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I know the state of a system at a time T1, and perform a measurement at a later time T2. My question is this: is there a maximum uncertainty on what state I could expect to measure the system?

Of course, I'm aware of the Minimum Uncertainty Principle. Is there another side to that coin?

Thanks!

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  • $\begingroup$ Depends on what values you can measure. If only a finite number of measurement outcomes is possible, then your maximum uncertainty is finite. In any measurement, the maximum uncertainty can be achieved by not doing the measurement, and instead randomly guessing a value. $\endgroup$ – probably_someone Dec 7 '17 at 21:53
  • $\begingroup$ What would be the case if the "system" in my question has an infinite amount of states? Would the maximum uncertainty simply be infinite? Or could it somehow be less than infinite? $\endgroup$ – Thomas Murphy Dec 7 '17 at 22:05
  • $\begingroup$ It doesn't depend on the number of states, but rather the range that they occupy. If an infinite number of states only cover a finite range of values (e.g. $\{1/n,n\in\mathbb{N}\}$), then the maximum uncertainty is finite (in the example, it's 1). $\endgroup$ – probably_someone Dec 7 '17 at 22:07
  • $\begingroup$ This greatly clarifies things. $\endgroup$ – Thomas Murphy Dec 7 '17 at 22:16
  • $\begingroup$ @probably_someone How does randomly guessing a number lead to a maximum measurement uncertainty? $\endgroup$ – jjack Dec 8 '17 at 1:37
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Since you have measurement uncertainty: if it is given as a continuous probability/frequency distribution, how would you pick the worst case from the tail of the distribution? This would have to involve probability of occurrence. If you have a discrete distribution for the uncertainty with a maximum value, then you could just use that one.

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  • $\begingroup$ 1.) Maximum value $\neq$ maximum uncertainty. 2.)In the continuous case, the maximum uncertainty is infinite. $\endgroup$ – probably_someone Dec 8 '17 at 1:44
  • $\begingroup$ Wikipedia says, uncertainty is not a well-defined concept. You claim otherwise. en.m.wikipedia.org/wiki/Uncertainty $\endgroup$ – jjack Dec 8 '17 at 1:49
  • $\begingroup$ In physics, we mean something pretty specific when we talk about uncertainty. NIST confirms this: physics.nist.gov/cuu/Uncertainty/glossary.html. In most cases, it's the standard deviation of the probability distribution of measurement outcomes (indeed, this is the sense in which it is used in the Heisenberg Uncertainty Principle). In some other cases, we use some other measure of the half-width of the distribution. My explanation given above only depends on uncertainty being some sort of measure of width. $\endgroup$ – probably_someone Dec 8 '17 at 1:55
  • $\begingroup$ @probably_someone So in physics "standard uncertainty" as defined by NIST is used? $\endgroup$ – jjack Dec 8 '17 at 1:58
  • $\begingroup$ Generally yes, unless specified otherwise. As an aside, these are specified by ISO, not NIST; it's just that the NIST website places them in an easier-to-reach spot than the ISO site. $\endgroup$ – probably_someone Dec 8 '17 at 2:00

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