Quantum Electrodynamics (QED)

What it claims: QED is the quantum field theory of light and charged matter — photons and electrons (and other charged leptons) interacting via the electromagnetic field, built on Dirac’s 1928 relativistic electron equation and completed by Feynman, Schwinger, and Tomonaga in the 1940s (shared 1965 Nobel Prize). It’s widely considered the most precisely tested theory in the history of science.

Catalog status: Proven Systems. The flagship result is the electron’s magnetic moment (its “g-factor”). Dirac’s original equation predicts exactly $g=2$. Schwinger’s 1948 calculation added the first quantum correction, $g=2(1+\alpha/2\pi)\approx2.00232$ — the first proof that a point particle’s magnetic moment isn’t quite the classical value, and the beginning of QED’s precision-test tradition. Modern measurements (Hanneke, Fogwell & Gabrielse, 2008) agree with QED’s full multi-loop prediction to about 10 significant figures — an agreement often described as the most precisely verified prediction in physics.

The objection its own founder never withdrew

QED’s precision record is real and is not in question above. But the man whose 1928 equation the whole theory is built on spent the rest of his life refusing to accept how that precision is obtained, and said so publicly in lectures recorded on tape. Leaving that out would make this page’s “Proven Systems” status read as more settled than Paul Dirac himself thought it was.

The problem is where the numbers come from. Solve QED’s equations by the standard perturbation method and several of the second-order terms — the electron’s self-energy and the correction to its charge — come out as infinite integrals. Dirac’s own reading of that was blunt: as he saw it, the equation has no solutions, and after decades of effort nobody had found one. The working answer physics adopted is renormalization: the infinity is interpreted as an infinite contribution to the electron’s own mass, and it is subtracted, leaving a small finite correction that turns out to match experiment — the Lamb shift, and (separately) the anomalous magnetic moment above. Not every QED prediction needs this treatment — Schwinger’s leading-order $\alpha/2\pi$ correction to the g-factor is itself finite, with no infinity to subtract — but the theory as a whole, including the electron’s own mass and charge, is built on the renormalization procedure Dirac objected to.

Dirac accepted the arithmetic and rejected the reasoning. In a 1975 lecture on quantum electrodynamics he put it this way — quoted directly from the recording, not paraphrased: “this so-called ‘good theory’ does involve neglecting infinities which appear in its equations, neglecting them in an arbitrary way. This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity when it turns out to be small — not neglecting it just because it is infinitely great and you do not want it.”

The rest of this section is paraphrased from the recording and reflects this vault’s own listening and notes — treat it with correspondingly less certainty than the quoted sentence above, which is independently corroborated in multiple secondary sources. By this account, he also named a concrete alternative: impose a cutoff — stop the divergent integrals at a finite upper frequency rather than letting them run to infinity — which would make the theory mathematically well-defined again, at the cost of breaking the theory’s exact relativistic invariance. This is consistent with Dirac’s broader, well-documented program of pursuing cutoff-style alternatives to standard renormalization (see Kragh’s biography of Dirac), though this vault has not independently confirmed that this specific 1975 lecture states the relativity trade-off in exactly these terms.

His conclusion was that the basic equations must be wrong somewhere, and that the fix required would be as drastic as the passage from Bohr’s atom to quantum mechanics — a comparison Dirac is known to have made more than once, not necessarily confined to this one lecture.

Why this belongs on a page marked “Proven.” It doesn’t downgrade the status. QED’s predictions are confirmed to roughly ten significant figures and that isn’t in dispute. What Dirac’s objection separates out is a distinction this site cares about everywhere else: a calculational procedure that demonstrably works is not the same thing as a derivation from first principles with no unexplained steps. QED has the first beyond argument. Its own founder did not believe it had the second.

Where PBT touches this: Paper 6 uses the exact formula $g=2(1+\alpha/2\pi)$ and the resulting precession frequency directly — this is Schwinger’s real 1948 result, reused as-is. The 2026-07-21 site audit flagged that no derivation of this number from PBT’s own aether-vorticity mechanism is shown; the paper borrows the number rather than independently deriving it. Paper 7, 8, and 12 separately reference the real Fermilab muon g-2 anomaly (Aguillard et al., 2023, $\approx2.51\times10^{-9}$) — a distinct, still-actively-studied discrepancy between the muon’s measured and Standard-Model-predicted magnetic moment, not fully explained by QED alone and not the same number as the electron g-factor above.

References

1. Dirac, P.A.M. (1928). “The Quantum Theory of the Electron.” Proc. R. Soc. A 117, 610–624.
2. Schwinger, J. (1948). “On Quantum-Electrodynamics and the Magnetic Moment of the Electron.” Phys. Rev. 73, 416.
3. Hanneke, D., Fogwell, S., Gabrielse, G. (2008). “New Measurement of the Electron Magnetic Moment and the Fine Structure Constant.” Phys. Rev. Lett. 100, 120801.
4. Aguillard, D.P. et al. (Fermilab Muon g-2 Collaboration). (2023). “Measurement of the Positive Muon Anomalous Magnetic Moment to 0.20 ppm.” Phys. Rev. Lett. 131, 161802.
5. Dirac, P.A.M. (1975). Lecture on quantum electrodynamics, delivered during his Australia/New Zealand visit, August–September 1975. Published in Directions in Physics, eds. H. Hora and J. R. Shepanski (Wiley, 1978). The quoted sentence above is taken from the recorded lecture audio directly; the surrounding paraphrase is this vault’s own listening notes.