Mario Hubert
American University in Cairo
We show that in the Maxwell–Lorentz theory of classical electrodynamics most initial values for fields and particles lead to an ill-defined dynamics, as they exhibit singularities or discontinuities along light-cones. This phenomenon suggests that the Maxwell equations and the Lorentz force law ought rather to be read as a system of delay differential equations, that is, differential equations that relate a function and its derivatives at different times. This mathematical reformulation, however, leads to physical and philosophical consequences for the ontological status of the electromagnetic field. In particular, fields cannot be taken as independent degrees of freedom, which suggests that one should not add them to the ontology.
Keywords electrodynamics  Maxwell-Lorentz  ontology  fields
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Reprint years 2021
DOI 10.1093/bjps/axy060
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References found in this work BETA

Ockham’s Razors: A User’s Manual.Elliott Sober - 2015 - Cambridge University Press.
Time’s Arrow and Archimedes’ Point.Huw Price - 1996 - Philosophical and Phenomenological Research 59 (4):1093-1096.

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