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

yrt

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

Lyem

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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