The shapes of things and the thing-in-itself

Quantum mechanics and the manifestation of the world

In a recent post I discussed an experimental arrangement quite analogous to the following. It features particles of the same type, particles that lack properties by which they can be distinguished and re-identified. Initially one particle is found moving Northward and the other Southward. The next thing we know — and can know under the experimental conditions envisaged — is that one particle is found moving Eastward and the other Westward. Once again, the obvious question is: “Which incoming particle is identical with which outgoing particle?” There are two possible answers, illustrated below, and neither is correct. Once again, we are asking a meaningless question.

One strategy to avoid asking the meaningless question goes back to Schrödinger,¹ who insisted that “the ultimate constituents of matter have no ‘sameness’ at all”: “If I observe a particle here and now, and observe a similar one a moment later at a place very near the former place, not only cannot I be sure whether it is ‘the same,’ but this statement has no absolute meaning.”

Schrödinger’s strategy is supported by the following fact, pointed out in another post: every measurement is genuinely unpredictable not only with regard to its outcome (which may in fact be predictable) but also, and more significantly, with regard to its actual occurrence. There is no certainty that an attempted measurement will succeed. Redundancies built into the measurement setup can make it very likely that there will be an outcome, but there are no causally sufficient conditions that make is necessary for there to be an outcome.

The actual situation thus is the reverse of what we are disposed to believe. Not particles but clicks come first, and the clicks aren’t caused by particles. Every position-indicating event is, in the words of Ole Ulfbeck and Aage Bohr,² an event that “comes by itself, out of the blue” and is “entirely beyond law.” What is not beyond law is the statistical correlations between position-indicating events, and they are such that under suitable experimental conditions these events form tracks. This makes it permissible “for all practical purposes” to talk as if the events constituting a track did indicate the passage of a particle, and even to talk as if the events were caused by the passage of a particle, while in reality this manner of speaking is but a concession to the object-oriented language of classical discourse, as we have seen in this post.

Another strategy to avoid asking the meaningless question “Which is which?” is to affirm the numerical identity of all particles of the same type. On this view, the meaningless question arises because we assume, falsely, that initially there are two things, one moving Southward and another moving Northward, and that afterwards there are again two things, one moving Eastward and another moving Westward. If there is only one thing that initially is moving both Southward and Northward, and that afterwards is moving both Eastward and Westward, then to ask, “Which is which?” obviously doesn’t make sense.

Furthermore, the “miraculous identity of particles of the same type,” which according to the great textbook by Misner, Thorne, and Wheeler³ should be regarded as “a central mystery of physics,” need not be confined to particles of the same type. There is no compelling reason why the numerical identity of particles should cease when it ceases to have observable consequences due to the presence of identity tags (i.e., conserved properties by which they can be distinguished).⁴ We are free to take the view that a fundamental particle observed here with these properties and a fundamental particle observed there with those properties are one and the same thing. If fundamental particles are indeed the ultimate constituents of the physical world, as most physicists believe, then nothing stands in the way of the claim that the number of ultimate constituents of matter is one.

Note: A particle is called “fundamental” if it lacks internal structure, which means (in particular) that it is not composed of other particles. According to the current standard model of particles and forces, quarks and leptons are fundamental. A nucleon (proton or neutron) is often said to be composed of three quarks, though the truth of the matter is more intricate. The leptons comprise electrons and the particles known by the Greek letters μ and τ, as well as three corresponding types of neutrinos.

To convey some idea of why the truth of the matter is more intricate, it is customary to invoke a metaphor according to which particle accelerators enable one to “see” subatomic structure as through a microscope: the higher the energy of the particles used, the shorter is the wavelength used for “seeing,” and the smaller are the structures that can be “seen.” Thus, while at a certain energy the atomic nucleus “looks” as if it were made of neutrons and protons interacting by exchanging pions, a closer “look” reveals that the protons, neutrons, and pions are made of quarks and antiquarks interacting by exchanging gluons. Further increasing the energy of the particles used for “looking into” protons and neutrons increases the number of quarks, antiquarks, and gluons that are “seen.” Here is how Brigitte Falkenburg⁵ sums up the matter: “our classical construal of physical reality necessarily gives a distorted picture of subatomic structure. It simply makes us look into the atom through the wrong glasses. Unfortunately, we do not have any better tools.”

Now recall that the form of a quantum object consists of spatial relations between its component parts and thus, ultimately, of spatial relations between formless components. Let’s put two and two together: on the one hand, the shapes of things resolve themselves into spatial relations between formless constituents; and on the other hand, the ultimate constituents of matter are one. What follows is that the shapes of things resolve themselves into reflexive relations (meaning self-relations) entertained by a single Ultimate Constituent, which is formless.

