# Maximum Uncertainty of a Measurement?

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!

• 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. – probably_someone Dec 7 '17 at 21:53
• 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? – Thomas Murphy Dec 7 '17 at 22:05
• 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). – probably_someone Dec 7 '17 at 22:07
• This greatly clarifies things. – Thomas Murphy Dec 7 '17 at 22:16
• @probably_someone How does randomly guessing a number lead to a maximum measurement uncertainty? – jjack Dec 8 '17 at 1:37

• 1.) Maximum value $\neq$ maximum uncertainty. 2.)In the continuous case, the maximum uncertainty is infinite. – probably_someone Dec 8 '17 at 1:44