It is shown that the wave function describes the state of the statistical ensemble E[S] of individual particles, or the statistical average particle . This result follows from the fact that in the classical limit h=0 the Schroedinger equation turns to the dynamic equations for the statistical ensemble of classical particles. The statement that the wave function describes the state of an individual particle is incompatible with the quantum mechanics formalism. It is shown that the statistical interpretation of quantum mechanics is a corollary of the fact, that the QM formalism is the technique of the statistical ensemble description, restricted by constraints of the dynamic equation linearity.
This article concerns the problem of identity and individuality of quantum particles. It has been suggested that ensembles of indistinguishable particles (e.g. electrons) can be treated in the way that is analogous to the way we refer to continuous matter using so-called mass terms (such as “water”). In the article I give several arguments against interpreting quantum predicates as mass terms. While the ontological interpretation of quantum objects as mass density fields determined by their wave functions is not uncommon in quantum mechanics (it features e.g. in the GRW interpretation of quantum theory), it is controversial to treat fragments of these fields as representing genuine entities picked out by quantum predicates. I point out that proper parts of electron matter-fields do not possess the same kinds of properties as whole electrons. Also, there are some measurable properties of ensembles of particles that cannot be recovered by describing a homogenized distribution of mass density. This problem affects both entangled and non-entangled states. In conclusion I opt for an approach (known as heterodoxy) according to which it is possible to individuate same-type particles momentarily using symmetric projectors.
xi 4.5.24.5.3The double-slit experiment The microscope 4.6 Meaning of the 'complementarity' concept 4.6.1 4.6.24.6.34.6.44.6.5 4.6.6 4.6.7 Two meanings of 'to determine' Heisenberg's disturbance theory of measurement Complementarity according to Bohr Particle-wave duality Parallel and circular complementarity Complementarity and the projection postulate Complementarity and consciousness 4.7 Critique of the complementarity principle Einstein Margenau Ballentine Recent developments Complementarity and empiricist interpretation The Einstein-Podolsky-Rosen problem 6 Individual-particle and ensemble interpretations of quantum mechanics 275 6.