4D Fock Space: Don’t Underestimate Doctor Strange

Yesterday, Luda suggested: Why not watch Doctor Strange again in Netflix? Now that you have been to Kathmandu, and really experienced how authentically weird it can be, why not compare the movie more with the real place and the real thing? So, OK, I did.

Of course, many confident intellectuals would be horrified to imagine anyone truly serious watching such a movie, let alone thinking about it in a serious way. In the session on Culture at the Federal Foresight Community of Interest (FFCOI) two weeks ago, one speaker expressed total disdain for the most popular movie series, like Avengers (which includes Dr. Strange) and Star Wars and such -- “totally out of touch with reality.” Maybe, maybe not. Who is actually more out of touch with reality, folks in Washington DC who assume they know all of what is really going on, or the folks who write those movies? In actuality, it is not always obvious. Stan Lee probably does not know what is REALLY going on, but neither do I, and I know enough to know what is obviously wrong about so many other things people confidently think they know. Even in Kathmandu.

One small thing: just as Doctor Strange crosses the threshold to a whole new world in Kathmandu, Mordo warns him: “Forget everything you thought you knew.” In fact, when I was asked to give a nice brief overview of “the new AI” and machine consciousness -- of the best of what we really have learned in decades of pioneering that area -- I properly summarized the lessons learned by a quote from Mark Twain: “It ain't what you don't know that gets you into trouble. It's what you know for sure that just ain't so.” (For the details of that story, see
https://www.facebook.com/paul.werbos/posts/1924099547620453 .)

But what the movie reminded me of most was about physics. Serious physics. Very serious, fundamental questions about mathematical quantum physics. Lots of people write hundreds of equations about quantum physics, but even now I keep remembering one of the proposals I handled at NSF where the guy crammed about 100 equations into 15 pages but clearly did not really understand what any one of them actually meant. It is not so easy to understand what certain equations really mean. People get away with writing equations they do not understand because few others do either, and we all just muddle through. Even a movie can be helpful in stimulating us to ask what we really think our equations might be telling us.

Do you find that hard to believe? Do you assume that nothing could be hidden there in the math? Well, a few decades ago, mainstream people thought they understood everything really important and basic about ordinary differential equations (ODE), the standard way of describing the dynamics of any system made up of a few variables fluctuating with time. “Dynamical systems theory.” Huge texts were written by people like Jay Forrester trying to convey the wisdom of ODE to people like industrial managers and policy makers. But then came “chaos theory.” Work on “chaos theory” showed us that simple ODE systems can generate behavior much weirder than anyone used to believe -- weirdness which is a real part of our life on earth.

But ODE systems vary in time, not space. At any moment of time, they assume a world made up of just a few mathematical variables. That’s not our world. The most basic mathematical description of systems which vary both in space and time are Partial Differential Equations (PDE) -- well known to anyone in serious mathematical physics or engineering (or many other areas). Calculus 1b? One thing I have come to appreciate more and more is that the surprises awaiting us in the world of PDE are much much stranger and bigger than mere chaos theory. Maybe even just as strange as those strange movies like Dr. Strange. Maybe even stranger than quantum mechanics as such, even though quantum mechanics assumes that we live in a cosmos which SOUNDS much stranger than the mere 3+1 dimensional space time of Einstein’s PDE models.

The most solid form of quantum mechanics, used as the foundation of the electronics and photonics industries today, assumes that we live in a kind of infinite dimensional “multiverse,” or “Fock Space.” (Are you skeptical that I really know what I am talking about here? See https://arxiv.org/abs/0709.3310. For years, I got to probe in depth what people really do in that industry, and it’s not about philosophical interpretations of verbal discussions between electrons, like what you see in a lot of the quantum philosophy or Vedanta literature.) The basic idea is that you and me and the transistors in your radio actually exist in a state called “quantum superposition”. There are multiple versions of us existing in parallel, in the larger cosmos. The simple three-dimensional world which we seem to inhabit at any one time may be called a “universe” -- but there is an infinite number of versions of ourselves, and “universes”, inhabiting one very much larger “multiverse” (Fock space). (And, by the way, the Dr. Strange movie talks explicitly about multiverse quite often, and its sequel Infinity Wars centers on that very same concept.)

When I first learned about the idea of Fock space, in the late 1960’s, I was very intensely skeptical of it. Like Einstein and De Broglie and Schrodinger, I felt that Heisenberg’s weird equations must be a colossal mistake of some kind. Above all: couldn’t those weird wave functions defined over “Fock space” actually be statistical correlation matrices of some kind, really just describing the emergent weird behavior of a simpler real world governed by “simple” plain old PDE? They do look a lot like correlation functions…

So now let me be honest, even though I know most people will kill anyone who is too honest. As I get older, there are some things I should say, regardless, because otherwise they might be unsaid forever by humans.

The hardest core evidence now available clearly tells us two things, a crucial core paradox: (1) that quantum dynamics over Fock space CAN be explained as statistical correlations over Fock space (e.g. https://arxiv.org/abs/1402.5116); and (2) despite that, the empirical evidence is overwhelming that macroscopic Schrodinger cats exist (http://drpauljohn.blogspot.com/2017/10/questions-of-day-cats-imp-and-tibetan.html ). (That second link is to a review, with very hard core physics citations, written for some of the folks I met in Kathmandu, as I lived a life as close as anyone has ever come on earth to a real life Dr. Strange. There are parts of Kathmandu which now look more like movie scenes set in Hong Kong.)

