Today I will try to explain in simple, everyday terms how I learned what really goes on at the nuclear level in “low to moderate energy systems” like thermonuclear explosions. This may sound like a dangerous subject for an open (though obscure blog), but for me it is actually a break from things which I view as far riskier. Just an instructive romp through the realities of science life today, and of what we know about the universe. Yes, it involves thermonuclear devices in a very practical way, but if you think H-bombs are scary, you have no idea what else is on the horizon today in ever so many directions! (Yes, the H bombs still could kill us all, but that’s more a story about politics than about physics at this point.)
Last week, I gave a heavy, dense seminar to pure mathematicians on the current status of our effort to understand how the universe really works. It was such a pleasure to go back and speak in my native language, mathematics... but don’t worry, I won’t inflict that on you here (though maybe I will post those slides somewhere at some point). Instead, I will tell some stories... which came up during the seminar...
Mainly I will tell the story of how my thoughts and my life were changed by reading a book called The Skyrme Model, by Makhankov, Rybakov and Sanyuk (MRS), which came out from Springer in 1994. The yellow book... At that time, I had some other connections through to the Joint Institute for Nuclear Research in Russia (JINR, Dubna), the “Los Alamos of Russia,” where Makhankov was a division director, but I will spare you the distraction for now (sigh). That yellow book was a huge turning point for me, in many many ways.
MRS was the hardest book to read and understand which I ever read in my entire life, and that’s saying a lot. A whole lot. On the first day I started reading it, I went to bed deeply and vastly discouraged. “I imagined I could make some contribution here, in developing the mathematics to explain what protons and neutrons really are, but as I read this book, it looks as if I won’t even be able to understand what has ALREADY been done in Russia on that subject.” But about 3AM that night, in my bedroom in College Park, I engaged in my usual nightly practice of “cosmic consciousness” or “conversations with God” or “posthuman state” or whatever you may call it. (At this moment, I am almost finished reading a sci fi, Count to a Trillion, by John Wright, which uses that last term... familiar issues... ). In that state, I saw an image of what MRS **MIGHT** be talking about. The next day, I cross-checked, and yes, it was exactly like that theory! MRS were not like mathematicians, proceeding from axioms through logic to predictions or theorems... but by doing it right in my own mind, I could get to the same place. Finally, after three or four really intense days, I was able to disentangle it, and see further than the authors on some important aspects. I don’t remember ALL of what is in that book....but what I do remember is important enough.
Some parts of the book were easy to understand. I will simplify a little... and laugh to myself at the idea you might try to read it yourself. Please read the cautionary tales first if you do...
“We in Russia, like physicists in America, will of course begin our sacred proceedings with a prayer to that great God in the sky, Quantum Chromodynamics (QCD)...”
In case you don’t know about QCD, here is a quick summary. You probably know already that human science knows about five types of basic force in the universe – electric force, magnetism, weak nuclear force, strong nuclear force and gravity. By the start of the twentieth century, even before quantum mechanics was developed, physicists learned that electric force and magnetic force are really just two sides of the same force, electromagnetism. (Can’t I display just one iddy-bitty covariant vector field here? No, I promised everyday language.) Weak nuclear force is basically what comes out when radioactive material decays to a lower state; over time, that radiation can kill you, but it’s not explosive. Strong nuclear force is what holds the nucleus of an atom together, and also what propels an H-bomb. In the 1950s, three people (one of them Schwinger, one of my teachers at Harvard) got the Nobel Prize for developing Canonical Quantum Electrodynamics (QED or KQED), which is the modern quantum mechanical theory of how electromagnetism works. QED is the real workhorse of the electronics and photonics industries. But now, we recognize that QED is just a useful approximation, like Newton’s theory of how gravity works. NASA still uses Newton’s theory to predict the orbits of planets and spacecraft, and industry still uses QED, but we know that those theories are not the exact truth. Mainstream physicists today talk a lot about the current “standard model of physics,” which is a pasting together of two quantum field theories: (1) Electroweak Theory (EWT), which is an extension of QED to predict weak nuclear force and electromagnetism, in a unified way; and (2) QCD, the “second quark theory,” due to Gellman, used to describe strong nuclear forces. There is a lot of debate about how to paste together or unify the standard model of physics with gravity, which seems to be well-described by Einstein’s theory of general relativity (GR), but GR is not a quantum mechanical theory.
