Check out something is rotten in the state of QED. It’s a paper by Oliver Consa, who has done some excellent detective work on the history of quantum electrodynamics (QED). He has delved deep into the claims that QED is the most precise theory ever, and what he’s come up with is grim:

Consa says the much-touted precision of QED is based on measurements of the electron g-factor, but that *“this value was obtained using illegitimate mathematical traps, manipulations and tricks”*. I think he’s right. I think he’s discovered where the bodies are buried. I think his paper is forensic physics at its finest.

*The devil’s seed had been planted*

Consa sets the scene by telling how after World War II, American physicists were regarded as heroes who could do no wrong. Such physicists were no longer harmless intellectuals, they were now *“the powerful holders of the secrets of the atomic bomb”*. Consa says the former members of the Manhattan Project took control of universities, and enjoyed generous state funding and unlimited credibility. He also says *“the devil’s seed had been planted”*. That’s because their hypotheses were automatically accepted, even when it concerned quantum field theory (QFT). This had been regarded as a complete failure in the 1930s because of the problem of infinities. However the physicists swept it under the rug using “renormalization”. Consa gives an analogy wherein Indian mathematician Srinivasa Ramanujan has claimed that the sum of all positive integers is not infinite, but is instead -1/12. It’s wrong, it’s absurd, but renormalization has now been accepted, and is even sold as a virtue.

*Meaningless explanations*

Consa rightfully points out that it comes with a long list of meaningless explanations such as the polarization of the quantum vacuum, electrons and photons interacting with their own electromagnetic fields, particles travelling back in time, the emission and reception of virtual photons, and the continuous creation and destruction of electron-positron pairs in a quantum vacuum. I share his sentiments. It pains me that people believe this garbage. See Karen Markov’s quora answer. It’s lies to children, and pseudoscience junk.

*Experimental results contradicted the Dirac equation*

Consa’s paper isn’t. He tells us about the 1947 Shelter Island conference, where experimental results contradicted the Dirac equation. Questioning the validity of the Dirac equation meant questioning the validity of quantum mechanics. Questioning the validity of quantum mechanics meant questioning the legitimacy of the Manhattan Project heroes. Consa tells us how the conference attendees *“devised a compromise solution to manage this dilemma by defining QED as the renormalized perturbation theory of the electromagnetic quantum vacuum”*. But for this to work, *“it was necessary to use the QED equations to calculate the experimental values of the Lamb shift and the g-factor”*.

*Bethe’s fudge factor*

He then tells us about Bethe’s fudge factor. On the train home from the conference Hans Bethe famously came up with the Lamb shift equation, obtaining a result of 1040 MHz. His paper was on the electromagnetic shift of energy levels. Consa tells us that the values in Bethe’s equation were known physical constants, except for the value of 17.8 Ry. He also says *“t**he origin of this value is unknown, but it is essential to obtain the desired result”*, and that *“**Bethe’s fantastic calculation is based on data that was calculated later, data that Bethe could not have known on his train journey”. *The bottom line is that it’s* “a value that was entered ad hoc to match the theoretical value with the experimental value”. *Now that is fighting talk. And there’s more of the same.

*Schwinger’s numerology*

Consa then tells us that a few months later Julian Schwinger devised an even more epic calculation to yield the g-factor of the electron. Check out the Wikipedia article on the anomalous magnetic dipole moment. Consa says Schwinger’s one-page paper was on quantum-electrodynamics and the magnetic moment of the electron. This is the paper where Schwinger said *“the detailed application of the theory shows that the radiative correction corresponds to an additional magnetic moment associated with the electron spin of magnitude δμ/μ = (½π)e²/ħc = 0.001162. It is indeed gratifying that recently acquired experimental data confirm this prediction”*** .** Schwinger said prediction even though it was obviously a postdiction. A retrofit. Consa points out that Schwinger didn’t explain how the value had been obtained, and suspects

*“that Schwinger did not publish the theory because he had no theory”*. The suspicion is that all he had was numerology, which is why he failed miserably at the 1948 Pocono conference. As did Feynman. Then came Tomonaga muddying the waters further. But then came Freeman Dyson to the rescue with his paper on the radiation theories of Tomonaga, Schwinger, and Feynman:

