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.

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