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.

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.

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 computation. 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 "computation."

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.

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.

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.

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.

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.

What do I mean by ambiguity? Like Wittgenstein's duck/rabbit:

Or the optical illusion of a Necker cube, appearing now extending inward, now outward from the page:

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.

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!

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?

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.

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.

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"?

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...)

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.

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 situations, 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.

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.

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.

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.

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.

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.

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.

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.

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, 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 "inward experience" 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.)

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.

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.

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 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 on the decades long difficulty in formulating relativistic quantum field theory. But ordinary quantum mechanics is already compatible with a relativistic spacetime. It is often incorrectly portrayed that the "instantaneous collapse" of the wavefunction is in conflict with relativity, 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 pair, 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 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 even dream of, if you hadn't been forced 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.

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".)

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 dead.

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."

Why I'm not a Bohmian*¶

Why I'm not a Bohmian^*¶