A True Story of Reaching for the Stars – Physically, Literally

-->

This is a true story of a boy who reached for the stars. I am writing this story because I think of some things I never told to any of my children. The story is a true story of one part of my life, but only one part. I hate having to simplify it, and leave out lots of things important to me, but that’s life. The bottom line is that the most painful part of this great quest has been accomplished,  and you who are younger and who also know some mathematics have an opportunity to change the future more than you may imagine yet. This is about me, but it is for you.

I grew up in the 1960’s, possibly the time of greatest optimism and true heroic feeling in American history.  I refused to accept the old wet blanket “realism” where people said “the best anyone can do is get a nice house in the suburbs, and give up the unrealistic idea of making a big difference to the future.” I was deeply inspired by the space program, by key parts of the vision of John Kennedy, and by stories of humanity someday settling space even beyond our solar system.

At age 8, I learned that I had some very unique abilities in mathematics. I was also inspired by some books in astronomy, most notably Hoyle’s paperback “The Nature of the Universe.” (It took me awhile to assimilate the last chapter, but I had read far enough to be on an upwards trajectory regardless.)  My father once said: “Well, if your two big interests are mathematics and astronomy, you should be an astrophysicist.”

By age 12, I had a deep interest in philosophy, which has also been a big part of my life. But I remember thinking: “Philosophy is basically about what you want to do with your life. If you spend your whole life figuring out what it is, you won’t have time to actually DO it! I need to figure this out… but I also need to make space for actually doing it.”

By the end of age 16, I had enough college credits in mathematics (from Princeton and the University of Pennsylvania, including a graduate course in logic from Alonzo Church, and some computer science) to meet most college requirements for a major in that subject, but I asked myself: “What now? What is the MOST that I could contribute, based on my own special comparative advantage?” I read some of the work of John Von Neumann, who said that there are three great opportunities for mathematics to revolutionize our understanding of science and reality – the mathematics of mind, the mathematics of the ultimate laws of physics, and the mathematics of life and self-organization as a universal phenomenon.

By 1968, I resolved to get a PhD in Applied Mathematics, to try to fulfill that kind of heroic vision as best I could. I still felt that reaching the stars, literally and physically, would be a huge advance in human history, far more heroic and important and worthwhile than anything else I could imagine. I also knew that our present knowledge of physics would make that extremely difficult, if at all possible.

Having read a little book on first year quantum mechanics in the summer of 1968, I knew it would be an incredible mess – but concluded that this mess REQUIRED new mathematical insight.  Perhaps humans never will make it to the stars – but to maximize whatever hope we have, the next prerequisite, the critical path, lies in FIRST cleaning up the mess in physics, THEN building a more complete model of how the universe works based on a new more powerful foundation, and THEN the actual insight in design and engineering leading up to an actual starship.

I remember, when my older children watched Star Trek, I said: “All this is exciting and great. But remember – the real hero, the person who changed the galaxy, was not the captain who steered the starship, but the person who built it in the first place. You, my child, could be that hero, that greatest hero in human history  -- IF you learn your mathematics and physics, and if I finish developing tools you will need to be able to do it.” My part would be the most painful and boring, and socially unrewarding, trying to create order out of chaos, and bringing it up to the level where more socially accepted work IS NOW POSSIBLE – by following up. But stage one (my stage) took a lifetime, and the next stage also takes a lifetime to totally fulfill – and I don’t have another lifetime left here. Maybe it all dies here, and maybe no one ever gets to the stars.  But I’ll keep trying, between other things which are also important.