Consa tells us that Dyson said that the Heisenberg S-matrix could be used to calculate the electron’s g-factor, transforming it into the Dyson series. It was an infinite series of powers of alpha, where each coefficient could be calculated by solving a certain number of Feynman diagrams. Consa also tells us that enthusiasm returned to the American scientific community, but that some were critical. Like Paul Dirac, who said *“How then do they manage with these incorrect equations? These equations lead to infinities when one tries to solve them; these infinities ought not to be there”*. And Robert Oppenheimer, who thought *“that this quantum electrodynamics of Schwinger and Feynman was just another misguided attempt to patch up old ideas with fancy mathematics”. *Another critic was Enrico Fermi who said this: *“There are two ways of doing calculations in theoretical physics. One way, and this is the way I prefer, is to have a clear physical picture of the process you are calculating. The other way is to have a precise and self-consistent mathematical formalism. You have neither”. *Well said Enrico.

*More fudge factors*

Consa then describes how in 1950, Bethe published a new calculation of the Lamb shift that adjusted his fudge factor from 17.8 Ry to 16.646 Ry. And *that “other researchers, such as Kroll, Feynman, French and Weisskopf, expanded Bethe’s original equation with new fudge factors, resulting in a value of 1052 MHz”*. He says this strategy of adding new factors *“of diverse origin with the objective of matching the theoretical and experimental values has been widely used in QED”.* The strategy is known as perturbation theory.

*Kroll and Karplus deliver **a theoretical result that was identical to the experimental result*

Consa then talks about John Gardner and Edward Purcell, who obtained a new experimental result which yielded an electron magnetic moment of μ_{s}=(1.001146±0.000012)μ_{0}. That was in their 1949 paper A Precise Determination of the Proton Magnetic Moment in Bohr Magnetons. That meant Schwinger’s result was no longer considered accurate. But that didn’t matter to Feynman, because according to Dyson’s QED reformulation *“Schwinger’s factor was only the first coefficient of the Dyson series”*. The calculation of the next factor in the series was performed by Norman Kroll and Robert Karplus, two of Feynman’s assistants. Their 1950 paper was Fourth-Order Corrections in Quantum Electrodynamics and the Magnetic Moment of the Electron. They came up with a new theoretical value of 1.001147. It was almost identical to the Gardner and Purcell’s experimental result. Now take a look at footnote 23 at the bottom of page 13:

Kroll and Karplus said the calculations had been performed independently by two teams of mathematicians who had obtained the same result. Consa says it wasn’t possible *“to imagine that a theoretical result that was identical to the experimental result could have been achieved by chance”.* And that *“this was the definitive test. QED had triumphed*”. He says logic had been renounced, rigorous mathematics had been dispensed with, but *“there was nothing more to discuss. Feynman’s prestige dramatically increased, and he began to be mentioned as a candidate for the Nobel Prize”*.

*The QED calculations had matched the experimental data because they were manipulated*

Consa goes on to tell us that Dyson had doubts, but that his claim that the series was divergent did not diminish QED’s credibility. Nor did a 1956 paper by Sidney Liebes and Peter Franken on the Magnetic Moment of the Proton in Bohr Magnetons. This provided a very different value of 1.001165. Hence the coefficient calculated by Kroll and Karplus was wrong. Hence QED must be incorrect. And *“there was no explanation for why Kroll and Karplus’s calculation provided the exact expected experimental value when that value was incorrect. It was evident that the QED calculations had matched the experimental data because they were manipulated*”. Consa also says “*the creators of QED refused to accept defeat. QED could not be an incorrect theory because that placed them in an indefensible situation”*. Ouch. So what happened next? Andreas Petermann wrote a paper in 1958 on the Fourth order magnetic moment of the electron. Consa says Petermann found an error in the Kroll and Karplus calculations, as did Charles Sommerfield in his 1957 paper on the Magnetic Dipole Moment of the Electron. Consa also say this: *“Once again, two independent calculations provided the same theoretical value. Miraculously, QED had been saved. For the third time in 10 years, experimental data had contradicted theoretical calculations”*. And *“for the third time in 10 years, a theoretical correction had allowed the reconciliation of the theoretical data with the experimental data”*. Wince.

