Is this statement about the Uncertainty Principle correct?

In summary, the conversation discusses the Uncertainty Principle and its manifestation in the macroscopic world. It also explores the connection between the Uncertainty Principle and the Pauli Exclusion Principle and the concept of degeneracy pressure. The correct statement of the Uncertainty Principle is also clarified.
  • #1
Vannay
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I was reading the Feynman Lectures awhile back and I remember reading something he said about the Uncertainty Principle and it seemed slightly odd to me. I don't remember the exact quote and combing through some of the lectures online I can't quite find it. I've heard it more than once from different sources so I know it's something someone said. It is roughly as follows:

A way the Uncertainty Principle manifests itself in the macroscopic world is when you are applying an increasing force on a floor, you are reducing the Δx of the atoms. This causes the Δp to increase or increasing the range that the momenta of the atoms can take. So, due to this compression in x and gradual increase in the range of p, the floor will push back more and more as the force increases.​

Now, I understand this from a classical point of view with electromagnetic forces and the properties of solids but can this quantum phenomenon be applied as a legitmate explanation for this macroscopic phenomenon?
 
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  • #2
It makes sense qualitatively, but I am not sure that one could make quantitative predictions with the idea.

Why do different materials have a different delta x for a given delta p?
 
  • #3
It wrong - the reason the floor pushes back is the Pauli Exclusion principle as was sorted out by Dyson:
https://en.wikipedia.org/wiki/Electron_degeneracy_pressure

The correct statement of the uncertainty principle is the following. Suppose you have a large number of similarly prepared systems ie all are in the same quantum state. Divide them into two equal lots. In the first lot measure position to a high degree of accuracy. QM places no limit on that accuracy - its a misunderstanding of the uncertainty principle thinking it does. The result you get will have a statistical spread. In the second lot measure momentum to a high degree of accuracy - again QM places no limit on that. It will also have a statistical spread. The variances of those spreads will be as per the Heisenberg Uncertainty principle.

Thanks
Bill
 
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  • #4
bhobba said:
It's wrong - the reason the floor pushes back is the Pauli Exclusion principle as was sorted out by Dyson:
https://en.wikipedia.org/wiki/Electron_degeneracy_pressure

I don't think it's wrong. The electron degeneracy pressure and the uncertainty principle are closely linked. Both can be formulated in reference of the phase space volume of a system. Heisenberg's uncertainty says the phase space volume of a single electron is not compressible. Pauli's exclusion says that even the combined phase space volume of many electrons is not compressible. So from a phase space geometry point of view, the two are closely related and you can ultimately reduce the idea of degeneracy pressure to the phase space volume of a single electron being incompressible (plus identical particle symmetry).

Cheers,
Jazz
 
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  • #5
Jazzdude said:
I don't think it's wrong. The electron degeneracy pressure and the uncertainty principle are closely linked. Both can be formulated in reference of the phase space volume of a system. Heisenberg's uncertainty says the phase space volume of a single electron is not compressible. Pauli's exclusion says that even the combined phase space volume of many electrons is not compressible. So from a phase space geometry point of view, the two are closely related and you can ultimately reduce the idea of degeneracy pressure to the phase space volume of a single electron being incompressible (plus identical particle symmetry).

Good point.

Thanks
Bill
 

FAQ: Is this statement about the Uncertainty Principle correct?

What is the Uncertainty Principle?

The Uncertainty Principle, also known as Heisenberg's Uncertainty Principle, is a fundamental principle in quantum mechanics that states that the more precisely the position of a particle is known, the less precisely its momentum can be known, and vice versa.

Is the Uncertainty Principle a proven scientific concept?

Yes, the Uncertainty Principle has been extensively studied and confirmed through numerous experiments and observations. It is considered a fundamental principle of quantum mechanics and has been incorporated into many aspects of modern physics.

Can the Uncertainty Principle be violated or overcome?

No, the Uncertainty Principle is a fundamental limitation of nature and cannot be violated or overcome. It is a consequence of the wave-particle duality of matter and the probabilistic nature of quantum mechanics.

How does the Uncertainty Principle affect everyday life?

The effects of the Uncertainty Principle are not noticeable in everyday life, as it only applies to very small particles such as electrons and photons. However, it has had a major impact on our understanding of the nature of the universe and has led to many technological advancements.

Are there any exceptions to the Uncertainty Principle?

While the Uncertainty Principle applies to most physical systems, there are some exceptions. For example, the principle does not apply to macroscopic objects, such as a baseball, as their position and momentum can be known with high precision. However, for subatomic particles, the Uncertainty Principle holds true and is an essential part of our understanding of the quantum world.

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