Back in graduate school, at Harvard, I started my first year taking an intermediate level graduate course in quantum mechanics, from Richard Wilson, a nuclear physicist.  Then courses from Schwinger and Coleman, among others.  I learned that the best official theory of physics then available was something called “the canonical version of quantum field theory” (developed mainly by Schwinger and Feynmann, with some help from Dyson supporting Feynman). It is based on strange objects called field operators or operator fields, based on creation and annihilation operators over a strange infinite dimensional space called Fock space. I also learned that Feynmann and Schwinger felt a great discomfort, which I shared, about the ugly and unnatural feeling of that version; we all wanted to find some way to reformulate quantum theory over the usual three dimensions of space and one dimension of time. More precisely, we wanted to find a theory defined over the elegant four dimensional version of space-time that Albert Einstein taught us all about. Schwinger’s efforts became things he called “source theory” or “functional integrals,” which were later called “the advanced form of Feynman’s path integral formalism.”

Schwinger never claimed that source theory or functional integrals would be a plausible model of how the universe works, at a fundamental level. “It is just a phenomenological tool for us to use for the time being when, in our ignorance, we do not know enough to do better.” (That’s what he said in class, but I think I saw similar words in his book on source theory.) I made up my mind to “bite the bullet,”

to face up to the fundamental challenge which other folks kept veering away from – the challenge to find a way to do it right. But by the third year of graduate school, I realized I could not make enough progress fast enough to do a PhD thesis on that subject. For my thesis, I defended the two other mathematical topics which I felt would be most important, but doable. Most people who know about my Harvard PhD thesis view it as an incredible act of ambition for a graduate student – but for me, it was a fallback position, to retrench towards something older, more familiar and easier.

I remember, in graduate school, fully understanding the importance of the question “what is an electron?” In other words, finding a mathematically valid description of the electron as a kind of vortex of force. Finding a way to PREDICT the mass of the electron by the equation E=mc**2, by adding up the energy in the force fields of that vortex.  I remember being deeply intrigued by the mathematics of that question, but overwhelmed by the difficulty of trying to find a way forward in time for a PhD thesis. The difficulty was very depressing to me – and I suspect that my fiancée of the time changed her mind ultimately because of how depressing it was to be unable to solve the problem at the time, and to have to give up (for a time!) and retrench. I made up my mind I would never give up this high quest – but would make a living in another area, working on the basic physics on my own time as best I could.  Of course, it did help a lot much later when NSF asked me to take some responsibility for areas of engineering-oriented physics (like engineering quantum computing) which helped me put more energy into the challenge,  learn more about the best empirical data we now have, and stimulate my thinking in many ways.

So now, after lots of false starts and lots of intermediate scaffolding, I have put together a new paper, under submission to a leading journal, joint with my wife Ludmilla, which brings it all together, and lays out the way forward – the opportunity for the next generation – in the clearest way we know how to do (given the complexity of the subject).  It starts out with four new Lagrangians, two of which have never appeared anywhere (not even in obscure blogs or scribd or such); one of those two is my best guess for the ultimate laws of physics. It is the first genuinely plausible candidate for that which I have ever seen anywhere – but in real science, plausibility is only a starting point, because empirical data is what should be driving us. The new Lagrangian and accompanying tools are open to that exploration, especially by making it possible to take advantage of empirical data which today’s standard model basically does not even try to address. (e.g. medium-energy nuclear physics, little things like nuclear fusion.)  Section 2 of the new paper is practically a work plan.

But at the end of the day – I remember the time, decades ago, when I walked into the office of Marvin Minsky and other leading scientists, with a simple elegant solution to the problems in neural networks which had blocked progress in that field. I remember having a new equation (the chain rule for ordered derivatives) every bit as powerful and fundamental in its area as E=mc**2 – and hoping that this simple easily understood solution would catalyze a huge immediate change. I remember learning how resistant even the most brilliant of humans seem to be to new ideas, even new ideas which fulfill what seemed to be frustrated goals of their lives.

Based on that experience, I do not feel great confidence that the journal will accept the new paper (despite the logic, and the commitment of true science to the exploration of transformative new ideas and worked-out heresy, one of the themes of Dyson’s great videos on the web cited at http://en.wikipedia.org/wiki/Freeman_Dyson), or that members of the next generation with enough horsepower will carry the baton forward. But maybe. Given the huge importance of what is at stake, I can only try… between other things.

