Quantum Physics and Integral Knowledge

Transcription

1 Quantum Physics and Integral Knowledge Ulrich Mohrhoff Presented at the International Seminar on Integral Paradigm and Other Approaches to Knowledge, Organized by University of Human Unity, Auroville, January 5 8, 2012 Abstract While science uses a conceptual framework that formulates questions and interprets answers, the question whether this is the right framework, or even what the criteria for rightness are, cannot be determined by its methods. Making sense of quantum mechanics is particularly challenging. The attempt to interpret its formalism in a materialistic framework of thought has had disastrous results. While the majority of physicists have therefore given up on making sense of the theory, New Agers have made matters worse by latching onto a materialistic interpretation and coating it with a spiritual veneer. In this presentation I will explain (in outline) how quantum mechanics in its entirety follows from the fundamental affirmations of the integral framework of thought due to Sri Aurobindo. I will then show (in outline) that the theory itself suggests a spiritual interpretation, which is very different from that peddled by New Agers, and which cannot be found if one accepts a materialistically prejudged version of the theory as one s starting point. 1 Preamble Science presupposes a conceptual framework in which questions are formulated and answers interpreted. Whether this framework is the right framework, or even what the criteria for rightness are, cannot be decided by the methods of science. Making sense of quantum mechanics is particularly challenging. Here are testimonies by three well-known physicists: It is safe to say that no one understands quantum mechanics (Richard Feynman). It is often stated that of all the theories proposed in this century, the silliest is quantum theory (Michio Kaku). The one thing that can be said against [the theory] is that it makes absolutely no sense (Sir Roger Penrose). It seems to me that the sentiments expressed here highlight the difficulty of making sense of quantum mechanics within a materialistic framework of thought. The conceptual framework I shall adopt is indebted to Sri Aurobindo s integral idealism. By showing in 1

2 outline how the validity of quantum mechanics is actually implied by this framework, I hope to be able to convey to you why the theory has the form that it does, and what it is trying to tell us about our world. 2 Conceptual framework There is an Ultimate Reality call it Brahman, Sachchidānanda, the Divine, whatever. Intrinsically ineffable, this Ultimate Reality relates to the world in a threefold manner: 1. as substance (Sanskrit: sat), it constitutes the world, 2. as consciousness (Sanskrit: chit), it contains the world, 3. as an infinite bliss/quality/value (Sanskrit: ānanda), it expresses and experiences itself in the world. The particular world in which we live is special in that it is evolutionary. Evolution presupposes involution: supermind in mind, mind in life, life in matter. Supermind is the consciousness-force (Sanskrit: chit-tapas) by which Sachchidānanda manifests the world. Its action is primarily qualitative and infinite and only secondarily quantitative and finite. Essentially, mind is this secondary, limiting and dividing action. Sachchidānanda adopts several poises of relation between self and world. In the primary poise (vijñāna), there is but one self. This is coextensive with the world and identical with the substance that constitutes the world. In the secondary poise (prajñāna), the single self adopts multiple viewpoints within the content of its consciousness. Through a multiple concentration, it acquires the aspect of a multitude of situated selves. In a further poise, the multiple concentration becomes exclusive. The result is a multitude of seemingly separate selves. Supermind is now involved in mind. Involution can be carried farther. To indicate the main steps, it helps to subdivide the process of creation the emergence of finite forms out of infinite quality into successive stages: infinite quality expressive idea executive force finite form. In the secondary poise, prior to involution, the individual s self-awareness is centered in its particular infinite quality (svabhāva). Once supermind is involved in mind, the consciousness of the individual is situated at the level of mind, concerned with the formation of ideas, while the qualities these serve to express are subliminally supplied. A veil of Ignorance (with a capital I, avidya) has fallen between infinite quality and the realm of expressive ideas. 2

