Abstract
At the present time, the Fokker-Wheeler-Feynman theory of electrodynamics and its generalizations provide the only relativistic alternative to a non-relativistic Lagrangian based classical dynamics theory of multi-particle systems. This formulation has particle interchange and time reversal symmetries and the equations of motion are properly Lorentz covariant. However, these equations of motion contain a central time plus relatively advanced and retarded times for each particle. An insistence on a Newtonian interpretation of the various terms results in a non-causal interpretation of the theory for few particle systems. In order to test the validity of the above interpretation, two classes of double time delay systems are examined. First, a series of three model problems of increasing complexity are studied that have fixed retarded and advanced time delays. All of these models have exact closed form solutions, implying a causal interpretation in which the past both drives the system forward in time and defines an irreversible arrow of time. Second, the Fokker-Wheeler-Feynman theory of electrodynamics and its generalizations are re-examined and found to satisfy this alternate interpretation. It is concluded that these theories are the relativistic counterpart of the classical dynamics description of systems of point particles with fundamental interactions.
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Moore, R.A. (1998). Causality in Relativistic Multi-Particle Classical Dynamic Systems. In: Hunter, G., Jeffers, S., Vigier, JP. (eds) Causality and Locality in Modern Physics. Fundamental Theories of Physics, vol 97. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0990-3_33
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DOI: https://doi.org/10.1007/978-94-017-0990-3_33
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