Quantum redux

A eulogy

Willis Lamb was an American physicist who won the Nobel Prize in Physics in 1955 “for his discoveries concerning the fine structure of the hydrogen spectrum." Lamb was able to calculate a surprising shift in electron energies in atomic hydrogen, which is now known as the Lamb shift. In a 1969 Physics Today paper¹ he wrote:

I have taught graduate courses in quantum mechanics for over 20 years at Columbia, Stanford, Oxford and Yale, and for almost all of them have dealt with measurement in the following manner. On beginning the lectures I told the students, “You must first learn the rules of calculation in quantum mechanics, and then I will tell you about the theory of measurement and discuss the meaning of the subject.” Almost invariably, the time allotted to the course ran out before I had to fulfill my promise.

So here is what I want you to know right away.

Many theoretical physicists have been taught the way Lamb’s students were taught, and they teach their students more or less the way Lamb did. This includes those who have written popular books on the subject or are holding forth, on TV or in other public forums, on the meaning and philosophical implications of quantum mechanics.

If there is a way of correctly characterizing quantum mechanics, it is as a calculus of correlations. It is a mathematical tool for calculating the statistical correlations which obtain between the possible outcomes of measurements that can be performed on quantum systems. What these theoretical physicists have studied and now teach therefore boils down to a medley of techniques for calculating such correlations. That’s what they are good at, that’s where they strive to outcompete each other, that’s where they try to come up with ever more sophisticated methods, theories, and — God forbid — another “theory of everything.”

What they are not good at is explaining why quantum mechanics — which, after all, is the fundamental theoretical framework of contemporary physics — is essentially a calculus of correlations, or why the corresponding correlata are measurement outcomes. Having never been trained for this, having in fact been discouraged from thinking about such questions, they obviously lack the competence to address them.

The metaphysical or epistemological issues raised by quantum mechanics were avidly discussed by its founders, including Bohr, Einstein, Heisenberg, and Schrödinger. The reigning motto of the post-war period until the late 70s, on the other hand, was “shut up and calculate.” The tide began to turn again with the experiments of Alain Aspect and collaborators in the early 80s, but with a different emphasis. Now the dominant issue wasn’t the special status of measurements; it rather concerned the common-sense defying implications of the correlations between measurements.

Among the protagonists of the first period of metaphysical head-scratching, Niels Bohr stands out. Bohr insisted, and rightly so, that “the emphasis on the subjective character of the idea of observation is essential” [BCW10:496].² In quantum physics, measurements have the special status that they do because measurement outcomes are observations, and this not in the sense that an observer becomes aware of an outcome that would also be indicated by the measurement apparatus in the absence of an observer. To Bohr, to make an observation was to have the experience of the outcome-indicating position of the apparatus pointer. Whether and in what sense this was more than a subjective experience, was a question for further consideration.

To Bohr, the reason why the description of atomic phenomena has “a perfectly objective character” was that “no explicit reference is made to any individual observer” [BCW10:128, my emphasis]. Atomic phenomena are perfectly objective because the observations of different observers agree. To Bohr, objectivity meant intersubjective agreement.³

To the proverbial person in the street, an object exists in itself, independently of how it is experienced, yet all by itself it is more or less as it is experienced. Physicists aren’t that naive or inconsistent. They will tell you that things are not as they seem.

Take, for instance, Arthur Eddington’s two tables. The first table “has extension; it is comparatively permanent; it is coloured; above all it is substantial.” The second table “is mostly emptiness. Sparsely scattered in that emptiness are numerous electric charges rushing about with great speed....” In his 1929 book,⁴ from which these quotes are taken, Eddington stated that “modern physics has by delicate test and remorseless logic assured me that my second scientific table is the only one which is really there — wherever ‘there’ may be.”

If this was progress, it wasn’t much. Heisenberg once wrote something to the effect that if microscopic objects are to explain macroscopic objects, they cannot be miniature versions of macroscopic objects. (Remember the dated model of the atom as a miniature solar system?) Heisenberg had learned from Bohr that (i) our concepts owe their meanings to a significant extent to the spatiotemporal structure of sensory experience — a point Immanuel Kant had made a century and a half earlier — and that (ii) “the facts which are revealed to us by the quantum theory ... lie outside the domain of our ordinary forms of perception’’ [BCW6:217]. By “our ordinary forms of perception” Bohr meant “the conceptual structure upon which our customary ordering of our sense-impressions depends and our customary use of language is based” [BCW10:xxxv–xxxvi].

