{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Why I'm not a Bohmian*\n", "\n", "*In what follows, I'm not arguing against the philosophy of David Bohm himself, much of which I agree with, but rather the specific interpretation of quantum mechanics known as \"Bohmian mechanics.\"\n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since it's come up so much, I'd like to offer a few words about why I am left unsatisfied by Bohmian mechanics. Some of my reasons are mathematical, others philosophical, and still others are personal.\n", "\n", "When I was a teenager, and still primarily a poet, one of my best friends and I would have interminable arguments about determinism, about the role of formal logic with its axioms and the force of its theorems, and about the nature of consciousness. Even as I say I was primarily a poet, I'd been programming computers since I was 12 years old, first in BASIC, graduating to C++, doing odd jobs in Java, eventually settling on python as my language of choice, which it still is today. Computer programming as much as literature attracted me as it seemed to promise the ability to actually *create worlds*. Indeed, for months, like Linus Torvalds, I carried around Andrew Tenenbaum's famous book \"Operating Systems: Design and Implementation\"--since I was above all interested in foundational matters. When I was 14, I think, I did some programming work for money (generating simple natural language reports from forms that doctors would fill out about patients with heart problems), and my mentor at the office took apart a computer in front of me, showing me the memory, the CPU, the hard drive, all the components, and how they fit together. What at first seemed like a metaphysical mystery lay exposed before me: when I pressed keys on the keyboard, electrical signals would be sent into the machine, routed to different places by the CPU, flipping little bits in the memory according to absolutely definite rules, depending on which electrons would be fired at the CRT screen, creating colors that I would see with my eyes. I at once realized that there was no *mind* in the computer: that the whole experience depended on *me* sitting there, conceiving ideas, typing away, enjoying the visuals, and typing some more--that for this circuit to be live, *I* had to be plugged into it.\n", "\n", "And from that point on, I was absolutely convinced, and have been convinced ever since, that \"consciousness,\" whatever it is, cannot be reduced down to what my laptop does. Memory, sure: reasoning, attention, even emotion, I was willing to grant could be mechanized: but the fundamental experience of uniquely being in the world itself was not something reducible to a classical computation.\n", "\n", "My very good friend, however, was then convinced that the world was entirely reducible to definite, essentially computational rules, and we spent many, many hours having it out. When I finally came to take introductory physics in high school, I was charmed by the inclined planes and right hand rules, but I had a basically cavalier attitude towards it. These scientists think everything is about rules, and while certainly a lot of things are about rules, *everything* can't be. And being a computer programmer, I ultimately had a dismissive attitude towards the study of physics: after all, in the end, they're just running computer simulations, and if I took the time to look at their code, I had no doubt that I could understand it, and so why bother at all.\n", "\n", "Meanwhile, I'd read Douglas Hofstadter's book \"Gödel, Escher, Bach,\" and in Gödel, I found vindication: here a proof, no less, that no single set of formal axioms could exhaust the boundless domain of truth. And this deeply affected me, not just the result, but the nature of it: that a *formal mathematical proof* could be given that formal mathematics itself was incomplete. In other words, this wasn't simply the prejudice of a poet who hadn't taken the time to learn to calculate, but a fatal attack from within the very citadel of reason itself.\n", "\n", "For the next half a decade, before and after my undergraduate years, I busied myself with the business of literature, writing novellas, short stories, poetry in every form, reading everything I could get my hands on. I'd tinker with neural networks often with an eye to their application in digital art from time to time, but the hard sciences I left to the side. \n", "\n", "In my engagement with literature, ambiguity itself was my muse. I was fascinated by how James Joyce could pack 16 different meanings simultaneously into a single word, how the implications of a sentence or a scene were inseparable from their context, always at risk of being revised, appearing now in one light, now in another, how a single stray line of dialogue could cause a whole interpretation of a character to collapse, how stories were structured against seemingly natural flow of time, with foreshadowing at the beginning, and callbacks at the end, how for a story to be satisfying, it had to follow a causal logic of its own, even as to not be boring the characters couldn't appear like puppets of the author, but to have a free will of their own, exercised against a background of significance supported by the cross connections between symbols studded like stars throughout the text--and above all, by how so much of literature was an attempt to express the inexpressible fact of being *here*, an attempt to point beyond the text itself, and yet to touch the reader in the heart, wrestling a lightning flash of clarity out of a world uncertain, vague, always slipping free out of every attempt to define it completely.