Conductivity of metals at 0 kelvin?

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Discussion Overview

The discussion centers around the conductivity of metals at absolute zero (0 Kelvin), exploring theoretical implications, experimental observations, and the role of entropy and quantum mechanics in this context. Participants engage in a mix of theoretical reasoning and hypothetical scenarios, examining the behavior of metals as temperature approaches absolute zero.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest that conductivity will be zero at 0 K due to the cessation of motion and entropy being zero.
  • Others argue that applying a voltage would introduce energy, preventing the system from remaining at 0 K and potentially leading to superconductivity.
  • It is proposed that the purity of the metal affects conductivity, with very pure metals having high conductivity limited by surface scattering.
  • A participant mentions that for non-superconducting metals, resistance at 0 K is not zero in practice, referencing residual resistance.
  • Some contributions highlight the complexity of the question, indicating that answers vary based on the level of understanding (high school, undergraduate, graduate/professional).
  • There is a discussion about the implications of the uncertainty principle on entropy at 0 K, with differing views on whether zero entropy is a valid concept.
  • Mathematical formulations are presented, including entropy calculations and their relation to quantum states, with some participants challenging the assumptions made in these calculations.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the conductivity of metals at 0 K, with multiple competing views and ongoing debate regarding the implications of quantum mechanics, the role of impurities, and the nature of superconductivity.

Contextual Notes

Limitations include unresolved assumptions about the definitions of entropy and conductivity at absolute zero, as well as the dependence on the purity of metals and the conditions under which measurements are made.

  • #31
mfb said:
It can be different from zero (with a degenerate ground-state), but it does not have to.

I don't think there are actual thermodynamical systems whose true ground state is degenerate. Usually at sufficiently low temperatures some very weak interactions break the degeneracy.
 
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  • #32
That is true. I just keep track of that special case as it is not forbidden.
 
  • #33
It is possible to calculate that all physical wavefunctions satisfy the (p,x)-uncertainty principle. This is related to the mathematics of Fourier transformations. Alternatively, it is possible to derive it in a pure algebraic way as well.
every one knows that.
Source?
It been time.I think it was written in vol. 1 of his and early chapters.
 
  • #34
andrien said:
I think it was written in vol. 1 of his and early chapters.

If you could provide a page number, chapter number or something like that that would be helpful, but either way I'm going to check this out when i next visit a suitable library, because i would have expected better of Feynman!
 
  • #35
psmt said:
i would have expected better of Feynman!

He was unambiguously referring to zero point energy, not entropy.
 

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