Something is rotten in the state of QED

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 “the 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 μs=(1.001146±0.000012)μ0. 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.


This Post Has 25 Comments

  1. You 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).

    1. the physics detective

      Point 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.

  2. oliverconsa

    Hi 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.

    1. Great 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.

  3. Greg R. Leslie

    Bravo 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.

    1. Thanks 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.

  4. Greg R. Leslie

    Yes 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.

    1. the physics detective

      Thanks 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.

  5. Charles

    Much 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. 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)

    1. That 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.

  6. Greg R. Leslie

    O.K. John, time for another question, but not one based on headlines.
    For quite awhile I’ve been puzzled by what does a nutrino actually do ? How does it make its living; what is it’s usefull purpose in the quantum world?
    After scouring your past articles,other websites including Wikipedia, all I can come up with is a consensus of what most physicists consider a nutrino to be; what happens to it during and after annihilation occurs. Not what it does prior to annihilation.
    I did come up with a crude,basic possibility,but I am not quite ready to be laughed out of town .LOL !

    1. As far as I know Greg, a neutrino is something like a photon. It has no mass and no charge, and it moves at the speed of light. Only whilst a photon is a transverse-wave soliton, a neutrino is a rotational wave soliton. A breather. Something like the Large amplitude moving sine-Gordon breather. As for its purpose, I don’t know. Neutrinos don’t interact with normal matter much. Not like photons do.

  7. Greg R. Leslie

    Thanks John for introducing me to a new concept, that of breathers. They fit nicely into my ideas,at the least breathers don’t appear to contradict them. My rudimentary hypothesis is based on what I learned from you concerning knot zoos and knot theory. My interpretation of of the moebius strip/continous loops of pure energy going around and around inside of photons and elctrons,ect…are that in essence the knots are basic little machines: self- perpetuating engines/ motors. And what do many heat and friction producing motors possess to help combat excessive heat/friction? BALLBEARINGS and BUSHINGS ! I postulate that could be how neutrinos make their livings in the quantum world. Let the guffaws and belly laughs begin……..

    1. the physics detective

      I think of them as the twists, Greg. I think of the photon as a transverse wave soliton propagating linearly through space at c, and I think of the electron as a 511keV photon trapped in a “trivial knot” configuration. I think of the proton as the next knot, the trefoil, which needs a more energetic photon. The neutrinos come in when you mangle an electron into a proton to make a neutron. You need a twist to keep it in there. Only if the neutron is a free neutron which is not held tight by the surrounding protons, it works itself loose like a slip knot, and the components separate. Neutron decay is the jumping popper of particle physics!

  8. Greg R. Leslie

    Oh, o.k., so in a very basic sense nutrinos do serve as part of a twisting control process in the nuclei; and are sort of a waste byproduct of the decay process or annihilation process ?

  9. Greg R. Leslie

    I was concentrating too much on the more basic diagrams of knotts and was trying to apply my knowledge of macroscopic pioneering and sailing rope knotts to the quantum world. My nutrino would have been in the dead center of the energy knot,compressed into a smaller size, helping to control the flow(waves) of pure energy. And other compressed nutrinos in the outward loops as well, one for each color or flavor said of quarks, all at different wave lengths according to need. When let free they would merge into the one known larger traveling size, this would account for the three oscillating sizes.
    I should’ve paid more attention to the diagrams and GIFs of the torus rings with waves within waves?
    Still, it was great fun pretending to be a real scientist for a few days,thanks for putting up with me John !

    1. LOL, always a pleasure Greg. As for sailing, you know how a sailor pulls on the rope to control the mainsail? IMHO that’s like the way a neutron in a nucleus is held tight by the surrounding protons. As for quarks, have you read the proton. I think quarks are the crossing points in the knots. That’s why you’ve never seen a free quark. And never ever will. I should pay more attention to TQFT.

  10. Greg R. Leslie

    Time for a few questions again, John.
    1.) ATLAS experiments concerning the supposed Higg’s Bozo-ons supposedly decaying into beauty quarks ? ( There’s not enough quantum lipstick to slap onto this here beauty queen pig.)
    2.) Heidelberg U. using cold atoms to construct building blocks to simulate complex physical phenomena? ( More virtual computer smoke and mirrors to prove another virtual theory ? ).
    3.) Stephen Wolfram’s radical new computational concepts to explain super- symmetry? ( Is he trying to replace Einstein’s elastic space/stress-energy-momemtum tensor concepts; or just modify them ?).

