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What's the difference between The phenomenon of decoherence and the quantum wave function collapse ?

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Wave function collapse is used for interactions of a limited number of elementary particles which are described by a wavefunction , optimally using Feynman diagrams for calculating probabilities of interaction. The "collapse" is one entry in this probability distribution.

Decoherence for quantum states is a general term for many particle ensembles that can be described by a collective wavefunction, which is built up by combining many particles, usually with the density matrix formalism. Decoherence happens when the phases are lost between the individual wavefunctions.

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Not coherence between waves happens when their difference in phase is not constant in time.

A system described by a wave function collapses in one of its state functions when a quantity belonging to it is observed.

Decoherence hypothesis says that in a elapsed time the coherence between state functions of a system will fade and all of the states that compose the system described would be not be coherent anymore (even if at the beginning of the considered time they were). Differentiation in ortonormal state functions is expected a priori at the beginning, in the collapse hypothesis; every state function that form the complete base system has its probability to be found as collapsed-state once you measure a quantity in the system.

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