BORN AND STRUCTURAL INVARIANTS

BORN AND STRUCTURAL INVARIANTS

Nevertheless, by the early 1930s the 'Received View' of quantum particles as non-individuals had propagated from specialist to more popular texts: Darwin, in his 'semi-popular' presentation of the new mechanics understands the Exclusion Principle as insisting that ". we ought not to talk about electrons as having any individuality". ¹³⁷ He notes, however, that as it stood then, the Principle was expressed in a manner that would probably come to be seen as rather clumsy: "The description consists in starting as though the electrons had full individuality, and then showing that this individuality did not matter". ¹³⁸ The idea is familiar: we first assume the electrons are individuals and can be labelled as such in constructing the wave function for the assembly and we then symmetrize à la Schrödinger, effectively denying the individuality by imposing the anti-symmetry condition. I 15115t1911p nterestingly, Darwin then offers an alternative 'rough and ready' account which avoids this clumsiness by denying the individuality of the electrons from the very start. At the heart of this account is the idea that the Exclusion Principle represents the quantum replacement of the venerable Impenetrability Assumption (as discussed in Chapter 1), with the twist that since the relevant wave functions can overlap, two electrons can be in the same place at the same time, as long as they are not "doing the same thing". ¹³⁹ If they are, then there is a kind of repulsion and the Coulomb force between electrons comes to be seen as an aspect of

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Exclusion. ¹⁴⁰ This suggestion of a connection between the Exclusion Principle and Coulomb repulsion is only the first step, however, and the goal is to arrive at a theory in which the electron, as a particle, emerges, in some sense, as a result of observation:

As far as concerns the wave aspect there will cease to be electrons at all, but only a sort of electrical juice. It will be the step from wave to particle which automatically cuts the juice into units, and thus it will be the observation that creates the electron. In some such way as this, the electrons would have no individuality from the very start, which is what we would like. ¹⁴¹

It is hard to resist the temptation to read into these remarks something like an early form of the quantum field theoretic view of particles.

We have already noted Born's advocacy of the Received View and in his 1943 defence of the role of experiment in physics, ¹⁴² he not only argues, again, that quantum particles lack individuality but emphasizes the experimental basis of this conclusion. Thus, in his outline of the development of statistical mechanics, after noting that the description of the relevant statistical weights is simpler for quantum systems than for classical ones in that ". each state of given energy which by no physical means can be split into several states has the same weight", ¹⁴³ he insists that if photons are treated as ". having an individuality of their own", ¹⁴⁴ we would not obtain Planck's (experimental) law for black-body radiation. ¹⁴⁵ Instead, he continues, we must assume ". that two states which differ only by the exchange of two photons are physically indistinguishable and have statistically to be counted only as one state. In other words, photons have no individuality". ¹⁴⁶

As extended to particles by Bose and Einstein, this assumption would have remained a 'theoretical speculation' because of the experimental difficulties in attaining the requisite conditions. However, Pauli's exclusion principle gives much more direct evidence for the "lack of individuality of particles", ¹⁴⁷ resting as it does on such 'facts of observation' ¹⁴⁸ as the non-existence of the lowest state of the helium atom as well as 'innumerable consequences' such as, and most importantly, Bohr's account of the periodic table.

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Now, Born's defence of the Received View of particle (non-) individuality is particularly significant because it is to Born, of course, that the orthodox, Copenhagen, interpretation owes its understanding of the wave function: namely as giving the probability of obtaining a given result on measurement, such as the position of an electron, say. The ontology here is that of particles and was conceived of and presented as the alternative to Schrödinger's problematic wave-based world-view. But now a tension arises within this orthodox view: if an electron, for example, can no longer be regarded as an individual, how can this particle ontology be maintained? As we shall see, Schrödinger took this tension to undermine the orthodox interpretation and invoked non-individuality to support the later development of his own view. Born himself suggested a way of removing the tension, which, although rather tentative, does bear some similarity to one aspect of Schrödinger's later interpretation.

The broadly philosophical context of Born's ideas is made explicit in subsequent reflections, delivered as a talk in 1958. ¹⁴⁹ Again Born states quite bluntly that "particles have no individuality" ¹⁵⁰ and in the very next line repeats the point about the non-classical counting. Here, however, he raises the question how we are to talk of electrons, say, as particles of a certain kind, given this lack of individuality. His answer has two features to it. The first is straightforward and involves the 'widening' of concepts, in the sense that the concept of 'number' for example, has been extended to include transcendental and imaginary numbers. The justification for this extension lies in the fact that some subset of relevant properties is shared. And so, "[w]e call an electron an elementary 'particle' because it has many, even if not all, of the properties particles exhibit in the tangible world". ¹⁵¹

The second feature is more significant and concerns the ontological nature of particles, as things which are not individuals yet can be said to 'have' properties, and here an interesting structuralist element emerges. He begins with an analysis of the trans-temporal identity of perceptible objects, such as a bird or a dog, and drawing on both Gestalt psychology and then current research in the physiology of perception, argues that what we are 'given' are not separate sense impressions-as the positivists believed-but rather 'certain invariant characteristics' of these impressions, which we then describe as 'objects'. ¹⁵² Moving along the epistemological spectrum to the unobservable, we again

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seek for 'invariant traits' but now they must be revealed through mathematical analysis: ¹⁵³

The properties of the postulated physical reality, which are independent of the reference system, are the invariants which can be obtained by the analysis of coordinates or projections. ¹⁵⁴

Reality is 'projected' via experiments, in general, and in the quantum context, by complementary experiments in particular. By making such complementary experiments we can obtain 'sets of invariant magnitude' which allows us to talk of electrons, protons etc. as particles of a certain kind. Thus objectivity in quantum physics is grounded not in an ontology of individual objects but in one of structural invariants. ¹⁵⁵

It is not difficult to find other expressions of the Received View during this period, particular in popular expositions where physicists felt they could 'cut loose' philosophically, or historically. Oppenheimer, for instance, noted how the modern notion of 'elementary particle' deviates from earlier understandings with respect to both elementarity and identity:

We are continuing the attempt to discover, to identify and characterize, and surely ultimately to order, our knowledge of what the elementary particles of physics really are. I need hardly say that in the course of this we are learning again how far our notion of elementarity, of what makes a particle elementary, is from the early atomic ideas of the Hindu and Greek atomists, or even from the chemical atomists of a century ago. We are finding out that what we are forced to call elementary particles retain neither permanence nor identity, and they are elementary only in the sense that their properties cannot be understood by breaking them down into subcomponents. ¹⁵⁶

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