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Quantum Waves Explained

[This is a slightly edited version of an email in which I tried to answer some of Jennifer’s questions about “Quantum Waves, Hegel’s Intuition and the Gospel of John: The Personal Account of a Mystical Experience”]

March 24, 2007.

Dear Jennifer,

[…]

Now, concerning your questions, I will try to answer them as well as I can.

I frankly do not think that “quantum complications” are due to nature but to people. I believe that what nature tells us in the microscopic realm studied by quantum physics is so distant from the expectations with which Western man and, in general, “monotheistic” man, has been approaching the world for the last two or three millennia that much convoluted theorizing and epistemology has been produced in order to erect an intellectual barrage against the idea that the “ground reality” of which we, our experience and the visible world are manifestations, is an undivided whole.

One of the closest things to what quantum physics reveals us about the world is the Chinese concept of “Tao,” and I should rather call it a hint or a clue, than a concept.

Like the “ground reality” suggested by quantum mechanics, the Tao is all pervading but no one can seize it or use it.

Let me start answering your questions by undoing a misunderstanding: quantum particles are not special particles. Electrons, neutrons, protons and photons are quantum particles. Atoms are quantum particles as well, and even massive molecules may behave as quantum particles. What distinguishes quantum particles is the fact that, by their size or the low density (in particles) of their environment, they are not constantly interacting with other particles. Their behaviour is markedly different from the behaviour of macroscopic bodies (described by classical physics) and it can be ― probabilistically ― predicted through wave functions and “state vectors,” which are (practically equivalent) mathematical expressions from quantum mechanics.

However, we can predict the behaviour of a body of any size with the help of quantum mechanical formalism: if we are dealing with macroscopic bodies (and a speck of dust may be considered a macroscopic body), the rate of external and internal interaction of its constituent particles makes them behave in the manners described by classical physics; in their case the quantum formalism will yield predictions similar to the predictions of classical physics. “Quantum particles” is just the shorthand for “particles behaving in manners predicted by the mathematical formalism of quantum mechanics but unaccountable in terms of classical Newtonian physics.” Of course, there is also the apparently discrete character of “state transitions” (like the transition of an electron from one atomic orbit to another) and of energy exchanges (like the emission or the absorption of one or more quanta of light, or “photons,” when an electron falls to a lower orbit or jumps to a higher one) at the quantum level, which gave quantum mechanics its name.

Quantum waves are a problem. They were conceptualized by Bohr and Heisenberg as being simply a description of our knowledge about a particle at a given time in a given setting. Now, some people made (what I believe to be) an entirely arbitrary jump from there and concluded that those waves, which are essentially mathematical entities, are the particles when undetected. The particle would “spread out,” taking the wave’s shape, and when this wave collided with a detecting body (like a photographic plate), the probability of finding the particle in a given point would dependent on the wave’s intensity at that location. Indeed, with the same “preparation” (i.e. with the same experimental settings), we do see more impacts where the wave is more “intense” and less where it is less intense.

Within this realist reinterpretation of quantum mechanical formalism, the particle impact is construed as the wave “collapsing” into a localized point. Unfortunately, neither the identification of the particle with the wave, nor the idea of a “collapse” of the wave is contained in the mathematical formalism of quantum mechanics. Nevertheless, this is the source of, and the ground on which rests, the famous claim according to which not only light but also every kind of particle would have a “dual nature”: that of a wave and that of a particle. This is also the origin of the famous paradox of “Schrödinger’s cat.” Since nothing in the mathematical formalism accounted for the postulated wave collapse (into a single impact point on a photographic plate, for example), some eminent people like Von Newmann decided that it must be the observer’s consciousness that collapses the wave into a point. If you make the life of a cat depend on that collapse (through the means of a cascade of consequences triggered by one of two equally probable quantum measurements and ending up in the breaking of a bottle with poison which will kill a cat inside a closed box) and you believe that, unless you look inside the box, the initial wave and all the resulting consequences will not “collapse” into a definite state, then you end up with a cat that is neither alive nor dead, or maybe both at the same time! So much mental energy wasted over a questionable postulate: “the wave equals the particle!”

