first fundamental constant
m1  m2
force  G 
2
r
G  6.674 10
11
3
m
2
kg  s
first basic
constant
Discovery of electron
m(electron )  0.511 MeV
second basic
constant
atoms
atoms =>
quantum electrodynamics
Arnold Sommerfeld, 1916
3.constant
  e 2 / hc
2
2
e
1
 

4
137
h, c  1
Sommerfeld

Einstein
1/   137
1958
Pauli
Nr 137
Kanton-spital
Zürich
Richard Feynman
alpha
one of the biggest secrets
in physics - a magic number,
written by the hand of God
2
e

hc
e  A

Gauge group
i ( x )
U (1)  e
one gauge boson => photon

me
4 gauge bosons
1
1
2
1
mass of weak boson
mass of “Higgs” boson
coupling constants
Electron mass
proton
u
u
d
d
Fritzsch / Gell-Mann
proton
mass
field energy
(gluons and quarks)
E( gluons )  E(quarks)  M p c
2
M  const.   c  860 _ MeV
c
fundamental
constant
c
M p  c    cu mu  cd md  cs ms  celm 
 u  c  t 
 ... ... 
d
s
b
     
7 fundamental constants
in strong interactions
____  c ___
mu
mc
mt
md
ms
mb
III
3 families
of
leptons
and
quarks.
II
I
Johannes Paul II
Newtons constant G
fine structure constant
coupling constant of strong interaction
coupling constant of weak interaction
mass of W boson
mass of Higgs boson
masses of 6 quarks and 6 leptons
flavor mixing of quarks
flavor mixing of leptons
1
1
1
1
1
1
12
4
6
md
ms
mb
me
m
d
u
2
mu
Mw

s
 sun
 atm
GN


m
w
MH
3
l
mc
 chooz
m2
m3
mt
m1
md
ms
mb
me
m
d
u
2
mu
Mw
s

 sun
 atm
GN


m
w
MH
3
l
mc
 chooz
m2
m3
mt
m1
Mw

GN
w
MH
s
Higgs boson ?
weak bosons
quarks
leptons
 1.8 billion years
( Gabon, Africa )
Natural Reactor
3.7% U 235 (today 0.72 %)
Moderator: water from river Oklo
  (Oklo)   ( now) 
7

  10



Change of alpha:
 /   10
16
/ year
(if no other parameters change)
???
Observation :
fine - structure
of atomic levels
Quasars
5-7 billion years back
Quasar absorption spectra
Light
Fine structure of Fe, Ni, Mg, Sn, A Quasars, back to 11 bn years in time
 /   ( 0.54  0.12)10
  /   1.2 10
15
/ year
5
 /   ( 0.54  0.12)10
  /   1.2 10
15
/ year
Oklo reactor ?
5
?
grand
unification
grand
unfication
Grand
unification

 8  s

GUT



const
.

2
2

3 s
 GUT
Calmet, Fritzsch
Langacker, Segre
(2002)

 8  s

GUT



const
.

2
2

3 s
 GUT

8  s


2
2

3 s



 38.8 


change of magnetic
moments of atomic nuclei
(per year)
3,9  10
14
Change of unification scale



 31 


change of
change of
 ~ 10
15
 ~ 10
14
/ year
/ year
Time
=>Cesium clocks
Hyperfine transition
magnetic moment of cesium nucleus
Difference: 3 CS oscillations per day
MPQ-Experiment
486 nm dye laser in hydrogen
spectrometer
Reference: cesium clock Pharao LPTF
Paris
Hydrogen: 1s - 2s transition
2 466 061 413 187 127 (18) Hz
:
magnetic moment

 /    / 
d  / dt :   (2.4  6.8) 10
15
yr
1
d  / dt :   (2.4  6.8) 10
d  / dt :   2 10
14
15
yr
1
d  / dt :   (2.4  6.8) 10
d  / dt :   2 10
14
15
yr
1
Simultaneous change:
unification coupling constant
unification scale
Partial
Cancellation?
(Superstrings)
E. Witten

8  s


GUT


const
.

2
2
3 s

 GUT


15
   3  1  10 / year

 
Reinhold et al. PRL 96 (2006)
2 quasars - 12 billion years 

mp
me
 /   ( 2  0.6)  10
5
  /   3  10
  /   3  1015 / year
15
/ year
===>MPQ
Grand Unification
QFD
QCD
time variation
alpha
time variation
QCD scale

15
 3  10 / year

  /   3  1015 / year
fundamental „constants“
functions of time?
Murray
Gell-Mann
Fundamental
Constants
Cosmic
Accidents ?
Gn
me

s