What is "smearing" and what is a "smeared field"

[Sicktoaster]

I've seen these terms in connection with quantum mechanics a lot. I've looked them up but it's hard to find just a straightforward definition of them.

 

[DaveC426913]

That's because they're not really definitions, they're analogies.

All word descriptions of the subatomic world are necessarily inaccurate because there are no analogies with anything in our experience. The only accurate descriptions of anything are the formulae themselves.

So I guess the "definition" of smearing is the equation that describes a Bose-Einstein condensate.

 

[Sicktoaster]

That's because they're not really definitions, they're analogies.

All word descriptions of the subatomic world are necessarily inaccurate because there are no analogies with anything in our experience. The only accurate descriptions of anything are the formulae themselves.

So I guess the "definition" of smearing is the equation that describes a Bose-Einstein condensate.

That's still a definition if that is the definition. I'm not looking for familiarity just as long as there is a definition even if the definition is anything that fits such-and-such equation. Even if I can't accurately picture it happening (which as you pointed out is impossible) what I'm looking for is to understand the definition mathematically and hopefully at some point understand how these mathematical equations can be applied to current or potential technology.

So is "smearing" as used in QM literature perfectly synonymous with the Bose-Einstein condensate equation?

 

[DaveC426913]

So is "smearing" as used in QM literature perfectly synonymous with the Bose-Einstein condensate equation?

I'll defer to professionals in the field for accuracy in termonology, but yes, in a nutshell, when atoms are cooled to near 0K they smear out into a BEC. As their motion approaches zero, HUP dictates that their position becomes indistinct. You can no longer tell one atom from another. In fact, it becomes meaningless to try.

 

[mfb]

You can use "smearing" to describe what happens during Bose-Einstein condensation, but you get similar effects without BECs as well. Therefore, they are not synonyms.

 

[Sicktoaster]

You can use "smearing" to describe what happens during Bose-Einstein condensation, but you get similar effects without BECs as well. Therefore, they are not synonyms.

Care to elaborate?

Also why is the word "smearing" used to refer to it? I understand it's not the same "smearing" you'd see in everyday life but there has to be some reason they chose that word. I've seen colored graphs of Bose-Einstein Condensates forming and I don't see how it's even analogous to smearing. It seems like it concentrates more in the middle. Smearing you think of it smearing out to cover a wider area, which it does not appear to do.

 

[mfb]

Care to elaborate?

"Smearing" is not well-defined enough for that.

If it just refers to wave functions spread out in space, then the double-slit experiment is enough to find something similar. Or a simple electron orbital in an atom.

Smearing you think of it smearing out to cover a wider area, which it does not appear to do.

Compared to classical arrangements of atoms (every atom has a single place), it is certainly much wider.

 

[dextercioby]

Another possibility: In your typical Wightman axioms context, field operators are said to be 'smeared' distributions with the help of test functions.