Escutcheons of Science
 Klaus-Olaf von Klitzing

Klaus-Olaf von Klitzing  (b. 1943)
German physicist  (Nobel 1985)

The above is a copyrighted picture reproduced here by permission.  © 2007   by Jochen Wilke.

Or, three Hungarian caps  [Tatarenmützen]  Gules lined Argent.
D'or, à trois bonnets hongrois de gueules retroussés d'argent,
le sommet orné d'un bouton du même.
Casque couronné
.   [Rietstap]

Klaus von Klitzing was awarded the  (unshared)  1985 Nobel prize for physics  for his 1980 discovery of the quantized Hall effect, or  Integer Quantum Hall Effect  (IQHE).

The  classical  Hall effect was first described in 1879, by the American physicist Edwin H. Hall (1855-1938) as part of his doctoral dissertation, which was published in 1880.

In a magnetic field, a ribbon carrying a current along its length develops a potential difference across its width which is proportional to that current.  The coefficient of proportionality is called the  Hall resistance.  What Klaus von Klitzing discovered is that the Hall resistance varies in discrete steps at low remperature under strong magnetic fields.  This allows an accurate realization of a resistance  (equal to twice the reciprocal of the  quantum of conductance  Go)  whose value depends only on two fundamental constants:  The elementary charge  (e)  and Planck's constant  (h).  This is called the  von Klitzing resistance standard.

RK   =   2 / G0   =   h / e2   =   25 812.8074434(84) W     (CODATA 2010)

Since 1990, the following value has been used by makers of precision instruments:

RK-90   =   25812.807 W

Because the  von Klitzing constant  depends on the charge of the electron, which is a measured value in SI units, the above value  (or any other  de jure  value)  will not yield a consistent system of units.  Electrical units based on the above merely allow very accurate measurements to be recorded and compared against each other.  However, the resulting numbers cannot be multiplied and divided freely as if they were expressed in true SI units.

The discrepancy is probably best illustrated by considering that the dimensionless  fine structure constant  (a)  is simply equal to half the ratio of the  characteristic impedance of vacuum  to the actual  von Klitzing resistance.  Now, the  characteristic impedance of vacuum  has an  exact  value in SI units  because it's simply the product of the speed of light by the magnetic permeability of vacuum  (both factors are known exactly in SI units, because of the definitions of the meter and the ampere, respectively).  Therefore, exact knowledge of the  von Klitzing resistance  in ohms (SI) would be equivalent to  perfect  knowledge of the  fine structure constant,  a dimensionless number whose exact value remains a mystery to this day.  For the record:

25812.807 W  ´ 2 / mc = 137.0359967203403618113165872...
1 / a= 137.035999074(44)

By contrast, a  de jure  value of Planck's constant would amount to a suitable replacement for the current definition of the kilogram (the only SI unit still based on a unique artefact).  This would maintain perfect consistency of the system of units.  In fact, it has been proposed that SI units should be updated exactly this way  (this may have been enacted by the time you read this).

In a metrological context, the above value of  25812.807 W  is just an arbitrary point against which the actual measured value of the  von Klitzing constant  can be compared.

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