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

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

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

Magnetic Induction B (T) Quantum Hall effect Rxy 0 10 Magnetic Induction B (T) Rxx i=2 i=3 i=4

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

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

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.

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.

Maxwell Equations SI: CGSG:

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

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 2.10-8 and that of εJ of the order of 2.10-7 with important uncertainties.

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.

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

RK determination with the Lampard

Determination of h/mat by Ramsey-Bordé atom interferometry 16 uncertainties (x 10-9) 0.008 2.1 0.2 15 Determination of the fine structure constant

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

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.

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