electrical and magnetic machines is to realize that electrical current actually
consists of two currents coupled together. Our treatment of an electric charge as a coupled system (Ø)(m) also means that electron current i = dq/dt is comprised of two coupled components [(dØ/dt)(dm/dt)]. This follows from simply invoking the operator d/dt; i.e., d/dt[(Ø)(m)] = (dØ/dt)(dm/dt), which is the same as [(dØ/dt)(dm/dt)]. The component (dØ/dt) is the known but not well understood massless displacement current, while the component (dm/dt) is the mass displacement current, and the coupling operator means "coupled to" or "trying to couple to". The coupling operator represents a real physical operation: the exchange of virtual photons between the vacuum potential and the charged mass. Any potential Ø1 is considered to be a potential that is superposed upon the ambient vacuum potential Ø0 , to provide a potential (Ø0+Ø1). The ambient vacuum potential does not disappear merely because we add another potential to it!
Confusion In Present Electrical Physics
We point out that, in physics books of note, the overt coupling effect is essentially unknown or ignored because physics presently has not defined either the scalar potential or the electrical charge. The conventional theory simply uses an "inert" expression dØ/dt to represent the displacement current (and another inert expression q for a charged mass), and most theoreticians are uncomfortable even with that. The displacement current is also confused with force by equating the displacement current dØ/dt to dE/dt. In turn, this means that dØ/dt is confused with mass, hence with dm/dt, which latter is also a component of dq/dt. m is always an \internal component\ of force, as is known in foundations of physics but this fact continues to remain completely oblivious to the electricians. [Good electrical theorists do admit that there is no force in the vacuum; and that the force associated with the E-field is evidenced only in the interacting mass. However, they continue to maintain the E-field (force per point-coulomb of charged mass) in the vacuum, when there are no point-coulombs of charged mass there!
Mass Is an Internal Component of Force
It is easy to show that mass is always a component of force: We will simply define force precisely. We first insist that no equation can be used as a definition; an equation simply states that the magnitude of one of its sides and the magnitude of the other side are equal. (The length of a board and the length of a human may be equal, but writing that as an equation has absolutely nothing to do with the definition of either a board or a human). So we will insist that any true definition must be an identity.
We define force F as Fd/dt(mv), whereupon mass is a component of force a priori. It follows that, if we define the E-field E as the force per coulomb, we are defining it as the force existing at a point and having a point-coulomb of charged mass as one of its major components. We may accurately now define E as E-[(Ø)(q)]/|q|, where the absolute value symbol in the denominator is essential, q/|q| being one point-coulomb. [We leave as an exercise for the reader the further reduction of this definition by treating q as (Øm)].
At any rate, with the new and correct definition of the E-field, one can see that the flow of displacement current (dØ/dt) upon a collector such as a rigid capacitor, containing a fixed charge (Øm), will result in the formation of an excess Ø upon those restrained charges in the capacitor plate, so that there is created an E-[( Ø)(q)]/|q|. Since the conventional theory considers the antigradient of the potential as an E-field, then one can now see the exact mechanism that creates this E-field that grows upon the capacitor (across its plates) as it charges. In fact, the q/|q| cannot change in a capacitor if its plates and dielectric are immovable. Instead, in that case, the Ø portion of the trapped (q) changes, producing the ( Ø) change. Since the ( Ø) component is coupled to the mass component of the fixed q as (Ø+ Ø)m, then an E-