Anomalies in the calculations of the anomalous magnetic moment of the electron

People regularly send me Alexander Unzicker videos. He’s a grouch and gadfly of similar timber. Unlike me Unzicker seems to have remained a professional physicist of some kind, or at least he seems to identify as such, which if you believe modern knuckleheads, should be good enough for him to be taken at face value. He’s written a  book warning of physics gambling its credibility away. I haven’t read it, more or less because I don’t think physics has much credibility left, at least other than among the type of people who somehow manage to remain enthusiastic 1950s style Science Fiction fans who think the future is right around the corner. I think Unzicker has come to his conclusions fairly recently, though he appears to be a guy who has always tried to get to the bottom of things based on his publications. I am guessing he’s dismissed as an outsider by the physics community, but he appears to be a bright guy, and he certainly knows more field theory than I do. I haven’t seen more than a couple of his videos, but have enjoyed the ones I’ve seen. This one got me to read a couple of amusing papers:

You can watch it or not; it’s based on the work of a gentleman by the name of Oliver Consa. Consa’s paper is a quick read (quicker than watching the video, at least for me: I absolutely despise how much time podcasts waste –only the bapcast is worth the time), though it must have involved painstaking scholarship over the course of many months in a good physics library. It’s an important topic: that of the anomalous magnetic moment of the electron.

History lesson time, all larval physicists take a course on quantum mechanics and they solve the Schroedinger equation for the the spectrum of the hydrogen atom: there are closed form solutions with Spherical harmonics and Laguerre polynomials. The spin and angular momentum of the electron is sort of folded in space around the central potential of the proton of the nucleus, and you get answers which are more or less the energy levels of hydrogen. You basically can’t do this closed form trick with any other atoms without making all kinds of approximations (OK fine, you can kinda do lower levels of the helium spectra with higher dimensional spherical harmonics, treating the two electrons as one in a higher dimensional space), but it’s such a beautiful result, it makes for great indoctrination for young fizzy-cysts. We then use the basic ideas developed here to solve all kinds of other atomic and scattering problems.

Later in your coursework you slap on some relativistic corrections called “fine structure” they tell you comes from the Dirac equation which you may or may not eventually fool around with, but which everyone should. You chug along and make corrections to the spectrum of hydrogen bringing it in greater agreement with the observed values. At some point they mention something called the Lamb shift, which, since it is small, is called “hyperfine structure.” It is related to the anomalous magnetic moment of the electron mentioned in the title. You can see that it’s proportional to various spin orbit couplings, and so you more or less concentrate on those, perhaps getting a bit of inadvertent group theory on SU(2). They tell you that this further correction has something to do with the quantization of the electromagnetic field itself. You then go on to forget all this and do something else unless you’re an atomic guy (like me) or a particle guy.

If you’re a particle guy, or an atom jockey getting above his station, you will eventually get to the dreaded course on quantum electrodynamics (QED): this is the so-called second quantization where the fields themselves are quantized. The Dirac/Schroedinger equations are matter quantization -the fields remain classical and continuous. I won’t bore you with the hocus-pocus that goes on here, but if you make it through your course (Itzykson and Zuber for me -I assume some other text is now canonical since my $120-in-the-90s book is now $21 from Dover) you eventually run up against something that literally everyone knows is nonsense called “renormalization.” In renormalization you do some ridiculous thing where you subtract one infinity from another done in a special way which just happens to produce the “correct” answer. When you come up against it, if you have any thumos, you will say “hey this sure looks like bullshit; you’d give me a D on a test if I thought that up on my own.” If your professor has any soul, he will agree with you. You then both shrug and move on, assuming that people more intelligent than you have done the work and think it is OK. Nobel prizes have been handed out for this, which, after all, somehow gives the “right” answer. One of the things about this course is that any nontrivial calculation is  astoundingly complicated; involving pages and pages of solution of differential equations, Greens functions, trace formulas and probably other things I’ve forgotten. You go on to do a couple of simple Feynman diagrams in the course, then either stop thinking about it (me) or continue with this baloney and become some kinda particle weirdo who should probably all neck themselves for the shame of it at this point, assuming they haven’t found gainful employment outside the particle physics communitay.