\n", "\n", "When I finally came to quantum mechanics, it had the character of a revelation: here was what I had always been looking for: the precise mathematical theory of *ambiguity* itself, yet another victory against the false clarity of the classical world from within the fortress of logic itself. I realized that actually some of the smartest people in the world were on *my* side in the great debate, and that far from being like a computer program, a better metaphor for the world would be: a book always yet being written and revised.\n", "\n", "What do I mean by ambiguity? Like Wittgenstein's duck/rabbit:\n", "\n", "\n", "\n", "Or the optical illusion of a Necker cube, appearing now extending inward, now outward from the page:\n", "\n", "\n", "\n", "So too the wave function of a quantum particle can't be reduced to signifying the particle's position nor its momentum, but both simultaneously, manifesting as one or the other in different contexts. In itself it was neither the one, nor the other, but: both. The framework of quantum mechanics allows us to deal with such situations, where Aristotle's \"law of the excluded middle\" is apparently violated, in a rigorous way, situations where no single metaphor, or single picture can do justice to the underlying reality.\n", "\n", "Indeed, the mathematics of quantum mechanics itself has a deeply protean, meta-ambiguous character, appearing like some ancient goddess under different names, different avatars. One can work with Heisenberg's matrices, Schrodinger's wave equations, Feynman's many paths, Everett's many worlds, Bohm's trajectories, and each mathematical picture has something interesting to contribute to the story: but quantum mechanics can hardly be reduced down to any single one of these mathematical fables. In fact, each is a source of useful--but quite possibly misleading intuitions!\n", "\n", "For instance, tracking Bohmian trajectories might give you a more satisfying mental image of what happens during a double slit experiment, but on the other hand, it would be rather painful to use it to discuss any of the spin phenomena we've spent so much time on. The more ecumenical standard approach can easily quantize the space of spin states, making use of simple finite dimensional vectors and matrices, allowing one to discuss a great deal of quantum magic in just those terms. In the Bohmian picture, one can't speak about anything without talking about \"positions,\" even if one just wants to talk about the spin, and so the differential equations get quite unncessarily hairy and complicated. And while this might be a feature if you really want to believe the world is made up of \"particles in space,\" it prevents you from doing any interesting generalizations! Why not quantize a string instead of a point particle, or a membrane? Am I not allowed to discuss quantum polyhedra without also specifying the \"positions\" of the spins that represent their faces, situating them in some already existing space? You can't even pose many of the deep questions about the origin of spacetime itself in Bohmian terms. For that matter, has Bohmian mechanics *ever* been used to discover anything new, or is it always playing catch-up to results more elegantly and easily obtained by Heisenberg's matrices since 1927? \n", "\n", "Moreover, even if it can be proved that under certain strong assumptions, one can extract from Bohm's framework the very same predictions as ordinary non-relativistic quantum mechanics of positions and spins, the reliance on imagining \"pilot waves\" in 3D space can very often lead one astray if one doesn't actually go through the calculations. For example, I've mentioned the fact that if you send a particle with spin through a Stern-Gerlach apparatus, if you don't measure its position immedietly afterwards, you can't say that the particle's spin was irreparably filtered by the apparatus, since if instead of measuring the position, you were to recombine the two beams leading from the up port and down ports, you'd be able to recover the original spin state intact, \"erasing\" the apparent measurement. Analogizing to a double slit in the Bohmian picture, you might then further imagine that if the particle does leave the Stern-Gerlach along both paths, there would be interference in their positions, since you've been encouraged to imagine all these waves propagating together in 3D space. But the proper home of (non-relativistic) quantum mechanics is the tensor product of Hilbert spaces. And the state of the particle after leaving the Stern-Gerlach, isn't $\\mid pos \\uparrow \\rangle + \\mid pos \\downarrow \\rangle$, which you could add together and get interference, but rather $\\mid spin \\uparrow \\rangle \\mid pos \\uparrow \\rangle + \\mid spin \\downarrow \\mid pos \\downarrow \\rangle$. These two states will always be at right angles since $\\mid spin \\uparrow \\rangle$ and $\\mid spin \\downarrow \\rangle$ are at right angles, regardless of the positions. Therefore when you add them, there won’t be any interference effect in the positions. As I say, to me the great danger of using Bohmian guidance waves as a source of intuition is that one is often led to incorrectly picture these waves unfolding together in 3D space, and to misapply our intuitions about how that works. The two waves might each be propagating in 3D, but in two different “universes” as it were (to use some “Many Worlds” intuition), each kept separate since one is associated with the spin being up and the other is associated with the spin being down.