Let’s set off on a different tack. In the 17th century, John Locke introduced the distinction between “primary qualities,” which were independent of the perceiving subject, and “secondary qualities,” which bore no similarity to sensations but had the power to produce sensations in the perceiving subject. In his epochal Critique of Pure Reason (1781/1787), Immanuel Kant insisted that all sensory qualities are secondary in Locke’s sense. Nothing of what we say about an object describes the object as it is in itself, independently of how it affects us. Nor does Kant stop at saying that if I see a desk, there is a thing-in-itself that has the power to appear as a desk, and if I see a chair in front of the desk, there is another thing-in-itself that has the power to appear as a chair. For Kant, there is only one thing-in-itself, an empirically inaccessible reality that has the power to affect us in such a way that we have the sensations that we do, and that we are in a position to “work up the raw material of sensible impressions into a cognition of objects”.⁶

Kant’s contemporaries and his idealistically inclined successors were quick to point out what appeared to them to be a major weakness of Kant’s philosophy. Without the presupposition that our sensations are caused by the unknowable thing-in-itself, Friedrich Jacobi wrote,⁷ “I could not find my way into the [Kantian] system, whereas with it I could not stay there.” The reason Jacobi could not stay there was that within the Kantian system causality is a relation between sense impressions, a relation which (together with the relation between substance and property) makes it possible to “work up the raw material of sensible impressions into a cognition of objects.” (For a more detailed account of how that is supposed to work see this post.) But if causality is a relation between sense impressions, then it cannot also be a relation between the thing-in-itself and sense impressions.

Kant of course could not explain how the thing-in-itself affects us (or our subconscious minds) in such a way that we (or our subconscious minds) are able to organize our sensations into a seemingly self-contained system of objects that interact and change in accordance with causal laws. But quantum mechanics can, provided that we identify the aforesaid Ultimate Constituent with the thing-in-itself, and provided that we reconceptualize the relation between it and the experienced world. In any case, it does make sense to distinguish between two kinds of causality: a causality by which the world is manifested to us, in our conscious experience, and a causality that correlates events and states of affairs within the world that is manifested to us.

The two domains

To Kant, the objectivity of science rests on the possibility of organizing our sense impressions into a self-contained system of objects, and doing so requires the use of concepts that everybody can understand because they owe their meanings to structures that are common to all: the logical or grammatical structure of thought or language and the spatiotemporal structure of human sensory experience. To Niels Bohr, on the other hand, the objectivity of science rests on the possibility of communicating “to others what we have done and what we have learned”,⁸ and this involves the use of the very same concepts. Bohr departed from Kant’s theory of science in only one respect: while Kant had assumed that the spatial resolution of human sensory experience was potentially unlimited, Bohr realized that it was limited. Beyond the domain that is directly accessible to sensory experience there lies a domain that is not — at any rate, not directly — accessible to sensory experience, which therefore cannot be expected to conform to concepts that owe their meanings to the structure of sensory experience.

To Bohr, “the physical content of quantum mechanics is exhausted by its power to formulate statistical laws governing observations obtained under conditions specified in plain language”.⁹ There are, however, ontological conclusions that can be drawn from these laws. And one of them is that the shapes of things resolve themselves into reflexive relations entertained by a single Substance.

1. Science and Humanism, in E. Schrödinger, Nature and the Greeks and Science and Humanism, pp. 103‒171 (Canto Classics, 2014).

2. O. Ulfbeck and A. Bohr, Genuine Fortuitousness. Where Did That Click Come From? Foundations of Physics 31, 757‒774 (2001).

3. C.W. Misner, K.S. Thorne, and J.A. Wheeler, Gravitation, p. 1215 (Freeman, 1973).

4. The presence of distinguishing characteristics suppresses the interference phenomena which would reveal the numerical identity. But absence of evidence is not evidence of absence, as they say.

5. B. Falkenburg, Particle Metaphysics: A Critical Account of Subatomic Reality, p. 160 (Springer, 2007).

6. I. Kant, Critique of Pure Reason, p. 136 (Cambridge University Press, 1998).

7. F.H. Jacobi, On transcendental idealism. In B. Sassen (Ed.), Kant’s Early Critics: The Empiricist Critique of the Theoretical Philosophy, pp. 169–175 (Cambridge University Press, 2000).

8. Niels Bohr: Collected Works Vol. 10, p. 128 (Elsevier, 1999); also Vol. 7, p. 349 (Elsevier, 1996) and elsewhere.

9. Niels Bohr: Collected Works Vol. 10, p. 159 (Elsevier, 1999).