Christian J. Bordé. Bruxelles, mai 2018

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unités of Units de (SI): base: de la géométrie Matter-wave

1 A consistent Fondations unified théoriques framework for de the la new métrologie International et du système System d unités of Units de (SI): base: de la géométrie Matter-wave et des optics nombres Christian J. Bordé Bruxelles, mai 018

2 Base units of the SI (Système International) m cd kg K s mol A

3 Emergence of quantum metrology: numbers and geometry All base quantities of metrology, length, time, mass, electrical quantities, temperature are ultimately measured by optical or matterwave interferometers: - Optical interferometry - Atom interferometry - Optical clocks - Josephson effect - Watt balance - Doppler broadening thermometry - Aharonov Bohm and Aharonov Casher phases - Sagnac effect - Gravitational red shift... Future fundamental metrology will thus deal essentially with phase measurements i.e. invariant numbers. All measured quantities enter these phases through geometrical properties of a 5D space-time which combines 4D space-time and the internal space of objects.

4 Relativity Gravitation Atomic Physics m at, c, G R Electrodynamics e, 0 Quantum Mechanics Action: Thermodynamics Statistical Physics Entropy: k B 5D-Optics, k, c, m, e B at

5D-Optics, k, c, m, e B at G Gm e m e 1.

5 5D-Optics, k, c, m, e B at G Gm e m e c mp 45 e e c qp 137 t m c Natural units of Planck 1 kb c,, lp ctp, mp, qp 0c T m c G P 4 P P P

6 Ἀγεωμέτρητος μηδείς εἰσίτω ds g dx dx, 0,1,, 3 Pythagore (Πυθαγόρας) Que nul n'entre ici s'il n'est géomètre! L'École d'athènes de Raphaël, g metric tensor

7 Flat Minkovski space-time (no gravito-inertial field): g g 00 ii 1, 1 c dt dx c d t coordinate time, proper time For light: c dt dx

8 VIRGO (Cascina) GRAVITATIONAL WAVE DETECTION

9 ENERGY E(p) 4 E( p) m c p c Mass E mc 1905 MOMENTUM p

10 ˆ p E c p p p mc ( /,,,, ) x y z ˆ 0,1,,3,4 E ˆ p pˆ 0 mc p

11 x ˆ ( ct, x, y, z, c ) dx ˆ dx ˆ t c dt dx ds 0 s c ds c dt dx 0 x

12 Quantum mechanical phase factor exp i S exp i mc de Broglie- Compton frequency 0 mc h

13 E(p) b a Recoil energy h / m c m b c m a c h / p //

14 Atom Bordé-Ramsey interferometers Laser beams b beam a

15 Atom Bordé-Ramsey interferometers Laser beams b beam Action T a

16 Atom Bordé-Ramsey interferometers Laser beams b beam a

17 Determination of h/m at by Bordé-Ramsey atom interferometry T h m at Atomic recoil: Hall and Bordé, Chu, Biraben

18 Rydberg constant R mc e h

20 Bridging the gap to the 4 K R J K macroscopic h world C M K h c 1 4 f 1 f ( v T / c)

21 Mc A h N 8 M /( a³) Si N Si m c h Escher 1935

(c) Flat etalon Flat etalon Sphere IMGC (b) Flat etalon Sphere

22 Volume measurement by optical interferometry Different types of interferometers (a) Flat etalon Flat etalon Sphere NMI-A (c) Flat etalon Flat etalon Sphere IMGC (b) Flat etalon Sphere Flat etalon NMIJ (d) Fizeau lenses Sphere Fizeau lenses PTB NMIJ PTB

$splitter mirror analyzer transmission diffraction x silicon single-crystal$

23 Principle of lattice spacing measurement by x-ray interferometer incident x-ray splitter mirror analyzer transmission diffraction x silicon single-crystal displacement

24 Les effets quantiques de la métrologie électrique Effet Josephson Prix Nobel 1973 f Effet Hall quantique Prix Nobel 1985 V nk 1 J f n h e f R H R i K 1 i h e i= courant 0 f 1 tension R xy (W) Rxy i=4 i=3 Rxx R XX (W) B(T) 0