*Keeping Petermann’s theoretical value within the margin of error*

But things were set to get worse. Consa tells us how a research team from the University of Michigan performed a new experiment in 1961. The relevant paper was Measurement of the g factor of free, high-energy electrons by Arthur Schupp, Robert Pidd, and Horace Crane. They said g is 2(1+a) and a=0.0011609 ±0.0000024. Consa says the experiment was revolutionary in its precision, but *“the authors were cautious with their results, presenting large margins of error”*. Consa says in doing this they were keeping Petermann’s theoretical value within the margin of error to avoid *“creating a new crisis in the development of QED”*. Then in 1963 David Wilkinson and Horace Crane (again) came up with a new improved version of the experiment. This yielded a result which matched Petermann’s theoretical calculation. Their paper was Precision measurement of the g factor of the free electron. The experimental result was 0.001159622 ± 0.000000027, which was nearly the same as Petermann’s theoretical value.

*A conscious manipulation of the experimental data*

Consa says* “this experimental result is incredibly suspicious. It was obtained after a simple improvement of the previous experiment, and it was conducted at the same university, with the same teams, only two years later. The margin of error could not have improved so much from one experiment to another, and it is extremely strange that all the measurements from the previous experiment were outside the range of the new experimental value. Even stranger, the theoretical value fit perfectly within the experimental value. Most disturbing, this value is not correct, as was demonstrated in later experiments”.* He also says *“it appears to be a conscious manipulation of the experimental data with the sole objective of, once again, saving QED”. *And that* “after this experiment, all doubts about QED were cleared, and, in 1965, Feynman, Schwinger and Tomonaga were awarded the Nobel Prize in physics”.*

*A temporary and jerry-built structure*

Consa also says the cycle was repeated a fifth time and a sixth time. It sounds like whack-a-mole to me. Theoreticians come up with a calculation that exactly matches an experiment. Then a later experiment shows that the earlier experiment wasn’t quite correct. Then the theoreticians change their calculation to match the new experiment. And so on. Consa concludes with a Feynman quote: *“We have found nothing wrong with the theory of quantum electrodynamics. It is, therefore, I would say, the jewel of physics – our proudest possession”. *Only it isn’t. Consa also quotes Dyson from 2006: *“As one of the inventors of QED, I remember that we thought of QED in 1949 as a temporary and jerry-built structure, with mathematical inconsistencies and renormalized infinities swept under the rug. We did not expect it to last more than 10 years before some more solidly built theory would replace it. Now, 57 years have gone by and that ramshackle structure still stands”*. It still stands because it’s been propped up by scientific fraud. Here we are fourteen years later, and it’s still the same, and physics is still going nowhere. How much longer can this carry on? Not much longer, because now we have the internet. Yes Oliver, winter is coming. There may be trouble ahead.

## Richard David Gill

17 Mar 2020You write “Consa gives an analogy wherein Indian mathematician Srinivasa Ramanujan has claimed that the sum of all positive integers is not infinite, but is instead -1/12. It’s wrong, it’s absurd”. I think that’s a little unfair. It depends on how you define the sum of positive integers. Ramanujan introduced “Ramanujan summation” and never claimed it gave the same answers as conventional summation. Ramanujan summation is useful and interesting! (But not for computing infinite sums in the usual sense).

## the physics detective

17 Mar 2020Point noted Richard. But we all know that 1+2+3=6 and 1+2+3+4=10 et cetera. See this plus maths article for details. The bottom line is that the sum of positive integers just isn’t minus a twelfth. So I think the analogy is pretty good, especially since the article uses the Casimir effect as an example.However it’s a pity that it says

“the vacuum isn’t empty, but seething with activity. So-called virtual particles pop in and out of existence all the time”. It isn’t true. Vacuum fluctuations aren’t the same thing as virtual particles. See Cathryn Carson’s peculiar notion of exchange forces part I and part II. Hydrogen atoms don’t twinkle, magnets don’t shine.## oliverconsa

18 Mar 2020Hi John,

I am the author of the paper. Great job!