\n", "\n", "On the other hand, the \"Many Worlds\" picture, of parallel universe branching off from each other, itself has its limitations: since as we've seen in the case of the recombined spin state, the different \"parallel universes\" can in fact *rejoin*.\n", "\n", "Now certainly, one can incorporate spin into the Bohmian story, but not only would the argument given above be much more tortuous and unnecessarily mathematically involved, it also seems to me to defeat the entire philosophical purpose of the Bohmian picture: if you're allowed to introduce another dimension to these pilot waves, one for each dimension of a spinor, then in what real sense are we still talking intuitively about \"trajectories in 3D space\"? \n", "\n", "That said, thinking about trajectories can be very useful. One might wonder if there were an analogous Bohmian-type picture for just the spin of a particle, without reference to its position. Ironically, I've already given it to you: for an isolated spin, one can describe its unitary evolution as the classical evolution of the trajectories of \"Majorana stars\" on the surface of the sphere. But as soon as one comes to think about entanglement, this intuitive picture falls apart, and one's intuitions about what's going on have to be sourced from elsewhere. (Although one wonders how far one could push the picture by always working in the total angular momentum basis, so as to keep continuity with the stars of multiple spins...)\n", "\n", "In other words, the point isn't that Bohmian mechanics isn't always useful. The point is that again and again quantum mechanics forces us into a situation where a certain metaphor is useful up to a point--but no further, and then a different point of view has to be taken--and then another--and then another. There is no one single over-arching ontology that can do justice the world as revealed by quantum mechanics.\n", "\n", "Indeed, quantum mechanics is not a theory of physics--to quote Scott Aaronson, quantum mechanics is like the *operating system* that our theories of physics run on, a mathematical framework that allows us to relate radically different perspectives under a common heading, the concept of perspective itself being massively generalized to encompass the different experimental conditions under which we can elict answers from nature. It is a most powerful method: one identifies the symmetry groups relevant to the physical systems under consideration, one finds unitary representations that act on vectors in the so-called Hilbert space, whose sets of basis states correspond to sets of outcomes to experiments; one models observable quantities as linear operators on this Hilbert spaces, and each can be associated with a time evolution that conserves some quantity. The algebra of operators encodes the interrelationships between different experimental arrangements, and so one can deal with a situation where the underlying \"states\" are always unobservable, but only reconstructible in the limit after many mutually exclusive interventions.\n", "\n", "And whereas classical physics emphasizes *things evolving in space and time*, quantum physics instead throws the spotlight on *relationships*, *perspectives*, and *processes*. Quantum mechanics is not a theory about \"things\": rather, as Bohr will tell you, it is the theory of how *to communicate precisely and clearly about a fundamentally vague and uncertain world*, where the separation between observer and observed is always provisional, contested and mutable. \n", "\n", "The framework may be abstract, but its very generality is its power. At the same time, one pitfall I've often found people fall into is that they can get too distracted by the language of \"experiment\" and \"outcome,\" forgetting what the underlying mathematics represents. Indeed, one often works with representations of very intuitive and familiar symmetry groups. As I've again and again emphasized, to say that a spin is \"both $\\uparrow$ and $\\downarrow$ simultaneously\" seems like a metaphysical paradox, until you realize that geometrically this means: the spin is pointed to the $\\rightarrow$. To use quantum mechanics correctly, one must always be simultaneously attuned to the geometry encoded in the representations, even as this geometry is always intimately related to *the outcomes of experiments*. It's this intertwining of geometry and experiment that makes quantum mechanics what it is.