Heisenberg's uncertainty principle

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Discussion Overview

The discussion revolves around Heisenberg's uncertainty principle, particularly exploring examples and variations of the principle, including its application to energy and time, as well as the differences in formulations encountered in various sources.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that energy and time might serve as another example of the uncertainty principle, referencing Einstein's box example.
  • Another participant introduces electron spin as an example, noting that knowledge of one spin component leads to uncertainty in the others.
  • A question is raised about the difference between the equations Δx * Δp = h/2π and Δx * Δp = h/4π, with a participant indicating that their high school textbook uses the former.
  • Some participants propose that the differences in equations depend on conventions used in derivations, mentioning the use of h and h-bar.
  • There is a suggestion that there is no standard formula for the uncertainty principle that applies universally, as various forms are encountered.
  • One participant remarks that the uncertainty principle is not typically used in practical problem-solving contexts.

Areas of Agreement / Disagreement

Participants express differing views on the applicability and interpretation of the uncertainty principle, with no consensus reached on the standard formulations or their use in practical scenarios.

Contextual Notes

Participants highlight the dependence on conventions in derivations and the potential for multiple formulations of the uncertainty principle, indicating that assumptions may vary across different contexts.

filippo
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As the above principle says, momentum and position can't be known both at the same time (Δx Δp ≥ h/4π); I am trying to find another example and I was thinking of energy and time following Einstein's box example...does anyone have an idea on whether it'c ocrrect or just another example?
 
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A great example is electron spin. An electron has 3 non-commuting spin components: x, y and z. Knowledge of anyone means there is complete uncertainty in the other 2. You will often find it easier to appreciate the HUP if you consider spin rather than p or q. Ditto for photons.
 
Just to recover that thread and not create a new one, can you please answer my question here?

What's the difference between the Δx * Δp = h/2pi and Δx * Δp = h/4pi equations I find everywhere on the internet and textbooks?

My High School book has the first one, yet I seem to meet the other one more frequently.

Thanks!
 
depends on conventions in the derivations I guess. I can derive so one get Δx * Δp > h-bar/2

Please note that sometimes you have h and sometimes h-bar.
 
Yea so far I've seen these candidates for the place after >=

1)h
2)h-bar
3)h/2pi
4)h-bar/2

Interesting, so there isn't any standard formula you can use in any occasion? Or can you use any of these approximately?
 
well, you don't "use" HUP while solving REAL things ;-)

So it is no big deal.
 

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