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Quantum Distance? (See me derive it.)

  1. Oct 28, 2012 #1
    As per: https://en.wikipedia.org/wiki/Elementary_charge
    Charge is quantum.

    As per https://en.wikipedia.org/wiki/Magnetic_flux_quantum
    Magnetic flux is quantum.

    Magnetic flux is measured as follows:
    [itex]Magnetic flux = \frac{Energy * Time}{Charge}[/itex]

    [itex]\frac{Charge}{Magnetic flux}[/itex] is quantum. (Quantum/Quantum = Quantum)

    It has the measurement:
    [itex]\frac{Charge}{Magnetic flux} = \frac{Charge ^{2}}{Energy * Time}[/itex]

    As per: https://en.wikipedia.org/wiki/Von_Klitzing_constant
    Conductivity is quantum.

    Conductivity is measured as follows:
    [itex]Conductivity = \frac{Charge ^{2}}{Energy * Time * Distance}[/itex]

    Taking the top two questions:
    [itex]Conductivity = \frac{\frac{Charge}{Magnetic flux}}{Distance}[/itex]

    Quantum = Quantum / Distance
    Quantum / Quantum = Distance = Quantum

    Distance is quantum.

    Anybody see anything wrong with this?

    Thank you,
  2. jcsd
  3. Oct 28, 2012 #2


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    "is quantum" does not make sense. I think you mean "is quantised".

    Conductivity can show quantum effects, but this does not mean that there are fundamental steps of conductivity.
  4. Oct 28, 2012 #3
    Indeed this is what I meant.

    Instead of there being fundamental steps of conductivity, conductivity is noted to be rational. (You can express it as a fraction of quantised values.)
    Can the same be said for distance then, as per what was shown above?

    Thank you,
  5. Oct 28, 2012 #4


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    Staff: Mentor

    As resistance due to the quantum hall effect, in two-dimensional systems at low temperature and strong magnetic field.

    There is a way to generate a quantised resistance, but it does not mean that resistance IS always quantised as charge is.

    Oh, and I found an error in your dimensional analysis:

    Electric charge: e
    Magnetic flux quantum: Φ = h/(2e)
    Quantum hall effect constant: e^2/h

    No, you don't get a length here. In more basic units, conductivity is charge^2 time^3/(mass length^2).
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