Heisenberg principle, little question

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    Heisenberg Principle
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Discussion Overview

The discussion revolves around the Heisenberg uncertainty principle, specifically focusing on the relationship between the uncertainties in position and momentum of an electron. Participants explore the implications of relativistic effects on these uncertainties and the definitions of mass used in the context of the principle.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that as the uncertainty in position (\Delta x) approaches zero, the uncertainty in momentum (\Delta p) should tend to infinity, raising questions about the implications of the speed of light limit.
  • Another participant clarifies that \Delta p represents the uncertainty in momentum, which can be large, and emphasizes that the non-relativistic momentum formula (p=mv) cannot be used in conjunction with relativistic constraints.
  • A further contribution explains the relativistic momentum formula and points out that as velocity approaches the speed of light, momentum approaches infinity, which complicates the relationship between position and momentum uncertainties.
  • The initial poster acknowledges a misunderstanding regarding the use of relativistic mass and expresses confusion about their earlier statement regarding limits on velocity.
  • There is a recognition that \Delta p should be considered in the context of relativistic momentum, indicating a shift in understanding among participants.

Areas of Agreement / Disagreement

Participants exhibit some agreement on the need to consider relativistic effects when discussing momentum and uncertainty, but there remains uncertainty regarding the implications of these effects and the definitions of mass used in the discussion. The conversation reflects a mix of clarification and ongoing confusion.

Contextual Notes

There are unresolved aspects regarding the definitions of mass (rest mass vs. relativistic mass) and how they apply to the uncertainty principle. Additionally, the implications of approaching the speed of light on the uncertainties in position and momentum are not fully resolved.

fluidistic
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[tex]\Delta x \Delta p \geq \frac{\hbar}{2}[/tex].
Say I want to measure the best I can the position of an electron, in detriment of its momentum (i.e. velocity since I assume that I know its mass quite well).
When [tex]\Delta x \to 0[/tex], [tex]\Delta p[/tex] should tend to [tex]+\infty[/tex] but there's the c limit so that I can't make [tex]\Delta x \to 0[/tex]. Unless I should consider the relativistic mass of the electron and not the rest mass in the [tex]\Delta p =mv[/tex] part of the inequality? So m would tend to [tex]+\infty[/tex] and I'm not really limited by a maximum limit of velocity and I can get a very precise measure for [tex]\Delta x[/tex].
 
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fluidistic said:
[tex]\Delta p =mv[/tex]

[tex]\Delta p[/tex] is not a particle's momentum but it's uncertainty in its momentum and it can be huge.
 
You can't assert [tex]p=mv[/tex], which is the non-relativistic momentum, and then assert that [tex]v \leq c[/tex] (and hence [tex]p \leq mc[/tex]) because of relativity.

Relativistic momentum is [tex]p = \frac{m_0 v}{\sqrt{1 - \frac{v^2}{c^2}}}[/tex], so [tex]v \rightarrow c[/tex] as [tex]p \rightarrow \infty[/tex].
 
maxverywell said:
[tex]\Delta p[/tex] is not a particle's momentum but it's uncertainty in its momentum and it can be huge.
I know.
alxm said:
You can't assert [tex]p=mv[/tex], which is the non-relativistic momentum, and then assert that [tex]v \leq c[/tex] (and hence [tex]p \leq mc[/tex]) because of relativity.

Relativistic momentum is [tex]p = \frac{m_0 v}{\sqrt{1 - \frac{v^2}{c^2}}}[/tex], so [tex]v \rightarrow c[/tex] as [tex]p \rightarrow \infty[/tex].

Ah ok. My m standed for the relativistic mass. That's what I meant in
Unless I should consider the relativistic mass of the electron and not the rest mass in the [tex]p =mv[/tex] part of the inequality? So m would tend to [tex]+\infty[/tex] and I'm not really limited by a maximum limit of velocity and I can get a very precise measure for [tex]\Delta x[/tex] .
Though now I don't understand what I meant by "I'm not really limited by a maximum limit of velocity".
Anyway I get the idea. And the [tex]\Delta p[/tex] is the relativistic momentum, which is what it seems I was doubting on.
Thanks guys, question solved.
 

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