As for space – I have learned enough about the “thick skulls” out there to realize I have a comparative advantage in something much simpler, like being able to see that it’s better to build an airplane with an engine than without, and that reentry vehicles don’t work so well if they melt every time they go through the atmosphere. Things which ought to be obvious – but create an additional burden of responsibility for those who can see straight.  (See the earlier blog post on how NASA decided to build an airplane without an engine. Hey – I was there; it’s real!) Who knows?

There is plenty of room for one person who sees straight to make a difference, simply BECAUSE there are so few of them…

Best of luck,

   Paul

P.S. Just in case anyone ever does see the paper I submitted… I also have a  version in my files which is slightly more clear about wave functions versus density matrices in the many worlds version of quantum theory, as in the seminal work of David Deutch of Oxford, the real founder of quantum computing. Also, I wish I had added a few sentences about WEINBERG’S recollections on canonical versus functional integral quantum field theory, which appears in his standard text on quantum field theory; it seems that the one and only “empirical” support for path integrals over canonical QFT was the method of renormalization of electroweak theory developed by ‘tHooft; however, the evidential value of that disappears when we do not need renormalization any more in the basic laws of physics, because, among other things, we have a finite mass for the electron, and can use PDE simulations to make predictions.

I suppose I should write something more concrete and easier to understand about how to manage the boundary conditions in PDE simulations for scattering in the general case – but if people do not follow up on other aspects, I probably won’t be motivated. The information is out there anyway. Or maybe the Bell’s Theorem experiment with imperfect polarizers should be a focus. So many things to do…
The biggest hole in this story is that it does not say enough about the essential role of Ludmilla, who taught me aspects of quantum field theory which they never taught me at Harvard (some because they were more recent).  Having someone to talk to, who really understands and contributes, is really essential to energizing the human brain.
Speaking of which, Luda notes some interesting passages in the book by Lawrence Krauss, "Quantum Man: Richard Feynman's Life in Science":
(1) page 159, Feynman says: "It was the purpose of making these simplified methods of calculating more available that I pblished my paper in 1949, for I still didn't think I had solved any real problems.. I was still expecting that I would some day come through the other end of my original idea... and get finite answers, get that self-radiation out and the vacuum circles and that stuff straightened out.. which I never did.
  (2) page 198, Krauss says:"Gellman.. suggests that Feynman's approach to renormalization, which he had always thought was just an artificial kluge that one day would be replaced by a true fundamental understanding of QED, instead reflected..."
(3) page 254, Feyman replies in effect: "String theorists don't make predictions, they make excuses!... It doesn't look right." (The passage in-between gives the important explanations... but if you are interested, I recommend reading the book.)
Women also played a crucial role in energizing Feynman's thought, though in a different way; for that, Luda recommends other sources.

X-rated joke about Obama

X rated? That means... I listen to lots and lots of sources, some socially acceptable, some unspeakable. This one is unspeakable, not because of anything like sex, but because it comes form the Buddhist thought stream, where we heard...

"Of course Obama is the reincarnation of Abraham Lincoln. Isn't it obvious?
The senator from Illinois, experiencing the obvious extension of the three main themes of his life.
First, the relations between black and white. Second, the karma, learning his lesson for what he did
when he created the Republican party. And third, trying to get it right and not set off a civil
war this time, without going back to slavery and the redneck feudalism of the old south."

looking for dice in the universe and stability of particles

Good morning!

This one is not written for a broad audience. Sorry. At some times, I need to get straight to the frontier, without providing much background. This one is like a personal journal entry.

I meditated a little on two mathematical questions this morning: (1) what is the easiest way to truly prove (or disprove) the claim that variational solitons exist in models such as the system which gives the famous BPS monopole, or the four new systems I discuss in a new paper under submission?
(i.e. to prove that such models do explain why stable particles can exist at all in some universes);
(2) how could we rationally look for "dice" -- underlying stochastic disturbance -- in the universe?
("Does God throw dice with the universe?")