\n", "\n", "Furthermore, I find political implications in this debate. Nothing having to do with Bohm's supposed dalliance with communism or the prejudices of academic funding, but instead this: I'd argue that classical physics is intimately tied to the European imperial system which has ravaged the world since even before the days of Newton. Empire's project was the collapse of diversity itself, the reduction of the many tongues of Earth to one common universal language (I leave aside the more utopian projects of certain harmless philosophers), enforced and overseen from above, predictable and determinable in all particulars. Man was seen as innately of a brutal nature, requiring submission to a higher authority, uncaring and impassive, for peace and prosperity, necessitating the use of coercion and force to ensure that the trade continued apace, that money wouldn't be counterfeited, and that the supremacy of white rationality be secured.\n", "\n", "In contrast, the world of quantum physics is a world of consensus. Entanglement is like a contract between two particles, which both affords them a degree of freedom, even as it constrains them, for example, to always point in the opposite direction. Such a contract doesn't require any higher authority to enforce it: rather, the systems *themselves* keep track of their relationship, which is in itself a private matter between them, not in itself open to the panoptic eye of some all seeing God, which has forseen everything in advance.\n", "\n", "As I emphasized in my discussion of decoherence, \"facts\" in a quantum world are mutable things: in other words, the consistency of a story where \"definite outcomes occur\" and \"single paths are taken\" is always provisional, up to revision. Facts are stable to the extent that someone can't reverse them: hence the stability of the results obtained by our macroscopic measuring devices, which act like intricate knots in the quantum web, preventing quantum coherence from being restored. But at the microscale, facts are always reversing themselves: and once a fact is reversed, it is as if it never was: since there is no all seeing God to keep track of what has happened, but only: the things themselves, in their relationships, who may or may not remember. While such a picture might be terrifying, particularly in our current world of fake news, I'd say this is actually a hopeful notion. To deny a problem isn't to solve it, it is to leave oneself vulnerable to it. If anything, the last four years have taught us that we can't take facts for granted, that we have to do the hard work of bringing people to consensus, building up the kind of shared reality that we all want to live in. And we can take inspiration from quantum mechanics, which suggests that the world itself is based in consensus, that the world is a cosmic democracy of perspectives, where both observer and observed are each afforded a degree of freedom in how they fulfull the contracts they enter into.\n", "\n", "It seems to be that people are always projecting their social conditions onto their metaphysics, and importing their metaphysics into their social conditions. If we really believe that underneath it all, the world is governed from above by fixed, immutable, deterministic laws to which we either conform or die, then the kind of society we build will reflect that: and I think we've seen the effect of this kind of thinking all around us, where it is taken for granted that we are all self-interested uncooperative automata requiring a government whose sole purpose is to enforce contracts by threat of violence. Instead, if we really believe that the world is a shared experience we all participate in and contribute to, each in our uniqueness, then I think the kind of society we will build will put to shame every political system in the past.\n", "\n", "Some would argue that compassion is necessarily founded in a kind of determinism: a shared recognition that we are all governed by forces outside our control, and so must be forgiven for our behavior. But to me this feels like giving up, an acceptance of external authority, a renunciation of responsibility, a reconciliation to the demands of Empire, which asks us to submit ourselves wholly to the system in which we happen to live, confusing chance for fate. I think rather universal compassion can be founded in our common condition, which we share with the plants, the animals, and the electrons: of being given freedom, and not knowing what to do with it, of being contrained, not by fate, but by the past decisions of those we share the world with.\n", "\n", "I return now to the original issue I brought up in my story about my first dissecting a computer. I didn't know it at the time, but I was following in the footsteps of Leibniz, whose famously asked us to imagine a brain blown up to the size of a building, with stairways and hallways we could explore, and how even if we could somehow see all its inner workings laid bare, we'd never find anything to \"point to\" and say: there it is, that's consciousness. In other words, Leibniz was talking about what we'd call today the \"binding problem\": how is it that a bunch of neurons which, although they are connected by axons and synapses, are nevertheless distributed across space, and yet give rise to a holistic experience of inward perception? I have no definitive answer to this question, except to say that: whereas classical mechanics, in beginning by separating mind from matter, can't even pose this question except as a paradox, quantum mechanics allows us to begin to explore the issue. Since after all, quantum mechanical systems relate to each other via entanglement independently of spatial separation--even entirely other quantum systems can be encoded holographically \"within\" other systems, like we've seen in the case of a spin's constellation being encoded \"within\" $2j$ separated, yet entangled spin-$\\frac{1}{2}$ particles. So that the question of \"inwardness\" is eminently posable with the framework of quantum mechanics: the tensor product of quantum systems has a \"depth\" to it, coalescing out of the relationships between the systems, and not just the states of the individual systems themselves: indeed, the individual states can't be fully specified without considering the whole, the latter being strictly greater than the sum of its parts. And so, the \"binding problem\" is brought within the domain of science, and is revealed to be not even the more fundamental mystery: the fact that one finds oneself being anything in particular at all, being the particular you, that you are. One can begin to discuss this insofar as \"quantum information,\" unlike classical information is not fungible, replacable, copyable sight unseen: indeed, each quantum system is in a way uniquely picked out by its relationships, by its entanglement with the rest of the world, and this cannot be duplicated, counterfeited, forged in any way. And so, one can actually define what it means to be an \"individual\" in quantum mechanics. (Although even this is relative to some perspective: since entanglement itself is observer dependent, depending, for example, on one's non-inertial state of motion--that said, it can't be destroyed by a perspective shift, but only shunted around in accordance with a changing definition of space, time, and particle. Perhaps then one should say that the particles don't keep track of their entanglement just by themselves, but rather that all the observers who see them that way track it; but either way, this is more democratic than the absolute oversight of a classical God: it's us, looking out for each other.) \n", "\n", "But of course, even all this doesn't touch on the fundamental issue of: being *this* participant in the grand theater of reality, where we are both actor, writer, and spectator, all in one, together.\n", "\n", "Indeed, as far as neuroscience goes, the difficulties there are even greater than in physics. Like an electron, to ask someone a question is to intervene dramatically: there are no passive observations, and often people respond to questions with answers even they'd never dreamed of before the moment of interrogation. But unlike quantum systems in a lab, no experiment on a person can be perfectly reproduced, there is no way to have thousands of identical preparations waiting to be measured in order to nail down a quantum state. Instead, there is just one of each of us, and we have a long memory. We are what we are, and no one else has access to that like we do: at the end of the day, no amount of poking at our brains will allow anyone do deduce whether we are conscious of something without *asking us to confirm that we are conscious of it*. And by then, we are a different person entirely.\n", "\n", "One might argue that perhaps all this can be incorporated into a Bohmian picture because of its intrinsic nonlocality. But I find the nonlocality being proposed by Bohmian mechanics to be patently absurd. The whole trajectory of physics has been towards a deeping of the principle of causal locality, the primacy of \"hereness.\" Even post-Newtonian classical physics had replaced action at a distance with an intervening field or ether whose motions herded forces from place to place. Now, this isn't an argument in itself, and after all quantum mechanics is itself nonlocal, insofar as particles keep track of entanglements across space and time, giving rise to correlations in the answers they freely give to measurements. But this nonlocality is of a very particular sort, one deeply compatible with the principles of relativity. It is often framed like quantum mechanics sits uneasily with special relativity, but this is perhaps an accident of history, a reflection of the decades long difficulty in formulating relativistic quantum field theory. But ordinary quantum mechanics is already compatible with a relativistic spacetime. Indeed, it is often incorrectly portrayed that the \"instantaneous collapse\" of the wavefunction is in conflict with relativistic principles, since evidently by measuring one half of an entangled pair of spins in the singlet state to be $\\uparrow$, the other half will \"instantly\" collapse to $\\downarrow$ wherever it is, in defiance of Einstein. But this is not the case. One has no way of knowing locally that a measurement has been performed on the particle's twin, and the fact that the results of measurement are random guarantees that no information can be transmitted by this method, and so violate relativistic causality. The measurement on the one particle could happen before the other, or the other way around, the two events could be re-ordered in time, and no conflict would arise, since the relationship between the particles is completely symmetrical. For although there are non-local correlations, these can't be detected locally. Indeed, only by bringing the results together and comparing them later, in other words, bringing the results together locally, can the non-local correlations be discovered. In other words, the unique interplay of indeterminism and entanglement allows ordinary quantum mechanics to be