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What this question is about: (Simple) models that show that decoherence is the reason for the non-observability of superpositions of macroscopic states use the simplification, that the Hamiltonian that describes the dynamics only consists of a part that describes the dynamics of the interaction between a system and an environment. Parts, that describe the intrinsic dynamics of the system und the environment, apart from the interaction, are neglected (said to be zero).

This comes from the fact, that it is well known by now that this model results in the fact that primarily eigenstates of position become the pointer basis (rather than energy eigenstates or a mixture, which leads to considerations of phase space).

The question: Let's say for a minute, one has no idea of the superselection behind all that but rather wants to find out about decoherence in the first place. Could it be allwed to argument for the used hamiltonian in the following way? Is there a better explanation (that doesn't consider the pointer basis emerging from the hamiltonian) for why exactly this hamiltonian is used?

In the macroscopic domain, the system always (very often) interacts with the environment (because there are so many photons, air molecules, etc. (let's also not forget gravity)). The timescale in which a proper interaction has taken place is much smaller than the timescale on which system or environment change apart from the interaction. The dynamics therefore is governed by the interaction itself. Therefore it is allowed to neglect hamiltonians that describe the intrinsic dynamics of the system und the environment (apart from the interaction).

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I think the example of superconductors contradicts the entire idea that there is such a thing as a simple theory of decoherence, let alone the possibility that we can neglect the properties of the free system Hamiltonian in general.

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