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Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
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Base units of the SI, fundamental constants and modern quantum physics

Published:04 August 2005https://doi.org/10.1098/rsta.2005.1635

    Abstract

    Over the past 40 years, a number of discoveries in quantum physics have completely transformed our vision of fundamental metrology. This revolution starts with the frequency stabilization of lasers using saturation spectroscopy and the redefinition of the metre by fixing the velocity of light c. Today, the trend is to redefine all SI base units from fundamental constants and we discuss strategies to achieve this goal. We first consider a kinematical frame, in which fundamental constants with a dimension, such as the speed of light c, the Planck constant h, the Boltzmann constant kB or the electron mass me can be used to connect and redefine base units. The various interaction forces of nature are then introduced in a dynamical frame, where they are completely characterized by dimensionless coupling constants such as the fine structure constant α or its gravitational analogue αG. This point is discussed by rewriting the Maxwell and Dirac equations with new force fields and these coupling constants. We describe and stress the importance of various quantum effects leading to the advent of this new quantum metrology. In the second part of the paper, we present the status of the seven base units and the prospects of their possible redefinitions from fundamental constants in an experimental perspective. The two parts can be read independently and they point to these same conclusions concerning the redefinitions of base units. The concept of rest mass is directly related to the Compton frequency of a body, which is precisely what is measured by the watt balance. The conversion factor between mass and frequency is the Planck constant, which could therefore be fixed in a realistic and consistent new definition of the kilogram based on its Compton frequency. We discuss also how the Boltzmann constant could be better determined and fixed to replace the present definition of the kelvin.