The amount of relevant information in the paper makes it very difficult to summarize without losing important data.

## The physics detective

18 Mar 2020Great Job yourself Oliver! Yes, your paper was difficult to summarize. But heck, it deserves some publicity. And some time from a guy like me. The more people who say something about this on the internet, the better.

## Greg R. Leslie

19 Mar 2020Bravo Oliver and John ! One of these days one or both of you will probably discover charlatans who were reading tea leaves, using Ouija Boards, and/or Phrenology. No wonder last years Nobel Dyn-O-Mite award in quantum physics went to a group of ASTROPHYSICISTS.

## The physics detective

20 Mar 2020Thanks Greg. I was just reading the Nobel press release and noticed this:

“The results showed us a universe in which just five per cent of its content is known, the matter which constitutes stars, planets, trees – and us. The rest, 95 per cent, is unknown dark matter and dark energy. This is a mystery and a challenge to modern physics”. I know what that is! Space is dark, it has its vacuum energy which has a mass equivalence, and there’s a lot of it about.## Greg R. Leslie

20 Mar 2020Yes Sir, you certainly do know, and have explained it most profeciantly at the most highest academic level for professionals and students; and most profeciantly at a much lower level for we gormless(LOL). Along with how gravity really works; what photons really are; what electrons really are; and many other facts and concepts that I now have a much better grasp of. By the way,your last essay on Oliver’s paper does not show up on my Physics Dective feed as a new topic,it only shows up in the comments section of the previous blog. In another week or so I will send in some more questions on current headlines, everyone please stay healthy until then.

## the physics detective

21 Mar 2020Thanks Greg. I’m not sure I’ve got the photon quite right, but hey, it’s a start. Sorry I’ve been under pressure at work recently, and didn’t add the last two essays to my list of articles. I’ve now done that, and put in the NEXT links. Yes, stay healthy. The situation in Italy looks grim, and it could be like that here in the UK soon. It rather focuses the mind, methinks.

## Charles

21 Mar 2020Much of this is completely true (I won’t say all, but only because then I would have to check every detail). However, it is possible to fix the the divergence problems of qed, using the rigorous mathematical methods of C19th analysis (taking limits. It is intricate by quite doable). I have shown how to do so in this paper. http://www.ejtp.com/articles/ejtpv10i28p27.pdf. The extraordinary thing to me is that physicists are not interested. They would rather sweep the issues under the carpet. Probably the main part of the problem is that doing so also shows that qed is really just relativistic quantum mechanics, that there is no justification for qft as a separate theory, that the idea that fields are fundamental is a nonsense, that there is indeed no reason or justification for renormalisation, and that pretty much everything currently taught about qft is based on the bits of qed which don’t work. It only gets worse in string theory, where they claim that it must be true that the sum of positive integers equals -1/12 because it is a physical result! (this was said in a famous numberphile video on Youtube)

## The physics detective

21 Mar 2020That looks interesting Charles. I shall read that. Meanwhile can I say that it’s sad that physicists aren’t interested in how you’ve fixed the divergence problem. They aren’t interested in how gravity works either. Or what the electron is. I know too many good people who can’t get their papers published. The situation is not good, and meanwhile physics is withering on the vine. Because there can be no admission of fault, because that would be bad for physics. So they’ve been harming physics for decades. There’s a dreadful irony to it.

.

No, I think there’s no justification for QFT as a separate theory. I too think the idea that fields are fundamental is a nonsense. Yes, there is indeed no justification for renormalization. In fact I now think QFT is so badly wrong it’s should be abandoned. We should start again, from classical electromagnetism. I’d like it if there was some material here that you found useful. I’d like to see people like you with top notch maths working on some of the stuff I’ve dug up. Starting from the photon, then moving on to pair production, then the electron, and so on. I think there;s a necessary sequence to getting the foundations right, and that QFT doesn’t have any.

## Greg R. Leslie

23 Mar 2020Go for it Charles !