Is the Preferred Basis selected by the environment?
We show that in a quantum measurement, the preferred basis is determined by the interaction between the apparatus and the quantum system, instead of by the environment. This interaction entangles three degrees of freedom, one system degree of freedom we are interested in and preserved by the interaction, one system degree of freedom that carries the change due to the interaction, and the apparatus degree of freedom which is always ignored. Considering all three degrees of freedom the composite state only has one decomposition, and this guarantees that the apparatus would end up in the expected preferred basis of our daily experiences. We also point out some problems with the environment-induced super-selection (Einselection) solution to the preferred basis problem, and clarifies a common misunderstanding of environmental decoherence and the preferred basis problem.
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