    References

    • Barger R.L& Hall J.L. 1969Pressure shift and broadening of methane line at 3.39 μm studied by laser-saturated molecular absorption. Phys. Rev. Lett, 22. 4. Crossref, ISI, Google Scholar
    • Becker P. 2001History and progress in the accurate determination of the Avogadro constant. Rep. Prog. Phys, 64. 1945–2008. Crossref, ISI, Google Scholar
    • Becker P. 2003Tracing the definition of the kilogram to the Avogadro constant using a silicon single crystal. Metrologia, 40. 366–375. Crossref, ISI, Google Scholar
    • Becker P, et al.2003Determination of the Avogadro constant via the silicon route. Metrologia, 40. 271–287. Crossref, ISI, Google Scholar
    • Bize S. 2004Advances in atomic fountains. C. R. Phys, 5. 813–820.(Special issue on fundamental metrology.). Crossref, ISI, Google Scholar
    • Bordé Ch.J. 1970Spectroscopie d'absorption saturée de diverses molécules au moyen des lasers à gaz carbonique et à protoxyde d'azote. C. R. Acad. Sci. Paris, 271B. 371–374. Google Scholar
    • Bordé Ch.J. 1989Atomic interferometry with internal state labelling. Phys. Lett. A, 140. 10–12. Crossref, ISI, Google Scholar
    • Bordé Ch.J. 2002Atomic clocks and inertial sensors. Metrologia, 39. 435–463. Crossref, ISI, Google Scholar
    • Bordé Ch. JMétrologie fondamentale: unités de base et constantes fondamentales. C. R. Phys, 52004a813–820. Crossref, ISI, Google Scholar
    • Bordé Ch.JQuantum theory of atom-wave beam splitters and application to multidimensional atomic gravito-inertial sensors. Gen. Relat. Gravit, 362004b475–502. Crossref, ISI, Google Scholar
    • Bordé Ch.J& Hall J.L. 1974Ultrahigh resolution saturated absorption spectroscopy. , Brewer R.G& Mooradian AIn Laser spectroscopyNew York:Plenum Press125–142. Crossref, Google Scholar
    • Bordé Ch.J& Kovalevsky JC. R. Phys, 52004789–931.(Special issue on fundamental metrology.). Crossref, ISI, Google Scholar
    • Bordé Ch.J, Houard J.-C& Karasiewicz A. 2000Relativistic phase shift for Dirac particles interacting with weak gravitational fields in matter-wave interferometers. , Laemmerzahl C, Everitt C.W.F& Hehl F.WIn Gyros, clocks and interferometers: testing relativistic gravity in spaceBerlin:Springer403–438.and gr-qc/0008033. Google Scholar
    • Bradley M.P, Porto J.V, Rainville S, Thompson J.K& Pritchard D.E. 1999Penning trap measurements of the masses of 133Cs, 87Rb, 85Rb, and 23Na with uncertainties <or=0.2 ppb. Phys. Rev. Lett, 83. 4510–4513. Crossref, ISI, Google Scholar
    • Brillouin L. 1959La science et la théorie de l'information. Paris:Masson et Cie. Google Scholar
    • Carlberg C, Fritioff T& Bergstrom I. 1999Determination of the 133Cs and proton mass ratio using highly charged ions. Phys. Rev. Lett, 83. 4506–4509. Crossref, ISI, Google Scholar
    • de Beauvoir B, Schwob C, Acef O, Jozefowski L, Hilico L, Nez F, Julien L, Clairon A& Biraben F. 2000Metrology of the hydrogen and deuterium atoms: determination of the Rydberg constant and Lamb shifts. Eur. Phys. J. D, 12. 61–93. Crossref, ISI, Google Scholar
    • DeWitt Bryce S. 1966Superconductors and gravitational drag. Phys. Rev. Lett, 16. 1092–1093. Crossref, ISI, Google Scholar
    • DiFilippo F, Natarajan V, Boyce K.R& Pritchard D.E. 1994Accurate atomic masses for fundamental metrology. Phys. Rev. Lett, 73. 1481–1484. Crossref, PubMed, ISI, Google Scholar
    • Eichenberger A, Jeckelmann B& Richard P. 2003Tracing Planck's constant to the kilogram by electromechanical methods. Metrologia, 40. 356–365.(Special issue: mass.). Crossref, ISI, Google Scholar
    • Evenson K.M, et al.1974Speed of light from direct laser frequency and wavelength measurements: emergence of a laser standard of length. , Brewer R.G& Mooradian AIn Laser spectroscopyNew York:Plenum Press143–156. Crossref, Google Scholar
    • Gill PIn Proc. of the 6th Symp. on Frequency Standards and Metrology2002Singapore:World Scientific. Crossref, Google Scholar
    • Gläser MMetrologia, 402003a299–386.(Special issue: mass.). Crossref, ISI, Google Scholar
    • Gläser MTracing the atomic mass unit to the kilogram by ion accumulation. Metrologia, 402003b376–386.(Special issue: mass.). Crossref, ISI, Google Scholar
    • Guinot B. 1997Application of general relativity to metrology. Metrologia, 34. 261–290. Crossref, ISI, Google Scholar
    • Guinot B. 2004Metrology and general relativity. C. R. Phys, 5. 821–828.(Special issue on fundamental metrology.). Crossref, ISI, Google Scholar
    • Hall J.L& Bordé Ch.J. 1974Direct resolution of the recoil doublets using saturated absorption techniques. Bull. Am. Phys. Soc, 19. 1196. ISI, Google Scholar
    • Hall J.L, Bordé Ch.J& Uehara K. 1976Direct optical resolution of the recoil effect using saturated absorption spectroscopy. Phys. Rev. Lett, 37. 1339–1342. Crossref, ISI, Google Scholar
    • Huber A, Gross B, Weitz M& Hänsch T.W. 1999High-resolution spectroscopy of the 1S–2S transition in atomic hydrogen. Phys. Rev. A, 59. 1844. Crossref, ISI, Google Scholar
    • Jain A.K, Lukens J.E& Tsai J.S. 1987Test for relativistic gravitational effects on charged particles. Phys. Rev. Lett, 58. 1165–1168. Crossref, PubMed, ISI, Google Scholar
    • Jeckelmann B& Jeanneret B. 2001The quantum Hall effect as an electrical resistance standard. Rep. Prog. Phys, 64. 1603–1655. Crossref, ISI, Google Scholar
    • Kautz R.L& Lloyd F.L. 1987Precision of series-array Josephson voltage standards. Appl. Phys. Lett, 51. 2043–2045. Crossref, ISI, Google Scholar
