THE IMPACT OF QUANTUM STATISTICS: QUANTUM NON-INDIVIDUALITY
As we have seen, it was perceived quite early in the history of quantum mechanics that quantum statistics raised a number of fundamental issues regarding the nature of the quanta and their independence. With the formalization in terms of symmetric and anti-symmetric state functions, these issues could no longer be avoided. Thus, in 1926, Born, while defending the corp 15215w2216p uscular as opposed to wave-like conception, acknowledged that these corpuscles could not be identified as individuals. 84 Likewise, Heisenberg noted, in the same year, that Einstein's theory of the ideal quantum gas implies that the "individuality of the corpuscle is lost". 85 Shortly after, Weyl, in his typically evocative fashion, wrote that,
. the possibility that one of the identical twins Mike and Ike is in the quantum state E 1 and the other in the quantum state E 2 does not include two differentiable cases which are permuted on permuting Mike and Ike; it is impossible for either of these individuals to retain his identity so that one of them will always be able to say 'I'm Mike' and the other 'I'm Ike.' Even in principle one cannot demand an alibi of an electron! 86
This understanding of what the new quantum statistics apparently implied-that quantum particles have in some sense lost their identity and cannot be regarded as individuals-was so ubiquitous that we shall refer to it as the 'Received View' of particle (non-) individuality.
That this view sits at the heart of attempts to come to grips with the new physics can be seen if one takes a look at the proceedings of the Solvay Conference of 1927 at which the 'Copenhagen Interpretation' effectively came to be cemented into place. 87 There we find Langevin, for example, commenting on the difference between the 'old' and 'new' statistics. 88 With regard to the former, he highlights the essential role played by the supposition of the individuality of the constituents of the system, 89 but then notes that, in the new statistics, this individuality of the constituent particles must be abandoned, to be substituted by the individuality of the 'states of movement'. If whatever number of 'constituents' are allowed to occupy a single such state one obtains Bose-Einstein statistics and if only one particle can occupy a state, Fermi-Dirac statistics results. 90 A further distinction can then be established between photons and material particles in that the latter, but not the former, are 'impenetrable'. 91 In either case, however, what this new 'mode of representation' implies is that by virtue of being completely identical (or indistinguishable in our terms), individuality cannot be attributed to the particles themselves, but only to the states of motion. 92 This point, that the loss of individuality of the particles was accompanied by an attribution of individuality to the states, was also emphasized by Schrödinger, as we shall see.
Consideration of these issues is not restricted to
commentaries on the nature of the new physics but also arises in the context of
its applications. One of the most significant was Heitler and
end p.105
homopolar, bond in terms of
anti-symmetric wave functions. 93 It was clear that the
attraction between two hydrogen atoms could not be accounted for in terms of
Coulomb forces. The solution to the problem lay with the non-classical exchange
integral, introduced by Heisenberg in the work recorded above. The
understanding of this concept underwent a shift from the idea of a literal
exchange of electrons to the perception that its basis lies in the
non-classical indistinguishability of the electrons. 94 Heitler
and
Several years later, in his analysis of what has come to be
known as the 'measurement problem', co-authored with Bauer and written with the
intention of rendering von Neumann's classic work accessible to physicists, 97
London insisted that although we can attribute pure states to those
particles which have been prepared using a suitable measurement arrangement, we
cannot know which atoms have the property in question since the preparation
never puts any individual object into a new pure state. Thus, our attribution
of the pure state is bought at the cost of the individuality of the object,
which remains absolutely 'anonymous'. 98 As we shall see in
subsequent chapters, this notion of the anonymity of quantum particles crops up
again in recent philosophical discussions of individuality in quantum
mechanics. According to
end p.106
measurements are not to do with the properties of individual systems but rather with general properties of species of systems. They conclude:
Quantum mechanics, truly a 'theory of species', is perfectly adapted to this experimental task. But given that every measurement contains a macroscopic process, unique and separate, we can hardly escape asking ourselves to what extent and within what limits the everyday concept of an individual object is still recognizable in quantum mechanics. 99
This latter question was addressed by Bohr and we can see in
these remarks by
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