Oops. How do we reconcile that? And how do we navigate the realm of really huge weirdness it implies? Furthermore -- the more we really understand, the more flexible and creative we can be in developing new technologies, such as technology to manipulate time, including some experiments which have already been done but have produced results so weird they are not yet ready to publish. (A few of them coming to light soon, I hope.)

In 2014, I first faced up to this paradox, just in time to update an invited paper in press in Russia (www.werbos.com/Mind_in_Time.pdf.) It suggests a shocking possibility, many steps beyond what physics proper is really ready for yet: that we DO inhabit a very weird “simple” PDE universe, in a way, but “we” are actually just POSSIBILITIES in the set of space-time histories that the underlying (Lagrangian) optimization program gives consideration to. We are like the shadows in Plato’s cave, and not that one simple reality. It turns out that those PDE which emerge from the mathematics of optimization (the modern extension of the old mathematics of Lagrange) are especially weird, and our very lives may be an echo of that weirdness. Sorry, folks, but that's how mathematical modeling works out; with better understanding, we don’t always find that we are the center of the universe! (I also noted the scene in the Dr. Strange movie where the Ancient One says to the Doctor: “You need to get it through your head that it’s not about you.” Of course, that is another one of those things I myself need to be conscious never to forget.)  Right now, all of this points towards a need to be very practical in physics, and clean up what we do in Fock Space (which is mostly a good enough guide for the “spiritual” level of reality as well, at least for most of my life so far), putting the PDE stuff back to the future, leaving just a few bread crumbs about the workings of the PDE in notes I may or may not ever post (going well past a few possibilities in papers published years ago). I have learned a lot about how to say “meow” like a proper Schrodinger cat, especially as concerns the physics of time. (Another reason for downplaying the PDE level now: it points directly to dangerous possible technologies, ways to make it real what Nicholas Manton of Cambridge sometimes hints about, which could kill us all on earth, especially given daily reminders by political authorities all over the earth how irresponsible they are.)

But the movie reminded me last night of yet a further paradox: the usual multiverse math all assumes a “Fock space” across three-dimensional space. It assumes time is fundamentally different from space. When we manipulate time as if it were different from space, we fail to understand a few things. It seems as if we are trying to cope with a vast infinite dimensional “firehose of information” squeezed through a narrow hose of one-dimensional time. Even in my 3AM most conscious meditation, the “firehose of information” was really getting to me -- until Luda said: “Stop thinking of it as a firehose of information. Think of it as an Ocean.” Oh, duh, 4D, not 3D. And oh, duh, what of those folks who talked about the “ocean” level of consciousness? 4D.

To some extent, I have already been experiencing things in 4D (i.e. reconstructing my mental images of reality in that more complete representation) already since then, but the movies (Dr. Strange and Infinity War) remind me that manipulating time in the usual 3D_Fock+1D_time way of thinking misses important aspects of what is going on. Even if we need to think in terms of Fock space reality for practical life, is 3D enough? In fact, true mathematical physicists (the kind who know what axiomatic quantum field theory is, Haag’s Theorem, constructive quantum field theory and all that) are all aware of a classic little book by Streater and Wightman which attempted to develop FOUR dimension-based Fock space more rigorously. (The Feynmann path version of quantum field theory, described in the authoritative text Quantum Field Theory by Weinberg, is a very hands-on practical attempt to be four dimensional, which drives mathematicians batty due to the unbounded hand-waving shortcuts.) But even Streater and Wightman was grossly incomplete… so to understand things better do we have to clean THAT up, before getting to PDE?

Just a few zingers before I move on.

Years ago, before I spent years trying to reach BACKWARDS to where the mainstream now lives (e.g. in https://arxiv.org/abs/1402.5116), I first developed the mathematics of PDE versus Fock space in the FULL FOUR DIMENSIONAL version. I quickly learned that a full up four dimensional version of Fock space was incomprehensible to mentally resistant mainstream hands-on users of hands-on Schrodinger equations, and so I spent time translating back to something more comprehensible to them. The arxiv paper using 3D Fock space was intelligible to folks like Marlan Scully (world’s top practical quantum optics theorist), and I was delighted to be invited to present that generalization in their elite Princeton workshop in 2014 and 2015. (I am sorry I did not realize they just wanted a rerun in 2015; I made the mistake of trying to move on to some wild new experiments, which people may be ready for in just a few years.) But the 4D version is there, in my scanned papers… maybe I will publish it someday, maybe not. I should think more about the empirical implications… just for my own enlightenment, maybe possibly to help me kibbitz the folks doing real work…

And: OK: one more even crazier thing.

I have come to believe that the best, most workable explanation for what people call “psychic” or “spiritual” experience and life is the evolution of life in the great ocean of dark matter and energy which we now know pervades the entire cosmos, in a vast network connecting (and creating!) all the galaxies. http://drpauljohn.blogspot.com/2017/08/where-we-really-come-from.html. (And yes: creating. Read the recent work on how weak star formation is in the few protogalaxies that lack dark matter.)  But oops: just last night I noticed the “dark” stuff in the Dr. Strange movie. Oh, dear!! Is Stan Lee really just afraid of his own shadow, and creating imaginary monsters in his mind? Or is it all in the realm of dreams, like the final scene of one of the acts in Kathmandu?

Who knows? Lots to think about and play with.