The concept of indistinguishable particles in classical and quantum physics

Dennis Dieks, Andrea Lubberdink

According to classical physics particles are basic building blocks of the world. Classical particles are distinguishable objects, individuated by physical characteristics. By contrast, in quantum mechanics the standard view is that particles of the same kind ("identical particles") are in all circumstances indistinguishable from each other. This indistinguishability doctrine is motivated by the (anti)symmetrization postulates together with the assumption (``factorism'') that each single particle is represented in exactly one factor space in the tensor product Hilbert space of a many-particles system. Although the factorist assumption is standard in the literature, it is conceptually problematic. Particle indistinguishability is incompatible with the everyday meaning of ``particle'', and also with how this term is used both in classical physics and in the experimental practice of physics. The standard view requires quantum particles of the same kind to remain indistinguishable even in the classical limit, so that a transition to the classical picture of the world seems impossible. Earlier we have proposed an alternative conception of quantum particles that does not rely on factorism and that avoids these and other problems. We further explain and develop this proposal here. In our view, particles in quantum theory are not fundamental but \emph{emergent}. However, in those situations where the particle concept is applicable, quantum particles---identical or not---are distinguishable in the same way as classical particles.

Alexander Bach

Dennis Dieks, Andrea Lubberdink

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.

Simon W. Saunders

Particle indistinguishability has always been considered a purely quantum mechanical concept. In parallel, indistinguishable particles have been thought to be entities that are not properly speaking objects at all. I argue, to the contrary, that the concept can equally be applied to classical particles, and that in either case particles may (with certain exceptions) be counted as objects even though they are indistinguishable. The exceptions are elementary bosons (for example photons).