I obviously do not buy into this and I agree with a minority of physicist who believe that this idea of a particle-wave duality is essentially the result of a reckless realist reinterpretation of Bohr’s and Heisenberg’s antirealist interpretation of quantum mechanics. These two great physicists, and especially Heisenberg, were “operationalists”: for them, quantum mechanics was not a description of “independent reality” but simply a way to describe, predict and communicate human experience acquired within precisely defined experimental conditions. Firmly entrenched in their epistemological position, they resisted any kind of discussion or speculation about the eventual reality corresponding to the mathematical wave and its relation to the detected “particle” on the grounds that none of that was represented in the quantum mechanical formalism which they took for the last word on the subject – no more knowledge of quantum reality could be acquired by humans. I think that this kind of biblical “Thou shall not go any further” involved in a sibylline epistemology which few physicist dared to defy was one of the main reasons for the adoption of a sketchy realist interpretation ridden with insoluble paradoxes.

There are however alternative propositions to Bohr’s and Heisenberg’s antirealist interpretation (also called the Copenhagen interpretation or the standard interpretation of quantum mechanics) and to the epistemologically naïve realist reinterpretation of their approach. The most important one was advanced by the French physicist Louis de Broglie and later taken up and developed by the American physicist David Bohm, who finally gave it its last expression in collaboration with his disciple, the British physicist Basil Hiley. They argued for the reality of both the wave and the particle¹. The wave does “spread” out in space and has a varying structure of intensity that depends on its source and on its potential targets. If you consider the case of a photon, for example, this automatically implies the idea of a faster than light correlation between the particle and its environment since the particle is guided by the wave in a way that is comparable to the behaviour of a ball rolling on a solid undulated surface, “reacting” to the crests and to the troughs according to the angle with which it approaches them, its accumulated kinetic energy (resulting from the movement multiplied by its mass), and the gravity pull.

What about the collapse of the wave, you may ask. Well, there simply is none in this interpretation since we assume the wave and the particle are not the same thing. When the particle hits another one (which may be an atom on a photographic plate, starting a chain reaction that will eventually modify an area on the plate big enough to allow the detection of the event with our “macroscopic eyes”), their respective waves combine. At that moment, the two particles become entangled since they are driven by the same combined wave, described by a single wave function or state vector (two mathematical representations that essentially yield the same results). This means that if they fly apart after having interacted, they will still be strongly connected, no matter how far they are. (This strong connection, known as entanglement, will last until one of them interacts with a third particle, and a fourth and so on, which are themselves correlated with the rest of the universe, drastically obliterating the perceivable and mathematically conceivable entanglement of the initial two particles.)

However, the wave function does not give us a full description of a particle’s behaviour. If we go back to the comparison with the ball rolling over the undulated surface, we may think of the wave function as providing a close (but, I think, only approximate) description of that surface. It does not tell you, for example, the exact angle from which the particle is coming, nor its exact velocity. In addition, if you change the shape or the orientation of the detecting device positioned on the particle’s potential path, you will instantaneously change the whole configuration of the undulated surface (that is, the wave).

According to quantum formalism, the wave function of any given particle spreads out indefinitely in space. Since the particle's wave instantaneously reacts to its environment (and particularly to the particle’s origin and to its most probable targets), that means it directly connects the particle to every other particle in the universe. Of course, this applies to every particle, which means the connection of each particle to the whole is direct and indirect (through other particles' connexions to the whole). This leads us to the obvious conclusion that even the quantum wave of entangled particles (which are flying apart after having interacted but have not yet “bumped” into anything else) is, at any time, reacting to the whole “quantum wave sea” from which it is never really separated.

I believe this is one of the reasons for the indeterminacy of the behaviour of every particle. The other reason for this indeterminacy is the fact that, at the scale of quantum events, the kind of interactions you need to perform measurements, significantly disturb the particle’s properties. It is like measuring the behaviour of a flying soccer ball using soccer fields as measuring devices. If you think that, even before the impact, the massive “detecting soccer field” greatly influences the properties of the wave driving our tiny “soccer ball,” you will understand why the observed quantum reality depends on the act of observation. Through our material intervention, we become part of a process of which the particle’s detected properties are just another part. Given nonseparability, this process is coextensive with the whole universe. The exact prediction of all the properties of a given particle would imply that a part (the observer) of the whole (the universe) would have a complete “grasp” of that whole, which is logically impossible.

