Understanding Electron Movement with Heisenberg's Uncertainty Principle

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Discussion Overview

The discussion centers around the movement of electrons in atoms, specifically addressing why electrons do not collapse into the nucleus, with a focus on the implications of Heisenberg's Uncertainty Principle (HUP). Participants explore both theoretical and conceptual aspects of quantum mechanics and its interpretations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant calculates the implications of HUP using specific values for position and momentum but expresses confusion about how to interpret changes in velocity (Δv).
  • Another participant clarifies that they are not using relativistic momentum, as their confusion lies with classical momentum.
  • A later post suggests that HUP describes the limitations of information we can obtain from a system rather than the system itself.
  • One participant raises a question about the apparent contradiction between high-precision measurements of particle velocities at the Large Hadron Collider and the principles of HUP.
  • Another participant responds by explaining that while collision points are known, the exact details of the interactions are not, referencing the statistical interpretation of quantum mechanics by Max Born.
  • A participant shares links to resources related to atomic orbitals and their connections to HUP, suggesting further reading.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of HUP and its implications for electron behavior and measurement in quantum mechanics. There is no consensus on the resolution of these points, and the discussion remains open-ended.

Contextual Notes

Participants have not fully resolved the implications of their calculations or the relationship between precision measurements and HUP. There are assumptions about classical versus relativistic momentum that are not fully explored.

Who May Find This Useful

This discussion may be of interest to those studying quantum mechanics, particularly in understanding the implications of HUP on electron behavior and measurement techniques in high-energy physics.

jaydnul
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I'm trying to work out why electrons don't crash down into the nucleus using HUP. So if we take 10^-10 meters, the diameter of hydrogen, and use 10^-13 meters as our Δx, the HUP should come out unequal.

So I get Δp=10^-35*10^13 or

Δp=10^-22 and p=mv, so

Δv=10^10

This is where I am confused. I don't know how to think about the Δv. What values do we choose for v final and v initial?
 
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Also, I didn't use the relativistic momentum because that is not what I am confused about. I thought it would be simpler with just the classical momentum.
 
Nevermind, think I figured it out. HUP doesn't describe the actual system, it describes the information we can get from the system.
 
Some time ago I saw a video relating the large hadron collider. They said that the particles could be accelerated to a velocity of 99.999% the speed of light and they also added that the measured velocities were to an extremely high degree of accuracy. They also showed where the particles actually collide( to be precise, made to collide). If they were so accurate in measuring simultaneously the velocity and position of the particles, are they not violating the uncertainty principle?
 
Rishi Gangadhar said:
They also showed where the particles actually collide( to be precise, made to collide).

Where they collided was not known to much accuracy.

The way such things are calculated is by so called in and out states. We know the states going in, and calculate the transition probabilities of states going out - what's going on in between, and exactly where it occurs, we don't know.

Interestingly this was one of the first things figured out in QM by Max Born leading to the statistical interpretation:
http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Born_1926_statistical_interpretation.pdf

Thanks
Bill
 
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