Abstract. Uncharged particles, traveling in a circle, speed up with the passing of time???
Long before most of us were born, scientists were intrigued by parallels between mass/mass interactions and charge/charge interactions. Cavendish and Coulomb found that the forces between resting bodies were in both cases inverse square. The clear difference is of course that like-signed charges repel, whereas like-signed masses attract. From the field vector point of view, the electric field of a positive charge points away from the charge, whereas the gravitational field of a mass traditionally points toward the mass.
Usually it is taken for granted that the field vectors in such cases are attributable to particles other than the one being acted upon. However, it is not difficult to show that an electric charge may experience an electric force in its own electric field when it moves in certain ways. This self-field, predicted by and consistent with Maxwell’s equations, is a consequence of the manner in which the charge’s fields vary in time.
By way of a specific example, we might consider the case of a charge traveling around a circular path at a constant speed. In such a case there is a motion-induced electric field right at the charge, said field pointing opposite to the charge’s velocity at all times. For reasons to be touched upon shortly, Abraham and Lorentz referred to this field as the radiation reaction field.
Of course according to the Lorentz force law, the charge should experience a component of electric force acting opposite to its velocity at all times. Evidently it should slow down. The only way the charge’s motion can be maintained is for some external agent to non-electromagnetically counteract the radiation reaction force, or for another E field to cancel out the radiation reaction field.
An agent force, acting in the same direction as the charge’s velocity at every moment, does a certain amount of work every cycle. If the charge’s fields at a distance beyond the orbit are calculated/computed, it turns out that there is a radiative component. Indeed, the flux of field energy per cycle outward through an enclosing surface precisely equals the work done per cycle by the agent force. (Hence the term "radiation reaction force" for the electric self-force.)
Now if we assume that the fields of a neutral (net charge of zero) mass are also governed by Maxwellian equations, then the question immediately arises as to the effect of the analogous field and force when a mass travels around a circle at constant speed. Consistent with the case of interacting, multiple masses, we might suppose that the mass feels a self-force parallel to its velocity at every instant. The effect of this force would be to speed the mass up! And here again, only by counteracting this force could the mass’s constant speed be maintained.
If such a force is manifest in nature, then a certain amount of work per cycle should be done on the agent providing the required counteraction. Whence the source of this work? One suggestion is that it flows inward from the environment, or, more specifically from the gravitational field.
According to a Physics News Update, there is evidence that an orbiting mass, in the absence of a counteracting agent force, does indeed speed up with time. This "anomaly" has been a matter of conjecture ever since its discovery. Might it be explained by the parallels suggested above? The whole matter warrants additional consideration.