The Electromagnetic Field
We concluded the previous chapter with the hope that the field may provide the way out of the paradoxes of thermodynamics. We point out that various intuitive ideas underlying field theory, such as action by ‘contact’, the idea of ‘locality’ or a ‘chain of causes’, or the mechanical model provided by the field, are respectively unintelligible, illusory, and redundant. Consequently, there is nothing ‘spooky’ about action at a distance.
We are left only with the differential equations of field theory, which admit both retarded and advanced solutions. In the context, the advanced solutions cannot be rejected on grounds of ‘causality’, and we state some of the paradoxes of advanced action: the pond, grandfather, and Wheeler-Feynman paradoxes.
We point out the divergences, due to self-action, in field theory. The Abraham-Lorentz model of the extended electron failed, while the action-at-a-distance approach is equivalent to time-symmetric fields. Even with Dirac’s approach, using the equivalence of advanced and retarded representations, the electron preaccelerates. Thus, consideration of interactions propagating into the past seems forced, and, prima facie, the introduction of the field seems to create more problems than it solves.
KeywordsRadiation Field Relativistic Generalization Advanced Action Closed Timelike Curve Mental Construct
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Notes and References
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