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Comité Science et métrologie Académie des sciences 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 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

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

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

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R xy 0 10 Magnetic Induction B (T) R xx i=2 i=3 i=4 Quantum Hall effect

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

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

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On electrical units: In the present SI, the values of μ 0 and ε 0 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 This system is perfectly adapted to the propagation of light in vacuum: no charges but also no ether. gives the radiation pressure and gives the intensity and the number of photons

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Let us now introduce charges. dimensionless constant imposed by nature, extraordinarily well-known today since its present uncertainty is 0.7x 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. The values of μ 0 and ε 0 are related to the positron charge e by the fine structure constant: is just another way to write the positron charge choice adopted by field-theory experts.

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Maxwell Equations CGSG: SI:

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Validity of expressions for R K and K J

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On electrical units: It clarifies future issues to introduce a specific notation for the approximate theoretical expressions of R K and K J : in order to distinguish them from the true experimental constants R K and K J which are related to the previous ones by: Fix h and e would fix the constants but not R K and K J 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 R K and K J. Let us recall that the present estimate of the value of ε K is of the order of and that of ε J of the order of with important uncertainties.

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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.

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243 nm HYDROGEN ATOM

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R K determination with the Lampard

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Determination of h/m at by Ramsey-Bordé atom interferometry 16 uncertainties (x ) Determination of the fine structure constant

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10 Janvier 2006Académie des Sciences 17 Validation of the expression of R K from the fine structure constant

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Conclusion on electrical units: Even if e is fixed, there remains a large uncertainty for R K and K J 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 μ 0.

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Les effets quantiques de la métrologie électrique Effet Hall quantiqueEffet Josephson

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