Toward a Stable Electron Model?
A question that has stimulated much thought over the years is how charged particles can exist. For charge repels like-signed charge, and any finite distribution of charge should dissipate into space. How can electrons persist?
There are two facts about "elementary" charged particles that may provide clues: (1) Charge (of either sign) always occurs in multiples of +1.6 x 10-19 coulombs. (2) Every charged "elementary" particle has a magnetic dipole moment.
Regarding clue no. 1, Dirac reportedly was able to demonstrate (in theory) a link between the quantization of electric charge and the existence of magnetic charge. A problem at this writing, however, is that no one has been able to isolate magnetic charge. If it exists, it always exists in tightly bound, equal amounts of both signs, so that the B field flux out of any measurable volume is zero.
With regard to the second clue we may safely conclude, in the absence of any non-electromagnetic constraint, that the charge in an elementary charged particle is somehow circulating. For no static distribution of electric charge can exist without some sort of non-electromagnetic constraint. Unfortunately the same appears to be true in the case of circulating charge. Many heroic attempts have been made to come up with a current configuration that holds together under the tug of its own internal interactions. All have failed. (Einstein reportedly pondered whether gravity might provide the needed, non-electromagnetic constraints needed to explain how electrons can persist in time.)
But what if we admit the possibility that magnetic charge exists (even though no one has detected an isolated sample of one sign or the other)? For example, what if we admit the possibility that true magnetic dipoles might exist … equal magnitude oppositely signed magnetic charges intimately bound but not completely superimposed. Fig. 1 illustrates. The distance s would of course be very very small. (The primes signify magnetic charge.)
A Magnetic Dipole
If the distance s in Fig. 1 is small enough, it will be impossible to detect a divergence of B out of any measurable volume. This being the case, the Maxwell equation, div B = 0, becomes a statement of what is practically observable, versus what is absolutely true.
Of course Fig. 1 immediately raises the question of what holds q+’ and q-‘ apart. For presumably the two hypothetical magnetic charges attract one another. In the generally accepted current theory, where there is no magnetic charge, we have the problem of what keeps electric charge from dissipating away. And if we admit the possibility that at least magnetic dipoles might exist, then we have the added problem of explaining what keeps the magnetic charges apart.
Interestingly enough, insight into both problems might be gained by considering a combination of circulating electric charge and magnetic dipoles. Fig. 2 depicts a rotating, circular, negative electric line charge midway between magnetic positive and negative charges. The positive and negative point charges are located at y=s/2 and y=-s/2 respectively. The ring of negative electric charge, of radius r, has an angular velocity in the negative y-direction. For obvious reasons we have supposed the negative electric charge to have a magnitude of e=1.6 x 10-19 coulombs.
A Magnetic Dipole/Electric Current Loop Combination
Let us first consider how the distance between q+’ and q-‘ might remain constant. q+’ is attracted in the negative y-direction by q-‘. But it is clear that the current loop’s B field points in the positive y-direction (on its spin axis). Thus q+’ experiences a force in the positive y-direction in the current loop’s B field. Equilibrium occurs when the downward force from q-‘ is balanced by the upward force from the current loop. Similar remarks apply to q-‘.
But what about the ring of electric charge? What keeps it from expanding away into infinite space? The magnetic dipole B field points toward negative y at every point on the current loop. Thus every increment of the (negative) rotating loop experiences an inward magnetic (Lorentz) force in the magnetic dipole’s field. And of course every increment of the loop experiences an outward electric force owing to the rest of the loop's electric charge. Equilibrium occurs when the inward and outward forces balance.
Does Fig. 1 suggest a model that can be expected to persist with the passage of time? Perhaps. If so, all of the dimensions must be extremely tiny. For experimentally the electron acts like a point electrically charged magnet. Thus s, the distance between the hypothetical magnetic point charges, and r, the radius of the hypothetical current loop, must mutually be too small to measure. Nonetheless the possibilities are intriguing and warrant more detailed study. The quantizations of both the electron’s charge and its magnetic dipole moment might be good starting points.