Position vector r and uncertainty principle

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Discussion Overview

The discussion revolves around the interaction of atomic-scale particles through gravitational and other forces, particularly in the context of the uncertainty principle in quantum mechanics. Participants explore how uncertainty in position affects the calculation of forces and interactions at this scale.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions how gravitational interactions can be defined when the position (r) is not known with complete certainty, suggesting that the force might also have an uncertainty component.
  • Another participant argues that in quantum mechanics, particularly when applying the uncertainty principle, classical forces are not used to describe interactions, and outcomes are treated statistically through operators.
  • A participant notes that the gravitational attraction between sub-atomic particles is negligible, referencing interference experiments that demonstrate the effects of gravity on quantum mechanics.
  • There is a discussion about the use of potential functions for forces, with one participant questioning whether this implies that forces are still being used to describe interactions.
  • Another participant emphasizes that different models can describe interactions in various ways, and they highlight the small scale of uncertainties involved in the Heisenberg Uncertainty Principle (HUP).
  • One participant suggests that at scales where the uncertainty principle is significant, electromagnetic interactions are better described using photons and Feynman diagrams rather than classical laws like Coulomb's Law.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of classical forces in quantum mechanics and the significance of gravitational interactions at atomic scales. The discussion remains unresolved, with multiple competing perspectives presented.

Contextual Notes

Participants acknowledge the limitations of classical descriptions in quantum contexts and the small magnitudes of uncertainties involved, but do not resolve the implications of these factors on the discussion of forces.

MHD93
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Hi physicists,

How can two atomic-scale particles interact through gravitation (Gm1m2/r^2) or any other force that is a function of r if r isn't know with complete certainty. Is it that the force itself also comprises uncertainty in its value?

Thanks
 
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In the model where the uncertainty principle is used, we don't use "forces" to describe interactions. The classical equations like the one you used for an example are not used. These are considered to be obeyed only on average.

What happens is that the uncertainty in relative position and momentum leads to an uncertainty in the outcomes of the interactions. Interactions are described by operators on a range of possibilities and the outcome is treated statistically by summing over all possible outcomes.
 
Also the gravitational attraction between two sub-atomic particles is absurdly negligible. Although you can demonstrate the effect of say Earth's gravity on quantum mechanics through some neat little interference experiments, I believe Shankar (or is it Sakurai) discusses this.
 
Simon Bridge said:
In the model where the uncertainty principle is used, we don't use "forces" to describe interactions. The classical equations like the one you used for an example are not used. These are considered to be obeyed only on average.

What happens is that the uncertainty in relative position and momentum leads to an uncertainty in the outcomes of the interactions. Interactions are described by operators on a range of possibilities and the outcome is treated statistically by summing over all possible outcomes.

If we use the potential function for such forces (such as the electrical force potential), Doesn't that mean that we use "forces" to describe interactions?
 
No - it doesn't.
There are lots of different ways to describe situations and interactions - to be true they have to be related to each other. The different descripton lend themselves to different models... eg. compare analyzing a object sliding down a hill via conservation of energy and by Newton's Laws. But, you know, if you want to think of using mv2/2 = mgh is the same thing as using mgsinθ-μN=ma then I'm not going to argue with you ;)

I do want to echo, and add to, @Many_S_Theory's observation - you realize how small the uncertainties in HUP are right? We are not talking about really big variations.

You could argue that "OK, maybe not gravity - but how about electric fields then" in which case I'd want to respond that in the scale where HUP is important, we do not use the electric potential or Coulombs Force Law and so forth ... on that scale the electromagnetic interaction is described in terms of individual photons and Feynman diagrams.

However, I believe:
What happens is that the uncertainty in relative position and momentum leads to an uncertainty in the outcomes of the interactions.
... answers your original question.
 
Last edited:

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