If physical concepts — both the kinematical/descriptive ones and the dynamical/explanatory ones — depend for their meanings on the spatiotemporal structure of (human) sensory experience, and if the facts revealed to us by the quantum theory lie outside the domain of our ordinary forms of perception, then the conceptual structure on which our customary use of language is based must not be expected to be applicable to the facts which are revealed to us by the quantum theory. Therein lies the real difference between these facts and those that are accessible to direct sensory experience.

This brings us to the reason why measurement outcomes (or outcome-indicating devices) enjoy the special status accorded to them by quantum physics: they are accessible to direct sensory experience and therefore capable of being described in the language at our disposal. How outcome-indicating events are related across space and time, on the other hand, is not amenable to the familiar language of everyday discourse, nor even to the less familiar language of philosophical discourse. The only language through which we can deal with the relations between measurements is the language of statistical correlations. As to what actually happens between measurements, Ludwig Wittgenstein’s phrase applies: “Whereof one cannot speak, thereof one must be silent.” In the words of Niels Bohr:

[T]he physical content of quantum mechanics is exhausted by its power to formulate statistical laws governing observations obtained under conditions specified in plain language. [BCW10:159]

[T]he quantum-mechanical formalism … represents a purely symbolic scheme permitting only predictions … as to results obtainable under conditions specified by means of classical concepts. [BCW7:350-351]

By “classical concepts” Bohr did not mean concepts proprietary to classical physics but concepts that owe their meanings to our forms of perception.

All of this appears to exceed the comprehension of most of today’s public-facing physicists. What is worse, the incompetent pronouncements of these popular figures on philosophical matters are lapped up like manna from heaven by the public, which apparently can’t be disabused of the superstition that theoretical physics holds the key to ultimate metaphysical truth — a superstition these physicists do little to discourage.

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Today the task of making sense of quantum mechanics is seen as one of grafting a metaphysical narrative onto its mathematical formalism, in a language that is sufficiently vague philosophically to be understood by all and sundry. A crucial part of this task is to figure out how the mathematical formalism, assumed to represent the very foundation of physical reality, accounts for what happens in the laboratory and in the wider macroscopic world. Bohr, on the contrary, instead of asking how the formalism yields outcome-indicating events — a question to which there is no satisfactory answer —inquired how outcome-indicating events and their connections could be mathematically represented. The idea that the classical features of quantum measurements are sufficient for generating the mathematical formalism of quantum mechanics was developed further by others, among them Josef Jauch,⁵ Walter Franz,⁶ Asher Peres,⁷ Julian Schwinger,⁸ and last as well as least by Yours Truly.⁹

Not to put too fine a point on it, but to transmogrify a calculational tool into the foundation of physical reality is downright absurd. In fact, the very notion that there is such a thing as the quantum-mechanical wave function of the universe — which is what is generally reified — is absurd. In quantum mechanics, a wave function serves to calculate statistical correlations between possible outcomes of measurements performed either on different physical systems or (successively) on the same system, and the universe as a whole isn’t a system on which measurements can be performed. (If it were, the measurement apparatus wouldn’t belong to the physical universe, and by definition there isn’t anything physical that isn’t part of the physical universe.)

Nor does the wave function represent a physical process connecting outcome-indicating events. There are several reasons why this notion, too, is absurd, among them the fact that the wave function of a system with N degrees of freedom would “exist” or “propagate” in an N-dimensional space. (Even the wave function of a system made up of just two particles “propagates” in a 6-dimensional space, rather than between the respective positions of the particles in 3-dimensional space.) Another reason is that the time dependence of the wave function is not the dependence on time of a physical state that exists in and changes with time; the time on which a wave function depends is the time of the measurement to whose outcomes it serves to assign probabilities.

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Because I studied physics close to the beginning of the second period of metaphysical head-scratching, I knew little at the time of Bohr’s profound reflections on the relation between the knowing subject and the known world. Instead, I was duly bothered by the common-sense defying implications of Bell’s theorem. (A distinguished Princeton physicist once said: “Anybody who’s not bothered by Bell’s theorem has to have rocks in his head.” This doesn’t mean that I don’t have rocks in my head.)  Having though fairly long and fairly hard about these implications, I came to the following conclusions.

