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The Dangerous Intuition of David Bohm

A few months before Einstein died, he wrote about an unpopular intuition in physics which went against everything he considered sacred. An intuition surfaced by an otherwise ostracised physicist, David Bohm.

“[If it is true] then nothing will remain of my whole castle in the air including the theory of gravitation, but also nothing of the rest of contemporary physics.”

To Einstein, Bohm’s intuition was downright dangerous.

The Twitter watering-hole erupted last week when a prominent union minister dismissed mathematical figures of a lagging economy by quoting how “math never helped Einstein discover gravity”. Does math help explain the economy? Perhaps. Did math really help Einstein (re)discover his equations of gravity? David Bohm, who this essay is about, would vehemently claim that it didn’t. That would be among the very few ideas on which both Einstein and Bohm would agree.

To understand this, one must first understand how a gyroscope works.

One way to understand it is to write down the three equations that the book tells you about. Make sure angular momentum is conserved on all sides. Then mechanically derive the final result. Formulaic. Works every time. Can be taught en masse. Very efficient.

David Bohm was the kind of physicist who would never understand it that way. He would imagine himself as the gyroscope, standing on his toes, perched on a gimbal, arms stretched far, pirouetting swiftly in circles, making small muscular movements to keep his balance. He would feel the behaviour of the gyroscope, understanding it’s motion through some form of muscular interiorization. The math and formulae would come later, almost as a pedestrian way of communicating that insight to others. Second-hand intuition.

Bohm was a throwback to the earlier days of physics which was unusual even in his time – An era of physics devoid of reams of astronomical data, quantum supercomputers, and well-intentioned “practical” problem solving. While a Feynman would jump on any opportunity to a solve a practical problem through complicated Feynman diagrams, Bohm would actively resist formalising his intuition, letting the muscle memory of the insight simmer, evolve, and manifest in unexpected ways.

“Dave always arrives at the right conclusions, but his mathematics is terrible. I take it home and find all sorts of errors and then have to spend the night trying to develop the correct proof. But in the end, the result is always exactly the same as the one Dave saw directly”.

Basil Hiley, Bohm’s colleague at Birckbeck College

Perhaps all discovery happens this way. In the most messy, ad-hoc, inefficient manner possible, outside the sanitised corporate innovation labs. It is not surprising that when Bohm met Einstein years later, Einstein would confirm Bohm’s predilections. “Matter tells space how to curve, and curved space tells matter how to move”, the basic principle behind his general theory of gravity, Einstein confirmed, was not arrived at by years of objective, rational thought. It was an irrational feeling, a series of subtle, internal muscular sensations about four-dimensional space-time that the world didn’t yet have the mathematics to describe.

This aspect of discovery doesn’t get discussed in polite company because it is impolite to attribute the profound to the irrational. There are always more convenient explanations fit for the industrialised age – like IQ, degrees, and the act of being European. How else does one justify the bizarre amnesia of high-school syllabi? Einstein’s equations explained the abnormalities in the behaviour of gravity, and predicted blackholes, and gravity waves – but this came much later. The muscular intuition came first. It is merely human to rationalise irrationality in hindsight.

That said, this essay is not about how Einstein sympathised with Bohm, or vice versa. It is rather about the exact opposite.

Feeling Causality

Gary Marcus, a vocal critic of the currently most popular approach to artificial intelligence – deep learning – wrote in The New York Times recently about how computer systems need to understand time, space and causality to be more..well, intelligent. What he means is that instead of learning by repetition that anything with two eyes, two ears and whiskers is a cat, it should learn that mammals have these features and hence anything with those features is a mammal, which breathes, excretes and reproduces, and a cat is just a special instance of such an mammal. Deep learning doesn’t posit an artificial intelligence to understand what causes a cat to be a cat, and hence it is brittle, narrow and quite dumb.

Do human beings have intuitive understanding of how causality works? David Bohm would disagree. We have an explicitly local understanding of how causality works. In everyday speech, “locality” is a slightly pretentious word for a neighbourhood, town, or other place. But its original meaning, dating to the seventeenth century, is about the very concept of “place.” It means that everything has a place, a location. You can always point to an object and say, “Here it is.” If you can’t, that thing must not really exist. At any point we can localise the different features of a cat – it has ears, eyes, whiskers, and a tail. So we would want our AI to do this intuitively too.

It is one of the strongest intuitions of the human experience – at any point of time, we have a strong sense of place, and of the relation between spaces. We feel a strong sense of separation from those we love, and a particular kind of impotence at being unable to affect things far away.

