1. The Constancy of Constants

2. 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 N = a·(F c /F g ) 2 = b·(t U /t e ) 2 = c·(R U /R e ) 2 (a, b, c of order unity)

3. Fundamental Constants Central to a given theory Cannot be calculated No idea where it comes from Not always well-defined, definitely time-dependent Conventional: e, m e, m p, h, c, N A, k B, G, ε 0, µ 0 SI: µ 0 = 4π * 10 -7 Hm -1 (def.), ε 0 * µ 0 = 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 (g s, g w, g 1 )

4. Theory 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 No reason for (fundamental) constants to be constant! Constants in theory often related to geometry/symmetry Example Inflation Model: electron mass changed during inflation of early universe

5. Dimensions units = constants Measurement of dimensional quantity is comparison Measurement itself is always dimensionless: quantity/units = number Measurement of dimensional quantity needs a “yardstick” to compare to Dimensional constants: value depends on units Dimensionless constants are just numbers Constants can be used to create “natural” unit systems“natural” unit systems Question: Can a change of a dimensional constant be measured?

6. Alpha dimensionless Electromagnetic coupling constant 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)

7. Experiments

8. Atomic Clocks H. Marion et al., Phys.Rev.Lett. 90 150801 (2003) Compare hyperfine structure of 133 Cs and 87 Rb during 5 years using atomic fountain clocks with an accuracy of ~10 -15. Relativistic corrections of order (Zα) 2 http://www.obspm.fr/actual/nouvelle/may03/varalpha.en.shtml Next step: go into space (PHARAO project), increase sensititvity by about 100 Same limit for the quantity

9. Hydrogen spectroscopy High precision (10 -15 ) measurements of 1S-2S transition in atomic Hydrogen over a period of 4 years. Hänch et al., Phys. Rev. Lett. 92 230802 (2004)

10. OKLO Low abundance of 235 U in mines Natural nuclear reactor almost 2 billion years ago Requires neutron capture by 149 Sm (Shlyakhter, 1976) Resonance energy very sensitive to change in alpha Sm isotopic abundances  149 Sm neutron absorption cross section  neutron capture resonance energy  Δ  / . Present limit:  /  =(-0.04±0.15)×10 -7 (Fujii, Int.J.Mod.Phys. D11 1137 (2002)

11. Meteorites Olive et al., Phys.Rev. D66 045022 (2002) Compare age of meteorites using Rhenium dating with other dating methods 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 187 Re most sensititve Usually: Re/Os ratio is measured Osmium used as “anchor”

12. Distant Quasars To Earth Quasar 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 CIV SiIVCIISiII Ly  forest Lyman limit Ly  NV em SiIV em Ly  em Ly  SiII CIV em

13. Webb/Murphy Improved method (AD => MM) & improved laboratory measurements Webb et al., Phys. Rev. Lett. 87 091301 (2001) 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

14. M p /M e Again, it started “fluffy”… F. Lenz, Physical Review 82 554 (1951) A very short article

15. 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 –H 2 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

16. Back to the question… Can a change of a dimensional constant be measured?

17. Natural unit systems “Stoney” Independent of ħ “Schrödinger” Independent of c “Planck” Independent of e All related via  ! Back