1. If (in our minds) we keep partitioning physical space, we reach a point where the distinctions we make between regions of space cease to correspond to anything in the physical world — they can no longer be objectivized (that is: they can no longer be thought of as real or objective). And much the same goes for intervals of time. The spatiotemporal differentiation of the physical world is incomplete; it doesn’t go “all the way down.”

2. By the same token, if (in our minds) we go on decomposing a physical object, we reach a point where the distinctions we make between its parts cease to correspond to anything in the physical world — they can no longer be objectivized. Eventually the parts become identical in the strong sense of numerical identity. This can also be expressed by saying that the number of “ultimate constituents” of the universe is one.

I reached the first conclusion through analyzing the two-slit experiment. Here the sixty-four-dollar question is: if, without modifying the experimental conditions, it is impossible to find out through which slit an electron went, are we allowed to assume that it went through either the left slit or the right slit?

As discussed in this post, Bohmians make this assumption. They resolve the notorious particle–wave duality by insisting that particles and waves are equally real, and this in a way that does not depend on the experimental conditions in which they are observed. In addition to classical particles (which follow definite paths and pass through definite slits), Bohmian mechanics features a modified version of the wave function, to be regarded as physically real and subsistent as particles. This “pilot wave” passes through every open slit, and it steers electrons in ways that depend on which slits are open. Bohmians belief this to be the best of all possible physical worlds, though in reality it’s the worst (assuming that it even is a possible world).

So, the right answer is, no, we aren’t allowed to assume that the electron went through either the left slit or the right slit. The electron went through both slits, not in the sense that it went through the left slit and through the right slit, but in the sense that it went through the undivided union of the two slits. The distinction we make between the two slits, or more generally between nonoverlapping regions of space, is one that the electron does not make (metaphorically speaking). But this means that space cannot be an intrinsically partitioned expanse. (If it were, its parts would exist for the electron, in which case the electron couldn’t simultaneously be in, or pass through, different parts of space.)

The differentiation of the physical world — the extent to which we are justified in regarding the physical world as objectively partitioned into nonoverlapping parts — therefore depends on the extent to which a region of space can be partitioned by a physically possible array of detectors. And this extent is limited by the uncertainty principle. This is why the differentiation of the physical world — not only with regard to space but also with regard to time — is incomplete. It does not bottom out; it does not go “all the way down.”

I reached the second conclusion by analyzing scattering experiments. What is characteristic of scattering experiments is (i) that a set of incoming particles gets transformed into a set of outgoing particles, and (ii) that it’s impossible to find out what happened between the observation of the incoming set of particles and the observation of the outgoing set of particles.

The simplest such experiment (discussed here and here) features two incoming particles and two outgoing ones. If the two incoming particles lack distinguishing characteristics, and if there is no other way to find out which incoming particle is identical with which outgoing particle, then the sixty-four-dollar question is: are we allowed to assume that a particular incoming particle is identical with a particular outgoing particle?

Quantum mechanics tells us that the answer is negative. The question “Which incoming particle is identical with which outgoing particle?” is meaningless. When we ask this question, we assume that the reason two simultaneously observed particles are two particles is not only that they are observed in different places but also that they are intrinsically distinct. This assumption was false even in classical physics, but because classical particles possess a definite position and a definite momentum at all times, it could not be falsified. But it is readily falsified by doing experiments with particles lacking distinguishing characteristics.

To avoid asking the meaningless question or making the false assumption, we have to acknowledge that what seem to us to be two intrinsically distinct things (one detected here, the other detected there) is really one and the same thing (once detected here and once detected there). Nothing therefore prevents us from taking the view that even the particle observed here with these properties and the particle observed there with those properties are not intrinsically distinct; intrinsically, they are one and the same thing. And if we go along with the notion that particles are the ultimate constituents of the physical world, then nothing stands in the way of drawing the conclusion that the number of the world’s ultimate constituents is one. (As we shall see presently, the conclusion that there is but one ultimate constituent stands, even though the notion that particles are the world’s ultimate constituents does not.)

From this, several further conclusions emerge. For I am now in a position to answer the following questions: What are we talking about when we talk about atoms and subatomic particles? They certainly aren’t like the objects of sensory experience, only smaller. And again, why is the general theoretical framework of contemporary physics a probability calculus, or why are the correlations between outcome-indicating events probabilistic? If they weren’t probabilistic, we would be back to classical physics. So why quantum physics?

