Classical field theories

Olivier Darrigol

in Physics and Necessity

Published in print May 2014 | ISBN: 9780198712886
Published online June 2014 | e-ISBN: 9780191781360 | DOI:
Classical field theories

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This chapter develops the consequences of a specific Faradayan condition of measurability for fields: that the physically relevant properties of fields should all be testable by point-like particles. Under this condition, and if the field dynamics derives from a Minkowski-invariant action principle, the only possible field theories are Nordström’s theory for scalar fields, Maxwell’s electromagnetic theory for vector fields, and Einstein’s gravitation theory for tensor fields. Nordström’s theory can be eliminated by slightly sharpening the measurability condition. In the tensor case, the assumed Minkowskian metric is a mere fiction, because the tensor fields affect geodetic measurements in a manner compatible with the pseudo-Riemannian metric of general relativity. A further section of this chapter explains the relationship of the Faradayan derivation of Einstein’s equations with the somewhat similar derivations by Gupta (1954), Feynman (1963), and Deser (1970). Lastly and most daringly, the chapter shows that a sharpened Faradayan principle and the action principle directly lead to Einstein’s theory of gravitation and electromagnetism when applied to a pre-metrical continuum of events.

Keywords: classical fields; Electromagnetism; general relativity; Nordström; Einstein; Gupta; Feynman

Chapter.  12120 words. 

Subjects: History of Science and Technology

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