In physics, I have several times discussed my shock last year in being forced to accept the
reality of "Plato's Cave" or else something even weirder in physics. That was my last blog posting.
Call that a "left wing realization," learning to accept empirical and mathematical reality
weirder than what my provincial common sense felt comfortable with. As bad as learning how to swim when you have spent your whole life on land.
Today is the opposite shock for me, learning to accept a kind of right-wing materialist heresy, which it seems is ALSO true and also takes a whole lot of swallowing. To accept and appreciate both Plato and Einstein, the "left wing" heresy of Plato's metaphor of the cave (or worse, but the cave is enough for me to assimilate for now) and the "right wing" heresy of Einstein's zitterbewegung. I long ago learned to accept time as just another dimension, neither left nor right but orthogonal to that line.
Einstein talked about that all the time, the core of his picture of the electron. It is somewhat connected to the view of De Broglie and Vigier, in their book on the linear and nonlinear wave and pilot waves and such, which I cite sometimes. (50s or 60?). I actually have letters form De Broglie to me in my few remaining old hard copy files, though I digitized and compressed them as I was departing NSF. But Einstein's picture seemed a bit incredible, My emerging view of the mathematics of the electron (as in my chapter in Chua's festschrift) was perhaps weirder (in a right wing sense) than De Broglie's but less weird than Einstein's.
Einstein's zitterbewegung idea...
The idea that the electron is something like a small hard core nonlinearity (like a vortex on the order of 3 femtoseconds wide) which zips around faster than the eye can see, like a competent feudal landlord surveying his domain -- the realm in which his pilot wave or wave function penetrates.
Zipping around and accelerating and decelerating at incredible speed, not emitting radiation except to sustain his fields, which would be impossible if the usual linear models were complete; however, the idea is that they are incomplete, that unknown nonlinear terms become dominant in the nonlinear core. De Broglie did try to describe possible field theories with the required properties; I wentr further in my chapter for Chua's festschrift, but have better options in new papers in my files, for a later stage of our discussions.
But really... zipping around faster than the eye could see?
I accepted that the full bosonic density operator for the full electron (assuming any of the PDE models in Chua's festschrift or better new versions) would explain the "pilot wave" as a kind of envelope wave, not a real wave, like the low-frequency envelopes one sees in analyzing an AM radio signal. That was clear from the mathematics of classical-quantum correspondence (as in my arxiv paper extending the Glauber-Sudarshan P map). But zipping around faster than the eye can see...?
But this morning I know better. If I have enough fortitude. Do I? So soon? But logic is logic.
Yesterday I began by asking myself a basic question: for what solitons in 3-D space would we expect the full statistics (as in my extended P map) to predict something like double slit or two-channel interference, following a picture like that "AM wave picture?" It does seem to get back to zitterbewegung.
If you believe zitterbewegung, then "seeing" the universe at small enough time scales would be like
slowing down a movie, in a way. What looked like one kind of continuous motion suddenly becomes something very different. Could such a thing possibly make sense? Is it logically plausible, even after we admit it violates some kind of provincial common sense? Must we stretch yet again, and accept something not as old or hoary or weird as Plato but still old and hoary and weird enough?
I had the advantage of remembering what happens when we look at 3 femtometers, in high energy electron-electron scattering, which simply does not agree with those beautiful predictions of QED (as in Bjorken and Drell) which they told us were so perfect in school. Perfect until the energies get to probe 3 femtometers. Probe an AM radio wave... and the 2000 hertz sound waves which appear as an envelope in an oscilloscope... are supplemented by something else, the real thing, the carrier and sideband waves at megahertz frequencies or higher. What if we probed the electron in time? Could
we suddenly get a very different picture there as well?
And then... I post this at about 5AM, from thoughts about 4AM in bed... (about one minute of thought this all is, except for memories of yesterday)... I realized: maybe this experiment is not a matter of "what if." The movie has ALREADY been slowed down. This May in Princeton, I heard the results of the world's most advanced experimental work to "slow down the movie," to record fluctuations in electric current down at the femtosecond level. (People did this before with optics, but for electrical currents, it required use of a high-speed electro-optic nonlinear crystal.) In a previous blog post, I even gave the address in Konstanz of Alfred who did the work.
Based on the magnitude of the currents he observed, Alfred calculated energies on the order of 10 watts per cubic centimeter, or 10 megawatts per cubic meter, "in free space." It would be truly delightful, from the viewpoint of energy economics, if that turned out to be a real source of energy,
and then if we could somehow extract it. (I have ideas about how, IF it is a real energy source.)
This is nothing at all like the "Zero Point Energy" or "Casimir energy" one reads about in some other places, which I view as a theoretical epicycle. This is empirical, and different. But what is it?
Perhaps... not the most exciting to an economist.. it is "merely" our first empirical window into zitterbewegung, which requires rewriting our models to even a more drastic degree, as we get to femtosecond electronics and below. A whole new world. Weird, in a right-wing sort of way.