3 Next comes a poise in which the veil of Ignorance has fallen between the realm of expressive ideas and the executive force. As a result, mind is involved in life. Next comes a poise in which the veil of Ignorance has fallen between the executive force and the finite forms it creates and sustains. Although life is now involved in matter, finite forms may retain their ability to manifest beauty, as they do in a subtle physical world. But if involution is carried to its absolute extreme, the executive force at work in the individual ceases. And since this is responsible for the existence of individual forms, what results is a multitude of formless individuals, the so-called fundamental particles of physics. The stage for the drama of evolution has been set. 3 A probability calculus Evolution is not simply a reversal of involution. A particle does not turn into an organism. Evolution begins with the formation of structured aggregates. And here we face a problem. If life is to manifest itself, we need objects that occupy space and have forms. How to create such an object out of a finite (or even a countably infinite) number of particles that, individually, occupy no space? We need an attractive force to bind the particles together, but we also need something to prevent them from sitting right on top of each other. The trick is to let both the positions and the momenta of the particles be indefinite or fuzzy. The attraction between the particles causes the fuzziness of their positions to decrease. The fuzziness of their momenta, on the contrary, causes the fuzziness of their positions to increase. The existence of stable composite objects is made possible by an equilibrium between these two tendencies. But the equilibrium must also be stable, and for this we need Heisenberg s uncertainty relations although uncertainty is not quite the right word, for what fluffs out matter is not our subjective uncertainty about the values of positions and momenta but the objective indefiniteness or fuzziness of these observables. What then is the proper way of dealing with a fuzzy quantity? It is to assign probabilities to the possible outcomes of a measurement of this quantity. This is the principal reason why quantum mechanics is a probability calculus, and why the events to which it serves to assign probabilities are measurement outcomes. Probabilistic predictions can be made for two reasons. In classical physics we resort to probabilities because of a lack of knowledge a subjective uncertainty. Quantummechanical probabilities, by contrast, arise from an objective indeterminacy. If we start with the probability calculus of classical physics and take this into account, we arrive at the 3

4 probability calculus of quantum physics via a minimal, straightforward extension of the former. Quantum systems are thus described by probability algorithms in general density operators, in special cases state vectors or wave functions. You may think of them as computing machines with inputs and outputs. Insert the times and outcomes of measurements that have been made, insert the time and the possible outcomes of a subsequent measurement, and out pop the probabilities of those outcomes. While the fundamental theoretical framework of contemporary physics tells us how the probabilities of possible measurements outcomes depend on actual measurement outcomes, it offers no clue to how by what mechanism of process measurement outcomes determine the probabilities of measurement outcomes. This worries some, but it should not come as a surprise to us. If the force at work in the world is an infinite force, there is no need for any mechanism or physical process to explain how nature does it. If this force works under self-imposed constraints, as it obviously does, we need to know why namely, in order to set the stage for the adventure of evolution and we need to know why the constraints have the particular form that they do namely, for the same reason. 4 One substance Let us now apply the quantum-mechanical probability calculus to a couple of key experiments. Consider a physical system consisting of two parts. Suppose that initially each part is subjected to a measurement, with respective outcomes A and B, and that at a later time each part is again subjected to a measurement, with respective outcomes C and D. To make this more concrete, let s say that initially we find two things, one in region A and one in region B, and at a later time we find the same two things, one in region C and one in region D. Now which is which? Is the thing in C identical with the one that was in A? Or is it identical with the one that was in B? There has to be an answer, right? Well, there is an answer if the two things carry identity tags properties that make it possible to identify them across time. Whenever the two things are sufficiently large or complex, this is the case. But if they do not carry identity tags, then there also is no answer. Assuming otherwise leads to false predictions. It is customary to dismiss unanswerable questions as meaningless. But meaningless questions often arise from false assumptions, and it is surely worthwhile to identify the false assumptions that give rise to meaningless questions. 4

