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Will wave function collapse without measurement? Yes and no. Collapse is a sometimes useful fiction. Sometimes you can pretend a subsystem has evolved into a particular state, a collapsed state. Since all matters are described by wave functions, then in principle, I should be able to describe wave function collapse by Schrodinger's equation. (I ...

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According to the standard presentation of QM, yes, there is a collapse. The wave function evolves in space not in a local manner, in the way, say a particle travels along line, but in the way a balloon evolves when air is blown in. A measurement, or interaction is local; the wave-function - the balloon collapses, say where I pricked it with a needle. But ...

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Following von Neumann, the measurement process is just a special type of interaction between two systems, that follows special rules when it comes to averaging a specific observable $X$. Let $H$ be a Hilbert space, $(\Omega,\mathscr{B})$ a Borel space, with $\Omega\subseteq \mathbb{R}$ and $\mathscr{B}$ a Borel $\sigma$-algebra on $\Omega$. By means of the ...

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Better calibrated response: I'm a little confused about your first argument, that decoherence should somehow reduce entropy. Decoherence is the coupling of a system to a much larger system and of course adds entropy. Another way of putting it: if one ignores the environmental degrees of freedom, decoherence essentially maps pure states (zero entropy) to ...

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The quantum state is a vector in a Hilbert space. Each basis vector in the Hilbert space is a possible observation one can make. For example, when modelling the position of a free particle, we assign one basis vector to each point in space. The length of the shadow that the state casts upon each vector is the (square root of) the probability that a ...

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