Einselection

In quantum mechanics, einselection, short for environment-induced superselection, is a name coined by Wojciech H. Zurek for a process which is claimed to explain the phenomenon of wavefunction collapse and the emergence of classical descriptions of reality from quantum descriptions. In this approach, classicality is described as an emergent property induced in open quantum systems by their environments. Due to the interaction with the environment, the vast majority of states in the Hilbert space of a quantum open system become highly unstable to entangling interaction with the environment, which in effect monitors selected observables of the system. After a decoherence time, which for macroscopic objects is typically many orders of magnitude shorter than any other dynamical timescale, a generic quantum state decays into an uncertain state which can be decomposed into a mixture of simple pointer states. In this way the environment induces effective superselection rules. Thus, einselection precludes stable existence of pure superpositions of pointer states. These 'pointer states' are stable despite environmental interaction. The einselected states lack coherence, and therefore do not exhibit the quantum behaviours of entanglement and superposition.

Advocates of this approach argue that since only quasi-local, essentially classical states survive the decoherence process, einselection can in many ways explain the emergence of a (seemingly) classical reality in a fundamentally quantum universe (at least to local observers). However, the basic program has been criticized as relying on a circular argument (e.g. R. E. Kastner ). So the question of whether the 'einselection' account can really explain the phenomenon of wave function collapse remains unsettled.

Zurek has defined einselection as follows "Decoherence leads to einselection when the states of the environment ${\displaystyle |\epsilon _{i}\rangle }$ corresponding to different pointer states become orthogonal: ${\displaystyle \langle \epsilon _{i}|\epsilon _{j}\rangle =\delta _{ij}}$",

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