Weird like Einstein. Weird just for the smallest things.
Time to adapt and try to start with the new models?
===================== 30 minutes later:
No, time to work on deciding whether I really believe it or not. The rules change at this time scale, but have to make sense. If the PDE are quasilinear still (as in the standard model of physics and the variations of it I have been working with, before gravity is considered -- though gravity is nonquasilinear), there is of course still the speed of light limit on information flow. 300 meters per microsecond... maybe...
========================== later still
It's natural to ask: :How much of the energy of the electron is in the core, and how much in the "pilot wave"?
But again, it is so much a statistical phenomenon that static images are not always reliable. It's always important to remember the analogy to AM radio waves. What's more... even in a static image... the question "where is the energy?" turns out to be meaningless.
This is due to a fundamental mathematical property of field theory (even classical Hamiltonian field theory) which they never told me in my courses... maybe because it was too embarrassing, or maybe because I took the wrong courses.
Even when you have a definite classical field theory, with a definite Lagrangian and Hamiltonian... no, you cannot really answer the question "WHERE is the energy?" How could that be? Because Hamiltonians are only well-defined to WITHIN A NULL FORM. Whenever you write down a Hamiltonian, there is an infinite set of OTHER Hamiltonians which are mathematically equivalent in terms of anything one can predict in classical field theory -- the possible solutions for the fields over space-time or any specific thing which depends on them. A null form is just a function of the fields whose integral over space is guaranteed to be zero. (Remember integration by parts?)
This is somewhat embarrassing for gravity. Even if decide you agree with general relativity exactly, and you decide to couple gravity with the New Standard Model by using the well-known classical coupling defined by folks like Moshe Carmelli... even then, it suddenly MATTERS which of the equivalent Hamiltonians you use! And no, pure reason cannot tell you which one is right; even trying to do it that way is like the worst of medieval theology. It's an empirical issue.
For zitterbewegung, we do not know which is right of the equivalent Hamiltonians. What matters is the actual behavior, and the equivalent Hamiltonians work like alternative coordinate systems, all valid. If your intuition starts telling you the phenomenon makes sense in one frame but not another, that suggests a hole in your intuition. Certainly it is that way for the "radius" of a simple topological soliton like BPS, where we can SEE some paradoxes for intuition in a well-defined family of solutions. So perhaps the energy is more in the core for one frame, and more in the "pilot" (the envelope) in another. Move from 3D space to stochastic Fock space, and it gets even less trivial.
Still, if things vary by a factor of a billion, some of the usual expectations of how electrons behave may be off by a billionth. If we ask IN GENERAL what kinds of solitions give rise to interference behavior... the mathematics probably allow situations with less contrast between levels...
Also, re Alfred's work... it is WAY too early for any of us to be dogmatic about what he is REALLY measuring and seeing and why. It may well be a MIX of things, and a situation where disentangling the measurement device and what is measured will take a lot of time. It may also be interesting to compare, say, how it looks at 5 femtoseconds versus half a femtosecond, to help us guess the truth at even shorter time scales. What we DO see, however, is that things do not look the same at those time scales, and we should not be constrained by imagining that they do.
Change of plans.
Lately I have often compared the photon to the white rabbit in Alice in Wonderland, or to a rabbit in general. I compare the electron... more to Sonic the Hedgehog (for many reasons, from ziterbewegung to Skyrme though it is not a skyrmion)... and I now feel some reverance for the little plastic figure on Sonic which Luda has been putting on our coffee maker for years
to give signals about cleaning. Sonic (and Stitch of Lilo and Stitch) are still nice metaphors and part of our reality, from microscopic to macroscopic.. and Alfred's crystals should never be neglected...
How much is studying the electron's behavior like getting past Alice's rabbit to reaching the Mad Hatter? If I ever get to the real nucleus, will it be a Red Queen? We know whose cat is in this story.
But as of today, I have made a resolution for myself to go back to chasing rabbits until they are tamed further in some respects. No study of electron behavior until certain issues in photon behavior are further clarified at a basic level. I need to get into more detail of HOW people have generated three-photon entanglement (linked to all four key groups, the groups of Yanhua Shih, Zeilinger, Zeilinger's student and Fuli Li potentially). The roles of interference in fibers in Zeilinger's group and of beam splitters, certainly call for more modeling. And I also need to look for utterly nonclassical David-Deutsch style formulations for my time-symmetric triphoton example. And I even need to look closely again at Shih's Popper experiment, and its more recent versions -- which might actually be a lot more radical than triphoton!! Maybe. These are what we need most of all in the theory domain for real progress in nongravitational basic physics. Gravity is something else, not my specialty or karma as yet.
When do I go back to chasing electrons? Depends on progress with photons. Could be years from now, or hours.