The first aspect of this is “separability”. You can take four china plates and put each one in a different corner of the dining table. They will not cease to exist or lose any of their features—size, style, rigidity. The entire dining table derives its properties from the set of plates that make it up; if one hamburger can be put on each plate, then a set of four plates can serve four hamburgers. The whole is the sum of its parts.

The second aspect of this intuition is “local action,” which says that objects interact only by banging into one another or recruiting some middleman to bridge the gap between them. Whenever a distance separates us from someone, we know we cannot have any effect on that person unless we cross the distance and touch, talk to, punch—somehow, make direct contact with—that person, or send someone or something to do it for us. Modern technology does not evade this principle; it merely recruits new intermediaries. A phone translates sound waves into electrical signals or radio waves that travel through wires or open space and then get translated back into sound on the other end.

Locality was the foundation stone on which Einstein built his castle. His theory of relativity formalises the locality we intuitively take for granted. Per Einstein, the speed of light is the cosmic limit on the speed of causality. Nothing occurs at infinite speed, and hence the world does not start and end at the same time. Places and things are “separate”, and interact via “local action”, limited by this speed limit.

What, then, would be the opposite of locality? So convincing is locality, that it’s opposite is simply referred to with the prefix “non” : non-locality. In the non-local picture of the universe, nothing is separate. Every particle interacts instantly with every other particle. There exists no concept of time – the universe is created and ends at the same frozen instant of time. Similarly there exists no concept of space – nothing can be separated, and while the whole may be a sum of it’s parts, there is no way for someone who is a part of the universe to localise the parts from the whole. As the joke goes, while a stitch in time would just confuse Einstein, a non-local universe would be his worst nightmare.

David Bohm discovered a model of the universe consistent with all experiments, that is explicitly non-local. In a book he co-wrote a few years before his death, he called it the Undivided Universe.

Feeling Non-Locality

We shall indulge ourselves in the absolute minutiae of math to understand what Bohmian’s idea of mechanics says. Like most good ideas, it is so horribly simple, and yet so counter-intuitive that it’s philosophical meaning has completely eluded the mainstream.

Any theory of the universe can be described by how a state of set of particles is defined and how it evolves over time. In Bohmian mechanics, the state of a system of N particles (q1, q2, q3…qN) is described by its wave function ψ=ψ(q1,…,qN)=ψ(q) . The theory is then defined by two evolution equations: Schrödinger’s original equation that is basis of all of quantum mechanics:

And a secondary Guiding equation, that Bohm called the pilot wave equation, that doesn’t get included any of the QM textbooks:

Why does nobody like Bohmian mechanics? It’s predictions match up with all the other more popular interpretations of quantum mechanics, so there is no empirical reason to reject it. Most physicists say it’s because the guiding equation adds unnecessary complexity to the already elegant Schrödinger’s equation, hence it must not be required. The real reason is found in the outrageous meaning the equation makes explicit. If you look carefully, the trajectory of any particle “Q_k”, is dependent on all other particles in the system (Q1…..QN), mandated by the very simultaneity of the equality sign. No time-delayed dependence, as Einstein would like it. A speed limit isn’t even required. Explicit non-locality. This dangerous idea goes against every established idea in contemporary physics, and hence amounts to sacrilege, even though it is effective. This is what the above equation when applied to set of particles passing through Young’s infamous double split experiment looks like:

What the simulation in the video shows is the exact trajectories of a set of particles passing through either of two slits. The idea of determinate trajectories alone is alien to the world of mainstream quantum physics. Bohm’s equation further predicts how a quantum state deterministically collapses into a classical state. When mainstream quantum mechanics says that the choice of which slit the particle goes through is fundamentally random, what Bohm says is that nothing is random – if only we knew the initial position and current position of all particles in the universe, we could simply plug it into his equation to find which slit the particle would go through.

