Matter opposes any change in motion. A simple statement that has perplexed mankind since the dawn of history. Galileo's contribution was the observation that heavy objects fall at the same rate as light objects. Newton's contribution was to give mathematical form and substance to Galileo's observation. By the 19th century, this picture was completed with the kinetic energy equivalence of matter in motion. However, two questions have remained unanswered…
1. Exactly where is this energy stored and in what form?
2. How does the storage of this energy cause movement?
These are the question I shall endeavor to answer here.
Acceleration and Force:
Acceleration results from the application of mechanical force to a mass. Acceleration is nothing more than a measurement of "rate of change" in velocity.
And since acceleration results from the application of mechanical force.
[Eq. 2] F = M a
Therefore, under constant applied force, the acceleration of any object is a linear change in velocity over time, of the object.
The kinetic energy of any moving object, is related to it's motion by the equation:
[Eq. 3] E = ˝ M v2
The kinetic energy of any moving object scales proportionally with the mass of the object, and as the square of it's velocity.
If we wrap an insulated wire around a paramagnetic substance, we create an electrical device called an inductor, and a curious phenomena occurs when an electric current flows through the wire. The inductor opposes any change in the flow of current. Consider the circuit shown in figure 1A. Closing the switch, starts the flow of current through the inductor. However, the inductor opposes any change in the electric current flow, so the current rises linearly over time as shown in figure 1B.
Since current flow is defined as electric charge (Q) per second, or (Q/t), it follows that figure 1B is describing a change in charge (Q) per second, per second (per second squared). Therefore in figure 1 electric charge (Q) is changing as the second derivative of time, just as in mechanical acceleration [Eq. 1], length is changing as the second derivative of time. In other words, the flow of electric charge (Q) is accelerating. We shall use the symbol aQ to denote accelerated charge, and define it as:
And since AQ results from the application of electric potential (force), supplied by the battery, our force equation for figure 1 is:
[Eq. 5] e = L aQ
As we see from Eq. 4 & 5, the circuit shown in figure 1A has an equivalent mathematical form, and exhibits analogous physical dynamics to mechanical acceleration and force (1.2.1 Eq. 1 & 2).
Note: Dimensional units of the electric field are Newtons per Coulomb, therefore in the strict sense of the word, an electric potential is not a "force". The electric field creates a force on an electric charge.
The inductor shown in figure 1A acts as an energy storage device. The energy is stored as unpaired electron spin alignments of the paramagnetic material. This phenomena is known as paramagnetic polarization. A larger population of unpaired spins, yields a greater inductance and greater energy storage. The stored electrical energy of an inductor is related to current flow by the equation:
[Eq. 6] E = ˝ L i 2
The electrical energy scales proportionally with the inductance, and as the square of electric current flow. Again we see an equivalent mathematical form and analogous physical dynamics to kinetic (mechanical) energy (1.2.2 Eq. 3).
All matter is composed of atoms, that are in turn, composed of electrons, protons, and neutrons. All of these subatomic particles are electrically charged (covertly in the case of the neutron). Therefore we can treat any moving object as an electric current. Consider an object one meter in length, composed of Q electric charges, and having a velocity of one meter per second. This object represents a current flow of:
By making our object a unit length, we can derive an electric current flow equivalence to the object's mass and velocity. We conclude that all moving objects represent flows of electric current.
Space possesses the property of paramagnetic polarization. A detailed discussion of this subject is available in the companion paper titled Electrodynamic Structure Space - Parts 1 & 2, and therefore will not be covered here. Suffice it to say, that empty space behaves in an equivalent way to a paramagnetic material, and is capable of storing energy as paramagnetic polarization.
Momentum as Induction:
We have shown that an electrical inductor behaves in a manner that is fully equivalent to the momentum of physical mass. Electric charge accelerates through an inductor (1.3.1 Eq. 5) under the application of an electric force, just as a physical mass accelerates through space under the application of physical force (1.2.1 Eq. 2). Energy stored in an inductor is proportional to the square of current (1.3.2 Eq. 6), just as kinetic energy stored in mass is proportional to the square of velocity (1.2.2 Eq. 3). We have also shown that mass is composed of electric charge, and that a moving mass represents a flow of electric current (1.3.3 Eq. 7). Lastly we have shown that space is paramagnetic and can be polarized (1.3.4). Therefore, we have answered question one, posed above (1.1). The energy of a moving mass results from polarization, caused by the moving electric charges that comprise the mass, is magnetic in form, and stored as paramagnetic polarization in the space occupied by the mass.
Stays in Motion:
Returning to our circuit in figure 1A (above), when the switch is opened, current flow does not cease instantly. The inductor has stored energy in the polarization of the paramagnetic material, and this energy must be dissipated (removed) before current can cease to flow. An analogous situation exists for any physical mass in motion. The movement of mass represents an electric current flow (1.3.3), and that current flow has paramagneticly polarized (stored energy in) the space through which the mass is moving. If the mass was to stop moving, without the application of an external force, this would represent a violation of the law of energy conservation. Therefore we must remove the energy stored as paramagnetic polarization of space, by the application of a force in opposition to motion, in order to dissipate the energy stored in polarization of space, before the mass will stop moving. We have now answered question two (1.1) above.
That momentum is induction (1.4.1), and arises as a consequence of matter being composed of electric charge, and movement of mass representing an electric current flow (1.3.3). That kinetic energy is stored as paramagnetic polarization of space (1.3.4) occupied by the moving mass. That an object in motion, will remain in motion, until the energy of paramagnetic polarization is dissipated (1.4.2). To many readers this may all seem moot, since this formulation of inductive momentum does not appear to provide any added utility over the traditional mechanical treatment of the subject. However, when this formulation is coupled with the companion paper entitled Electrodynamic Structure of Space, many hitherto poorly understood relativistic phenomena flow as natural consequences of this formulation.