Re the first question -- the topological arguments which have been widely accepted as "proofs"
in physics (e.g. by folks citing E. Weinberg, not to be confused with S. Weinberg) do show that
there is no path of small perturbations which go from a state with topological charge to
the vacuum.  In other words, particles with topological charge simply cannot decay away to vacuum. The same can be shown easily for the four new systems, as I show in the new paper.
That's enough to justify working with these systems, but we really should try to know for sure, to develop proofs which meet a higher standard.

One thing which worries me is evidence to SUGGEST that there may be no "state" of minimum energy in the BPS system -- no well defined, C infinity function which minimizes energy. Could there be a whole family of states, starting with the usual BPS monopole state, of ever decreasing energy,
converging not to a function but to a "distribution" like the Dirac delta function? The "proofs" based on the work of Bogomolnyi ignore the energy in the Higgs term, which could conceivably be reduced
by states which reduce that term by bringing the asymptotic solutions ever closer to the origin,
approaching a limit which is not a "function" -- but perhaps is meaningful as some kind of distribution. I would guess, for good reason, that ALL five of these systems (BPS and my four)
actually have variational solitons (basically just states of local minimum energy) which are c infinity functions, but it may be much easier to prove the weaker claim that they have variational solitons within the larger space of distributions. It's a matter of exploiting the fact that sets of distributions are closed under limits, in a way that ordinary functions are not. Probably not so hard.

=

And then, the dice.

I am very grateful that the first text I studied on quantum field theory long ago
was Mandl's old book, Introduction to Quantum Field Theory. Lately I often cite the
newer classic Mandl and Shaw, which is mainly an expanded version.

Mandl began with the empirical, scientific approach. He noted that there were three great confirmations of quantum electrodynamics (QED), similar to the three great confirmations
of general relativity which everyone studying that subject knows about. For QED, the Lamb shift and the anomalous magnetic moment of the electron stand out in my memory. The key to getting the Lamb shift right was to calculate the "vacuum fluctuations" and "vacuum polarization" diagrams.
Many people have interpreted those words to mean that there is a huge amount of zero point energy out there, based on the noise terms in quantum field theory. But if you read Mandl's simple
presentation closely, you see that the correct predictions are based on the normal form Hamiltonian with that scalar noise term removed.  The correct predictions are based on the "normal form Hamiltonian." It is normal form Hamiltonian (plus renormalization) which explained what we see, not the songs and dances which preceded it. And -- it turns out that the normal form Hamiltonian exactly describes statistics of unknown fields with dynamics which do not involve random disturbance other than the usual thermodynamic background fluctuations one would have in any nonlinear dynamical system.

And so, I see no evidence out there in the empirical world to justify believing that
"God throws dice with the universe." Unlike Einstein, I have absolutely no religious objections to the ideas of the universe being governed by a stochastic model, if it is mathematically meaningful
(realistic). But I don't see any evidence for it either. Certainly the usual "quantum noise terms" postulated by the ZPE people have no empirical basis.

But... if there MIGHT be dice out there (which is mathematically and logically quite a reasonable possibility to consider), how would we find evidence for them?

It seems to me that the first step would be to study/develop mathematically meaningful theories
in that class, building more concretely on what we actually know from centuries of empirical
study.

One would start from the kind of real mathematics developed for stochastic systems.
I think immediately of the old work on stochastic differential equations, on mixed forward-backwards differential equations, and even of the book by Jacobsen and Mayne on
Differential Dynamic Programming which builds a bridge to concrete algorithms like much
of my work on RLADP.

This supports a kind of crude image... a stochastic model which is formulated by
assuming the existence of a kind of exogenous random number field, e(x-mu),
where e can be a random scalar, a random vector, whatever. The idea of a random field is
not new (e.g. see Markov Random Fields). The question would be how to
hook it up with physics.

There are lots of other formulations one might imagine, which entail asymmetries (e.g. with respect to time) for which there is no empirical support. Considering the possibility of dice is just one speculation, albeit a somewhat natural speculation; imposing new asymmetries at this time is much
more grossly speculative, and a detour from the core question about dice.

