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
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