MRS: “We know that QCD works very well in predicting what happens at very high energies, like two particles colliding at enormous energies in big accelerators, but because it is so complicated it cannot be used to predict what happens at low to medium energies. ‘Low to medium energies’ includes thermonuclear devices like what we develop here in Dubna, and so we cannot expect this great god in the sky to come and help us. In the real and humble engineering task of making predictions for what happens in humble experiments here in this lowly real world, beneath the level of lofty metaphysicists, we therefore use what they call ‘phenomenological models.’ We in Russia have less faith in the invisible gods than people in the West do, but really, that is not so important, since ‘phenomenological models’ are what we use for prediction of experiment anyway. “
“We are amused that interest in the Skyrme model (a phenomenological model of what a proton or neutron is) was very low in universities in the West, because of its religious incorrectness, until someone showed that the Skyrme model is equivalent to QCD in the limit where 3 equals infinity; this made it possible to call it an approximation to QCD, and discussable ... to a limited degree.”
Maybe here I should say more about just how important “phenomenological models” are to nuclear technology. In some fields of technology, like drug development or battery development, people have gotten away with mindless trial-and-error approaches on a huge scale. Try out a thousand possible drugs in the laboratory, and just see what happens. Computer simulation can help in those fields, but thousands and thousands of experiments are still used. (This reminds me of how China is far ahead of the US in battery development for now, but far behind in some other fields, like access to space, where a more analytic approach is needed.) But with nuclear weapons, trying out a few thousand designs without knowing what to expect is not such a good idea! For this reason, computer simulations have always played a very central role in nuclear technology development, civilian and military, in US and Russia (the two nations I know the most about on this subject). But what kind of model actually gets used in these computer simulations, to make predictions? Not QCD. The accuracy of phenomenological models is in fact crucial to the development of nuclear technology! It is not a coincidence that the biggest supercomputers in the US have been at two nuclear labs, Lawrence Livermore and Oak Ridge. My very first tenured job, at DOE, involved oversight of some of the computer codes at Oak Ridge. (I still remember my boss at DOE who said: “I used to be a strong supporter of nuclear power, but now that I know what kind of computer tools they use to ensure their safety, I am a lot more worried...”)
But back to MRS:
“We dedicate this book to the great British physicist, Tony Skyrme, one of the greatest physicists of the twentieth century, who is widely known and respected in Russia but almost unknown in the West. How did this happen? Skyrme worked at A.E. Harwell, the most deeply secret of all the British nuclear places, and he wrote his brilliant models and mathematics in a notebook, which he kept under lock and key in that secret facility. That is why the work became very widely disseminated and used in Russia, but almost unknown in the West. We hope that this book, in (broken) English, will help bring him to the higher level of recognition he deserves in his homeland..”
How did they get away with writing this kind of thing, discussing Russian nuclear S&T? In the early 1990’s, the US and Russia had a kind of honeymoon period, after the fall of the Berlin Wall, and hopes that the US and Russia could become strong allies. At NSF, we were encouraged to fund Russian scientists to work in collaboration with US universities, through subcontracts to grants to US universities; everyone (or almost everyone) in my Division at NSF did some of that, and I funded some people at Dubna. Now, under Putin, things have changed... but let me return to the science.
By the way, if you doubt what I am saying here about QED... I cited Mandl and Shaw in my seminar. The “infinite negative mass energy” is called dM, a “mass renormalization.” Sometimes people say “It isn’t really part of the theory, it’s just a number we put in there to make the calculations work out.” A number put in there as part of how predictions are made. Hmm. It reminds me of a talk I once heard form a guy named Aharonov at NSF: “My viewpoint yield totally different predictions from the usual ones, but I am still assuming the same theory. I just INTERPRET the theory differently...” When I learned about the scientific method, they would say that two different systems which yield different predictions are different theories, not just different interpretations. That’s part of the definition of the words “a theory.”
As the slide illustrates... there are three kinds of “soliton” model of interest in physics. Three ways of trying to describe or explain elementary particles as whirlpools of force. Mathematicians do not like to call these whirlpools “solitons,” because they have their own definition of the word “soliton,” different from what physicists use. So I said: “Hey, we agree that a sea horse is not a horse. So a topological soliton or a chaoiton (chaotic soliton) does not have to be a soliton.”