The youtube channel Veritasium, has done us all a brilliant service by creating this video about how to visualise the guiding (pilot) wave equation :

There’s another way to intuit Bohm’s notion of an undivided universe : un-mixing drops of ink in viscous corn syrup. A hollow glass cylinder is kept inside another, and the space between is filled with viscous fluid – corn syrup. Three drops of ink are injected into the corn syrup, in a way they appear separate (“localised”) from each other. On rotating the inner cylinder, the viscous corn syrup moves in layers, layers of liquid farther away from moving cylinder stay static, the ones near it move rapidly. As a result the drops appear to mix – they go from a state of less entropy to more entropy. They coalesce into a single colour, in a way it would be impossible to separate them in a traditional liquid. But corn syrup is viscous, hence on turning back the inner cylinder, the drops magically un-mix, and return to their initial localised positions. Here’s a video showing how this happens:

The experiment is just an analogy, but it resembles how David Bohm thought about the universe. In the experiment, there exists what Bohm calls an “implicate order” (the order of colours of the separate drops) that over time evolves and mixes into this non-local mixture (where nothing is separate, everything affect everything else). Nothing in the mixture appears separate, yet it is – if the universes trajectory was rolled back, it would separate into it’s constituents in a predictable, determinate manner to reveal the “implicate order” of all the particles since an initial Big Bang event. The order Bohm speaks of is timeless, exists all the time, yet is not apparent.

In Bohm’s view, all the separate objects, entities, structures, and events in the visible or explicate world around us are relatively autonomous, stable, and temporary “sub-totalities” derived from a deeper, implicate order of unbroken wholeness. Bohm gives the analogy of a flowing stream:

On this stream, one may see an ever-changing pattern of vortices, ripples, waves, splashes, etc., which evidently have no independent existence as such. Rather, they are abstracted from the flowing movement, arising and vanishing in the total process of the flow. Such transitory subsistence as may be possessed by these abstracted forms implies only a relative independence or autonomy of behaviour, rather than absolutely independent existence as ultimate substances.

(David Bohm, Routledge & Kegan Paul, London, Boston, 1980, p. 48.), Wholeness and the Implicate Order

Another metaphor Bohm uses to illustrate this implicate order is that of the hologram. To make a hologram a laser light is split into two beams, one of which is reflected off an object onto a photographic plate where it interferes with the second beam. The complex swirls of the interference pattern recorded on the photographic plate appear meaningless and disordered to the naked eye. But like the ink drop dispersed in the corn syrup, the pattern possesses a hidden or enfolded order, for when illuminated with laser light it produces a three-dimensional image of the original object, which can be viewed from any angle. A remarkable feature of a hologram is that if a holographic film is cut into pieces, each piece produces an image of the whole object, though the smaller the piece the hazier the image. Clearly the form and structure of the entire object are encoded within each region of the photographic record. Bohm suggests that the whole universe can be thought of as a kind of giant, flowing hologram in which a total order is contained, in some implicit sense, in each region of space and time. When Chinese billionaire Jack Ma recently gifted a hologram gift to his employees, he would have liked to have this notion in mind.

In perhaps the most important result in the history of quantum mechanics , John Bell in the 1960s theoretically proved through his infamous Bell’s inequality that one could not accept the findings of quantum mechanics without accepting the inevitability of non-local communication. He owed his proof to a singular man – David Bohm.

… conventional formulations of quantum theory, and of quantum field theory in particular, are unprofessionally vague and ambiguous. Professional theoretical physicists ought to be able to do better. Bohm has shown us a way.

J.S. Bell, Speakable and Unspeakable in Quantum Mechanics

Simulating Non-locality

Contrary to the misgivings mainstream physics has for the explicit non-locality of Bohmian mechanics, it is used a lot in one particular domain : visualising quantum mechanics via simulation. Everything from quantum tunnelling, to decoherence and time-dependent scattering, is easily plotted and evolved using perfectly deterministic classical computers. This youtube channel explores a lot of these in multicolour detail.

Why is Bohmian mechanics so useful in computer simulations of quantum mechanics? Because while non-locality might seem strange to physicists, it is not as weird to computer scientists. The scientific question of non-locality is, “How can two particles separated by half a universe be understood as connected such that they interact as though they were right on top of each other?”. If we analogise to a computer, the question would be, “How can two pictures at the far corners of the screen be understood as connected such that the distance between them is irrelevant?”

In fact, the measured distance between any two pixels (dots) on the monitor’s display turns out to be entirely irrelevant, since both are merely the products of calculations carried out in the bowels of the computer as directed by the programming. The pixels may be as widely separated as you like, but the programming generating them is forever embedded in the computer’s memory in such a way that the very concept of separation in space and time of the pixels has no meaning whatsoever for the stored information, similar to Bohm’s notion of non-locality. To those familiar with functional programming, written in pseudo code, the guiding equation we encountered earlier looks like any other computer function:

type particle {
   V velocity
   X position
}

function GuidingEquation(Q_1, Q_2, Q_3....Q_N) (Q_K particle) {
     ...
     return Q_K
}

The above function takes in the position and velocities of ALL the particles in the computer system, and returns the position of the k-th particle. It is almost trivial to understand how the universe would evolve if it was guided by an equation like this, as opposed to something which drew explicit difference between interdependencies based on a speed limit. Whether the universe is a computer simulation or not is the unfalsifiable subject of another debate, but it certainly gives us another intuition to why non-locality may not be as strange as it appears.

