Can individual elementary particles have individual properties?

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Abstract
Assuming the validity of conventional quantum theory, we may divide the laws of physics into laws of conservation and laws of change. The former, unmodified by quantum theory, are deterministic. The latter, according to quantum theory, are indeterministic for single systems, but curiously are deterministic for probability distributions in ensembles of particles. Elementary particles are characterized by invariant properties which are conserved. The question is discussed whether noninvariant observables, like momentum or spin components, at some chosen time can have definite instantaneous values. For investigating this, we discuss a simplified version of a thought experiment proposed some years ago by Wigner. This provides some answers to two questions: (1) In what sense is it usually insufficient to describe a beam of equally prepared particles as a collection of particles with certain given properties, instead of describing this beam by waves or by a state vector? (2) In case we know what value an observable has for a particle, when may it be useful to describe this individual particle quantum mechanically by ascribing to it the corresponding eigenfunction as its individual state vector?

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