Electromagnetism as Quantum Physics

Foundations of Physics 49 (4):365-389 (2019)
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One can interpret the Dirac equation either as giving the dynamics for a classical field or a quantum wave function. Here I examine whether Maxwell’s equations, which are standardly interpreted as giving the dynamics for the classical electromagnetic field, can alternatively be interpreted as giving the dynamics for the photon’s quantum wave function. I explain why this quantum interpretation would only be viable if the electromagnetic field were sufficiently weak, then motivate a particular approach to introducing a wave function for the photon :1914–1919, 1957). This wave function ultimately turns out to be unsatisfactory because the probabilities derived from it do not always transform properly under Lorentz transformations. The fact that such a quantum interpretation of Maxwell’s equations is unsatisfactory suggests that the electromagnetic field is more fundamental than the photon.



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Charles Sebens
California Institute of Technology

References found in this work

Time and Chance.S. French - 2005 - Mind 114 (453):113-116.
The Fate of 'Particles' in Quantum Field Theories with Interactions.Doreen Fraser - 2008 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (4):841-859.
Ontological Reduction and the Wave Function Ontology.Alyssa Ney - 2013 - In Alyssa Ney & David Z. Albert (eds.), The Wave Function: Essays on the Metaphysics of Quantum Mechanics. Oxford University Press. pp. 168-183.
Against Field Interpretations of Quantum Field Theory.David John Baker - 2009 - British Journal for the Philosophy of Science 60 (3):585-609.

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