Echoes From a Forgotten Past

Non-locality forces upon us an universe that by nature is undivided – but the concept of an undivided universe is not in itself new. Cause and effect have been important topics in all ancient schools of Indian philosophy, particularly Vedanta. All schools of Vedanta subscribe to the theory of Satkāryavāda, meaning that the effect is pre-existent in the cause. Alan Watts, a prominent Eastern philosopher describes in detail the intricate concept of Indra’s Net:

Imagine a multidimensional spider’s web in the early morning covered with dew drops. And every dew drop contains the reflection of all the other dew drops. And, in each reflected dew drop, the reflections of all the other dew drops in that reflection. And so ad infinitum. That is the Buddhist conception of the universe in an image.

Alan Watts

The metaphor of Indra’s Net originates from the Atharva Veda (one of the four Vedas), which likens the universe to a woven net. The net is described as being infinite, spreading in all directions with no beginning or end. At each node of the net is a jewel, so arranged that every jewel reflects all the other jewels – similar to Bohm’s hologram metaphor. No jewel exists by itself independently of the rest. Everything is related to everything else; nothing is isolated. This net describes the universe as a web of connections and interdependencies among all its members, wherein every member is both a manifestation of the whole and inseparable from the whole.

Other texts relate this to the idea of Brahman (not to be confused with brahmin, which is a caste identity). Even seemingly disparate elements are described as nothing other than reflections of this Brahman, and hence of one another. This notion of an organic unity – a non-locality – is a signature of Indian and most of Eastern philosophy, and distinguishes it from all major Western philosophies – that are explicitly local in nature.

Vidyāranya in his Panchadasi (V.4) explains the meaning of the phrase, or mahavakya, “Aham Brahmasmi“:

Infinite by nature, the Supreme Self is described here by the word Brahman (lit. ever expanding; the ultimate reality); the word asmi denotes the identity of aham and Brahman. Therefore, (the meaning of the expression Aham Brahmasmi is) “I am Brahman”.

Bohm was astute enough to know the difference between science and scientism. A communist who was literally and figuratively ostracised from America during the Cold War, and from the physics community at large, he knew that physicists harboured as much dogma as the mystic shamans. It is no surprise, that the technique of Bohmian Dialogue – which acknowledged that rigorous science and schools of philosophy both have similar goals – to arrive at an understanding of thought and reality. And so there must be a dialogue in a civilised space, reconciling differences in the absent of any judgement. His dialogues with his collaborator, Jiddu Krishnamurti, an Indian philosopher, have filled many books.

There is however one man’s intuition which Bohm’s notions of locality have never been reconciled with till date. A theory that was as popular as Bohm’s ideas were unpopular – Einstein’s theory of relativity. Explicit locality. Even today, the many bastions of mainstream physics reject Bohm on these grounds, as if their own vague theories of quantum mechanics are somehow perfectly consistent with relativity.

Bringing Back the Absolute Frame

Einstein’s theory of relativity says that the laws of physics work the same everywhere, regardless of the frame of reference i.e. (1) No frame of reference is privileged in relation to all other frames. (2) All frames of reference are privileged in relation only to themselves.

Prior to Einstein, most scientists believed in a “luminiferous ether”, posited by Lorentz’s ether theory. The ether was an unobservable all-pervading absolute frame of reference, such that time was definitive only when at rest in that “ether” rest frame. Time in this rest frame was the yardstick that time in all other frames in motion would be relative to. They assumed that as beings on the surface of the earth traveling in the ether rest frame , our timing measurements must be distorted, although it was not possible to know by how much. Einstein’s contribution was to note that even if there were an invisible ether rest frame that we were traveling through, we could still define our inertial rest frame to have all the characteristics of a ether rest frame so that our timing measurements were definitive while timing measurement made at rest in the elusive ether would be distorted. In other words, it didn’t matter whether there really was an ether or not, we could define our own inertial rest frame and everything would work out just fine. In fact the idea of “Lorentzian tranformations” used by Einstein to transform event in one frame of reference to another, is borrowed from Lorentz’s ether theory, which required there to exist an absolute frame of reference in the first place.