This would suggest that indeterminacy is only a result of our limited perspective and that reality itself may well be not only determinate but also deterministic and/or animated² or “something” else that we cannot understand.

Another feature that may make us suspect that we are somehow “off track” with our conventional representations of the universe is the “supraluminal” character of nonseparability, i.e. the fact that it seems to imply an interaction that is faster than light and virtually instantaneous.

Think again of two entangled particles, a hundred miles apart from each other. You cannot make something determinate happen to one by interacting with the other. One of the reasons for this resides in the fact that you cannot know all of the properties of a given particle. If we probe it with our “detecting soccer filed,” we will know one property as it was in that specific measuring configuration (or “preparation” as it is usually called); however, to measure another property, we will have to introduce a different measuring configuration in which we will not be able to assume the validity of the first measurement. In addition, we are unable to control completely all of the determinants influencing the particles’ behaviour since they are ultimately linked to the whole universe.

However, the fact that we cannot use entanglement to influence deliberately a distant particle by acting on its correlated pair does not imply that there is not a correlation. Bell’s theorem established the mathematical conditions under which the existence of a correlation could be established beyond any possible doubt. Several experiments conducted during the eighties and the nineties fulfilled those conditions, providing complete experimental confirmation of the correlation existing between entangled particles and proving that if correlation is the result of a spatially defined interaction, this interaction has to be supraluminal, possibly instantaneous.

Now, wonder what the phenomena of instantaneous correlation could mean. Ask yourself what could be a perfect example of an instantaneous correlation. Probably you have already guessed: two things are perfectly instantaneously correlated when they are… the same thing!

That is what the late David Bohm suggested with his example of the fish tank in a book entitled Wholeness and the implicate order (a must-read if you catch the wholeness virus!) Imagine a fish tank with glass walls and a fish swimming inside, being filmed by two perpendicularly oriented cameras (one pointed to the front glass wall and the other, say, to the right glass wall). We thus obtain two different images in two different screens. If a spectator, watching the two synchronized movies, does not know anything about the fish tank or about how the cameras were set, he may believe, at first, that he is looking at two different fishes. He will then notice that, when he sees the side of a fish on one of the screens, he will see the front or the back of the other fish on the other screen. As he is vaguely familiar with cameras and shooting angles, he will eventually realize that he is watching the same fish from two different angles.

This does not necessarily mean that the two entangled particles could be the same particle, but it suggests that they may be two different manifestations of the same “thing”…

…a thing whose self-correlation would be inversely proportional to the number of times it interacts with itself. Let me explain this: If we admit the idea of a Big Bang, we have there a perfectly self-correlated expanding whole which ― after some mysteriously providential disturbance breaks up the perfect symmetry of the first moments of the expansion ― de-correlates from itself as it increasingly interacts with itself. You may figure this as an expanding circle of synchronized water dancers that, at some point, start bumping into each other and begin forming smaller groups engaged in different local dance patterns. Yet, each dancer’s small gesture is somehow connected to the movement of each other dancer.

A pale “replica” of this perfect and primordial self-correlation of the whole will be recreated each time any two (or more) of the whole’s parts interact with each other generating an entangled pair (or more).

The apparently instantaneous character of the correlation uniting the entangled particles may indicate that space itself is no less an appearance than the appearance of locality (or separation) of which the former is the frame of reference. After all, if every “thing” in space is instantaneously correlated with every other thing, what does space become? For Kant, space and time were “a priori forms” of perception and of intellection, i.e. the innate moulds in which the mind would pour and organise the raw sense impressions. In the model of the universe we are discussing here, space would be an abstract or empty form of difference, that is, of manifestation.

Following the Kantian lead, we may also conceive of time as another abstract or empty form of difference ― i.e. of manifestation ― if we previously discard the (slightly immodest) idea according to which the probabilistic character of quantum mechanics does not reflect the limitations of our knowledge but an alleged ― and unexplained ― intrinsically indeterminate behaviour of quantum “particles” and restore, even if just as a working hypothesis, the old idea of full universal determinism.

Suppose you could rewind the “universal movie” and bring back a previous moment³. Now press play. What happens? Well: exactly what already happened when you played it for the first time. What we would have described as a random fluctuation on the quantum level would have been as determined as any other event. Its randomness would simply have been a reflection of our incomplete knowledge.

