The Constancy of Constants
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The Constancy of ConstantsThe Constancy of Constants
Dirac’s Large Number HypothesisDirac’s Large Number Hypothesis
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“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
80102.1 N
N = a·(Fc/Fg)2 = b·(tU/te)2 = c·(RU/Re)2
(a, b, c of order unity)
Fundamental ConstantsFundamental Constants
• Central to a given theory• Cannot be calculated
• No idea where it comes from
Not always well-defined, definitely time-dependent
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 mass3 coupling constants (gs, gw, g1)
TheoryTheory
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
Dimensions
units = constants
Measurement of dimensional quantity is comparisonMeasurement itself is always dimensionless:
quantity/units = number
Measurement of dimensional quantity needs a “yardstick” to compare to
Dimensional constants: value depends on unitsDimensionless constants are just numbers
Constants can be used to create “natural” unit systems
Question: Can a change of a dimensional constant be measured?
AlphaAlpha
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)
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ExperimentsExperiments
Atomic ClocksAtomic Clocks
11610)0.72.0(ln
yrt Cs
Rb
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
44.0
CS
RbSame limit for the quantity
Hydrogen spectroscopyHydrogen 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)
115109.29.0ln
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OKLOOKLO
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: /=(-0.04±0.15)×10-7 (Fujii, Int.J.Mod.Phys. D11 1137 (2002)
MeteoritesMeteoritesOlive 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
187Re most sensititve
Usually: Re/Os ratio is measured
Osmium used as “anchor”
Distant QuasarsDistant Quasars
To Earth
Quasar
Quasar: extremely massive (billion solar mass) black holesExtremely 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
CIVSiIVCIISiII
Ly forest
Lyman limit Ly
NVem
SiIVem
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Ly SiII
CIVem
Webb/MurphyWebb/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
MMpp/M/Mee
Again, it started “fluffy”…F. Lenz, Physical Review 82 554 (1951)
A very short article
Recent workRecent 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
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Back to the question…Back to the question…
Can a change of a dimensional constant be measured?
Natural unit systemsNatural unit systems
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“Schrödinger”
Independent of c“Planck”
Independent of e
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