25 Generalization in the presence of interactions ˆ xˆ ( ct, x, y, z, c ) G ˆ ˆ 4 g G A G 4 A G A A e / mc rapport gyromagnétique 5D action Sˆ G dxˆ dxˆ ˆ ˆ ˆ ˆ

26 The 5D action gathers all phenomena and constants of interest for a fully relativistic quantum metrology in an invariant phase through Planck's constant and this includes the dephasing arising from gravito-inertial fields (e.g. the Sagnac effect or the effect of gravitational waves) as well as those of electromagnetic origin (such as the Aharonov-Bohm or the Aharonov-Casher effect).

27 mc 4i pˆ ˆ4 ˆ i G c p d x mc f dt f dt * * 00 dt m m G 0 ˆ0 ˆ dt p dx Horloge+décalages Doppler relativiste et gravitationnel Gravimètre+Doppler Ondes gravitationnelles Aharonov-Bohm vectoriel Aharonov-Bohm Nouvelle contribution Aharonov-Bohm scalaire ˆ i0 i ij p j i4 pˆ ˆ ˆ 4 G c p i d x ki f dt f dt * * 00 dt m m G où la masse relativiste s écrit: Origine physique des déphasages 00 ij ˆˆ 1/ Sagnac * m m G uˆ f u ˆ uˆ= pˆ/ p i j i i 4 f ij ˆˆ G ij ˆˆ iˆ 0 0ˆj G G G 00 ˆ ˆ ˆ ˆ ˆ

30 Watt balance: principle A) Static mode B) Dynamical mode

31 En hommage à Alain PICARD BIPM WATT BALANCE Mechanical Power= Electrical Power

32 En hommage à Alain PICARD BIPM WATT BALANCE Mechanical Power= Electrical Power M gv K IU M c K h gvt c nn f e J

33 Atomic Gravimeter S pace c oordinat e z v 0 ' z 1 v 1 z 0 v 0 T Time coordinate t arm II z 1 ' v 1 ' arm I T' z ' v ' z v 7 k 1 M kgt kt gt v0 T z0

34 Cold Atom Gravimeter CAG Observatoire de Paris 34 LNE-SYRTE

35 ABSOLUTE QUANTUM GRAVIMETER World s first commercial sensor utilizing laser-cooled atoms Sensitivity: m.s - / t Stability < m.s - Continuous absolute measurements over months Production line of AQGs running at Muquans

36 Planck vs Boltzmann Action S Entropy S Quantum Quantum k Time t Temperature Liouville - Von Neumann equation: B 1/T i t H, p Bloch equation: H k B 1T

37 LASER SOURCE Amplifier Resonator Measurement of Boltzmann constant k B by absorption spectroscopy, 1/ Internal degrees of freedom Absorption cell v p Mv External motion Detector transmitted intensity D u c k T B mc Doppler width derivative spectrum SPECTRUM Frequency

38 Action mass m Entropy k B mc / h / mc clock phase recoil shift k B T / mc Doppler width proper time temperature T h / kbt Planck' s law for the black body radiation Thermal Decoherence

39 Conclusions Action and entropy are the two cornerstones of the future SI. They should be explicitly introduced in its formulation. The definitions for time and mass units are coupled. A natural theoretical framework for the redefinition of the SI is completely provided by the connection between 5D geometry, metric tensor and metrology, that we have outlined. This perspective incorporates naturally all relevant fundamental constants in a logical scheme.

Atom interferometry. Quantum metrology and fundamental constants. Laboratoire de physique des lasers, CNRS-Université Paris Nord

Atom interferometry. Quantum metrology and fundamental constants. Laboratoire de physique des lasers, CNRS-Université Paris Nord Diffraction Interferometry Conclusion Laboratoire de physique des lasers, CNRS-Université Paris Nord Quantum metrology and fundamental constants Diffraction Interferometry Conclusion Introduction Why using