And so... it is interesting to ask about the family of models generated by ordinary Lagrange-Euler equations (as with classical PDE) EXCEPT by the addition of the exogenous random e field.
This is a time-symmetric formulation.

What do we know about the properties of such systems?

For ordinary time-forwards dynamical systems, introducing noise typically would introduce
drift. Energy conservation would not be exact at the microscopic level. Laws of large numbers
might reduce the implied violation of energy conservation at the measured, macroscopic level,
but things similar to roundoff error can accumulate and cause instability. Would we really see
the rigid degree of energy conservation we see in low-level bubble chamber events
if there were that kind of disturbance?

And yet -- in a time-symmetric situation it is not quite as clear. The perfect "optimization"
performed by Lagrange-Euler equations might possibly result in a much tighter kind
of law of large numbers, preventing such large excursions in energy at the macroscopic
level. Even at the bubble chamber level.

But at this point, this is just a theoretical, hypothetical kind of possibility. 
I don't see any real reason to believe that there are "dice" out there in the basic laws of the universe.
I see that it COULD be possible, but I do not yet even see a path to testing the idea.
I did a paper once on "Q" versus "P" which is another way to get at the same issue,
leading to the same outcome for now.

There is some relation between this and the "stochastic chaos" work I discussed with Freeman
and Kozma years ago, in Biosystems and elsewhere. But on the physics side,
there are certainly more urgent areas for mathematical exploration at this time
(such as exploration of the four new systems which contain no dice).

An alternative formulation for "dice" might use the modern Hamilton-Jacobi-Bellman
equation in place of the old Hamilton-Jacobi or Lagrange-Euler equations, or -- given that
we seem to be seeing a mix-max system -- the Hamilton-Jacobi-Isaacs equation REVISED
for time symmetry. They sound entertaining, but perhaps the time-symmetric stochastic Lagrange-Euler system has more of the right properties. All speculative for now anyway.

Best of luck,

    Paul

How you could lose all your webmail and how to protect yourself

Just yesterday, I spoke to a very distraught guy who said he just
"lost his whole life" to to a hacking problem on the internet.
"I found out that 11 million people on gmail have been hacked just like me. The hacker shut me out of all access to all the information I had been counting on on the cloud. And google is a totally automated system; they could do nothing to help me or the 11 million others." This
guy was recently retired from NASA, and fully informed about regular security procedures
and technology, so it would be very risky to assume that you are safer than he is.

Suddenly I wish I had paid more attention to another friend, who casually mentioned that he
configured his gmail so that he uses it with Outlook. His gmail is still there on the cloud. He can still access it from anywhere on earth on his laptop or his desktops, which have been set up to run Outlook, using the google servers. But he can very easily make backup copies of all his folders
any time he chooses, so that he is safe, unlike my other poor friend. And the folder structure
lets him organize his life in a way that the default google interfaces do not. This is a serious matter, just as serious as backing up your hard drive.

And... it's easy. It does require searching on "gmail IMAP" and such on the gmail help pages and
web in general. But at the end of the day, it amounts to clicking on the "enable IMAP"
setting in gmail, typing in the names of the gmail servers into an Outlook account, and being sure
you are happy with your settings in Outlook. (like "leave mail on server.") And of course being prepared to wait a little the first time as it copies all your gmail to your computer.


I still don't know what you get from the usual gmail interface when you create folders
(exploit IMAP) for use in Outlook. There are things on that on the web, but not so clear to me.

I never did what my Outlook friend did, because I don't like Outlook very much.
(Not that Thunderbird and its ersatz Eudora are any better.) But the same thing can
be done with AppleMail.

I really wish google had bought out Eudora 7 when it was available cheap. They could
have cleaned up just a few things, and then offered their OWN IMAP client -- and made it
a lot easier for lots and lots of people to use it! A lot of former Eudora users would
pay for that option, just as they paid for Eudora, ""even" if it's "just" available
for use with gmail.