Quantum Electrodynamics
Quantum electrodynamics (QED) is the relativistic quantum field theory of the interaction between light and charged matter. It treats the electromagnetic force as the exchange of virtual photons between charged particles, and it is the model on which the rest of the Standard Model of particle physics was built.
The standard account
Paul Dirac opened the subject in 1927 by quantizing the electromagnetic field, and his 1928 relativistic wave equation for the electron supplied the other half. The resulting theory produced infinities: calculations beyond the leading order gave divergent integrals for quantities such as the electron's self-energy. The problem stood for twenty years until, between 1947 and 1949, Sin-Itiro Tomonaga, Julian Schwinger and Richard Feynman independently produced renormalized formulations in which the divergences are absorbed into redefinitions of the measured mass and charge; Freeman Dyson showed the three approaches to be equivalent. Tomonaga, Schwinger and Feynman shared the 1965 Nobel Prize. Feynman's diagrammatic method became the standard calculational language of particle physics.
The theory's reputation rests principally on two quantities. The Lamb shift, measured by Willis Lamb and Robert Retherford in 1947, is a small splitting between hydrogen levels that the Dirac equation says should coincide; QED accounts for it. The other is the anomalous magnetic moment of the electron, g−2, where the calculated and measured values agree to roughly ten significant figures — the closest agreement between theory and experiment anywhere in physics, and the usual answer when QED is challenged.
There are open questions. The perturbation series is believed to be asymptotic rather than convergent, so the expansion has no proven limit; the coupling (the fine structure constant) runs with energy and the theory has a Landau pole at extremely high energy, meaning QED is generally regarded as an effective theory valid below some cutoff rather than a complete one. The muon's anomalous magnetic moment has been the subject of a long-running discrepancy between measurement and the Standard Model prediction; as of the mid-2020s the disagreement turns substantially on how the hadronic vacuum polarization contribution is computed, and is not resolved.
On this wiki
The criticism gathered here is directed less at QED's numbers than at its method — specifically at renormalization, at the physical status of virtual particles, and at the claim that the g−2 agreement constitutes a proof.
The most detailed historical critique is by Oliver Consa, whose essay "Something is wrong in the state of QED" argues that the theory's celebrated precision rests almost entirely on the electron g-factor calculation, and examines the history of those computations — including the Karplus and Kroll episode, in which a published result later found to be in error had nonetheless been reported as agreeing with experiment — to question how independent theory and measurement really were. Consa's own work develops geometric alternatives: a ring and helical-solenoid model of the electron in which the g-factor follows from the particle's shape rather than from a loop expansion. This connects to the wider structural tradition here — see Toroidal Ring and Common Sense Science — where Paul Wesley and David L Bergman's Spinning Charged Ring Model of Electron Yielding Anomalous Magnetic Moment (Galilean Electrodynamics, 1990) derives the anomalous moment from an extended charged ring, and Harold Aspden's A New Approach to the Problem of the Anomalous Magnetic Moment of the Electron (1977) derives it from aether structure.
Paul Wesley rejects the underlying quantum formalism outright in The Failure of Quantum Mechanics (1996) and offers a classical replacement in Classical Quantum Theory (1996), in which particle motion follows the Poynting vector and quantization arises from standing waves. Randell L Mills attacks a specific QED-era argument in The Fallacy of Feynman's and Related Arguments on the Stability of the Hydrogen Atom According to Quantum Mechanics (2005).
Howard C Hayden takes up the relationship between QED and special relativity in Einsteinian and Quantum-Mechanical Observers (Galilean Electrodynamics, 1993), noting that the two great successes of twentieth-century physics assume incompatible things about observers and about Maxwell's equations. Richard Oldani presses similar consistency questions in his work on measurement and complementarity.
A separate line accepts field theory but disputes that Maxwell's abelian electrodynamics is the right starting point. Myron W Evans argued for a non-abelian electrodynamics with a longitudinal magnetic component, the B(3) field; with Lawrence B Crowell he set this out in Classical and Quantum Electrodynamics and the B(3) Field (2001) and in The Enigmatic Photon - Volume 2: Non-Abelian Electrodynamics, and summarised the programme in The New Electrodynamics (Apeiron, 2000). Charles William Lucas pursues a universal electrodynamic force law derived from finite-size charged structures rather than point charges in Symmetry of Nature Confirms Universal Electrodynamic Force (2012). The divergence problem that renormalization was invented to handle is itself an artefact of point charges, a point made in Alexander L Kholmetskii's Classical Electrodynamics of Point-Like Charges Without Divergences (2006) — and the collection Has the Last Word Been Said on Classical Electrodynamics? (2004) gathers the classical-side objections.
John F Kilpatrick's A Note on Quantum Electrodynamics (1989) and Lawrence B Crowell's Quantum Electrodynamics of Nonabelian Electrodynamics in a Cavity (1999) are catalogued here as citations in the Index of Papers Without Abstracts.