To answer these questions, I introduced the concept of manifestation — needless to say, not in the new-agey sense associated with the “law of attraction.” I attributed the necessity of distinguishing between a macroscopic (or “classical”) domain and a microscopic (or “quantum”) domain to the difference between the manifested world and its manifestation. I envisioned the manifestation of the world as a progressive transition from the undifferentiated unity of a single ontological substance — as we just saw, quantum mechanics tells us that there is such a thing — to a world which allows itself to be described in the object-oriented language of classical discourse. Formless subatomic particles, non-visualizable atoms, and partly visualizable molecules mark the stages of this transition. Instead of being constituent parts of the manifested world, they play an instrumental role in its manifestation.

How best can we talk about these things, or how best can we describe the intermediate stages of the transition? Through these stages, the definiteness of classical properties and the distinguishability of classical objects is gradually realized or brought into being. My answer to this question was (and still is) that whatever is not intrinsically definite and distinguishable can only be described in terms of probability distributions over something that is intrinsically definite and distinguishable, to wit: outcome-indicating events. What is instrumental in the manifestation of the world can only be described in terms of statistical correlations between events that happen (or could happen) in the manifested world.

This goes a long way towards explaining why the general theoretical framework of contemporary physics is a probability calculus, and why the events to which it serves to assign probabilities are measurements.

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Bohr would have been pleased as punch had he lived to see Bells papers of 1964¹⁰ or any of the many “no-go” theorems subsequently published. (Bohr died in 1962.) For Bell was the first to demonstrate in experimentally testable (and subsequently tested) ways what Bohr had established on epistemological grounds, to wit: that most if not all of the descriptive or explanatory concepts at our disposal, which work so well in the macroscopic domain, fail to apply to the quantum domain.

Consider the experiment that was first proposed by Greenberger, Horne, and Zeilinger. It features tree particles A, B, C in different locations and two measurements X and Y that can be performed on each particle. How, in this setting, is it possible to make the predictions that quantum mechanics allows us to make? Specifically, how is it possible to predict the value of X(C) by measuring Y(A) and Y(B), regardless of the order in which the three measurements are made, and regardless of the distances between the three particles?

We know of two kinds of explanation. The first is a common-cause explanation, according to which the three particles are created in a state that predetermines the outcome of each of the six possible measurements. The second is a spooky-action-at-a-distance explanation, according to which the outcomes of the Y measurements performed on two of the particles determine the outcome of the X measurement performed on the third particle. While the first explanation is ruled out by quantum mechanics, the second is ruled out by the theory of relativity.

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Because classical concepts (as defined by Bohr) are inapplicable to the quantum domain, the physical properties of quantum objects are contextual: they are defined in terms of the experimental arrangements by which they are observed, and they are unequivocally attributable to quantum objects only if and only when they are observed. In fact, quantum objects themselves are contextual in that they are individuated by the experimental contexts in which they are observed.

But the measurement apparatus is needed not only to define quantum observables, quantum objects, and the properties that quantum objects can possess. By his insistence on the subjective character of observations, Bohr has also shown that the measurement apparatus is needed to indicate the actually possessed value of a quantum observable or the actually possessed property of a quantum object. But no property or value can be indicated in the absence of a sentient observer to whom it is indicated. Hence, the reason why the objects and properties that make up the manifested world (including those by which measurement outcomes are indicated) are intrinsically definite and distinguishable, is that the manifested world is an experienced world. It is manifested to us.

And this brings me to the question of who we are — we, who appear to be correctly described in two incompatible ways, as subjects that create the objective world on the basis of their sensory experiences and in accordance with human logic, and as objects that exist in it.

The way I see it, the key to this seeming paradox can be found in the philosophy of the Upanishads, which describes ultimate reality in the triple terms of Being, Consciousness, and Quality/Delight: as Being (sat) it constitutes the worlds, as Consciousness (chit) it contains them; and as pure Quality or Delight (ānanda) it throws itself into them in order to experience and express itself. If consciousness were not coequal, and ultimately identical, with being, we would have no choice but to adopt one reductionism over another, the reductionism of the materialist or the reductionism of the idealist. And if quality/delight were not the very heart of reality, this world could not be much more than a living nightmare.