profoundly compatible with relativity and locality. It's completely beautiful and miraculous, the kind of loophole to the principle of locality that you'd never dream of, if you hadn't been guided into it by experiment. To then give all this up and return to an absolute Euclidian space, and accept that by fiddling around here, I can exert a force on particles miles away instanteously, seems like a step in precisely the wrong direction--and all for the sake of what? Determinism? It was even an insane proposition in the classical days, and connected either with fantasies of domination and control or else fatalistic submission to a God hungry for human sacrifice. Classical visualizability? If you really want to take a look at a room, you don't just sit in one place, and absorb the scene: you walk around it, and see it from as many angles as possible. That quantum mechanics asks us to see a system from many different ontological perspectives, under the heading of diverse metaphors, different domains of physical intuition, is not different in kind, but in degree. Quantum mechanics doesn't ask up to give up visualizability: it instead asks us to be as fluid as nature in moving from one vision to the next. And indeed, we've seen how pictures can be associated to quantum spins and quantum polyhedra built out of the expectation values of necessarily incompatible operators, and how quantum stories can be told using string diagrams, that do justice to teleological nature of the plots, states winding around the bend of entangled cups and caps.\n", "\n", "Finally, to return to the discussion about rules and laws, quantum mechanics provides us with definite rules for dealing with a certain kind of indeterminism resulting from ambiguous, intercontextual situations, and in doing so, opens up whole new vistas for scientific thought. But even this lawlessness is contained, as it were: it is the kind we can nevertheless communicate precisely about. But my deepest intuition is that there is something radically, more absolutely lawless at the heart of reality, that goes beyond physics, something that cannot be grasped, but only gestured towards. I won't be able to convince you of that by proofs, I can only lead you to the mountaintop in the clear air. (And suggest you read John Wheeler's \"Law without Law\".)\n", "\n", "So in conclusion, I'll say this, if by some miracle, it was proven that the Bohmian story (of point particles propagating deterministically in non-relativistic space and time, feeling nonlocal forces) was the only possible story one could tell about physics, I'd accept it, and of course learn what else there is to be learned from it, as a responsible citizen, but frankly, I'd go back to being a poet. I'd leave physics to someone else. It wouldn't do justice to *my* world. Indeed, everything that inspires me about physics would be more or less dead. \n", "\n", "But I have no fear of that happening. I say, as Hilbert said of Cantor's transfite set theory: \"From the paradise that [quantum mechanics] created for us, no one shall be able to expel us.\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "## Addendum\n", "\n", "Looking back on our discussion on Saturday (8/8/20), which I very much enjoyed, I feel like I should clarify my own position on a few things.\n", "\n", "I’m not necessarily claiming to “believe” in “free will.” There are numerous paradoxes involved in the concept of free will even before one brings in any quantum considerations. If my choices are not determined by my past, in what sense are they “my” choices? If my choices are determined by my past, in what sense are they free? What quantum physics seems to offer is a way to split the difference, in positing that the choices made by nature, including ourselves, have an element of freedom, while being constrained by the quantum space of probabilities, which may force agreement between different systems due to entanglement. One interesting twist it offers is the idea of a “joint decision”: for two entangled spins, the choice to be up or down can’t be assigned individually to either system, but to both, as if they had a “common will.”\n", "\n", "All the same, for humans, freedom is always defined with reference to human capacities, social systems, and morality: to say someone is free is to say that they faced no obstruction in their environment against acting, and so can be held responsible for their choices, rewarded or punished accordingly. And as such, I am wary of making overt claims about “free will,” insofar as the issue will always be politically charged. Similarly for determinism, which, insofar as it takes as granted a fixity to the ways of the world, allows those who speak “in the name of nature” to commit unspeakable crimes under the banner of “necessity.”\n", "\n", "In other words, there is no way to win. And so, as always, I return to Bohr, who again and again emphasized that it is not always possible in every case to resolve everything, but rather that one ought to explore the inherent trade-offs in any point of view. This is the principle of complementarity. Or what the Buddha would call: the middle path.