    • Kibble B.P. 1975A measurement of the gyromagnetic ratio of the proton by the strong field method. , Sanders J.H& Wapstra A.HIn Atomic masses and fundamental constants, vol. 5New York:Plenum Press545–551. Google Scholar
    • Kose V, Siebert B.R.L& Wöger W. 2003General principles for the definitions of the base units in the SI. Metrologia, 40. 146–153. Crossref, ISI, Google Scholar
    • Lach G, Jeziorski B& Szalewicz K. 2004Radiative corrections to the polarizability of Helium. Phys. Rev. Lett, 92. 233001. doi:10.1103/PhysRevLett.92.233001. Crossref, PubMed, ISI, Google Scholar
    • Luther H, Grohmann K& Fellmuth B. 1996Determination of thermodynamic temperature and 4He virial coefficients between 4.2 K and 27.0 K by dielectric constant gas thermometry. Metrologia, 33. 341–352. Crossref, ISI, Google Scholar
    • Martin J.E& Haycocks P.R. 1998Design considerations for the construction of an absolute radiation detector at the NPL. Metrologia, 35. 229–233. Crossref, ISI, Google Scholar
    • Mills, I. M., Mohr, P. J., Quinn, T. J., Taylor, B. N. & Williams, E. R. In press. Redefinition of the kilogram: a decision whose time has come. Metrologia. Google Scholar
    • Mohr P.J& Taylor B.N. 1999CODATA recommended values of the fundamental physical constants: 1998. J. Phys. Chem. Ref. Data, 28. 1713–1852. Crossref, ISI, Google Scholar
    • Moldover M.R& Ripple D.C. 2003Comments on “General principles for the definition of the base units in the SI”. Metrologia, 40. L9–L10. Crossref, ISI, Google Scholar
    • Niemeyer J, Grimm L, Hamilton C& Steiner R. 1986High precision measurement of a possible resistive slope of Josephson array voltage steps. IEEE Electr. Device Lett, EDL-7. 44–46. Crossref, ISI, Google Scholar
    • Niering M, et al.2000Measurement of the hydrogen 1S–2S transition frequency by phase coherent comparison with a microwave cesium fountain clock. Phys. Rev. Lett, 84. 5496. Crossref, PubMed, ISI, Google Scholar
    • Pendrill L.R. 1996Macroscopic and microscopic polarizabilities of helium gas. J. Phys. B, 29. 3581–3586. Crossref, ISI, Google Scholar
    • Piquemal F, et al.2004Fundamental electrical standards and the quantum metrological triangle. C. R. Phys, 5. 857–879.(Special issue on fundamental metrology.). Crossref, ISI, Google Scholar
    • Quinn T.J. 1999Practical realization of the definition of the metre (1997). Metrologia, 36. 211–244. Crossref, ISI, Google Scholar
    • Quinn T.J. 2003Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards (2001). Metrologia, 40. 103–133. Crossref, ISI, Google Scholar
    • Quinn T.J& Martin J.E. 1996Total radiation measurements of thermodynamic temperature. Metrologia, 33. 375–381. Crossref, ISI, Google Scholar
    • Reichert J, Niering M, Holzwarth R, Weitz M, Udem Th& Hänsch T.W. 2000Phase coherent vacuum-ultraviolet to radio frequency comparison with a mode-locked laser. Phys. Rev. Lett, 84. 3232. Crossref, PubMed, ISI, Google Scholar
    • Renaot E, Elgourdou M& Bonnier G. 2000Interlaboratory comparison of realizations of the triple point of water. Metrologia, 37. 693–699. Crossref, ISI, Google Scholar
    • Schwitz W, Jeckelmann B& Richard P. 2004Towards a new kilogram definition based on a fundamental constant. C. R. Phys, 5. 881–892.(Special issue on fundamental metrology.). Crossref, ISI, Google Scholar
    • Sterr U, et al.2004The optical calcium frequency standards of PTB and NIST. C. R. Phys, 5. 845–856.(Special issue on fundamental metrology.). Crossref, ISI, Google Scholar
    • Storm L. 1986Precision measurements of the Boltzmann constant. Metrologia, 22. 229–234. Crossref, ISI, Google Scholar
    • Stuhler J, Fattori M, Petelski T& Tino G.M. 2003MAGIA-using atom interferometry to determine the Newtonian gravitational constant. J. Opt. B: Quantum Semiclassical Opt, 5. S75–S81. Crossref, Google Scholar
    • Taylor B.N& Mohr P.J. 1999On the redefinition of the kilogram. Metrologia, 36. 63–64. Crossref, ISI, Google Scholar
    • Taylor B.N& Mohr P.J. 2001The role of fundamental constants in the international system of units (SI): present and future. IEEE Trans. Instrum. Meas, 50. 563–567. Crossref, ISI, Google Scholar
    • Trapon G, Thévenot O, Lacueille J.C& Poirier W. 2003Determination of the von Klitzing constant RK in terms of the BNM calculable capacitor—fifteen years of investigations. Metrologia, 40. 159–171. Crossref, ISI, Google Scholar
    • Tsai J.S, Jain A.K& Lukens J.E. 1983High precision test of the universality of the Josephson voltage-frequency relation. Phys. Rev. Lett, 51. 316–319. Crossref, ISI, Google Scholar
    • Tuninsky V.S. 2003Unit systems based on the fundamental constants. Metrologia, 36. 9–14. Crossref, ISI, Google Scholar
    • White D.R, et al.1996The status of Johnson noise thermometry. Metrologia, 33. 325–335. Crossref, ISI, Google Scholar
    • Wicht A, Hensley J.M, Sarajlic E& Chu SA preliminary measurement of h/Mcs with interferometry. & Gill PIn Proc. of the 6th Symp. on Frequency Standards and Metrology2002aSingapore:World Scientific193–212. Google Scholar
    • Wicht A, Hensley J.M, Sarajlic E& Chu SA preliminary measurement of the fine structure constant based on atom interferometry. Phys. Scr, 1022002b82–88. Crossref, ISI, Google Scholar
    • Wignall J.W.G. 1992Proposal for an absolute, atomic definition of mass. Phys. Rev. Lett, 68. 5–8. Crossref, PubMed, ISI, Google Scholar
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