Hall resistance and fine structre constant

[MathematicalPhysicist]

do they have any connection to each other (physically)?

im asking because i saw them mentioned in this webpage together:http://www.pha.jhu.edu/~qiuym/qhe/node6.html

 

[Tyger]

Yes, they do.

 

[heumpje]

The quantized Hall resistance goes like 1/[alpha]...

 

[MathematicalPhysicist]

Originally posted by heumpje
The quantized Hall resistance goes like 1/[alpha]...

have you given a look at the page i have given.
it states that alpha=e^2/2h*c*epsilon_0 and the hall resistance is h/e^2, and 1/alpha=2h*c*epsilon_0/e^2 isn't h/e^2.

 

[marcus]

Originally posted by loop quantum gravity
have you given a look at the page i have given.
it states that alpha=e^2/2h*c*epsilon_0 and the hall resistance is h/e^2, and 1/alpha=2h*c*epsilon_0/e^2 isn't h/e^2.

Hello loop, you are right that the q.Hall resistance is
h/e². There is no question about that. It is how it is
defined in the NIST listings of the Fundamental Physical Constants.

A modern term for q. Hall is the "von Klitzing constant" which
metrologists (the experts in this area) want to call it because
the q. Hall effect, and this constant, were discovered by von Klitzing (1985 Nobel for this) so the normal nomenclature would be to call it after Klaus von Klitzing

http://physics.nist.gov/cgi-bin/cuu/Value?eqrk
or google with keywords [CODATA Klitzing]


In the NIST listing the definition of fine structure const alpha
is

a = e²/(4pi e₀ hbar c)

That agrees exactly with what you said about 1/alpha.

So the two things are related---but not in a completely simple way. To get from one to the other you need some factors like c, the speed of light, and like epsilon-naught.

Formulas don't always convey physical insight but, for what its worth, here's the connection:
the quantum hall resistance = m₀c/2a

 

[marcus]

maybe you would like to get an impression of the physical meaning of these things

alpha as you surely know is a pure number------not dependent on any system of units-----in whatever units it always comes out to be around 1/137.036...

On the other hand, the von Klitzing constant is a RESISTANCE so its numerical value depends on what units you use to measure resistance. If you use a big unit then it will have a small numerical value and so on.

So there could not be a really simple-minded connection between the two-----one is a pure constant number (a bit like pi itself!) and the other is a resistance quantity that varies numerically all over the place depending on choice of scale.

If you use metric units then the von Klitzing is IIRC some
25,800 ohms.


If you use natural units setting the values of hbar, c, G, and e all equal to one, then the value of alpha will still come out to be
1/137.036...
but the von Klitzing (quantum Hall) resistance will come out to
be 2 pi resistance units.

The von Klitzing is 2 pi times the natural Planck-style unit of resistance.

If you are familiar with the COULOMB constant that could give you a handle on alpha. The fine structure constant alpha is just the numerical value of the coulomb constant when it is expressed in the same Planck-style units.

Or what amounts to the same thing it is an index, in universal terms, of the strength of the attraction/repulsion between two unit charges----e.g. the repulsion between two electrons expressed in terms of the fundamental constants hbar and c.

 

[MathematicalPhysicist]

Originally posted by marcus
Hello loop, you are right that the q.Hall resistance is
h/e². There is no question about that. It is how it is
defined in the NIST listings of the Fundamental Physical Constants.

A modern term for q. Hall is the "von Klitzing constant" which
metrologists (the experts in this area) want to call it because
the q. Hall effect, and this constant, were discovered by von Klitzing (1985 Nobel for this) so the normal nomenclature would be to call it after Klaus von Klitzing

http://physics.nist.gov/cgi-bin/cuu/Value?eqrk
or google with keywords [CODATA Klitzing]


In the NIST listing the definition of fine structure const alpha
is

a = e²/(4pi e₀ hbar c)

That agrees exactly with what you said about 1/alpha.

So the two things are related---but not in a completely simple way. To get from one to the other you need some factors like c, the speed of light, and like epsilon-naught.

Formulas don't always convey physical insight but, for what its worth, here's the connection:
the quantum hall resistance = m₀c/2a

hi marcus what does m0 stands for? (in mechanics it usually is the friction parameter i don't there is relation to the hall resistance phenomonon though).

 

[marcus]

hi marcus what does m0 stands for? (in mechanics it usually is the friction parameter i don't there is relation to the hall resistance phenomonon though).
------------------------------

Loop, human notation is influenced by custom, historical accidents and compromise and is sometimes unreasonably awkward

Are you familiar with (and comfortable with) the "coulomb constant" k_Coulomb?
If you are sure about that one, the mu and epsilon can be explained easily.

As you very likely know, the Coulomb constant relates the force and distance between two point charges in the simplest imaginable way

F = k_Coulomb multiplied by QQ'/R²

The force between the two charges is just equal to the two charges multiplied together and divided by the square of the separation and then multiplied by k_Coulomb.

Well people have the Coulomb constant dressed in some other guises, for slick formula-writing.

k_Coulomb = 1/4pi e₀

e₀ = 1/4pi k_Coulomb

m₀ = 4pi k_Coulomb/c²

If people would just use k_Coulomb , or if they pleased, 4pi k_Coulomb , consistently they would not need these epsilon and mu thingees. In some timetested systems of units the epsilon and mu don't exist---no one bothers with them and it works out fine.
The old metric system Gaussian CGS was like that
But in the presentday metric system these epsilon and mu things are dignified with important-sounding names and fervently believed in by engineers---they are called "magnetic constant" and "electric constant"
by the NIST (National Inst. of Standards and Tech.)
MU used to be called "magnetic permeability of the vacuum" but that was just a little too silly for the NIST so they recently started calling it simply "magnetic constant"

And EPSILON used to be called the "electric permittivity of the vacuum" (another styrofoam term) but thankfully the NIST has had the decency to stop using that wording and now simply calls it "electric constant"

http://physics.nist.gov/cgi-bin/cuu/Value?eqrk
or google with keywords [CODATA Klitzing]


In the NIST listing the definition of fine structure const alpha
is

a = e²/(4pi e₀ hbar c)

That agrees exactly with what you said about 1/alpha.

So the two things are related---but not in a completely simple way. To get from one to the other you need some factors like c, the speed of light, and like epsilon-naught.

Formulas don't always convey physical insight but, for what its worth, here's the connection:
the quantum hall resistance = m₀c/2a

 

[heumpje]

Originally posted by loop quantum gravity
have you given a look at the page i have given.
it states that alpha=e^2/2h*c*epsilon_0 and the hall resistance is h/e^2, and 1/alpha=2h*c*epsilon_0/e^2 isn't h/e^2.

Apparantly my post wasn't entirely clear. Fortunately it was explained by marcus. I said "goes like" which is different from "is equal to". As marcus said, there are some proportionality constants to be included. PS: I DID look at the page you mentioned and some links there.