Quantum Distance? (See me derive it.)

[LiteHacker]

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:
Magnetic flux = \frac{Energy * Time}{Charge}


Thus:
\frac{Charge}{Magnetic flux} is quantum. (Quantum/Quantum = Quantum)

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



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

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


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

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

Distance is quantum.

Anybody see anything wrong with this?

Thank you,
Veniamin

 

[mfb]

"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.

 

[LiteHacker]

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

Indeed this is what I meant.

Conductivity can show quantum effects, but this does not mean that there are fundamental steps of conductivity.

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

 

[mfb]

Instead of there being fundamental steps of conductivity, conductivity is noted to be rational. (You can express it as a fraction of quantised values.)

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).