
New math makes scientists more certain about quantum uncertainties - magoghm
https://spectrum.ieee.org/nanoclast/semiconductors/nanotechnology/new-math-makes-scientists-more-certain-about-quantum-uncertainties
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m-watson
Here is the arxiv paper for those interested:
[https://arxiv.org/abs/1907.05428](https://arxiv.org/abs/1907.05428)

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brink
Is there an easy way to explain why pi shows up here?

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MiroF
When taking the integral over a gaussian distribution, coincidentally the
distribution describing a single particle at minimum uncertainty, you get an
answer in terms of pi.

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hervature
Not a physicist, but don't you mean maximum? Gaussian distribution is entropy
maximum with finite mean and variance

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evanb
I am a physicist, and minimum is correct. Quantum uncertainty is not an
entropy measure.

Importantly, the 'minimum uncertainty' is not just about the width of the
wavefunction in position space---the uncertainty principle (roughly speaking)
says that the variance in position space times the variance in momentum space
has a lower bound. A gaussian saturates that bound.

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crmrc114
Translation for us quantum muggles?

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Koshkin
Quantum computers will be slower and/or further away than originally thought.

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gus_massa
Where did you find the relation with quantum computers? This looks like an
unrelated problem to me.

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empath75
An interesting result to be sure, but usually constant factors don't matter
that much experimentally and pi is approximately equal to one for any large n.
Am I wrong about this? What's the size of n in a typical measurement, are we
talking on the order of 10s or thousands or millions?

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ChrisLomont
>but usually constant factors don't matter that much experimentally and pi is
approximately equal to one for any large n

Not sure if you're joking, but this is not pi+n, in which case it doesn't
matter as much, but pi/n, limiting the the edge of knowability of mutually
measurable non-commuting observables by a factor of 3 in a direction against
what we would like.

And as the article mentions, experiments are within 56% of this, so they are
about to hit hard limits if the math is correct.

So it most certainly matters experimentally. There are many places this will
affect the current edge (and future) of technology (also, as mentioned in the
article).

Basically it put behind an impossibility theorem things people had expected to
use in technology.

