Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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]


    Thus:
    [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,
    Veniamin
     
  2. jcsd
  3. Oct 28, 2012 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    "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,
    Veniamin
     
  5. Oct 28, 2012 #4

    mfb

    User Avatar
    2016 Award

    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).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Quantum Distance? (See me derive it.)
  1. Quantum Distance (Replies: 2)

Loading...