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arXiv · 1409.7167

"Almost" Quotient Space, Non-dynamical Decoherence and Quantum Measurement

Yu-Lei Feng·Yi-Xin Chen
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Abstract

An alternative approach to decoherence, named non-dynamical decoherence is developed and used to resolve the quantum measurement problem. According to decoherence, the observed system is open to a macroscopic apparatus(together with a possible added environment) in a quantum measurement process. We show that this open system can be well described by an "almost" quotient Hilbert space formed phenomenally according to some stability conditions. A group of random phase unitary operators is introduced further to obtain an exact quotient space for the observed system. In this quotient space, a density matrix can be constructed to give the Born's probability rule, realizing a (non-dynamical) decoherence. The concept of the ("almost") quotient space can also be used to explain the classical properties of a macroscopic system. We show further that the definite outcomes in a quantum measurement are mainly caused by the "almost" quotient space of the macroscopic apparatus.

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Yu-Lei Feng, Yi-Xin Chen. 2014-09-25. "Almost" Quotient Space, Non-dynamical Decoherence and Quantum Measurement. https://arxiv.org/abs/1409.7167

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