Article ID: CBB322806876

When Fields Are Not Degrees of Freedom (2021)


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.

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Authors & Contributors
Lazaroff-Puck, Cameron
Rinat Magdievich Nugayev
Francesco Nappo
Marmottini, Donatella
D'Agostino, Salvo
Stanley, Matthew
Studies in History and Philosophy of Science
Substantia: An International Journal of the History of Chemistry
Ziran Kexueshi Yanjiu (Studies in the History of Natural Sciences)
Sudhoffs Archiv: Zeitschrift fuer Wissenschaftsgeschichte
Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
Spontaneous Generations
Pavia University Press
Blackwell Publishers
Cambridge University Press
University of Minnesota
Philosophy of science
Fields and field theory
Electricity; magnetism
Maxwell, James Clerk
Hertz, Heinrich Rudolph
Lorentz, Hendrik Antoon
Sommerfeld, Arnold Johannes Wilhelm
Gauss, Carl Friedrich
Weber, Wilhelm Eduard
Time Periods
19th century
20th century
Great Britain

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