5 In the present case the meaningless question arises because we take it for granted that initially there are two things, one in region A and one in region B, and that later there are again two things, one in region C and one in region D. The meaningless question Which is which? would not arise if we assumed instead that initially there is one thing present simultaneously in region A and region B, and that later there is the same thing present simultaneously in region C and region D. Let me ask a different question, one that has been debated for centuries. Suppose that in front of you there are two exactly similar objects. The only difference between them is that they are in different places. Is the fact that they are in different places the only reason why they are two objects, or is there another reason? If it is the only reason, then what there is in front of you is actually one and the same object in two places. To dodge this conclusion, it has been argued that the properties of objects belong to substances, and that the two objects are different not only because they are in different places but also because they are different substances. But how can one substance by itself, regardless of its properties differ from another? (I am referring here to a philosophical concept of substance that goes back to Aristotle. While, according to Aristotle, a property is anything in the world that can become the predicate in a sentence composed of a subject and predicate, a substance is anything in the world that can become the subject in such a sentence but not the predicate. The metaphysical relation between substance and property thus is a projection into the world of the fundamental grammatical relation between a subject and a predicate. Another idea is implicit in this concept. A property does not exist by itself. It exists if and only if it belongs to a substance. Substance therefore also connotes the idea of independent existence: it exists by itself, rather than being the property of something else.) Quantum mechanics has finally settled the question. Ultimately there is only one substance sat. Beginning its descent towards involution, the One becomes Many by assuming a multitude of properties, including different positions. Completing their descent into involution, the Many become again One by losing their differences. Some multiplicity remains, but it is neither a multiplicity of substances nor a multiplicity of properties but a multiplicity of relations. What remains is a multitude of spatial relations between the One and the One. The positions of particles relative to particles are self-relations of the One. You may, if you wish, think of the result of involution as the One turning itself inside out. Insofar as they are self-relations, relative positions between particles are internal to the One. To the extent that the particles are (or appear to be) separate individuals, their relative positions are external to them. But doesn t an electron differ from a neutrino or a quark? Not really, for the properties by which we characterize fundamental particles tell us nothing about what a particle is by 5

6 itself. They specify either of two things: relations between particles (such as relative positions or mass ratios) or the manner in which particles interact with particles (such as the various types of charge). 5 Two slits The famous two-slit experiment next. Particles are launched, one at a time, in front of a plate that contains two slits. They are detected, again one at a time, at a screen behind the slit plate. Pick any one particle and ask: through which slit did it go, the left slit (L) or the right slit (R)? There is an answer only if an answer is indicated by a measurement. If the answer is not indicated by any measurement, then there also is no answer. Assuming otherwise once again leads to false predictions. Since the particle has passed the slit plate without going through a particular slit, it must have gone through both slits. But how is that possible? It would indeed be impossible if L and R were different parts of space. Since it is, in fact, possible, L and R cannot be different parts of space and, by implication, space cannot be something that has parts. We are inclined to think that L and R are different. But how are they different? They are cutouts in a slit plate things that have been removed. What difference do they leave behind once they have been removed? The difference between the positions they previously occupied? But positions are not things; they are properties. And properties do not exist by themselves; they exist as and when they are possessed. We in fact readily agree that red, round, or a smile cannot exist without a red or round object or a smiling face, the Cheshire cat notwithstanding. Yet we appear to be just as ready to believe that positions exist by themselves, without being possessed. Quantum mechanics tells us that there we are wrong, and Sri Aurobindo tells us why, as we shall see in a moment. As said, the question Through which slit did the particle go? has an answer only if an answer is indicated by a measurement. For this to be the case, the setup must include two detectors, one for each slit: if the left detector clicks, the particle went through L; if the right detector clicks, the particle went through R. But indicating the slit through which the particle went is not the only function these detectors fulfil. Since in their absence the two slits form an undivided whole, it also falls to the detectors to make the slits distinct, to realize them as separate regions. Speaking in more general terms, measurement apparatuses are needed not only to indicate outcomes but also, and in the first place, to define the questions that can be asked, by making available the possible answers. Thus by realizing (or manifesting) a particular region of space, a detector makes it possible to attribute to an object the property of being in that region. 6