Of course, there is no playing device for the “universal movie.” At the most, we could say that the universe is its own playing device. The point I’m trying to make with this imaginary rewind of the universe is that, in a deterministic universe in which there is no absolute randomness ― and I do not know what randomness could be other than our own ignorance pressed into some kind of definite frame like an instrument measuring the consequences of a quantum event or a person flipping a well calibrated coin, ― all future and past events are implicit (to use David Bohm’s term) in every present time.

Nonlocality seems to imply exactly the same thing in spatial terms: every event is instantaneously connected with every other event, which means that every “sector” of universal “space” is somehow implicit in every other sector. Take a few cubic centimetres of air at the place P at the time t₁ with an exact configuration (x₁) of matter. Given nonlocality, most, if not all, physicists would agree that the configuration x₁ could not be dissociated from the configuration (U₁) of the whole universe at time t₁. (Many would object that, since the measurement of exact configurations is impossible, what I’m doing here is not physics but metaphysics, an objection with which I would cheerfully agree!) You cannot have the configuration x₁ at P at time t₂. Nonlocality makes this something more than a truism. The whole universe, in its present configuration, is implicit in each of its sectors.

To quote d’Espagnat:

“Already in year 1914, Emile Borel made the surprising observation that, just because of gravitational effects, shifting a small piece of rock as distant as Sirius by a few centimetres would radically modify the behaviour of the gas molecules contained in a vessel here on Earth.”

Speaking now of quantum effects, d’Espagnat adds:

“…even a speck of dust lying far away in interstellar space is not totally isolated due to its interaction with cosmic background radiation.” (On Physics and Philosophy, 2006, p. 181.)

To which we may add that, if we accept the Big Bang theory, every particle was at least once in contact with the rest of the universe, which means that even without cosmic radiation no speck of dust would ever be “alone”!

Lest I start divagating, let me summarize the consequences of Broglie’s and Bohm’s ontological interpretation of quantum mechanics for the meaning of time and space: If we accept nonlocality and assume determinism (which is at least as legitimate ― if not more ― as assuming indeterminism on the grounds of our limited knowledge) then time and space no longer appear to us as fundamental but as conditions or abstract forms of the manifestation of the whole to itself. However, whereas this whole manifests to itself as space and time, in itself it is neither in time nor in space.

Before closing the subject of quantum physics and nonlocality, I cannot resist adding that ― in spite of the lack of articulation between quantum physics and relativity (both special and general) and, particularly, in spite of the fact that nonlocality apparently contradicts the speed of light as the top limit for interactions between two points in space according to special relativity ― we find, in special and in general relativity, some important ideas which converge with the notion of a supra-temporal and supra-spatial universe in which time and space are just the “forms of manifestation” of being.

The most obvious convergence is the idea that, according to general relativity, time and space are not absolute frames of reference, indifferent to, and transcending the objects and events within them. On the contrary, space and time are literally moulded by large bodies like planets and suns. Moreover, they are not thought of as two separate sets of dimensions but as a single set of four integrated dimensions (three of space and one of time), and thus we have the notion of space-time.

However, it is in special relativity that one may find the most striking confluence with our view of a supra-temporal and supra-spatial undivided universe.

As you may know, according to the special theory of relativity, the speed of light is a constant (in the vacuum, I should add). That means that, if you have two observers moving at different speeds relative to a source of light, both will measure the same speed of light. Imagine you have a fixed light spot and two observers. Observer A is stopped and observer B is moving toward the light source at half the speed of light. Each will “see” the light beam moving in her/his direction at exactly the same speed. What does that imply? Simply that time flows half as slow to the observer B, who is moving at half the speed of light towards the light spot, than it does to observer A. If they had similar clocks and could compare them, clock A would have to count ten minutes for clock B to count five minutes.

Therefore, time slows down as you approach the speed of light. What happens then when you reach the speed of light? Theoretically, your mass should become infinite (this particular point derives, I believe, from general relativity). As for time… well, time would stop!