With that preamble in mind, and keeping in mind my coursework of almost 30 years ago is all I have to go on for this subject, I present to you this aforementioned work of Oliver Consa. You see, there is an old saw that QED is the most precisely verified theory in the history of the human race. This is, of course, bullshit for various reasons. One of the most important reasons is the one Consa covers; one I was dimly aware of -that the theorists have always had a hard time getting it right in their calculations, and often got it “right” in lock step with experimental errors; aka they got the same errors as the experimentalists did, meaning, more or less, they cheated at their homework. I knew this had happened; it also happened with the charge to mass ratio of the electron: Millikan reported an incorrect result and subsequent results were …. closer to his erroneous result and only crept towards the true result sequentially. People are chickenshit to publish stuff which contradicts established results. Also people with experience notice theorists are often over-eager to get the “right” answer -my own thesis advisor had a theorist collaborator (famous dude) who borked up a paper “explaining” some experimental results in a similarly embarrassing way.

It turns out the theorists for this allegedly ultra-precise theory have gotten the right answer almost exactly never, at least according to Consa’s scholarship. This I hadn’t realized. It looked like a jolly game of whack a mole where the experimentalists would come up with a new number, after discovering the secretary left the toaster on while performing the experiment or whatever, the theorists would claim to match the number and tell some shaggy dog story about how someone else checked their unpublishably long work and “no you can’t see it; maybe we’ll publish it one day.” Really: that’s how it happened. In fact, that’s happened any number of times and for all I know is still happening. The analytic results we accept as true are partially unpublished, and the people who did the original calculation are long dead. The precision claim rings pretty hollow when it changes every couple of years based on what the latest experimental results are.

“Look how big my brain is!”

I mention the didactic indoctrination that all physicists take above for an important reason. Pretty much every living physicist goes through that: a sort of psychological initiation or indoctrination. It’s how we are formed into physicists. To be clear, you go through 5 years of this crap, culminating in the quantum field theory: the thing done by “the important people” in the physics department. Feynman did it! We all love Feynman! It’s all presented to you as beautiful, inevitable even. Lots of physics really is beautiful and looks inevitable in hindsight, but QED and the rest of the standard model certainly ain’t: it’s a disgusting trash fire of nerds painting over errors and sawing off things that don’t fit together. It is hard to deal with, and only people of a certain kind of intelligence are able to do so in all its gory details. Such people are more like  medieval theologians than actual physicists with insight into, you know, physics: the science of matter.

If America were to fight a real war with flying saucers or the Chinese or whatever where we’d need to make actual progress, would we ask the “wicked smaht” field theorists or even the slightly practical experimental particle physics guys to help? I mean, assuming we wanted to actually win the thing. The particle dorks ain’t what they used to be: Feynman made real contributions to the War effort, even though he may have led us all down a useless rat hole with QED. I’m trying to imagine someone from current year field theory working on industrial production problems, or even coming up with something like neutron cross section heuristics using human calculators: having a hard time imagining it TBH. Working mechanical or electrical engineers: no problem. Working field theorists: absolutely not.

I think Consa gets the sociology right in the preamble: in the mid-late 1940s, American physicists were masters of the universe for having come up with nuclear weapons, the Loran navigation system, the proximity fuze and radar. Their prestige was unmatched and the money began to flow from the federal government in ways it never had before. At this moment in time, high energy physics became a racket: the field theorists were top of the pops for this. They had to come up with some kind of answers: it wasn’t possible to not know what the answer was -billions of dollars in research funding and thousands of jobs were at stake.  The guys who won the Nobel for QED more or less had to be right to justify the business. They themselves figured they were just showing the outlines of something better that would come later on; something without all the renormalization baloney and 90 page long calculations. That later thing never came about, so we’re stuck with this Nobel prize winning turkey. I think Consa works on some alternative to QED, which is a noble and brave, and probably necessary thing to do. He’s not the only person to notice this stuff; a trivial google turns up other examples of rather important people noticing.

Even when I was in grad school in the 90s, it seemed like high energy experimental physics should have been taken out back and shot like ole yeller. People working on it were usually bureaucrats tossed into a meat grinder: working preposterous hours and doing things not remotely recognizable as science for the payoff of getting your name on some ridiculous paper with 5000 “authors.” There was the fumes of a certain cachet to the field, but it was obvious back then only a fool would do this to themselves as a career. It’s not clear to me how the field will eventually die, but die it should.