\n", "\n", "From a sociological standpoint, I’m interested in the following historical fact. In the 19th century, if you were a scientist, given the information available to you, it would have been completely rational for you to assign very high credence to deterministic models of nature, and very low credence to indeterministic models. This, on the basis of the explanatory success of Newtonian mechanics, unweaving the rainbow with its impassive mathematics. One interesting consequence of this was an increasing split between intellectuals along the two poles of science and art, the former practically identified with a lawful, deterministic, objective picture of the world, the latter being the domain of the wild, free, subjective, and Romantic, if you will. But actually, these cultural formations are somewhat specific to the Enlightened European situation. In other historical contexts, for example, art was seen primarily as a formal craft, whose standards of objectivity had to do with the accurate portrayal of divine aspects; in other words, art was not the domain of individual self-expression, as it became almost entirely for the European world by the end of the 19th century.\n", "\n", "I bring this up, in part, to contextualize my own work. I’m neither artist nor scientist, but both. If I’m an “avant-gardist,” it is only because I too see in art the power to broaden and expand what is perceptible to human beings, augmenting our intuitions by bringing the untouchable into tangibility. Hence, my emphasis on the use of computer simulations, which I use primarily not as a means of discovery per se, but as a means of making interactive pictures, in hopes of breathing life into the mathematical symbols which can so easily lie dead on the page.\n", "\n", "But to return to my main point, if it was rational for a 19th century scientist to assign high credence to deterministic models, to the point where for many, the idea of an indeterministic model of nature was inconceivable, a contradiction in terms, the quantum revolution of the early 20th century flipped the probabilities completely. For the post-quantum scientist, determinism is not so much a lost cause, as a long shot. It is rational as a scientist today to assign high credence to indeterministic theories, and low credence to deterministic ones. And this is just to say: as a determinist, you’re going to face a very uphill battle, since the burden is on you to prove how indeterminism can’t work; whereas in the 19th century, the burden was on the indeterminist to come up with a theory at all. That alone is fascinating as a fact in the history of science.\n", "\n", "
\n", "\n", "I don’t believe that science is about discovering how the world “is”. Rather, science is the art of speaking clearly, speaking in such a way that others can understand our claims, and adjudicate those claims for themselves. In other words, the domain of science is the *communicable*.\n", "\n", "When I say science isn’t about how the world “is,” what I mean is that science as such can’t make substantial claims, about the “substance” of the world, but only structural claims, about the relationships between different parts of a structure. One comes up with formal structures, which one coordinates with other formal structures, using yet other formal structures to mediate between them, ultimately testing parts of those structures against the data of experiment. Even if such structures yield successful predictions, it would be a mistake to identify those structures with the “being” or “reality” of the world. \n", "\n", "I think what we really mean when we ask what something “is,” is: What part of my body should I use to understand it? If something “is” sound, I should use my ear. If something “is” food, I should taste it. If something “is” a pebble, I should roll it around in my hand. As we humans explore structures and attempt to apply them to the world, we first have to apply them to our bodies. \n", "\n", "Classical physics attempted to explain the world entirely using structures which we could understand using our kinesthetic and visual intuitions, our intuitions about how we move around in the apparent three dimensional space of our environment, our intuitions about how volleyballs arc when we serve them, our intuitions about how we can spy from afar with telescopes without being detected, our intuitions about how we can chart out a whole visible territory from above with a single map. These were the different capacities which were marshaled to bring Newtonian physics to life.\n", "\n", "Quantum physics requires different kinds of intuitions to augment these. To understand how a detector placed by a double slit can destroy an interference pattern, we can marshal our social intuition: even the silent presence of another person in a conversation speaks volumes. To understand the delicate perspectival interplay of entanglement, relating systems disparate in space, we can use our intuitions about social networks, contracts, kinship networks, which persist however we travel about--the tensor product can be unlocked via our linguistic intuition for counterfactuals, with their many possibilities explored in parallel—-we could even say that the improper mixed state of a quantum subsystem is like a pronoun whose referent hasn’t yet been specified. In understanding quantum plots, we can analogize operators as beads on a string. In understanding how Cooper pairs can gather in a condensed matter system into emergent higher order particles, we can analogize to the way the artist can lay different colors of paint on a canvas, after which the painting can propagate as a different kind of object altogether from the materials from which it was made. Indeed, to understand the emergent inner space of holography in AdS/CFT, we can analogize to our interior lives, you seeing the surface of my body, and me existing somehow “within” it.