BOHR'S VIEW OF PARTICLE INDIVIDUALITY
Bohr first mentioned his doctrine of 'complementarity' in an
early draft of his famous talk at
end p.107
exclusive but complementary aspects of the situation. 103 Let us consider what he meant by this assumption, in particular.
Bohr begins the substantive part of his paper (the version which was published in the proceedings of the conference) with a characterization of 'individuality' in terms of the 'essential discontinuity' of quantum mechanics:
Notwithstanding the difficulties which hence are involved in the formulation of the quantum theory, it seems, as we shall see, that its essence may be expressed in the so-called quantum postulate, which to any atomic process attributes an essential discontinuity or rather individuality, completely foreign to the classical theories and symb 22122h72w olised by Planck's quantum of action. 104
Bohr understood this postulate in terms of the unavoidable disturbance of atomic phenomena by an act of observation. This leads directly to the complementarity of space-time and causal descriptions, since to define the state of the system requires the absence of disturbance, but then "any possibility of observation is excluded". 105 If observation is allowed, then the interactions involved prevent us from giving an unambiguous definition of the state and "there can be no question of causality in the ordinary sense of the word". 106 Thus Bohr regarded his doctrine of complementarity as following from the quantum postulate which embodies the 'essential' individuality in the above sense of a fundamental discontinuity. However, there is more to his account than just this and it is more directly relevant to the theme of the present chapter.
Bohr continues by exploring this view in the context of the quantum analysis of the nature of light and material particles. Significantly, with regard to the latter he emphasizes that "[t]he individuality of the elementary electrical corpuscles is forced upon us by general evidence". 107 What he is referring
end p.108
to here is the sort of thing one sees on a scintillation screen for example: discrete flashes of light that lead one to suppose-given the classical metaphysics within which one is operating-that what is causing those flashes are individual particles, where individuality is to be understood in terms of Space-Time Individuality, as what the flashes indicate is the spatio-temporal location of the particles. Again, we shall return to this sense of evidentially based individuality in subsequent chapters. Nevertheless, Bohr acknowledges, there is also evidence-concerning the reflection of electrons, for example-which requires the use of " . the wave theoretical superposition principle in accordance with the original idea of L. de Broglie". 108 Hence the evidence presents us with a dilemma, which is resolved by accepting that what we are dealing with here are 'complementary pictures' of the phenomena. Furthermore,
. it must be kept in mind, that according to the view taken above, radiation in free space as well as isolated material particles are abstractions, their properties on the quantum theory being observable and definable only through their interactions with other systems. Nevertheless these abstractions are . indispensable for a description of experience in connexion with our ordinary space-time view. 109
These twin themes-of the complementarity between superpositon and individuality and the nature of both as essential abstractions-are returned to again and again in this work. 110
The final passage of this paper is particularly interesting with regard to our history of quantum statistics. Here Bohr records the introduction of the spin, or 'magnetic moment', of the electron which, together with Heisenberg's 'resonance' analysis of multi-electron atoms, have 'brought to completion' an understanding of both atomic spectra and the periodic table. 111 However, he notes, the 'intimate connection' between the Pauli Exclusion Principle and this understanding excludes the hope of an elucidation of the difference between the statistical behaviour of electrons and that of light quanta, that is, of the difference between Fermi-Dirac and Bose-Einstein statistics. This point is repeated in the version of the paper published in Nature, but, interestingly, there Bohr refers to " . the 'individuals' symbolised through the conception of light quanta" 112 and also notes that with regard to the 'recent development of statistical theories', the Exclusion Principle is just one among several possibilities.
An even more explicit reference to the new quantum statistics can be found in the published version of Bohr's 1930 address to the Chemical Society upon being awarded the Faraday Medal. 113 Thus he discusses the role of 'the so-called quantum statistics' 114 in explaining the spectra of molecules consisting of two 'identical' atoms and notes that for helium molecules, as for light quanta, the wave function must be symmetrical. Nevertheless, there is a crucial difference between photons and helium nuclei in that, in the former case, the statistics reduces in the limit to the classical treatment of electromagnetism, whereas in the latter, " . the new quantum statistics find no unambiguous application within the scope of ordinary statistical mechanics in which the existence of the action quantum is neglected and the particles are treated as individual dynamical entities". 115 Again, as with quantum notions in general, these new statistics have an "essentially non-visualisable character". 116
This non-classical aspect of the new statistics is then explicitly related to issues of identity in the context of the problem of β-decay: straightforward application of conservation of energy implies a variation in the mass of nuclei corresponding to the same radioelement. 117 Yet such a variation is ruled
end p.110
out on the grounds, among others, that the nuclei obey quantum statistics, which means that nuclei of the same kind (possessing the same charge and mass) " . are not to be regarded as approximately equal, but as essentially identical". 118 Furthermore, Bohr writes, "[t]his conclusion is the more important for our argument, because, in the absence of any theory of the intra-nuclear electrons, 119 the identity under consideration is in no way a consequence of quantum mechanics, like the identity of the extra-nuclear electronic configurations of all atoms of an element in a given stationary state, but represents a new fundamental feature of atomic stability". 120
How does this discussion of particle identity relate to Bohr's consideration of the notion of individuality in his presentation of complementarity? The latter notion is understood, at its most fundamental level, in terms of both discontinuity and unity, which hold for both processes and particles. 121 As applied to the former, this individuality is represented by the quantum of action which gives rise to a profoundly non-classical sense of discontinuity and indivisibility in the sense that every change of state of an atom, for example, should be regarded as an individual process which cannot be subjected to a more detailed description. 122 It was this sense of individuality which Bohr took up in subsequent discussions and carried into the debate with Einstein. 123 As applied to particles, it was to be understood likewise in terms of discontinuity, in the sense that a particle can be contrasted with a wave, and a fundamental kind of unity. It is interesting that with regard to the latter, Bohr draws an