Many years ago, I defined a new concept of “chaotic soliton” or “soliton” in papers in the journal Chaos, Solitons and Fractals. It was a very natural concept, like what a mathematician would expect here. A “chaoiton” could EITHER be a stable fixed pattern of forces concentrated in a small region of space, a pattern which goes off to zero far away from that region, or it could be a stable SET of patterns, oscillating between each other but still staying there and not just dissipating away.
But then I read the yellow book, MRS. MRS actually described TWO types of “topological solition,” the Skyrme model type and the “BPS” type. Both are a bit of a stretch for a mathematician. Both model an elementary particle as a kind of “knot” in space, a knot which simply cannot be unitied, because the knot connects the particle all the way to space infinitely far away from the particle itself. The force fields describing the particle include at least one field which does NOT go to zero far away from the particle.
MRS even included a “theorem,” the “Generalized Hobart-Derrick Theorem,” which argued that objects like chaoitons simply could not exist in ordinary models of physics without hard-wired topology. I looked at the two page “proof,” and did not believe it. I wondered whether Rybakov or Sanyuk might have worked out more of the details in their original work in Russian, or at least more explanation of what they were talking about.
And so, I tried to get more information. I spoke to the guy whom I funded who had a subcontract to Dubna, and visited the place often. He tried hard to bring back lots of information, but he really had nothing to say on this. But then... here in the US, at a conference, I met Ludmilla Dolmatova... whom I later married, but who did return to Russia and France in the meantime. In that mean time, she visited the offices of Rybakov and Sanyuk at Moscow State University, and obtained what they had, and had some good conversations -- but it did not really change the picture on that “proof”. (Yes, this was a huge thread in my life... but... back to the book...)
Can chaoitons exist, and could they be a possible model of electrons or quarks?
I made contact somehow with Prof. Pego of the University of Maryland, whose work on... solitary waves?... was perhaps the closest in the world then to what I had done with chaoitons. He had a PhD student, Lev Wertheim, whom I knew from Adelphi Quaker Meeting, who was also an all-Soviet mathematics Olympiad winner. We all agreed on a possible thesis project for Lev: to try to prove or disprove the alleged “Generalized Hobart-Derrick Theorem.” He already had access to my papers and Pego’s, through the usual US systems, but he needed, above all, the two pages of MRS stating the alleged Theorem and proof.
I intended to give Lev just the two pages, but life was very complex for me at that time, and I wasn’t able to get the xerox in a timely way, so as Quaker meeting I handed Lev the book and said: “Lev, I apologize, but I have to ask that you xerox those two pages yourself, and then return the book. But before I do, I want you to promise, PLEASE do not try to read the rest of the book. It is like a Godel-Escher-Back painting. It will drive you crazy if you try to make sense of it.” He promised.
A few days later, I was informed that he had been hospitalized, and I was invited to visit his apartment where his suitemates would return my book to me. “What happened?” I asked. “Well, he seemed normal and alert and intelligent as always, when he returned from Meeting. But then he sat down in that chair, and started to look at that yellow book. At first he looked at it, and then away, as if he was very torn about whether to open it. But then he did. He started paging through it... slowly at first... page by page... and his eyes started glazing over. And then... well... we had to call the mental hospital.” A few days after that, they reported that the mental hospital had decided he had to go back to Novosibirsk (Siberia) where his family was, and he never returned to physics after that. What kind of music did he take up then? I do not know. I imagine mournful old Jewish songs on ... old type string instruments.
So... reader beware.
For the seminar, I displayed instead a newer book, by Nicholas Manton of Cambridge University, which I hope would not be so risky for mental health. I do not know how easy that book would be to understand, for a first time reader, since I already knew much of the stuff when I bought it, and I read quickly up to chapter 11, which had some very exciting advanced new stuff. (Also some stuff much scarier than mere thermonuclear devices, for those who understand.) Manton talks BOTH about the Skyrme model and about the family of models related to the famous BPS topological soliton. And he talks about EWT, which makes contact with real experiments and predictions much more than QCD does.
