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.
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.
According to our understanding of the everyday physical world, observable phenomena are underpinned by persistent objects that can be reidentified (or tracked) across time by observation of their distinctive properties. This understanding is reflected in classical mechanics, which posits that matter consists of persistent, reidentifiable particles. However, the mathematical symmetrization procedures used to describe identical particles within the quantum formalism have led to the widespread belief that identical quantum particles lack either persistence or reidentifiability. However, it has proved difficult to reconcile these assertions with the fact that identical particles are routinely assumed to be reidentifiable in particular circumstances. For example, when two electrons move through a bubble chamber, each is said to generate a sequence of bubbles (a 'track') that is caused by one and the same particle. Moreover, 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. Here we propose the novel idea that both persistence and nonpersistence models must be employed in order to fully account for the behaviour of identical particles. Thus, identical particles are neither persistent nor nonpersistent. 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 these models, and by showing how reidentifiability emerges in a context-dependent manner. 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. Finally, we construct a precise parallel between these two complementarities, and detail their conceptual similarities and dissimilarities.
The mathematical rules used to handle systems of identical quantum particles bring into question whether the elementary constituents of matter, such as electrons, have the fundamental characteristics of persistence and reidentifiability that are usually attributed to classical particles. However, despite considerable philosophical debate, the metaphysical profile of these entities remains elusive.
Previous debates have taken the mathematical rules, and the language in which these are usually couched, as a starting point. Here, we argue that this methodology is inherently limited, and develop a new conception of identical particles based on a recent mathematical reconstruction of these rules. Using this reconstruction, we demonstrate that the special behaviour of identical particles originates in the confluence of identicality and the active nature of the quantum measurements. We propose that identical particles are appropriately viewed as potential parts of a whole, and show how this leads to striking consequences such as restricted transtemporal identity.
Abstract According to classical physics particles are basic building blocks of the world. These classical particles are distinguishable objects, individuated by unique combinations of physical properties. By contrast, in quantum mechanics the received view is that particles of the same kind (“identical particles”) are physically indistinguishable from each other and lack identity. This doctrine rests on the quantum mechanical (anti)symmetrization postulates together with the “factorist” assumption that each single particle is represented in exactly one factor space of the tensor product Hilbert space of a many-particle system. Even though standard in theoretical physics and the philosophy of physics, the assumption of factorism and the ensuing indistinguishability of particles are problematic. Particle indistinguishability is irreconcilable with the everyday meaning of “particle”, and also with how this term is used in the practice of physics. Moreover, it is a consequence of the standard view that identical quantum particles remain indistinguishable even in the classical limit, which makes a smooth transition to the classical particle concept impossible. Lubberdink (1998; 2009) and Dieks and Lubberdink (2011) have proposed an alternative conception of quantum particles that does not rely on factorism and avoids these difficulties. We further explain and discuss this alternative framework here. One of its key consequences is that particles in quantum theory are not fundamental but emergent; another that once they have emerged, quantum particles are always physically distinguishable and thus possess a physically grounded identity.
A remarkable feature of quantum theory is that particles with identical intrinsic properties must be treated as indistinguishable if the theory is to give valid predictions in all cases. In the quantum formalism, indistinguishability is expressed via the symmetrization postulate (Dirac P 1926 Proc. R. Soc. A 112 661 , Heisenberg W 1926 Z. Phys. 38 411 ), which restricts a system of identical particles to the set of symmetric states ('bosons') or the set of antisymmetric states ('fermions'). However, the physical basis and range of validity of the symmetrization postulate has not been established. A well-known topological derivation of the postulate implies that its validity depends on the dimensionality of the space in which the particles move (Laidlaw M and DeWitt C 1971 Phys. Rev. D 3 1375–8 , Leinaas J M and Myrheim J 1977 Il Nuovo Cimento B 37 1–23 ). Here we show that the symmetrization postulate can be derived by strictly adhering to the informational requirement that particles which cannot be experimentally distinguished from one another are not labelled. Our key novel postulate is the operational indistinguishability postulate, which posits that the amplitude of a process involving several indistinguishable particles is determined by the amplitudes of all possible transitions of these particles when treated as distinguishable. The symmetrization postulate follows by requiring consistency with the rest of the quantum formalism. The derivation implies that the symmetrization postulate admits no natural variants. In particular, the possibility that identical particles generically exhibit anyonic behavior in two dimensions is excluded.
In classical physics, the question whether there are subsets of identical particles is not particularly interesting. After all, whether the particles are identical or not, we can always track each of them at any time. As we shall see, in quantum mechanics identical particles are indistinguishable because we cannot track trajectories, and this fact induces some important symmetry properties on the total wave function describing the system of particles under consideration. Generally speaking, a symmetry is an effect of an invariance, that is, the system does not change if one effects certain transformations (see Ch. 8). In this case, the system is not modified under exchange of two identical particles. Moreover, such a symmetry yields a most interesting connection between spin and statistics. After a short introduction to the significance of statistics in quantum mechanics (in Sec. 7.1), we define the permutation operator and discuss the symmetry properties of the wave function of N identical particles (Sec. 7.2). In Sec. 7.3 we show that quantum particles, differently from classical particles (that obey the Maxwell–Boltzmann statistics), may be subject to two different statistics, namely the Fermi–Dirac statistics for fermions and the Bose–Einstein statistics for bosons. In Sec. 7.4 we treat the so-called exchange interaction and, finally, in Sec. 7.5 we consider some applications of the two statistics. Statistics and quantum mechanics Identical particles are those particles whose Hamiltonian is symmetric under exchange of one particle with the other.
Details of the many-particle system can also be read from my book titled “Quantum Field Theory: Feynman Path Integrals and Diagrammatic Techniques in Condensed Matter” [ 23 ]. The fundamental difference between classical and quantum mechanics relates the concept of indistinguishability of identical particles where each particle can be equipped with an identifying marker without influencing its behavior in classical mechanics. Besides in classical mechanics, the particle follows its own continuous path in phase space and so it is possible to determine the particular process taking place. So, principally, each particle in a group of identical particles can be identified which is not so in quantum mechanics. It is not possible to mark a particle without influencing its physical state, and worse, if a number of identical particles are brought to the same region in space, their wave functions will rapidly spread out and overlap with one another, thereby soon rendering it impossible to say which particle is where. One of the fundamental assumptions for many-particle systems is therefore that identical particles (i.e., particles characterized by the same quantum numbers such as mass, charge and spin) are, in principle, indistinguishable.