8 Particles

If the properties of the microworld are what they are because of what happens or is the case in the macroworld, rather than the other way around, then we cannot think of particles, atoms, and such as the constituents of the macroworld. Then what constitutes the macroworld? And what is a particle if it is not a constituent of the macroworld?

All we can know about particles is what we can infer from correlations between “detector clicks.” If we perform a series of position measurements, and if every position measurement yields exactly one outcome (that is, each time exactly one detector responds), then we are entitled to infer the existence of an entity O which persists in time. Things get more involved as soon as each time exactly two detectors click. Can we infer from this the existence of two persistent entities?

Previously we raised a similar question and concluded that we cannot. We calculated the probability with which two indistinguishable particles scatter at right angles, and we found that the question “which of the incoming particles is identical with which of the outgoing particles?” has no answer. But a question that has no answer is meaningless.

Here as elsewhere, the challenge is to learn to think in ways that do not lead to meaningless questions. Meaningless questions arise from wrong assumptions. The question “Which is which?” arises because we assume that initially there are two things, one moving northward and one moving southward, that in the end there are two things, one moving eastward and one moving westward, and that each of these things remains identical with itself.

What if we assumed instead that initially there is one thing moving both northward and southward, and that in the end there is one thing moving both eastward and westward? Startling though this assumption may be, it has this advantage that the meaningless question “Which is which?” can no longer be asked. At the same time it is the conclusion our interpretational strategy requires us to draw, for under the conditions stipulated by Rule B it implies that the distinction we make between alternatives does not correspond to anything in the actual world.

Thus if each time two detectors click, and if the question “Which of the particles detected earlier is identical with which of the particles detected later?” lacks an answer, we are in the presence of a single entity with the property of being in two places whenever we check — not a system “made up” of two things but a single thing with the property of being in two places every time a position measurement is made.

When I asked you to imagine two (exactly similar) objects in two (different) places, I used the word “two” once too often, for if in front of you there was what looks like two exactly similar objects, it would actually be one and the same object in different places. It is, however, virtually impossible to create two objects that are exactly similar if they are bigger or more complex than an atom or molecule. With such objects the conditions stipulated by Rule B are never satisfied. It is likewise virtually impossible to sufficiently isolate all but the smallest objects from the rest of the world. If light of a certain wavelength falls on an object, the reflected light makes it possible to discover the object’s location to within a wavelength. In the darkest corner of the universe, were the only light is the cosmic microwave background radiation, an object would still reflect light of wavelengths in the millimeter range, and this would make it possible to pinpoint the object’s location to within a few millimeters or less. For any two objects larger than this, it will therefore always be possible to trace their respective trajectories with sufficient precision to tell which is which.

Since, before quantum mechanics, it seemed always possible to keep track of the identities of objects, it seemed always possible to associate with each object a distinct substance. But this was completely unwarranted, for what accounted for the apparent distinguishability of things was the distinguishability of their positions rather than their being (let alone their being made of) distinct substances. Individuality is strictly matter of properties (not counting such gimmicks as the property of being “this very object”).

Hence if there is a substance (that is, if the word “substance” is of any use), there is exactly one substance. Quantum mechanics does not permit us to interpose a multitude of distinct substances between this one substance and the multitude of existing (“possessed”) positions or the multitude of existing (“possessed”) bundles of properties. A physical system, accordingly, is not made of component systems or constituent parts. The number of its so-called components or constituent parts is merely one of its properties. Whereas in a non-relativistic context this property is constant, in a relativistic setting it can come out different every time it is measured. Hence if we permit ourselves to think of the physical universe as a quantum system and to ask about the number of its constituent substances, there is just one. The rest is properties. Quantum mechanics therefore lends unstinting support to the central idea of all truly monistic ontologies: ultimately there is only one substance.

We arrive at the same conclusion if we consider a fundamental particle “by itself,” out of relation to anything else. What can we say about it? Apart from pointing out that it lacks a form, and that space does not contain it, the plain and simple answer is: nothing. For the properties that are attributable to fundamental particles are either relational, like positions and momenta, or characteristic of interactions, like coupling parameters (charges), or they have objective significance independent of conventions only as dimensionless ratios, like mass ratios. They all involve more than one particle.

According to a philosophical principle known as the Identity of Indiscernibles, what appears to be two things A and B is actually one and the same thing just in case there is no difference between A and B. Although there is nothing so obvious that a philosopher cannot be found to deny it, this principle strikes me as self-evident. If true, it implies that all fundamental particles considered by themselves, out of relation to anything else, are identical in the strong sense of numerical identity. (Numerical identity contrasts with qualitative identity or exact similarity. Examples of numerical identity are (i) the evening star and the morning star, (ii) Clark Kent and Superman.)

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