The main result of decoherence theory is that the non-diagonal elements of a quantum object's density matrix become zero due to uncontrolled interactions with the environment. For me, that only means that there will we no more interference effects between the superposed states. But there still remain the diagonal elements of the density matrix. So there is still a superposition of classical alternatives left. How does that solve the measurement problem ?
Moreover, doesn't the mathematical derivation of the decoherence effect involve an ensemble average over all possible environmental disturbances ? How does this help when we are interested in the behavior of a specific system in a specific environment ?
Of course it just means the coherence effect of waves only has finite length,
or quantum effects diminish with distance.
It servs as an explanatory bridge between macroscopic classical and microscopic quantum physics with scale.
Does not particularly illuminate anything else.
IMHO, decoherence does not solve the measurement problem. However, it is a prerequisite for the very concept of macroscopic measurement. It allows the measurement device to be regarded initially decoupled from, and uncorrelated with, the system on which the measurement is performed.
Having written this, I start wondering if this assumption is equally needed in any classical dynamical measurement theory. Not to be misunderstood, I mean not a brainless statement that "whatever appears in the theory may be measured without disturbance", but a real classical dynamical model of a particular measurement setup, accounting for all actions and back-actions.
Thanks to 'Juan Weisz' and 'L. I. Plimak' for your quick answers!
I just want to add that the reason for my question was an article ( https://arxiv.org/pdf/1612.00676.pdf ), in which physicists were surveyed about their attitudes concerning the foundations of quantum mechanics. I was shocked to see (in Fig.6) that 29% considered the measurement problem as solved by decoherence, and 17% considered it even as a pseudoproblem. I my opinion, the measurement problem is absolutely important, but still unsolved.
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