Uniform Acceleration Of Charge

Any complete theory of electromagnetism must include the zero-point energy, for ignoring it leads to contradictions and paradoxes at a very fundamental'level. One difficulty in electrodynamics is known as the equivalence paradox. Here a uniformly accelerated charge is recognized to radiate. However, a charge suspended at rest in a uniform gravitational field does not. According to general relativity, a uniformly accelerating system in free space should be equivalent to one at rest in a uniform gravitational field. Thus, in this case the principle of equivalence seems to be violated. This problem has been discussed in the literature at the classical level without adequate resolution. For example, Rolrhich,6 Atwater,7 and Ginzburg8 conclude that radiation is a function of the acceleration of the observer in relation to the source charge. But as Ginzburg asks, what are photons, and what propagates at the velocity of light if it can be made to appear or disappear depending on the acceleration of the observer? Boulware9 similarly suggests that "the way out of the paradox is to deny that the concept of radiation is the same in the accelerated and unaccelerated frames."9 This interpretation likewise throws out the independent existence of light by linking it to the motion of the observer.

C. M. Dewitt10 and B. S. Dewitt11 acknowledge the violation of equivalence but state that electric charge is an "unfair," i.e., scientifically invalid, test of the principle of equivalence since a real gravitational field is only uniform locally, but a charge's field persists to infinity. B. S. Dewitt11 also states that spinning neutral bodies also deviate from geodesic motion and they too are "unfair" tests of the principle of equivalence since angular momentum is a manifestation of a "nonlocal" phenomenon. It appears that either one must admit some of the laws of physics disobey the principle of the equivalence or that light cannot exist as an independent entity. The equivalence paradox has not yet been adequately resolved at the classical level.

An even more basic problem appears in classical electrodynamics regarding the uniform acceleration of charge. It is generally accepted that the radiated power is proportional to the square of the acceleration as computed by the Lar-mor formula:12

Yet the radiation reaction friction force experienced by the charge is proportional to the first time derivative of the acceleration:12

3 c3 dt

For uniform acceleration this derivative is zero while the acceleration is not. The particle radiates but does not lose kinetic energy. Where does the radiation energy come from? Fulton,15 Ginzburg,8 and Boulware9 conclude it has to come from the charge particle's source field. But Pauli,14 Vasude-vam,15 and Luiz16 come to the opposite conclusion, stating, "...we cannot accept the assumption of radiation from the charge because otherwise the internal energy of the particle should be exhausted."16 Luiz further argues, "The law of action and reaction is a fundamental law in physics and if the radiation reaction is zero, certainly there is no radiation."16 Ginzburg8 points out that this fundamental problem manifests itself in attempts to match theory with experiments measuring synchrotron radiation. Surprisingly, Leibo-vitz12 concludes that Maxwell's equations are incompatible with uniform accelerating motion! Electrodynamics clearly suffers serious problems at the classical level where the zero-point vacuum fluctuations are ignored.

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