7 6 Top-down rather than bottom-up No material object ever has a sharp position relative to any other object, or so the quantum mechanical probability calculus implies. Even the positions of detectors are fuzzy. We can therefore conceive of a partition of space into finite regions so small that none of them is realized by a detector. None of them, therefore, exists. This leads to the conclusion that the spatial differentiation of the world is incomplete it does not go all the way down. For at least twenty-five centuries, physicists or their predecessors have tried to model reality from the bottom up either on the basis of an intrinsically and completely differentiated space or spacetime, or out of ultimate building blocks. Quantum mechanics tells us that this approach is doomed. Recall: If we go on dividing material objects, they lose their differences, and along with that their separate individualities. And if we conceptually partition the world into smaller and smaller regions, we reach a point where the distinctions we make between regions no longer correspond to anything in the world. The so-called ultimate constituents of matter end up being numerically identical, and space ends up being an undifferentiated expanse. (Clark Kent and Superman are numerical identical; they are the same person.) The explanatory arrow of quantum mechanics thus points the other way: not from an original multiplicity to a semblance of unity but from a genuine unity to an apparent multitude. It tells us how the One becomes many by entering into spatial relations with itself and how form comes into being. After the plunge into involution, which ends with a multitude of formless particles, forms re-appear through aggregation first as forms that can be visualized only as mathematical abstractions, like the forms of atoms, then as partly visualizable forms, like the nuclear skeletons of molecules, and finally as wholly visualizable forms, like those in the familiar macroscopic world. 7 The macroworld The incomplete spatial differentiation of the physical world helps solve a conundrum that has beset quantum theory from the start the so-called measurement problem. A region of space must be realized made real, made to exist by something equivalent to a macroscopic detector if the property of being in that region is to be attributable to a microscopic object. Accordingly, microscopic objects have positions only if, and only to the extent that, their positions are measured, whereas the positions of macroscopic objects exist by themselves, without needing to be measured. So where does one draw the line? What accounts for the difference? How can we define macroscopic objects so as to rigorously distinguish them from microscopic ones without denying that both kinds of objects are subject to the quantum laws? 7

8 The problem is this: Given nothing but a probability calculus that correlates measurement outcomes, we have to synthesize a model of a world that contains measurement outcomes but whose existence is independent of measurement outcomes. As said, the solution hinges on the fact that the spatial aspect of the physical world is not differentiated all the way down. This implies the existence of objects whose trajectories are only counterfactually fuzzy: their trajectories would be fuzzy if there were a sufficiently differentiated spatial background. In actual fact, their positions are fuzzy only against an imaginary spatial background that is more differentiated than the actual world. Their positions therefore behave in accordance with the laws of both classical and quantum physics. The behavior of macroscopic positions agrees with both the predictions of the probability calculus of classical physics and the predictions of the probability calculus of quantum physics (except when a macroscopic position serves to indicate the outcome of a measurement performed on a microscopic system). 8 Manifestation While macroscopic objects are in some sense made of microscopic ones, it is also true that microscopic objects can only be described in terms of what happens or is the case in the macroworld, properly defined. This apparent circularity has occasionally been remarked upon, but it has never been adequately appreciated. We can clear up this mystery if we recall that the explanatory arrow of quantum mechanics points from unity to multiplicity. What the theory essentially tell us is how the world is manifested. The macroworld is the manifested world (or else an important aspect of it). The microworld extends from the one Ultimate Reality to the manifested world. On this path we encounter formless and numerically identical particles, non-visualizable atoms, and partly visualizable molecules, which, rather than being the world s constituent parts or structures, are instrumental in its manifestation. Since manifestation is a progressive differentiation of the undifferentiated, what is instrumental in the world s manifestation is to varying degrees indefinite and indistinguishable. But in order to describe, with mathematical rigor, the indefinite and indistinguishable, we have to resort to probability distributions over events that are definite and distinguishable, and such events only exist in the macroworld. In other words, what is instrumental in the world s manifestation can only be described in terms of the finished product, the manifested world. 8

