All of the statements of Heisenberg's uncertainty principle that I've read seem to state that there is a fundamental limit on the precision to which you can measure the values of conjugate pairs (like position and momentum)(adsbygoogle = window.adsbygoogle || []).push({}); at the same time.

So is this simultaneity necessary? I ask because the course book also says that if you prepare many identical systems in identical states, and perform measurements of position on half of them and momentum on the other half, the results will be consistent with the uncertainty principle. But doesn't this mean you are finding out these values at different times, and therefore not having to sacrifice precision of either one?

If you prepare two identical systems, and test one very precisely for position, then turn to the second system, will there be an inherent limit on the precision with which you can measure momentum? Or will you be able to achieve an arbitrary (but non-zero) level of precision as the measurements were not simultaneous?

Obviously I'm ignoring any technological limitations, as this is not really the point of the question.

Thanks for any help, this one is messing with my mind...

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# Simultaneity of Uncertainty Principle

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