end p.111
analogy with the individuality of persons:
. the apparent contrast between the continual onward flow of associative thinking and the preservation of the unity of the personality exhibits a suggestive analogy with the relation between the wave description of the motions of material particles, governed by the superposition principle, and their indestructible individuality. 124
This understanding of individuality allowed Bohr to talk of
'individual' light quanta, even though such quanta obey non-classical
statistics, as we have seen. It is also worth noting his emphasis that this
form of individuality is indestructible. In the 'introductory survey' to the
above volume he notes the fundamental dilemma presented by the experimental
confirmation of de Broglie's wave theory: that although matter may exhibit
wave-like characteristics, ". there can be no question of giving up the idea of
individuality of the elementary particles; for this individuality forms the
secure foundation on which the whole recent development of the atomic theory
depends". 125 Bohr continues by insisting that, "[t]he main
purpose of the article [namely the
What the sense of individuality as applied to processes effectively did was to cleave apart the two most notable descriptive characteristics of individual particles, whether they be light quanta or electrons in atoms. These have to do with acting as a carrier of energy/momentum and following a distinct spatio-temporal trajectory, respectively. It is in terms of these two characteristics-with the former understood as underpinning a causal description-that complementarity is originally formulated, as we have seen. However, Bohr effectively privileges the standard understanding of particle individuality in terms of a spatio-temporal description-that is, what we have called Space-Time Individuality-and thus this sense of complementarity is also spelled out as that which holds between superpositions and individuality, taken in these terms. The former allows us to understand the notion of stationary state and in particular its 'supramechanical' stability but its invocation precludes any spatio-temporal description and, in particular, any specification of the behaviour of the separate particles in the atom. Thus the two applications of individuality work together here: as applied to processes it underpins the very notion of a stationary state, but this precludes its application to particles.
end p.112
This approach allows an 'unambiguous definition' of the energy of the atom and the 'fundamental renunciation' of the space-time description is unavoidable when it comes to the interpretation of observations. On the other hand, in order to 'unambiguously use observations regarding the behaviour of the particles in the atom' one must neglect interactions and treat the particles as free and thus as distinct individuals, but then one cannot invoke stationary states or say anything about the overall energy. Likewise, outside the atom, the individuality of the particles seems forced upon us by the experiments but we recall that what these experiments register-by the (discontinuous) flash on the scintillation screen for example-is the spatio-temporal location of the particle. 127 Thus they preclude any consideration of the wave-like nature through superpositions. An account of the latter is complementary to that of (spatio-temporal) individuals and both superpositions and individuals are to be regarded as abstractions upon which our complementary descriptions rest. 128
Can we understand the 'superposition' half of the complementarity relationship as a kind of non-individuality? Certainly, if the nature of complementary relationships is cashed out in terms of mutually exclusive or even inconsistent notions, one would have to see superposition as somehow opposed to individuality. And, as we shall see, this is indeed how superposition has been regarded, if it, or more generally quantum 'entanglement', is understood as denying the separability of states which, it is alleged, Einstein, in his later debate with Bohr, took to be definitive of individuality. Can this idea of superposition-as-a-loss-of-individuality then be related to the acknowledged implications of quantum statistics? Bohr seems to have thought so: in a 1928 letter to Bohr, Schrödinger argued that, if Heisenberg's uncertainty principle is right, then the notion that there are discrete quantum states cannot be experimentally tested:
One may . verify this fact in a few simple cases, e.g., in the quantization of an ideal gas. If we allow the molecule a latitude in position of the size of the entire gas volume, then the uncertainty in the momentum becomes of the order of magnitude of the momentum difference of neighbouring quantum states. 129
To this Bohr replied by invoking the complementarity between spatio-temporal and causal descriptions where this is revealed by the 'apparent
end p.113
contrast' between the superposition principle and the individuality postulate. 130 A 'particularly striking' example is the 'absolute exclusion' between the application of the notion of stationary states and the spatio-temporal 'tracking' of the individual particles in the atom. 131 He writes:
In the article [his 1928 Nature paper] I have endeavoured strongly to stress the failure of classical pictures in the quantum theoretical treatment of the interaction problem, and to emphasize that our entire mode of visualization is based on the abstraction of free individuals-a point where, in my opinion, the relationship between classical theory and quantum theory is particularly evident. I might add further that just in the case, touched upon in your letter, of the quantization of a gas, this failure shows up so strikingly in the paradoxes of the new statistics. 132
And he concludes by rejecting Schrödinger's use of the uncertainty principle in this case, "because here of course the momentum variable conjugate to the coordinate does not have an unambiguous value". 133
In a later letter to Pauli, in 1929, he writes,
Thus one can pursue the reciprocity of the concept of individuality and the superposition principle to far-reaching consequences. One can show in general that any use of the former concept limits the application of the latter principle as an immediate consequence of the loss of phase resulting from every observation. Conversely, any consistent application of the superposition principle limits the possibility of a visualizable interpretation based on the principle of individuality, as it finds expression above all in the quantum theoretical treatment of systems with several identical particles. All this contains of course nothing really new. 134
In other words, the paradoxical implications of the new statistics have to do with the loss of a 'visualizable interpretation based on the principle of individuality', something to which Bohr subsequently refers in his later comments on these statistics. 135 Bohr insisted that one cannot rest content, as it were, with this loss of individuality, since the very foundation of a space-time description is provided by the 'abstraction' of free individuals 136 and this abstraction is pressed upon us by the experimental circumstances indicated above. What the loss represents is only one side of the complementary relationship, with individuality providing the other. In effect, then, Bohr encapsulated, within his complementarity interpretation, the two metaphysical packages that we will be exploring in this book.
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