Fortunately, photons are massless. But do you realize what the speed-of-light-stopped-time means? It means that, light goes nowhere. It never leaves, and it never arrives. For light, there is no time and there is no space. It is the representative of our undivided supra-temporal and supra-spatial universe par excellence.

If you consider the fact that the “photon” represents the minimal quanta of energy that can be exchanged between any two spatially and temporally situated particles or bodies and that the speed of light is the limiting speed for the “displacement” of any kind of particle or body, you realize that light is the hinge connecting the non-temporal and non-spatial undivided universe with its seemingly spread and apparently fragmented self-manifestation. Each time energy seems to be exchanged, each time a beam of light seems to cross the space, you have a glimpse of that timeless and spaceless undivided whole. Could it be “realizing” itself in and through your unique human awareness?

Enough of quantum physics, entanglement and nonlocality! Please forgive me – I get carried away when I start dealing with this kind of subjects. I hope I answered some of your doubts, tough I’m afraid I may have originated a few more with my clumsy writing…

[…]

Concerning universal connectedness, the paradox of not being able to use it and the comparison you draw with the American relation to history: no, it is not banal. In fact, that is, expressed in other words, the major realization of twentieth century philosophical hermeneutics (see Gadamer’s Truth and Method): you are never fully aware of your own historical and cultural ground. Yet, you can enlarge your awareness through contact and careful consideration of what at first is culturally or historically alien. You have been through such a process personally. Therefore, you must know what I’m talking about.

When you oppose quantum connectedness to the idea of DNA determinism you are obviously dealing with symbols. […] However, as you probably realized by reading the first part of this email (yes, I tend to serve quantum physics as a hors-d’oeuvre!), quantum connectedness is not contradictory with determinism. If you think determinism through and do not perform the Cartesian trick of making your ego an External and Transcendental (ET) entity by fiat, then you realize that you can never really use that determinism, for the reason that that determinism is also you… This is so mind-boggling that it is better no to pursue this line of thought without previously peppering it with an abundant amount of doubt… We have good reasons to doubt and question determinism, for how can we conciliate it with the idea of a non-temporal and non-spatial universe? Determinism is the realm of causality, but we cannot conceive of causality outside time and space⁴.

You are afraid your considerations ― those to which I have been trying to answer just now ― may be tangential to what I intended to communicate about wholeness and the consciousness of difference that separates us from it. I must confess to you that I consider all my words about nonlocality, nonseparability and the undivided whole as tangential to the very thing to which they point! Looking back to what I wrote in the previous email and in this one, I cannot say I’m satisfied. I see too much structure, too much definiteness. Physics is fun and interesting, but I will always prefer to it, as a metaphor for Reality, the Taoist image of the free flow of water, finding its way immediately, without hesitation, in perfect coordination with itself and its environment.

You ask me how I would define a conscious experience. I would answer that with the phenomenological conception of consciousness as an “arrow” actively pointing at something. This definition stresses the fact that consciousness tends to uphold something, implicitly separating it from the background. The great Eastern traditions of wisdom know this and try to remind us of the whole picture. Concisely, and to paraphrase Alan Watts, wisdom means knowing that for each silhouette there must be an equally important background, that in a definition what is left out is as fundamental as what is included, that you cannot have the Good without the Bad, consciousness without unconsciousness or eternity without finitude, and that meaning is simply the shape of the lines you draw (of the distinctions you operate) “on” the whole.

Consciousness implies, at least, two crossed lines: on the one hand, the line separating the consciousnesses of… (the arrow) from the “of” of consciousness, and, on the other hand, the line separating what the “consciousness of…” brings forth to awareness from what is (meaningfully) left in the shadow…

The baby’s consciousness to which you refer ― whether she/he is peacefully enjoying the fact of being there or crying or craving for food ― is just like water flowing without the constant feedback loops (self-awareness) we specialize in as we grow older. Nevertheless, these loops have their usefulness too ― the water never stops flowing…

You then address the matter of the relations between consciousness and distinction (and, I would add, separation), underlining some problematic aspects of the idea according to which consciousness generates distinction and separateness. You remark that consciousness is able to apprehend as a whole something that was generated through a “selective accumulation of parts,” like a painting, which is the result of an accumulation of brush strokes. However, you could also consider that the brush strokes, as gestures, are themselves abstracted and idealized wholes that you can break down into parts and connections like the particular technical intention in a given precise context of a work in progress, the metabolic processes going on in the muscles as the gesture is being accomplished, a memory that briefly surfaces as the brush approaches the canvas, the air entering the lungs as the tip of the brush is being pressed against the canvas and the precise pattern in which the painter’s neurons are firing and relaying electrical impulses during that quarter of a second.