During the early 1920s, Sri Aurobindo's brother Barin was doing some oil painting under the Mother's guidance. As was common practice, a small board was kept for depositing the paint left on the palette after each session. One day after Barin had finished his work, the Mother asked for the board covered with a random mix of old palette-scrapings and gave a few deft brush strokes to the center of the board. The result was this painting, to which the Mother gave the title “Divine Consciousness Emerging from the Inconscient.” She confirmed that the face was Sri Aurobindo's.

The reason I used the plural “worlds” is that our present habitation is not the only world. What sets our world apart is that it is evolutionary. This accounts for our peculiar cognitive status at this point in history. Our mental consciousness has not only evolved out of a primordial state of inconscience but also devolved from a supramental consciousness that is one with being, by a multiple exclusive concentration of consciousness. As Sri Aurobindo wrote,

In a sense, the whole of creation may be said to be a movement between two involutions, Spirit in which all is involved and out of which all evolves downward to the other pole of Matter, Matter in which also all is involved and out of which all evolves upward to the other pole of Spirit. [LD 137]

The consciousness-force (chit-tapas) at work in the world is an infinite force working under self-imposed constraints. This is why we can stop being spooked by the inexplicability of the quantum-mechanical correlations. There is no need for a mechanistic explanation of the working of an infinite force. What needs explaining is why it works under constraints, and why the constraints have the particular form that they do.

What can be inferred from the quantum correlations is that the shapes of the things we experience resolve themselves into reflexive spatial relations entertained by a single ultimate constituent. (Reflexive relations are self-relations.) If we identify this ultimately constituent with the Being that is one both with Consciousness and with Quality/Delight, and if the reason for the creation of our world was to embark on the adventure of evolution, then the well-established laws of physics can be shown to have more or less exactly the form they need to have if they are to set the stage for this adventure.¹¹

But a conscious force working under self-imposed constraints is also capable of lifting its constraints. Their purpose was to set the stage for the drama of evolution, not to direct the drama. We are actors in this drama, and if our free will is limited, it is not because it is illusory. To be sure, there is but one way in which freedom can be complete, and this is to be the sole determinant of all that goes on in the world. We are in possession of true freedom to the extent that we are not only consciously but also dynamically identified with the consciousness that is one with being. Absent this identification, our sense of being the owner of a libertarian free will is a misappropriation of a power which belongs to a deeper, subliminal self, and which often works towards goals that are at variance with our conscious intentions.

Thus, physics can make us understand how the stage for the adventure of evolution was set, but it knows nothing of the true nature of the drama’s characters, its audience, its plot, its reversals and complications, its denouement. It has nothing to say on what really matters. And since this now interests me way more than physics, I may have nothing further to say on the subject of physics.

1. W. Lamb, An operational interpretation of nonrelativistic quantum mechanics, Physics Today 22 (April 1969), 23–28.

2. Niels Bohr: Collected Works, Vols. 1–13 (1976–2008).

3. U.J. Mohrhoff, Niels Bohr, objectivity, and the irreversibility of measurements, Quantum Studies: Mathematics and Foundations 7, 373–82 (2020).

4. A.S. Eddington, The Nature of the Physical World, pp. ix–x (MacMillan, 1929).

5. J.M. Jauch, Foundations of Quantum Mechanics (Addison–Wesley. 1968).

6. W. Franz, Quantentheorie (Springer, 1971).

7. A. Peres, Quantum Theory: Concepts and Methods (Kluwer, 1995).

8. J. Schwinger, Quantum Kinematics and Dynamics (Westview Press, 1991).

9. U.J. Mohrhoff, The World According to Quantum Mechanics: Why the Laws of Physics Make Perfect Sense After All, 2nd Edition, Chapter 7 (World Scientific, 2018).

10. J.S. Bell, On the Einstein Podolsky Rosen paradox, Physics Physique Fizika 1 (3), 195–200 (1964); On the problem of hidden variables in quantum mechanics, Reviews of Modern Physics 38, 447–52 (1966). Though published after the 1964 paper, the second paper was actually written before the first.

11. U. Mohrhoff, Why the laws of physics are just so, Foundations of Physics 32, 1313–24 (2002); Quantum mechanics explained, International Journal of Quantum Information 7, 435–58 (2009); The World According to Quantum Mechanics: Why the Laws of Physics Make Perfect Sense After All, 2nd Edition, Chapter 25 (World Scientific, 2018).