Persistence and nonpersistence as complementary models of identical quantum particles

Abstract

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.