1. Comité Science et métrologie
Académie des sciences
Jean Kovalevsky Christian Bordé
Christian Amatore Alain Aspect
François Bacelli Roger Balian
Alain Benoit Claude Cohen-Tannoudji
Jean Dalibard Thibault Damour
Daniel Estève Pierre Fayet
Bernard Guinot Theodor Hänsch
Serge Haroche Yves Jeannin
Pierre Perrier Gabriele Veneziano
Marc Himbert Ian Mills
Terry Quinn Christophe Salomon
Claudine Thomas

2. COMITÉ « SCIENCE ET MÉTROLOGIE » DE L’ACADÉMIE DES SCIENCES
Effet Hall quantique
et métrologie
Colloque organisé par Christian Glattli

3. Quantum Hall effect
and the reform of the SI
Christian J. Bordé

4. Magnetic Induction B (T)
Quantum Hall effect
Rxy
Magnetic Induction B (T)
Rxx
i=2
i=3
i=4

5. Metrological triangle Quantum Ohm law
SET
effect
Josephson
effect
Quantum Hall
effect I

6. Watt balance: principle
A) Static mode:
B) Dynamical mode:
Mass
comparator I
Radial
field
E.m.f. U U U
Velocity
Interferometer
Interferometer
Position
Mechanical Power = Electrical Power

8. On electrical units:
In the present SI, the values of μ0 and ε0 are fixed and
thus the propagation properties of the electromagnetic field
in the vacuum are also fixed:
- propagation velocity
- vacuum impedance
electric and magnetic energy densities
and
gives the radiation pressure and
gives the intensity and the number of photons
This system is perfectly adapted to the propagation of light
in vacuum: no charges but also no ether.

9. Let us now introduce charges.
The values of μ0 and ε0 are related to the positron charge e
by the fine structure constant:
dimensionless constant imposed by nature, extraordinarily
well-known today since its present uncertainty is 0.7x10-9.
The free electromagnetic field is coupled to charges through
this constant, which thus appears as a property of electrons
and not as a property of the free electromagnetic field.
is just another way to write the positron charge
choice adopted by field-theory experts.

10. Maxwell Equations
SI:
CGSG:

11. Validity of expressions for RK and KJ
3.10-8
2.10-7

12. On electrical units:
It clarifies future issues to introduce a specific notation for the
approximate theoretical expressions of RK and KJ :
in order to distinguish them from the true experimental constants
RK and KJ  which are related to the previous ones by:
Fix h and e would fix the constants
but not RK and KJ which would keep an uncertainty.
This uncertainty is not that related to the determination
of e and h in the SI but to our lack of knowledge
of the correction terms to the expressions of RK and KJ.
Let us recall that the present estimate of the value of εK
is of the order of and that of εJ of the order of
with important uncertainties.

13. The fact that the universality of these constants has been
demonstrated to a much better level simply suggests that
possible corrections would involve other combinations of
fundamental constants: functions of α, mass ratios, …
The hydrogen spectrum provides an illustrating example
of a similar situation. The energy of the levels of atomic
hydrogen is given to the lowest order by Bohr formula,
which can also be derived through a topological argument.
Nevertheless there are many corrections to this first term
involving various fundamental constants.
It is not because the spectrum of hydrogen is universal that
we may ignore these corrections and restrict ourselves
to Bohr formula.

14. HYDROGEN ATOM
The fact that the universality of these constants has been demonstrated to a much better level simply suggests that
possible corrections would involve other combinations of fundamental constants: functions of α, mass ratios, …
The hydrogen spectrum provides an illustrating example of a similar situation. The energy of the levels of atomic
hydrogen is given to the lowest order by Bohr formula, which can also be derived through a topological argument.
Nevertheless there are many corrections to this first term involving various fundamental constants.
It is not because the spectrum of hydrogen is universal that we may ignore these corrections and restrict ourselves
to Bohr formula.
243 nm

15. RK determination with the Lampard

16. Determination of h/mat by Ramsey-Bordé atom interferometry16
uncertainties (x 10-9)
Determination of the fine structure constant

17. Validation of the expression of RK from the fine structure constant
10 Janvier 2006
Académie des Sciences
Validation of the expression of RK from the fine structure constant 17

18. Conclusion on electrical units:
Even if e is fixed, there remains a large
uncertainty for RK and KJ  and in addition
vacuum properties acquire an uncertainty.
There seems to be no real advantage
in fixing the value of e rather than that of μ0.

19. Les effets quantiques de la métrologie électrique
Effet Josephson
Effet Hall quantique
4 10-9