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On the first day of my upper level quantum mechanics class, I discuss exactly the sort of systems that you've asked about here. Unfortunately, it turns out that
by Steuard 13y ago
On the first day of my upper level quantum mechanics class, I discuss exactly the sort of systems that you've asked about here. Unfortunately, it turns out that "common sense" is not in fact an accurate guide to the behavior of our universe (especially on an atomic scale). This is deeply frustrating, but in the end, the universe doesn't care.
Specifically, I introduce the idea of a Stern-Gerlach experiment to measure the spin of an electron along specific directions. If you prepare an electron in (say) a "+z" state (which is absolutely unique and unambiguous) and then measure its spin along the perpendicular x-axis, the results are 50/50 (and completely unpredictable).
At this point, your intuition is crying out, "We must have just overlooked some distinguishing detail in that initial +z state!" But it turns out that there are experimentally testable predictions of that sort of "hidden information" theory that differ from the predictions of quantum theory (look up "Bell inequalities"), and experiments always come back saying that the quantum description is correct.
- flibble 13y ago"We must have just overlooked some distinguishing detail in that initial +z state!" - yes, or there is an external influence we have missed. The fact that the x-axis spin results are 50/50 strongly suggests something very specific and deterministic is going on. It would seem that we just aren't able to (pre)determine it without influencing it.
- Steuard 13y agoI completely agree that it suggests that we have overlooked something in the underlying state. However, if you take a course in quantum mechanics that includes a detailed mathematical discussion of the Bell inequalities (for instance), you will see that any possible deterministic system along the lines that you're thinking of here will give predictions that are measurably different from the predictions of quantum mechanics. These experiments have been done, and the results are incompatible with any deterministic model (regardless of how difficult we assume it is to measure those "hidden variables" without influencing them). I agree that this flies in the face of everything that seems sensible in the world. I loathed quantum mechanics for years for reasons along these lines. Nevertheless, the universe is under no obligation to obey my intuition for what is sensible, nor my sense of elegance and beauty. Much to my disappointment, experiments make it absolutely clear that we do not live in a universe where "common sense" arguments are at all trustworthy on the scale of individual particles. (Also, personally, I would say that the 50/50 result on the x-axis is purely a consequence of symmetry: nothing in the initial state or the measurement apparatus is set up to prefer +x over -x or vice versa, so it would be more or less impossible for it to split any way other than 50/50.)
- flibble 13y agoWe shall see :)