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
--
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 everything-list+unsubscr...@googlegroups.com
<mailto:everything-list+unsubscr...@googlegroups.com>.
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 everything-list+unsubscr...@googlegroups.com.
To view this discussion on the web visit
https://groups.google.com/d/msgid/everything-list/8ffd7c9b-d434-4a17-c131-e7a01d3a50cf%40verizon.net.
