# The Problem of Identical Particles

# The Problem of Identical Particles

Do the properties of a compound or aggregate supervene on the properties of its parts? Theories that imply a negative answer (or the states they attribute) are called ’holistic’. Besides the EPR paradox, Pauli's Exclusion Principle and quantum statistics (for aggregates of identical bosons or fermions) are all generally cited as establishing the holism of quantum theory. It has been conjectured both that the principle of Permutation Invariance accounts for the departures from classical statistics, and that if ’identical’ in ’aggregate of identical particles’ is properly understood, then it entails Permutation Invariance tautologically. It has also been thought that there can be a proof within elementary (non‐relativistic) quantum mechanics of the principle of Dichotomy, i.e. that only Bose and Fermi statistics, and not intermediate non‐classical ’para‐statistics’ can apply. All three conjectures are contested in this chapter and the next. This chapter is devoted to an exposition of the quantum theoretical foundations for this subject, with implications for limits to interpretation of the theory.

*Keywords:*
Bose statistics, boson, Dichotomy Principle, Fermi statistics, fermion, holism, identical particles, para‐statistics, Pauli's Exclusion Principle, Permutation Invariance, quantum statistics

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