9 9 Materialistic versus spiritual Recall now that the action of the supermind is primarily qualitative and infinite, and that mind, in its essence, is the supermind s secondary, quantitative, and finite action. Mind limits and divides. When mind is employed by supermind, it is used judiciously. Its tendency to divide ad infinitum is checked. This is why there are limits to the objective reality of the distinctions we make. But when mind is effectively separated from its supramental parent and left to run wild, as it is in us, it not only divides ad infinitum but also tends to take the resulting multiplicity for the original truth or fact. This is why we attempt to construct reality from the bottom up, on the foundation of an intrinsically and completely differentiated space or space-time, or out of a multitude of intrinsically distinct individuals. It is also why mind, when separated from its parent consciousness, is by default reductionistic and materialistic, for what I mean by materialistic is to take the multiplicity of things as fundamental, and to model reality from the bottom up. What I mean by spiritual, accordingly, is to take unity and identity as fundamental, and to model reality from the top down. As far as the ontological roles played by quality and value are concerned, this makes all the difference. In a materialistically conceived world, quality and value are strangers if not outcasts. To that which ultimately exists on this view a multitude of valueless particles or points various traditions have fittingly referred as dust. A spiritual world view like the Aurobindonian, on the other hand, places quality and value are the very heart of reality; their origin is the ānanda that expresses and experiences itself in the world. It is present, though involved, in every particle of matter, because every particle of matter is the one Ultimate Reality. 10 Quantum nonsense In the early 19th Century, mathematics was taken over by Cantorian set theory, and since then physicists, with negligible exceptions, think of space as a set of points, which is to say, as differentiated intrinsically and all the way down. Positions, which exist only if they are possessed by, or can be attributed to, objects, became the constituents of space. When it comes to making physical sense of the mathematical formalism of quantum mechanics, the consequences of this way of thinking have been disastrous. It has made it impossible 9

10 to discern the undifferentiated unity of space to understand why a particle can simultaneously pass through different slits to conceive of the objective fuzziness of positions and other observables to see that the physical world is structure from the top down but not all the way down and to comprehend the reason why the mathematical formalism of quantum mechanics is a probability calculus. Instead, this way of thinking has created a number of pseudo-problems, foremost among them the problem of what causes wave functions to collapse. The crucial question here concerns the time on which the wave function depends. In every possible test of the theory, the time that is plugged into the wave function is the time of a measurement. Wave functions and more generally, quantum states tell us nothing about what happens or is the case at other times, which is to say, between measurements. (Insofar as an interpretation of quantum mechanics tells us what happens between measurements, it is not even wrong to use Wolfgang Pauli s felicitous phrase, since we can prove it neither right nor wrong. But then, to quote Bertrand Russell, there is much pleasure to be gained from useless knowledge. ) On the other hand, if space is differentiated all the way down, then so is time. And if time is differentiated all the way down, then the wave function s dependence on time is the timedependence of an evolving state of some kind. And if that is the case, this state not only evolves but has two modes of evolution: (i) between measurements, wave functions change continuously and predictably; (ii) at the time of a measurement, they change discontinuously and unpredictably they collapse. Hence the mother of all quantum-mechanical pseudo-questions: what bestows on measurements the power to collapse wave functions? Under the influence of the positivism of the late 19th and early 20th Century, measurements had come to be called observations, and with the advent of the special theory of relativity, reference frames had come to be called observers. Thus when quantum mechanics arrived on the scene, there was a ready answer to this question: the collapse of the wave function is caused by the consciousness of an observer. Although it is but a gratuitous solution to a pseudo-problem, this story now seems to be part and parcel of the New Age canon. For the technical details see Ulrich Mohrhoff, The World According to Quantum Mechanics: Why the Laws of Physics Make Perfect Sense After All, World Scientific,