What is a brush stroke? What is an inkblot? What is a painting? No matter where you choose to draw the line around a provisional whole, you will inevitably “severe” potential connections, disregard details, discard potentially relevant contexts and limit you perception to a narrowly defined scale. Is the thing you have just singled out a part or a whole? It depends on the scale and on the set of relevancies with which you decide to evaluate the thing. It is the chosen scale and set of relevancies that make the thing or the “think,” as Alan Watts liked to call it. Language and concepts are useful but they are just abstractions. That is the reason why, even though I love surfing the world of language ― as you may have guessed, ― I try not to be caught in the formulations I end up concocting.

Now, concerning loneliness… You say you cannot understand how the sense of connectedness, of being a part of the whole universe could possibly lead to a feeling of loneliness. It cannot if you embed you “ego” in the whole but keep it circumscribed, so to say. There is still an “I” looking at the whole of which, she/he feels, she/he is a part. However, in my experience, that circumscription, that frontier, was opened, and the distinction between I and non-I was literally suspended. All and everything was saying “I” right there. It scared itself to death by finding out who it was! You are it. You are everything and beyond. There is nothing else and no one else out there. That is it. End of game. You found out who you are.

Turn the mirror away and now it is I, not you. Give it another turn: It is she. It is he. It is the frog I came across the other day (an old acquaintance, I should add).

Is it not fun? Is it not worth forgetting who I am once more and going back to the game? I think it is, but I only speak for this particular perspective in space and time. How could I speak otherwise?

Is this “nihilism,” as some say?

No. Nihilism supposes a separate human realm that is supposed to collapse unless an abstract set of values is cherished above everything else. I would agree that such a view, if it is rendered flexible enough, is often useful and that most of us do live, most of the time, in a sort of separate and abstracted human realm where we must build agreements about provisional sets of values. Still, let us not mistake the floor for the Earth or the ceiling for the sky!

Concerning my analysis of the Gospel of John, you are right to say that my interpretation cannot be a novelty. You are obviously right. The Cathars and the Bogomils that you mention seem to have been later branches of the Gnostic tree. Many researchers sustain that orthodox Christianity sprang from that same source only to sever itself from it in order to disguise its pagan origins and to present itself as a revolution of the stern prophetical Jewish religion, an eminently political religion that absorbed the imperial “essence” from the blows the successive Middle-Eastern empires inflicted on the Israelite people and, particularly, on the pride of its priestly intelligentsia…

I intend to learn more about all of that in the next decade or two if I can…

Moving forward: my experience near the sea reminded you of an experience you once had, also on the seashore. You had felt awful among humans and you were now by yourself, watching the sea lions enjoying themselves by plainly being what they were, with no self-conscious loops to complicate their existences. You also began watching a group of kids that were absorbed in the contemplation of the sea lions. Unexpectedly, the distinction separating the human realm from the animal realm collapsed:

“I suddenly realized that if there are no mediocre animals, how can we dismiss any human as mediocre? Is he mediocre only as much as he doesn’t live up to his potential? Why is their potential so important for some humans, thus making us miss so many opportunities to be just what we are?”

When a plant grows, it follows its potential; it is its potential as it unfolds. You cannot order a plant to grow. With humans, things work differently. They have those self-conscious loops that often seem to make their life messy and miserable. Some people say that humans should be ordered as little as possible, that they grow harmoniously when they are left alone. Others say that humans must be bent in a sense or another, that they need a certain amount of constraint and direction as they are growing. I suppose the truth is somewhere in the middle but I have no authority in the matter.

Maybe the only problem with those self-conscious loops is the fact that in them, we believe we are somehow outside the stream of life. We then look at the latter, anxious to keep it under control in order to avoid the worst catastrophes and we find ourselves in the middle of a spinning abyss without realizing that, after all, we were just passing through another elegant whirlpool in the stream.

[…]

Take care,

Miguel Montenegro

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