Translating Solenoids, Maxwell’s Aether and Electric Interactions
1. Translations of an Infinite Solenoid.
In a previous article x, the electromagnetic mass per unit length of an infinitely long solenoid, was calculated in the following way: (1) EMag, the magnetic field energy per unit length in the solenoid cavity was calculated; and (2) The rotational kinetic energy per unit length (x(meter)w2R2/2) was assumed to equal EMag.
Although not explicitly mentioned in that article, the electric field presumably equaled zero outside of the solenoid, which is to say the net charge per unit length presumably equaled zero. This in turn assumed an overlay of equal density positive and negative cylinders of charge. (If there is excess charge of either sign, then the electric field energy per unit length will be infinite outside of the solenoid.)
In view of the Hall Effect we might assume that the positively charged cylinder is at rest and the equal density, superimposed negatively charged cylinder rotates around the longitudinal axis at the angular rate w. The positive charge then contributes nothing to B in the solenoid cavity and thus is not a factor in the calculation of x, the electromagnetic mass per unit length of the negative charge.
In this article let us say that v is the solenoid’s rate of translation in the direction of its longitudinal axis. We shall assume that this axis coincides with the x-axis of "rest" frame K. If frame K’ moves in the positive x-direction of K at speed v, then the solenoid translates in the negative x’-direction of K’ at speed v.
A natural question is: Will the translational kinetic energy per unit length equal 2xv2/2 in frame K’? We might begin by hypothesizing that any translational kinetic energy also equates to magnetic field energy. Outside the translating solenoid we again have E’ = B’ = 0. And Gauss indicates that E’ is again zero inside the cavity. More pointedly, B’ = B. Evidently the translational kinetic energy is zero!
This result is theoretically general. No overlaid, equal density positive and negative charge distributions can have electromagnetic translational kinetic energy! Only rotational kinetic energy is possible under such circumstances. Furthermore, in the case of our infinite solenoid (with zero net charge density), if both w and v equal zero then we have no way of even knowing of the solenoid’s existence!
2. "Maxwell’s Sea."
The conclusion in Sect. 1 is of historic interest because of what Maxwell (mathematically developing Faraday’s ideas) suggested about "empty space." Maxwell theorized that all of space is actually filled with a sea of positive and negative charge, everywhere of equal but opposite density. So long as these two distributions do not move relative to one another we cannot detect their existence.
Maxwell dubbed the motion of one distribution relative to the other "displacement current." We might accordingly call the two vast seas of charge "displacement charge."
According to the Maxwell paradigm, finite distributions of "free" (shall we say) charge are injected here and there in the displacement charge sea. (Like Maxwell, we shall not speculate about what agency did the injecting.) If the injected free charge is positive, then it displaces (i.e. pushes out) positive displacement charge and overlays the negative displacement charge. Assuming the positive and negative displacement charges are elastically bonded to one another, any displacement of one from the other gives rise to restorative stresses. It is these restorative stresses that we refer to as the electric field.
3. The Net Charge of the Universe is Zero.
Assuming the net free charge and the net displacement charge in the universe are both zero, we must conclude that for every positive displacement there is, somewhere else, a negative displacement. It is the elastic, restorative stresses in the displacement charge that explains the apparent attraction of the positive and negative free charge distributions.
4. Free Charge/Displacement Charge Interfaces.
Another name for the universal sea of displacement charge is of course the "aether." Aside from the interesting fact that we cannot detect our motion relative to the aether, there is the theoretical "pressure" exerted on the surface of every distribution of free charge by the displaced displacement charge. While large distributions of free charge might tend to divide amoeba-fashion when subjected to such pressures, it is not unreasonable to hypothesize that adequately small distributions (quarks?) would resist further division. Perhaps the idea that no distribution of free charge can persist in time, without the counteraction of some mysterious, non-electromagnetic agent, is too extreme.
5. Aether Waves.
One of the consequences of Maxwell’s equations (first noted by Maxwell himself) is that "displacement waves" (or electromagnetic waves) can propagate through the aether, driven only by local displacements as the wave passes. According to the theory, such waves all propagate with the one speed c, regardless of their wavelength and/or the motion of their sources relative to the aether.
In a clever experiment Michelson and Morley attempted to detect changes in the Earth’s velocity relative to the aether at different times in its annual orbit around the Sun. The null results they obtained initially caused much confusion. In time the results were explained by the combined effects of length contraction, time dilation and the relativity of simultaneity. Although length contraction and time dilation were somewhat ad hoc at the time, it is not difficult now to demonstrate (using a computer) that certain admittedly simplistic models of the atom do indeed length-contract and time-dilate when in motion. The generalization to the (theoretical) rigid grids and distributed clocks of different reference frames follows.
6. Maxwell’s Paradigm for Electric Interactions.
In present times it has become standard practice to suggest that the existence of Maxwell’s sea of overlaid displacement charge distributions (or, in brief, of his aether) has been disproved. But the truth is that, given the electrodynamic phenomena of length contraction and time dilation (and the most natural way to synchronize spatially separated clocks), no one has devised an experiment to disprove the aether’s existence.
Maxwell believed that such a medium was the most reasonable and mathematically tractable substitute for instantaneous action at a distance. As he himself wrote in his seminal treatise, "Hence it is possible to account for the action of E2 on E1 by means of a distribution of stress in the intervening medium …" (Article 105, A Treatise on Electricity and Magnetism. Maxwell earlier identifies E2 and E1 as "…two electrical systems the mutual action between which we propose to investigate." As suggested herein, E2 and E1 would be two spatially discrete distributions of free charge.)