Manton may well be the most important thought leader in the Western world today on the Skyrme model, and on ways to use that model in real nuclear technology. He is mainly known for a huge cross-cutting consortium, which uses the Skyrme model to predict properties not just of proton and neutron but also of small nuclei. Predicting nuclei... is meat and potatoes for practical places like Dubna and Livermore. His consortium has done very large-scale computer simulations, all simulations of the Skyrme model in just three dimensions of space... which is a lot easier than computing with a theory like QCD which requires lots and lots of dimensions. But the accuracy is not so impressive. Errors on the level of 20% and 40% compare well enough with other phenomenological models, but they aren’t exactly correct. What’s more, even if we question the exact details of QCD, we do know very well from high-energy experiments that the proton and neutron are made up of smaller and harder elementary particles, called “partons.”. (Basically, these are scattering experiments, like what Rutherford used to show that the atom has a small nucleus. The word “parton” is a good search term to learn more about those experiments.) So the Skyrme model is useful, sort of, maybe, but we should be able to do better. The “quark” model is just one of many possible models of what partons are like.
After years of digesting MRS and other things... I now believe quite strongly that our best hope of understanding electrons and partons is to model them as the OTHER type of topological soliton, the “BPS” family. The Skyrme model has limited accuracy, and does not really model partons anyway. The mathematics is less rigorous than the BPS mathematics, and “less rigorous” really means “lots of stuff that may be dead wrong.” I now have a much better idea how to construct examples of chaoitons in simple, ordinary field theories... but I am not as motivated now to resolve that issue, because I don’t think they are as plausible as the BPS type of model. Above all, in real physics, we see a very amazing quantization of electrical charge, the exact same unit of charge for all kinds of particles and compound bodies. In principle, that quantization COULD be just an emergent outcome of field statistics... so maybe the electron could be a chaoiton after all... but for now it seems both easier and more promising to work with the BPS family, where the quantization of “charge” (the winding number of the knot in space) is strict and easy and natural.
The key to the BPS model is the inclusion of a term called the “Higgs term” or the “Higgs force,” which is similar in a way to the famous Higgs boson, but NOT EXACTLY THE SAME. The Higgs force is the one which does NOT go to zero even infinitely far away from the particle. The “knot in space” is the knot formed by the vectors of the Higgs field, considered in spheres surrounding the particle.
The BPS family of topological solitons, using Higgs terms and assuming Higgs fields, is very well known in physics. In addition to Manton’s book, there is a simpler review paper written by Erich Weinberg of Columbia University. The physicists assume they have proven “well enough to be sure” that all these Higgs type topological solitons are rock hard stable, just like the electron, but no, they haven’t, EXCEPT for the one specific case of the BPS example, which is the limiting case of a simple model in the case where the Higgs term actually goes to zero! (A mathematician at Harvard really proved stability for that case, I think, basically using special boundary conditions INSTEAD of a Higgs term.) Even if I think more like an engineer than a physicist these days.. even engineers often have higher standards of proof here. I can imagine how these “stable” solutions might actually collapse into a point, or diffuse away into nothingness, even without any change in the “winding number.” I am not convinced by the existing “proofs” that this would not happen for some of the Higgs types theories. I really wish a solid mathematician would get in here, and either PROVE what Weinberg says, or provide a counterexample, and give us some guidance about WHICH Higgs-field models actually work.
But none of that is all electron or a parton yet. **IF** we had a good Higgs-type model of the parton, we could use that for practical nuclear simulations, just what Mantyon has been doing, but hopefully a whole lot more accurate. I could imagine using such a model “tomorrow” to improve Livermore’s ability to predict what actually happens when a laser pulse hits a deuterium/tritium pellet target, a subject of immense importance in trying to develop a new safe energy technology here. (I hear that Livermore’s laser fusion work is funded based on its spinoff value in making nuclear weapons design easier and more reliable. I suppose the new model could be useful there as well.)
