Understanding the Mathematics of Locality and Nonlocality

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Discussion Overview

The discussion revolves around the mathematics of locality and nonlocality, particularly in the context of quantum field theory (QFT) and its implications for particle behavior. Participants explore definitions, examples, and the relationship between locality and concepts such as the uncertainty principle.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant requests an explanation of the mathematics behind locality and nonlocality, indicating a need for clarity on the context of the discussion.
  • Another participant mentions that locality in QFT is assured by a finite polynomial type of Lagrangian density, providing an example involving a scalar field and suggesting that certain forms may break locality.
  • A question is posed regarding the meaning of velocity for a nonlocalized tachyon, prompting a discussion about the implications of nonlocality and the uncertainty principle (HUP).
  • There is a suggestion that as the uncertainty in velocity or momentum increases, any particle could potentially be tachyonic, linking nonlocality to broader quantum concepts.

Areas of Agreement / Disagreement

Participants express differing levels of understanding and clarity regarding the concepts of locality and nonlocality, with no consensus reached on the definitions or implications of these terms.

Contextual Notes

Some participants indicate a lack of clarity regarding the context in which locality and nonlocality are being discussed, suggesting that assumptions about definitions and frameworks may be missing.

Flatland
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Can someone explain the mathamatics behind locality and nonlocality?
 
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In what context...?You should have specified that.

Daniel.
 
dextercioby said:
In what context...?You should have specified that.

Daniel.

I didn't know there were different context to it.
 
In QFT,the locality is assured by a finite polynomial type of a Lagrangian density.For example,the density for the scalar field:

[tex]\mathcal{L}(\varphi,\partial^{\mu}\varphi)=\exp [(\partial^{\mu}\varphi)(\partial_{\mu}\varphi)+\phi^{2}][/tex]

is said to break locality...

Daniel.
 
ummm...huh?
 
Ok explain to me what velocity means to a nonlocalized tachyon
 
What do you mean?"nonlocalized" ...does it refer to HUP...?Yes,in agreement with HUP,as the uncertainty in velocity/momentum goes to infinity,basically any particle could be tachyonic...

Daniel.
 

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