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New math makes scientists more certain about quantum uncertainties
- brink 7y agoIs there an easy way to explain why pi shows up here?
- MiroF 7y agoWhen 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.
- hervature 7y agoNot a physicist, but don't you mean maximum? Gaussian distribution is entropy maximum with finite mean and variance
- evanb 7y agoI 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.
- xdavidliu 7y agolast time I took grad quantum was Spring 2010, so I need a refresher. What does it mean for a particle to be "at minimum uncertainty"?
- peteradio 7y agoh < dPdX is generally true h = dPdX is case of minimum uncertainty I'm guessing that is what is meant by minimum uncertainty.
- liuhenry 7y agoFull derivation: https://physicspages.com/pdf/Griffiths%20QM/Griffiths%20Problems%2003.16.pdf https://physicspages.com/pdf/Griffiths%20QM/Griffiths%20Prob...
- empath75 7y agoAn 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?
- ChrisLomont 7y ago>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.
- m-watson 7y agoHere is the arxiv paper for those interested: https://arxiv.org/abs/1907.05428 https://arxiv.org/abs/1907.05428
- crmrc114 7y agoTranslation for us quantum muggles?
- Koshkin 7y agoQuantum computers will be slower and/or further away than originally thought.
- gus_massa 7y agoWhere did you find the relation with quantum computers? This looks like an unrelated problem to me.
- anticensor 7y agoIn addition to that, quantum algorithms are harder to design as your algorithm needs to be reversible; this adds many uncomputation stages into your algorithms.
- lacker 7y agoThis is just describing the limits more precisely for a certain type of repeated measurement. It does not seem to affect quantum computing.