What Are What Are Fundamental Fundamental Constants?Constants?

Cosmic Accidents?Cosmic Accidents?Determined by Dynamics?Determined by Dynamics?

Changing in Time?Changing in Time?Given by Self-Consistency?Given by Self-Consistency?

Calculable?Calculable?

nG

sem

Sommerfeld, 1916………Sommerfeld, 1916………

Pauli (1958): Nr 137, Pauli (1958): Nr 137, Zürich.............Zürich.............

L. Lederman, 137 Eola RoadL. Lederman, 137 Eola Road

Feynman: 137–how little we Feynman: 137–how little we

knowknow

137/1

/22

hce

03599976137

1

.

QED: Most successful theory QED: Most successful theory in science. Merging of in science. Merging of electrody-namics, quantum electrody-namics, quantum mechanics and special mechanics and special relativity.relativity.Renormalizable theory, Renormalizable theory, tested up to 1:10 000 000tested up to 1:10 000 000(Lamb shift, hyperfine splitting, (Lamb shift, hyperfine splitting, magnetic moments)magnetic moments)

Not expected by the creators of Not expected by the creators of the theory: Dirac, Heisenberg, the theory: Dirac, Heisenberg, Pauli, …Pauli, …

Quantum Field Theory:Quantum Field Theory:

Finestructure constant becomes Finestructure constant becomes function of energy or scale due to function of energy or scale due to quantum fluctuations of electron-quantum fluctuations of electron-positron pairspositron pairs

=> partial screening of bare charge of => partial screening of bare charge of the electron at distances less than the electron at distances less than the compton wavelength of the the compton wavelength of the electronelectron

Renormalization GroupRenormalization GroupContribution of electron-Contribution of electron-

positron pairspositron pairs

3

2

( , ) ( )ln( / )

( ) ...12

r

de q e e

d q M

QED

ee

3

2( ) ( . )

12

ee el myons tauons u d s c b

LEP: ~ 1/127LEP: ~ 1/127

( ) 1/127.8ZM

(200 )GeV

About 1.8 billion years ago, in Gabon, About 1.8 billion years ago, in Gabon,

Westafrika. Westafrika. Natural Reactor, which operated about Natural Reactor, which operated about

100 million years.100 million years. High concentration of uraniumHigh concentration of uranium 3.7% U 235 at that time (today 0.72 %)3.7% U 235 at that time (today 0.72 %) Moderator: water from river OkloModerator: water from river Oklo (off – on reactor, period about 30 min)(off – on reactor, period about 30 min)

Discovered in the 1970ties by frenchDiscovered in the 1970ties by french

nuclear physicistsnuclear physicists

It was found: It was found:

Uranium 235 had 0.717 %-Uranium 235 had 0.717 %-

Normally: 0.720 % Normally: 0.720 %

=> further investigation=> further investigation

Shlyakhter, Dyson and Damour (1996)Shlyakhter, Dyson and Damour (1996)Neutron CaptureNeutron Capture

Sm(149) + n =>Sm(150) + gammaSm(149) + n =>Sm(150) + gammaCalculation: cross section about 57 … 93 kbCalculation: cross section about 57 … 93 kb

very large cross section due to very large cross section due to nuclear resonance just above thresholdnuclear resonance just above threshold

E=0.0973 eVE=0.0973 eV

Resonance position cannot have changed muchResonance position cannot have changed much Change less than 0.1 eV =>Change less than 0.1 eV =>

alpha(Oklo)-alpha(now)/alphaalpha(Oklo)-alpha(now)/alpha

<1/10 000 000<1/10 000 000

Change of alpha per yearChange of alpha per year

must be less thanmust be less than

1/10 000 000 000 000 000 1/10 000 000 000 000 000

per yearper year

(if no other parameters (if no other parameters change)change)

=>constraint questionable=>constraint questionable

Thus far only one mechanism of mass Thus far only one mechanism of mass

generation established: generation established:

QCDQCDMass from „no-mass“Mass from „no-mass“

(dimensional transmutation)(dimensional transmutation)

„„Anti-screening“ of color – Anti-screening“ of color –

infrared slaveryinfrared slavery

:about 250 MeV:about 250 MeV

Mass: confined field energyMass: confined field energy

c

Nucleon Mass in limit of Nucleon Mass in limit of vanishing quark masses:vanishing quark masses:

const. calculable, but large errors at const. calculable, but large errors at present.present.

Exp: 938.272 MeVExp: 938.272 MeV

cconstM .

Nucleon Mass in QCD:Nucleon Mass in QCD:

Nuleon mass: QCD mass and massNuleon mass: QCD mass and mass

contributions from the quark massescontributions from the quark masses

Example: QCD u d s+c Example: QCD u d s+c QED)QED)

n u u d d s s elmM c c m c m c m c

938.272 (861.532 20.138 19.253 35.362 1.987)pM MeV MeV

The Dark Corner of HEPThe Dark Corner of HEPFermion Masses: ArbitraryFermion Masses: Arbitrary

L

R

lbGeVMeVme301000.22460000021.0511.0

6 Constants for stable matter

d

u

m

m

Atoms, Nuclei

em

G

um

s

w

dm

tmbm

em

m

cm

u

d

sm

m

wM

HM

Constantsof

Nature

2m

1m

3m

sun

atm

choozl

2

3

Quark Masses:Quark Masses:

