integral multiples of this basic unit, fee(t), of magnetic force (fractions are not allowed in a system of quantized elementary particles).
The smallest possible magnitude of gravitational force, fgg, appears to be caused by one masson, mg, separated from another masson by the SG unit of length, λg, such that fgg is proportional to, but not equal to, mg2·λg-2. The action is mg2·λg-2, the reaction, fgg. All other possible magnitudes of this type of force are positive, integral multiples of this basic unit, fgg, of gravitational force (fractions are not allowed in a system of quantized elementary particles).
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