Time: Towards a Consistent Theory pp 116-135 | Cite as

# Electromagnetic Time

## Abstract

In the previous chapter we saw that the introduction of the field creates more problems than it solves. Here we begin by disregarding the problems due to the field, and formulate the two-body problem of retarded electrodynamics, without radiation reaction. The resulting equations of motion are time-asymmetric, and fail to satisfy the ‘phase-flow’ hypothesis underlying the recurrence and reversibility paradoxes. We present a counter-example to show that the Lorentz-Dirac equation, resulting in preacceleration, may be invalid since it is derived by replacing a retarded ordinary differential equation (o.d.e.) by a higher-order standard o.d.e. obtained by Taylor approximation. The solutions of advanced o.d.e.’s branch into the future, implying in-principle unpredictability from the past and resolving Popper’s pond paradox. The branching and collapse of solutions of mixed o.d.e.’s suggests a resolution of the Wheeler-Feynman and grandfather paradoxes.

With a direct-action theory, or with Dirac’s definition of radiation damping, the elimination of advanced interactions is a serious problem. We present an exposition of (i) the Sommerfeld condition, pointing out its arbitrariness; (ii) the Wheeler-Feynman absorber theory, pointing out its internal inconsistency; and (iii) the Hogarth-Hoyle-Narlikar theory, pointing out its external inconsistency. The remaining absorber theory predicts the existence of rare advanced interactions. We compare this with the empirical results of Partridge, and suggest that experiment proposed by Heron and Pegg may now be revived.

## Keywords

World Line Null Cone Retardation Vector Time Asymmetry Advanced Radiation## Preview

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## Notes and References

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