\n", "\n", "In breaking with the purely visual and kinesthetic, quantum mechanics made it impossible to ignore how our *all* our “worldviews” were always quilts, patchworks of intuitions from different domains, different sense modalities, different ways of reaching out and grasping. What was surprising, and indeed, surprising only relative to the recent scientific history of the time, was that, for example, social and linguistic intuitions had any role to play in the study of the “objective world.” Indeed, quite aside from the issue of dividing the observer from the observed in quantum physics, there is the cultural issue of what a given social group regards as properly mental in contrast to the physical, what's a matter of perception vs. what's \"really out there.\" For example, an important move in the Scientific Revolution was to segregate material causes to the outside world and final causes in the inside. In other words, to talk about the “outside” world, one had to frame one’s explanation in terms of atoms knocking against each other; any sense of “teleology” was regarded as a mental construct at best. It is then shocking to find in quantum physics that one’s later choice of what measurement to perform conditions what can be objectively regarded as having happened in the past, a situation which has a distinctly teleological character. Moreover, the particular separation between the elements of the inner world and the elements of the outer world made by the scientists of the period can't be disentangled from the religious conflicts which did so much to forge the modern world. The disavowal of social intuitions about the natural world can be connected to the desire of the period’s intellectuals to distinguish themselves from the anthropomorphizing tendencies of the pseudo-pagan peasantry, as well as from the more canonical religious viewpoint which sees a divine intention behind every fall of a leaf.\n", "\n", "All that said, it is deeply incorrect to claim that quantum mechanics gives up on visual and kinesthetic intuitions altogether: rather, because they are embedded in a web of other intuitions, the visual images that one can form are of a cubist character, not always reconcilable as views of one common scene. But despite the limitations of any single image, the images we can form are crucial and decisive for our understanding. There’s no sense in which you’ll ever really understand quantum spins until you realize you can “see” their quantum states as constellations on the sphere, even as that simple picture must be renounced when one considers multiple spins, entangled. \n", "\n", "It’s worth dilating here about how we all have different “cognitive styles.” Some of us are classifiers, others system-breakers. Some of us have to take machines apart to understand them, others of us can intuit their working from blueprints seen in the mind’s eye. Some of us are entirely defined by our social lives, others of us can sit alone for hours. Some of us can read music, others of us can only play by ear. If I have any talent for quantum physics, perhaps it’s because of a highly developed linguistic intuition, turned rigorous by my also being a native speaker of computerese. All the same, I can tell you that I understood nothing of quantum mechanics except as an abstraction, until I started making my 3D visualizations, mapping quantum operators to the buttons and joysticks of video game controllers. \n", "\n", "One hopeful thing I see in all this is that precisely because our understanding of physics requires such diverse intuitions, everyone, whatever their cognitive style, has something to contribute. At the same time, the question remains how to make all our talents talk to each other in a rigorous way. The glue is mathematics. But one should be careful here: it’s a classic observation about mathematics that it’s always been been divided between the visions of the geometer and the symbol-shuffling of the algebraist. The point is rather that if we want to paste together our patchworks, we need to find representations that can make rigorous the interconnections between different representations. For example, we can use string diagrams so that by playing around with bits of string, we *can’t fail* to make correct statements about quantum systems. That’s precisely what makes them good representations. We can also use the axioms of Hilbert space to play around with vectors and matrices so that in the same way, we *can’t fail* to make correct statements about quantum systems. That there is a correspondence between these things comes out of category theory. But one could imagine a more specific domain where by playing around with some other toys, one *couldn’t fail* to make correct statements about the relationship between string diagrams and Hilbert spaces itself. This, in the end, is what mathematics is really about." ] } ], "metadata": { "kernelspec": { "display_name": "VPython", "language": "python", "name": "vpython" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 4 }