    1. As regards number 1) Greg, I’d say this: when a church needs a miracle, a church gets a miracle. It was similar for the W boson and the Z boson. Alexander Unzicker’s book is well worth a read, as is Gary Taube’s article. I don’t know what to say about 2). I had a quick look and saw which looked OK. Can you give me a reference? As for 3) I read about that last week and thought it looked interesting because he was starting simple and he said energy is real. However when I floated out an email, I got this reply:
      Thanks for reaching out to us! We really appreciate you taking an interest in our project. As I’m sure you understand, we’re concentrating on all the work we have to do in developing our own theory, so we don’t expect to allocate time to studying alternative theories.
      Alternative theories! When I’m the guy who’s forever quoting Einstein? Grrrr! Then there was this:
      If you think that your work directly informs what we’re doing (e.g. maybe it gives us deeper mathematical insight into the limiting structure of the multiway causal graph, perhaps it provides us with a more precise understanding of the correspondence between our models and the holographic principle…
      The holographic principle! At this point I thought FFS, these guys are a bunch of quacks who know nothing, and who aren’t listening. Not like Robert Close, see I was clearing out drawers the other day and came across his 2009 elastic space paper: Now there’s a guy who deserves a trip to Stockholm.

  11. Greg R. Leslie

    The 2.) question about Heidelberg U. was based on an article from Phys.Org , dated April,27th.,2020, John.
    Concerning 1.), you have clearly stated many times that carrier particles are bogus, I basically needed your conformation that I was reinterpreting things properly. I am just amazed by the length of time and the huge amount of money CERN keeps blowing thru perpetuating their myths. What would you suggest the LHC be looking into instead ?
    3.) As usual both of the links concerning Robert Close is 99.9% over my head. But I did comprehend that his research affirms the ” screw nature ” of the electromagnet spectrum because of rotational waves; the wave nature of matter; and that the aether is definately a ” something ” and not a ” nothing “. All in line with our beloved Uncle Albert’s theorems, just with a mostly new and exiting mathematical manifold interpretation?

    1. Thanks Greg. The PhysOrg article didn’t say much: It refers to this paper: which is available here: I didn’t like it. They claim they’re proving gauge invariance using cold atoms, when gauge invariance was a retrofit. Electromagnetism does not work because of a some mathematical symmetry or gauge invariance. They talk of electric fields and magnetic fields, not the electromagnetic field. They also talk of gauge fields and matter fields, even though the only field we’re dealing with is the electromagnetic field – either in the guise of a photon field variation or an electron standing field. They don’t know that the electron is field. There is no understanding of fundamental physics here. I’d say the experimental side of this is OK, but the theoretical side is cargo-cult mumbo-jumbo.
      Yes, those messenger particles are lies to children. They do not exist. Hydrogen atoms don’t twinkle. The electron and the proton attract one another because each is a “dynamical spinor”. Not because they’re throwing photons back and forth. As for what CERN should be looking at, I’d say it’s the history. If they read the papers I’ve read, they’d know the Standard Model is wrong. Perhaps some do, but they’re in a hole. Being critical of the Standard Model is viewed as being critical of particle physics, which is viewed as being critical of physics. The situation is not good.
      I think Robert Close is in line with more physics than people realise. What isn’t, is the Standard Model. It’s portrayed as a really successful theory, but it’s pretty much isolated from the rest of physics. When you’ve read up on classical electromagnetism, it’s amazing how different QED is. And amazingly, QED employs point particles. Even though it’s the wave nature of matter. See

  12. Greg R. Leslie

    Thanks again John for the clarifications,and also the link to the really cool chart. That chart is exactly what I need to study for a few steady weeks. Quiz on Friday you say ?

    1. That chart is yet more cargo-cult garbage, Greg. See the bottom righ corner where it says the origin of mass is an unsolved mystery? That’s bollocks. Because of a certain little something called E=mc². The mass of a body is the measure of its energy content. The Standard Model flatly contradicts that. It’s another example of how the Standard Model is pretty much isolated from the rest of physics.

  13. Greg R. Leslie

    Oh, man am I ever in over my head. But I am still having fun,and slowly but surely learning.

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