Observed:Observed:

m(c) : m(t) = m(u):m(c) m(c) : m(t) = m(u):m(c) 1/185 1/1901/185 1/190

m(s):m(b) = m(d):m(s)m(s):m(b) = m(d):m(s) 1/24 1/231/24 1/23

Relations among constants?Relations among constants?

e.g. flavor mixinge.g. flavor mixing( slight reduction of nr. of parameters)( slight reduction of nr. of parameters)

/u u cm m

/d d sm m

Higgs“ v.e.v.Higgs“ v.e.v.

v = 246 GeVv = 246 GeV(Fermi constant)(Fermi constant)

/ 2 174 ?tv m

Time Variation of fundamental Time Variation of fundamental constants:constants:

Dirac (~1930)Dirac (~1930)

1010

Observation offine structure of atomic levels

Quasars5-7 billion years back

Fine structure of Fe, Ni, Mg, Sn, AFine structure of Fe, Ni, Mg, Sn, A

Quasars, back to 11 bn years in timeQuasars, back to 11 bn years in time

(challenged by Reimers, Chile, (challenged by Reimers, Chile, investigating only one quasar)investigating only one quasar)

5

15

/ ( 0.54 0.12)10

_ .: / : 1.2 10 _ _Linear App d dt per year

SU(3)xSU(2)xU(1) < SU(5)SU(3)xSU(2)xU(1) < SU(5)

(G, G: 1974)(G, G: 1974)

SU(3)xSU(2)xU(1) < SU(3)xSU(2)xU(1) < SO(10)SO(10)

(F-M, G : 1975)(F-M, G : 1975)

O(10)

Electroweak theory:Electroweak theory:

SU(2) x SU(2) x U(1)SU(2) x SU(2) x U(1)

U(1): (B-L)U(1): (B-L)

Coupling Constants in SU(5) with Coupling Constants in SU(5) with SupersymmetrySupersymmetry

(similar in SO(10) – Theory)(similar in SO(10) – Theory)

If the scale of unification does If the scale of unification does not change, one finds:not change, one finds:

2 28 1/ : : ( .) _ / :

3 2s s Gut Gutd dt d const d dt

2 28/ : / :

3 s sd dt d dt

Calmet, F. - Langacker, Segre (2002)

Magnetic moments of atomic Magnetic moments of atomic nuclei would change nuclei would change accordingly, per yearaccordingly, per year

/ : 38,8 _ / :d dt d dt

143,9 10

If only the scale of unification If only the scale of unification changes, the sign changes:changes, the sign changes:

/ : 31_ / :d dt d dt

Time: measured by Cesium Time: measured by Cesium clocksclocks

Hyperfine transition, Hyperfine transition, involving the magnetic involving the magnetic moment of the cesium moment of the cesium nucleus.nucleus.

Would be affected by time Would be affected by time change of QCD scalechange of QCD scale

Comparison

Cs-

clockHydrogen

clock

Difference: 3 CS oscillations per day

Experiment at MPQ Munichand NIST Boulder

MPQ-ExperimentMPQ-Experiment

486 nm dye laser in hydrogen486 nm dye laser in hydrogenspectrometerspectrometer

Reference: cesium clock Pharao LPTFReference: cesium clock Pharao LPTFParisParis

Hydrogen: 1s-2s transitionHydrogen: 1s-2s transition2 466 061 413 187 127 (18) Hz2 466 061 413 187 127 (18) Hz

Expected in simple model:Expected in simple model:about 10 times moreabout 10 times more

Measurement:Measurement:15 1/ : (2.4 6.8) 10d dt yr

14/ : 2 10d dt

Simultaneous change of unif. coupling Simultaneous change of unif. coupling andand

unif. scaleunif. scalePartial Cancellation of effect? Partial Cancellation of effect?

(expected in superstring models)(expected in superstring models)

Indication for effect in the new exp. at Indication for effect in the new exp. at MPQ:MPQ: 15/ : (3 1) 10 /d dt year

2 28 1/ : / : ( .) _ / :

3 2s s Gut Gutd dt d dt const d dt

Very recently: Very recently: Reinhold et al. PRL 96 (2006)Reinhold et al. PRL 96 (2006)2 quasars, 12 bn. years away2 quasars, 12 bn. years away

Looking for time variation of ratio Looking for time variation of ratio proton mass / electron massproton mass / electron mass

One finds:One finds:

5/ (2 0.6) 10

Hänsch finds the same effect Hänsch finds the same effect

15/ 3 10 / year

SummarySummary

28 constants of nature, 24 of them mass 28 constants of nature, 24 of them mass parametersparameters

Grand unification relates elm., strong and weakGrand unification relates elm., strong and weakinteractions.interactions.

Time variation of alpha leads to time variation of theTime variation of alpha leads to time variation of theQCD scale and of the weak interactionsQCD scale and of the weak interactions

MPQ Experiment rules out simplest model, but effectMPQ Experiment rules out simplest model, but effectseems to be there, about a factor 10 less than naivelyseems to be there, about a factor 10 less than naivelyexpected, consistent mit observed variation of expected, consistent mit observed variation of electron-proton-massratio.electron-proton-massratio.

Necessary:Necessary:

Both unification scale Both unification scale

andand

unified couplingunified coupling

must change in time.must change in time.

(expected in superstring models)(expected in superstring models)