Even assuming it’s broadly correct, field theory itself is absurdly abstract and intellectually impotent, autistically going over the same glasperlenspeil ideas of the last 75 years rather than attempting something new. This is a statement rather beyond my previous sneerings at noodle theory: the whole broad category of “field theorists” and high energy physicists appear to be morally and intellectually bankrupt. Even assuming the field theory I learned in school is correct in some sense, and all these calculational blunders are a kind of progress or were illusory somehow: it is a subject irrelevant to virtually all of the practically observable world, quite unlike something such as quantum mechanics, special relativity and other 100 year old “modern” physics ideas which have numerous real world consequences we use daily. Second quantization is essentially irrelevant; some weird lines in the hydrogen atom -that’s it. The promise of physics is that sperging out on something like hyperfine structure in atomic spectra (or mesonic spectra or whatever) is going to each us useful things about the rest of the world, possibly bringing some other kinds of benefit or at least a deeper understanding of matter and the universe. The archetypical unified field theory was the theory of electricity and magnetism which brought preposterously huge increases in both human understanding and power over nature; almost immediately. Quantum field theory has done no such thing and seems unable to do such a thing. Unless it changes radically it will never do such a thing. At best it’s a glorified IQ test; though a double humped one -people who continue to do it after graduation certainly seem to exhibit a certain kind of stupidity.

 

 

I think a lot of the problem with this sort of thing is …. the process described above. By the time you’ve begun to master something like field theory, even at a low Itzykson-Zuber level like I did, you’re subsumed in sunk cost. Doing these calculations is hard; even solving simple Feynman diagrams makes you feel pretty damn clever: you’re just like the big boys of history. The problem is, what if those big boys were dead wrong? There’s plenty of historical precedent for large groups of intellectual workers wandering off on intellectual branches that don’t make any sense due to incorrect abstractions. Kabbalah, numerology, Marxist economics, Prolog constraint solvers, astrology, alchemy, the fountain of youth, Atlantis: these sorts of clownish bullshit are the norms for human beings, and actual physics done by men of power like Poincare is the exceptional weird thing that sometimes, apparently fairly rarely happens. Countless fortunes and lives of many thousands of very talented people were wasted on, say, alchemy. It is becoming clear that the same can be said for various forms of quantum field theory and “standard model” as an intellectual enterprise.

I mean, OK I get it, I’m one of the first people to make such an assertion in a strong way, and I’m just some guy. It seems pretty crazy with all those smart people “study hard differential equation” that none of the high profile ones could also come to the conclusion, though Unzicker and Consa (and Hossenfelder I think) certainly seem coming around to this. I could be wrong! Surely all this looks very suspicious. I know there are a few former field theorist types in my readership: feel free to tell me this is bullshit and Consa’s scholarship is wrong.

Putting aside these specifics, and the fact that all of these QED measurements boil down to measuring the fine structure constant – a number which would be there without QED, which it after all predates QED by a couple of decades: it’s something that turns up naturally in the presence of quantum mechanics of electric field related things.  If I were still in the game I wouldn’t look for particle soup “tests” of QED: those people are involved in a bureaucracy folie a deux with theorist nerds. A more potentially precise measurement, to say nothing of a more potentially relevant measurement, might be something like the Casimir effect, or other solid state test of QED. There are a few of these tests out there for various forms of Casimir effect. If they’re not looking for an anomaly they won’t find one, but that’s where I’d look. This also has the benefit of bringing ideas from QED into the relevant physical world of matter. Theoretically you should be able to do stuff with MEMS or other forms of lithography. Heck you could probably also do something with very macroscopic objects like Fabry-Perot cavities, Wheatstone bridges and cantilevers. I’m not going to think about this for long enough to make concrete suggestions or try to build something in my machine shop. For one thing, I have better things to do. For another there are people out there who make a living at this shit, and it’s what they should be doing if they weren’t chicken-hearted poltroons or unimaginative bureaucratic goblins. Further investigations of Casimir is even a relatively low-risk career move: you’re going to get something out of it by pulling 2nd quantization into the macroscopic world.  Maybe some adventurous person outside the degenerate welfare-queen anglosphere will figure it out.

Edit add (Mar 14 2023): this is a really cool recent measurement, not at all done in a particle physics way. No word on whether or not the theorists are adding digits: https://arxiv.org/abs/2209.13084