3 ms·

Potential dumb question ahead: how, or does, this relate to the Uncertainty Principle? My five-year-old brain says that freezing the electrons in a lattice so

Potential dumb question ahead: how, or does, this relate to the Uncertainty Principle? My five-year-old brain says that freezing the electrons in a lattice so that they don't move means that there's no momentum or velocity, and therefore we should have an infinite? uncertainty concerning position. Obviously something is wrong in my understanding or in the precision of the article's discussion. Can someone ELI5?

go_elmo 5y ago
maybe even dumber answer ahead: the lattice positions might be big enough not to cause any conflict with the uncertainty relation?
zamadatix 5y ago
The distances between electrons in this lattice are enormous compared to the electron, even bigger than the typcial distances between atoms in a lattice, so being essentially dead still in the overall lattice structure doesn't imply much about the certainty of the position of the electron at the scale the uncertainty principle implies.
frutiger 5y ago
The uncertainty principle says something different than the common understanding. It says that if you have an ensemble of identically prepared systems, the product of variances of non-commuting observables obtained by measuring different instances in this ensemble will have a lower bound.
- nextaccountic 5y ago
  What does "different instances" mean here? We can't talk about uncertainty principle if we have a single electron?
gus_massa 5y ago
They are not 100% frozen in a 100% perfect lattice structure. They still move a little around the positions where they "should" be. Something similar happens with atoms in a normal crystal.
- memling 5y ago
  > They are not 100% frozen in a 100% perfect lattice structure. They still move a little around the positions where they "should" be. Something similar happens with atoms in a normal crystal. Thanks for the explanation. In retrospect this seems like it should be obvious (at least for some definition of obvious); I was probably reading a little too hard.

go_elmo 5y ago

maybe even dumber answer ahead: the lattice positions might be big enough not to cause any conflict with the uncertainty relation?

zamadatix 5y ago

The distances between electrons in this lattice are enormous compared to the electron, even bigger than the typcial distances between atoms in a lattice, so being essentially dead still in the overall lattice structure doesn't imply much about the certainty of the position of the electron at the scale the uncertainty principle implies.

frutiger 5y ago

The uncertainty principle says something different than the common understanding. It says that if you have an ensemble of identically prepared systems, the product of variances of non-commuting observables obtained by measuring different instances in this ensemble will have a lower bound.

nextaccountic 5y ago
What does "different instances" mean here? We can't talk about uncertainty principle if we have a single electron?

gus_massa 5y ago

They are not 100% frozen in a 100% perfect lattice structure. They still move a little around the positions where they "should" be. Something similar happens with atoms in a normal crystal.

memling 5y ago
> They are not 100% frozen in a 100% perfect lattice structure. They still move a little around the positions where they "should" be. Something similar happens with atoms in a normal crystal. Thanks for the explanation. In retrospect this seems like it should be obvious (at least for some definition of obvious); I was probably reading a little too hard.