On Thursday, May 7, 2020 at 7:09:04 PM UTC-6, Brent wrote: > > > > On 5/7/2020 4:28 PM, Alan Grayson wrote: > > > > On Sunday, May 3, 2020 at 12:19:52 AM UTC-6, Brent wrote: >> >> >> >> On 5/2/2020 10:50 PM, Alan Grayson wrote: >> >> You mean to experimentally estimate it from the scatter of results? That >>> depends on how accurately you want to estimate. The error scales as >>> 1/sqrt(N). In most experiments with photons or electrons, it's easy to >>> make N big. But it's also hard to eliminate other sources of scatter that >>> have nothing to do with the UP. So only experiments deliberately designed >>> for maximum precision are going to push the UP bounds for simultaneous >>> measurements. >>> >>> Brent >>> >> >> If the experiment is designed for max precision, how large does N have to >> be to satisfy the UP? TIA, AG >> >> >> That doesn't quite make sense. It takes two to get an estimate of the >> variance and the first two you measure may satisfy the UP or they may >> violate the NP. The variance, and the std deviation estimators are random >> variables, obey a certain distribution. The bigger N the tighter the >> estimate. In almost all experiments there will be other sources of >> randomness and the estimate will converge around some uncertainty bigger >> than h, which is satisfying the UP. >> >> Brent >> > > Why doesn't my question make sense? You say that with an ensemble of 2, > the product of the standard deviations might violate the UP. So how large > must the ensemble be to guarantee satisfying the UP? AG > > > There's no such guarantee. You're not measuring the standard deviations > directly, you're measuring estimators of them. The estimators are random > variables. Suppose I said the average height of a human being is greater > than 175cm. How many people would you have to measure to guarantee that > was true? > > Brent >
Suppose I wanted to measure the length of a rod. Couldn't I use high frequency photons to measure its endpoints with as much precision as desired (short of inducing a black hole), and its length calculated from the length differences of its endpoints? Would this procedure violate the UP? AG > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected] <javascript:>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/ae628106-3287-4e48-a497-76597c60eb93%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/ae628106-3287-4e48-a497-76597c60eb93%40googlegroups.com?utm_medium=email&utm_source=footer> > . > > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/922a8ebd-5677-45ec-9c7e-11cfe72a87ff%40googlegroups.com.