In short, Einstein’s approach was decidedly positivist – if scientists with PhDs couldn’t observe the ether, then it meant that it did not exist, and hence wasn’t worth bothering about. Lorentz ether theory with an absolute rest frame made the same predictions as Einstein’s special theory of relativity, it was merely another interpretation of the phenomenon described by SR. In truth, there is nothing that prevents the existence of an absolute frame of reference, except Einstein’s postulates that explicitly say otherwise. The luminiferous ether hence was as quickly forgotten as Bohm’s ideas about mechanics.

In no matter of coincidence, the fundamental reason why Bohm’s notion of reality is inconsistent with Einstein’s relativity is due to the necessity of faster-than-light propagation i.e. non-locality inevitably picks out a preferred frame. The guiding wave described by Bohm’s guiding equation works non-locally in this absolute frame. This explicitly violates Einstein’s postulates. A postulate however, it should be noted, is not a divine truth, but merely an arrangement of words. There are those who believe rabidly in postulates given by men, but can an appeal to an authority that starts with an E instead of a G be really called the scientific method?

Could a neo-Lorentzian ether theory of relativity that explains gravity via an absolute frame, coupled with Bohmian mechanics result in a unified theory of everything? Perhaps. It would certainly do away with the locality-non-locality debate. But we would first need to reject every epistemological notion about physics we hold, and certainly those postulates handed down by science’s favourite neighbourhood genius, Albert Einstein. If that isn’t a controversial idea, then maybe 9/11 was indeed an inside job.

A Delicate House Of Cards

While critiquing Einstein is easy, it is also easy to forget that he was the first to notice the inconsistency. In his famous paper describing what is known today as the EPR paradox, he would list his problems with the inherent non-locality in quantum mechanics, or what he called “spooky-action-at-a-distance”. In so many words, his message was clear : “My intuition tells me this is wrong, and hence it is wrong(or incomplete)”.

In a recent biography of Indian freedom fighter, V.D. Savarkar, his biographer Vikram Sampath points out how Savarkar could be described as Mahatma Gandhi’s anti-christ. Not many know of the man, who saw rituals and cow worship as an abomination, advocated nuclearisation, industrialisation, militarisation and the abolishment of the caste system as the only way to develop India. Meanwhile, the Mahatma championed a rural aesthetic, the theatre of non-violence, and simple self-sustained living in the style of his many ashrams. Even today, many appropriate Gandhi to serve their own means, but looking around, India has largely gone down the way professed by Savarkar, a man deemed dangerous by both the British and the Indian establishment. Both were men of powerful intuition about what felt right. Both are villains and heroes of different fan followings, but Savarkar is mentioned in the same breath as Gandhi precisely because his intuitions were as powerful as Gandhi’s. As Leo Tolstoy would put it – “The best stories are not between the good and the bad, but between the good and the good.”

Albert Einstein’s intuition, the castle in the air that put locality above everything else, will perhaps attain a similar measure of piousness that Gandhi has. Bohm’s ideas too have mostly stayed outside the mainstream for mainly epistemological reasons, relegated to the elephant graveyard of physics, trying to make their way in. It is a crime of human bias, as John Bell puts it:

Bohm’s 1952 papers on quantum mechanics were for me a revelation. The elimination of indeterminism was very striking. But more important, it seemed to me, was the elimination of any need for a vague division of the world into “system” on the one hand, and “apparatus” or “observer” on the other. I have always felt since that people who have not grasped the ideas of those papers … and unfortunately they remain the majority … are handicapped in any discussion of the meaning of quantum mechanics. Why is the pilot wave picture ignored in textbooks? Should it not be taught, not as the only way, but as an antidote to the prevailing complacency? To show that vagueness, subjectivity, and indeterminism are not forced on us by experimental facts, but by deliberate theoretical choice?

John Bell

What happens to men who are firmly set in muscled intuition when they come across something counter-intuitive? It burns. Like a immune system violently responding to a pathogen. Those who’ve moved past science’s most loved high-school myth, that electrons move around a sun-like nucleus in planet-like orbits have come across the usual suspects of quantum mechanics – Bohr, Schrödinger, Heisenberg et al. None of them noticed this as much as the one person whom it burned the most – Albert Einstein. He was hence the first to point it out. The first real threat to his castle in the air. David Bohm merely aggravated it from an itch to a burn.

It takes one powerful intuition to counter another. Which is perhaps why we should listen to the most dangerous ones.