In fact, I do have two candidates for what that model might be, much better than the earlier candidates I played with in past years, published in various places. These two new models basically fix some problems I found when I studied the earlier models. (When I first learned about the BPS model itself, I had some hope for it; I had to fully understand WHY it is not a good enough model, even for grand unified theory, before I knew how to do better.) I have not published the new alternatives anywhere, in part because Luda has urged me not to do so until/unless a higher impact journal agrees to publish the details. I did include them in a paper I showed to Marlan Scully and a couple of other people, and I included one of them in the slides I showed at Memphis last week. A lot of very basic work is needed to work out what stable soliton solutions these two new models have, and what properties they predict for nucleons as combinations of such partons. (I have of course studied a lot of what is known about strong interactions as a filter here, EVEN THOUGH I still propose that we use EWT itself with changes only in the Higgs term and in the representation of what the key B and W fields couple to.) Of course, such work might point to a need for further upgrades or tweaks, before such models could actually do better in Livermore than what they already have. We could still simulate the new model in three dimensions, as with Skyrme model, but partons are a bit smaller than protons, and one would have to use multiscale modeling to make it as routine and easy as the present models. (It is still in three spatial dimensions, however, making it a whole lot easier than simulating QCD!)
That all is the normal part. If I were in graduate school, I would happily see how this could be a worthwhile life’s work... but as someone retired and close to 70, scheduled for cancer surgery next month, I just write it up and hope no one else will have to put in so much effort as I did to see how the pieces fit together.
A couple of quick notes. My old teacher, Julian Schwinger, had a different theory of what the partons are. I believe it is very important that we NOT have premature religious commitment to either his model or QCD at this early stage. Some Higgs-field models based on extending EWT would yield solitons more like quarks, and some more like Schwinger’s dyons, but it is too early to restrict our choices. The basic mathematics and tools need to be further developed, and we should start with the simplest models
(like the two I now have) which seem like they might work for now. Yes, we could insert many topological charges to fit QCD more precisely, but why? For now, two might work; it is easy enough to add more, if and when we have solid guidance on what kind of tweak is needed of that type, if it should be needed. (I doubt it.) Some Higgs type models of the parton (and electron) would also predict a rigid conservation of what physicists call “baryon number,” but others, like the Russian work described in chapter 11 of Manton’s book (probably held secret now in Russia) would not. My two versions probably would not. If not... as Manton describes, and many Russians attempt... then it may be possible to “burn down protons and neutrons themselves” for energy. Basically, that would allow construction of devices like thermonuclear weapons, but about a thousand times as powerful, potentially using any materials at all as fuel. Manton observes that this would require a special kind of coherent radiation as a catalyst. My slides for Memphis describe an extension of the Glauber-Sudarshan coherence theory (the basis for designing lasers) which would be applicable here. I am amused that one of the key Russian places working on this, according to Manton, is the Institute for Nuclear Energetics in Protvino, where Luda obtained her “first PhD.” But no, she did not work on that project. There is also some connection here to the lower-energy lower-frequency stuff which Schwinger worked with in the last years of his life, also pretty wild. See http://drpauljohn.blogspot.com/2016/02/korean-rocket-and-navy-lenr-illustrate.html . But hey, that’s for the further future. Testing the new Lagrangians mathematically and aiming to assist Livermore type of work is all I would write about at all, if I were more confident about either my personal long-term survival or the long-term survival of key actrivities in the US.
Final note: this whole post elaborates on some aspects of the first part of a 3-part presentation with 33 slides in all. Another slide elaborated on the various concepts and measurements of the radius of the electron -- after noting that the "radius" of a whirlpool can be defined and measured in a variety of ways, and noting how MRS discuss the different values for the radius of the proton, all valid, explainable by a topological soliton model.
The second part dealt with distribution functions in Fock-Hilbert space, basically explaining my paper at arxiv.org on my extension of the Galuber-Sudarshan methods to three and four dimensional space. Part of that is a theorem showing that the energy levels we get from simple computer simulations are close to identical to those predicted by canonical quantum field theory (and maybe exactly identical, depending on how we interpret the usual self-energy corrections, like what people use to predict the Lamb shift).
The third part dealt with more recent work, which is what my own thinking is drawn to more lately. I mentioned my joint paper with Ludmilla in the journal Quantum Information Processing, which came out just a few months ago. More people at Memphis also expressed interest in the third part, because it has a connection to their work in graph theory, stochastic graphs, and emergent behavior like sudden phase shifts (which they see as analogous to the sudden drop of an electron from a high energy level to a lower one in the atom). TBD.