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So let's say I have a spin-up and a spin-down filter one after the other, Stern-Gerlach style. I fire a beam of electrons. 100% of the electrons passing the spin-up filter have spin-up, and so 0% of them can get past the spin-down filter.

But, time evolution exists, or I'd have heard something about particles permanently keeping their measured properties before. I've never seen actual figures for these times. How much time would be needed for the spin-up electrons passing the first filter to become evenly split in spin direction again?

In general, how long does it take for quantum superposition to be dominant again after measurement? What order of magnitude or time frame are we talking here?

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So you can calculate this but I don't know the exact numbers. I would guess that a typical room has variations at maybe 0.3 gauss over human distances of ~30 cm of so? It's caused by things like wires in the walls, metal pieces of furniture, water pipes... So you're talking about 0.01 gauss/cm whereas I think actual S-G experiments are at like 10,000 gauss/cm? So something like a millionth of the effects?

Accordingly if the splitting in the Stern Gerlach experiment is happening over like 1 cm, the inhomogeneity has a similar effect over maybe a scale of kilometers? It's hard to think that you'd see it in laboratory conditions.

But again, these are pretty uninformed guesses, just to get kind of an order of magnitude of the effect.

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    $\begingroup$ Just to clarify for the OP, if they're new to the subject, time evolution could be completely trivial if the spin is not coupled to external effects. So, in principle, an isolated spin would remain in the measured state forever. Of course, as you mention, in practice, there would be all kinds of magnetic fields present which couple to the spin. $\endgroup$
    – user87745
    Commented Sep 14, 2021 at 9:21

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