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##### The Constancy of Constants

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**N = a·(Fc/Fg)2 = b·(tU/te)2 = c·(RU/Re)2**(a, b, c of order unity) Dirac’s Large Number Hypothesis “A New Basis for Cosmology” Proceedings of the Royal Society of London, A165, 199 (1938) Ratio between cosmological constants and atomic constants gives large numbers of equal magnitude**Conventional: e, me, mp, h, c, NA, kB, G, ε0, µ0**SI: µ0 = 4π * 10-7 Hm-1 (def.), ε0 * µ0 = c-2 Minimal Standard Model has 20 free parameters, among which: 6 quark masses (u, d, c, s, t, b) 3 lepton masses (e, µ, ) 1 Higgs mass 3 coupling constants (gs, gw, g1) Fundamental Constants Not always well-defined, definitely time-dependent • Central to a given theory • Cannot be calculated • No idea where it comes from**Theory**No reason for (fundamental) constants to be constant! Modern Unified Theories (e.g. String, M, KK Theories) invoke extra (spatial) dimensions. 3+1 dimensional constants related to scale sizes of extra dimensions Example M-theory: gravity acts in all 11 dimensions, other forces only in 4 Gives rise to variation in G on very small scales Constants in theory often related to geometry/symmetry Example Inflation Model: electron mass changed during inflation of early universe**Dimensions**Dimensional constants: value depends on units Dimensionless constants are just numbers units = constants Constants can be used to create “natural” unit systems Measurement of dimensional quantity is comparison Measurement itself is always dimensionless: quantity/units = number Measurement of dimensional quantity needs a “yardstick” to compare to Question: Can a change of a dimensional constant be measured?**Alpha**Electromagnetic coupling constant dimensionless 7.297 352 568(24) x 10-3 (NIST) = 1/137.035999 2 approaches: Laboratory experiments (short “look-back time” (years), high measurement accuracy) Or Astrophysical data (long “look-back time” (Gyears), larger systematic errors)**Same limit for the quantity**Atomic Clocks H. Marion et al., Phys.Rev.Lett.90 150801 (2003) Compare hyperfine structure of 133Cs and 87Rb during 5 years using atomic fountain clocks with an accuracy of ~10-15. Relativistic corrections of order (Zα)2 Next step: go into space (PHARAO project), increase sensititvity by about 100 http://www.obspm.fr/actual/nouvelle/may03/varalpha.en.shtml**Hydrogen spectroscopy**Hänch et al., Phys. Rev. Lett.92 230802 (2004) High precision (10-15) measurements of 1S-2S transition in atomic Hydrogen over a period of 4 years.**OKLO**Low abundance of 235U in mines Natural nuclear reactor almost 2 billion years ago Requires neutron capture by 149Sm (Shlyakhter, 1976) Resonance energy very sensitive to change in alpha Sm isotopic abundances 149Sm neutron absorption cross section neutron capture resonance energy Δ/. Present limit: Da/a=(-0.04±0.15)×10-7(Fujii, Int.J.Mod.Phys.D11 1137 (2002)**Meteorites**Olive et al., Phys.Rev.D66 045022 (2002) Compare age of meteorites using Rhenium dating with other dating methods 187Re most sensititve Usually: Re/Os ratio is measured Osmium used as “anchor” Rhenium lifetime changed < 0.5% during the life of the solar system => Δ/ < 10-7 over 4.6 billion years http://www.sciam.com/article.cfm?articleID=0005BFE6-2965-128A-A96583414B7F0000&chanID=sa008**Quasar**To Earth SiII CIV Lyman limit Lya SiII CII SiIV Lyb Lybem NVem Lya forest CIVem SiIVem Distant Quasars Quasar: extremely massive (billion solar mass) black holes Extremely bright due to material falling towards black hole Intervening gas clouds cause absorption spectrum mostly Hydrogen, but also metallic ions can be measured with telescope & spectrograph**Webb/Murphy**Webb et al., Phys. Rev. Lett. 87 091301 (2001) Improved method (AD => MM) & improved laboratory measurements Δα/α = (0.72 ± 0.18) × 10−5 over a redshift range of 0.5 – 3.5. Might be systematic effects (all data from Keck1), next step: use different telescope: VLT**Mp/Me**Again, it started “fluffy”… F. Lenz, Physical Review 82 554 (1951) A very short article**Recent work**• Ubachs et al., Phys. Rev. Lett.96, 151101 (2006) • QCD coupling varies vary faster than QED in some unification scenarios • Method similar to alpha • H2 spectra from quasars & interstellar clouds • Precise laboratory measurement • 3.5 σ C.L. that µ has decreased over the past 12 Gyear • Δµ/µ = (2.0 ± 0.6) · 10-5**Back to the question…**Can a change of a dimensional constant be measured?**Independent of e**Independent of ħ Independent of c “Planck” “Stoney” “Schrödinger” Natural unit systems All related via ! Back