# Quantum Distance? (See me derive it.)

1. Oct 28, 2012

### 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

2. Oct 28, 2012

### 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.

3. Oct 28, 2012

### LiteHacker

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

4. Oct 28, 2012

### 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).