Abstract
Classical mechanics is based on the notion that matter consists of persistent particles that can be reidentified (or tracked) across time. However, the mathematical symmetrization procedures (due to Dirac (1926 Proc. R. Soc. A 112 661) and Heisenberg (1926 Z. Phys. 38 411) and Feynman (1965 Quantum Mechanics and Path Integrals 1st edn (New York: McGraw-Hill))) used to describe identical particles within the quantum formalism are widely interpreted as implying that identical quantum particles are not persistent (so that the concept of ‘the same particle’ is not meaningful) or are persistent but not reidentifiable. However, it has not proved possible to rigorously reconcile these interpretations with the fact that identical particles are routinely assumed to be reidentifiable in particular circumstances—for example, a track in a bubble chamber is interpreted as a sequence of bubbles generated by one and the same particle (Mirman 1973 Il Nuovo Cimento 18B 110; de Muynck 1975 Int. J. Theor. Phys. 14 327; Dieks and Lubberdink 2011 Found. Phys. 41 1051; Jantzen 2011 Phil. Sci. 78 39). Moreover, these interpretations do not account for the mathematical form of the symmetrization procedures, leaving open theoretical possibilities other than bosonic and fermionic behavior, such as paraparticles (Messiah and Greenberg 1964 Phys. Rev. 136), which however do not appear to be realized in nature. Here we propose that the quantum mechanical behavior of identical particles is a manifestation of a novel kind of complementarity, a complementarity of persistence and nonpersistence. Accordingly, identical ‘particles’ are neither persistent nor nonpersistent; rather, these terms are to be understood as descriptors of different models of the same experimental data. We prove the viability of this viewpoint by showing how Feynman’s and Dirac’s symmetrization procedures arise through a synthesis of a quantum treatment of persistence and nonpersistence models of identical particle-like events, and by showing how reidentifiability emerges in a context-dependent manner. Finally, by drawing on a reconstruction of Feynman’s formulation of quantum theory (Goyal et al 2010 Phys. Rev. A 81 022109), we construct a precise parallel between the proposed persistence–nonpersistence complementary and Bohr’s wave–particle complementarity for individual particles, and detail their conceptual similarities and dissimilarities.
Highlights
According to our understanding of the everyday physical world, observable phenomena are underpinned by persistent objects that can be reidentified across time by observation of their distinctive properties
That is caused by one and the same particle. Neither of these assertions accounts for the mathematical form of the symmetrization procedures used to describe identical particles within the quantum framework, leaving open theoretical possibilities other than bosonic and fermionic behavior, such as paraparticles, which do not appear to be realized in nature
We further show that the persistence and nonpersistence models satisfy the key characteristics of Bohr’s concept of complementarity, and thereby propose that the behavior of identical particles is a manifestation of a persistence–nonpersistence complementarity, analogous to Bohr’s wave–particle complementarity for individual particles
Summary
As indicated in the Introduction, the quantum treatment of identical particles brings the assumption of persistence into question. We propose that the understanding of identical particle-like events requires a synthesis of complementary persistence and nonpersistence models, analogous to the way that localization (‘particle’) and delocalization (‘wave’) models need to be combined in order to understand individual microscopic entities. We assert that persistence and nonpersistence are complementary descriptions of identical particle-like events on the ground that the persistence and nonpersistence models satisfy the three key features of complementarity, as follows These two models are mutually exclusive in the sense that they make contradictory assumptions about whether or not successive individual detections are underpinned by individual persistent entities. One of these models permits an analysis of the situation into parts—‘the electron passes through one slit or the other slit’ or ‘the identical particles make a direct or indirect transition’ This analysis allows two distinct amplitudes to be defined and, in principle, calculated by making use of the Dirac–Feynman amplitude–action quantization rule [21].
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