The Relativity of Electric Charge
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Having covered the basics of electrostatics, we now want to consider the physics of electric charges in motion in order to prepare for a consideration of how Relativity affects the electric and magnetic fields. Let's begin with a look at the Relativity of electric charge itself. We have seen that motion affects the amount of mass carried by a body. Does relative motion also affect the amount of electric charge that a body carries?
We can explore that question in the laboratory of our imaginations. By conducting the right imaginary experiments we can seek an answer to that question. Imagine a ring floating motionless in space and imagine that we have given it a net electric charge Q. Now imagine that we make the ring spin at a high speed. Does the amount of electric charge on the ring change?
Assume that the charge Q increases as the ring spins up. At any point in the space around the ring the electric field generated by the charge must also increase in the same proportion. That means that a charged particle at that point would have a potential energy vis-a-vis the charge on the ring that increases inherently with the elapse of time; that is, the potential energy must be represented by an explicit function of elapsed time. But an inherently time-varying potential energy provides the basis for generating a timeward force, thereby violating the no-time-travel theorem. We must therefore dismiss as false to Reality our postulate that the charge Q could change and assert in its place its opposite, that changes in motion cannot change the magnitude of electric charge.
We thus infer that electric charge obeys a conservation law. Electric charge can be separated or neutralized, but neither created nor destroyed. Therefore, moving bodies carry the same charge they possess at rest.
That analysis applies to any property of matter that generates a forcefield. But we seem to have a dilemma if we include gravitation in that statement. We know that changing the speed at which a body moves changes that body's inertial mass. Now we need to ask whether the change in speed also changes the body's gravitational mass and, if so, how we can reconcile that fact with the statement that the source properties of forcefields do not change with changes in their motions.
Look again at the ring spinning in the laboratory of your imagination. To make the ring spin we had to put energy into it. And that energy had to come from some place away from the ring. We have already discerned that energy correlates with mass, so we know that the mass of the ring did not merely grow; we brought the extra mass into the ring by moving it through space. If energy, in whatever form we find it, generates a gravitational field, then the field of the ring did not grow as an inherent function of time but rather as an accidental function of time due to transport of the source.
But now we must ask whether energy-in-whatever-form actually gravitates, as I have tacitly assumed above. To ask that question is to ask whether light and forcefields generate their own gravitational fields. But if light generates a gravitational field, then conservation of linear momentum necessitates that it respond to a gravitational field, that in some sense it fall toward any gravitating body. So I need only prove and verify the proposition that gravity affects light.
Our sun glows four megatonnes of light into space every second from its photosphere. Let's imagine taking the helium made in the fusions that created that light and lift it out of the sun. And now imagine that we have trapped that light at a helium cracking plant located some distance from the sun and use it to split the helium back into hydrogen. Finally let's lower the hydrogen back down onto the sun, harnessing its gravitational energy, the work its weight does upon our hoist as it descends, as we do so. In accordance with the law of conservation of energy, the energy in the matter that returns to the photosphere must equal the energy in the helium and the light at our helium cracking plant. At the cracking plant we have the mass-energy of the helium (A), the energy we put into the helium in lifting it out of the photosphere (B), and the energy in the light (C). At the photosphere we have the mass-energy of the hydrogen plus any leftover helium (D = A+C) and the work done in lowering the matter (E). Because the mass of matter that we lower onto the photosphere is greater than the mass of the helium we lifted off the sun, the work it does on our hoist (E) is greater than the work we did to raise the helium (B). The additional work E-B must represent the work done by the energy that we obtained from the light when we split the helium, so we must infer that the energy the light had as it exited the photosphere equaled C+(E-B), so when the light reached the distant fission plant must have carried less energy than it had when it left the sun. Therefore, the light must have done work against the sun's gravitational field, which means that light responds to the gravitational force; that is, light has gravitational mass.
Now we know that we cannot
discern a difference between inertial mass and gravitational mass. That fact
will have a profound effect upon our understanding of General Relativity. But
for now we want to return our attention to the Relativity of Electricity.
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