AC Fundamental Constants

1
AC Fundamental Constants

• Savely G Karshenboim
• Pulkovo observatory (St. Petersburg)
• and Max-Planck-Institut für Quantenoptik
  (Garching)

2
Astrophysics, Clocks andFundamental Constants
3
Astrophysics, Clocks andFundamental Constants

• Why astrophysics?
• Cosmology changing universe.
• Inflation variation of constants.
• Pulsars astrophysical clocks.
• Quasars light from a very remote past.

• Why clocks?
• Frequency most accurately measured.
• Different clocks planetary motion, pulsars,
  atomic, molecular and nuclear clocks different
  dependence on the fundamental constants.

4
Astrophysics, Clocks andFundamental Constants

• Why astrophysics?
• Cosmology changing universe.
• Inflation variation of constants.
• Pulsars astrophysical clocks.
• Quasars light from a very remote past.

• Why clocks?
• Frequency most accurately measured.
• Different clocks planetary motion, pulsars,
  atomic, molecular and nuclear clocks different
  dependence on the fundamental constants.

But everything related to astrophysics is model
dependent and not transparent.
5
Optical Atomic Clocks andFundamental Constants

• Why atomic clocks?
• Frequency measurements are most accurate up to
  date.
• Different atomic and molecular transitions
  differently depend on fundamental constants (a,
  me/mp, gp etc).

• Why optical?
• Optical clocks have been greatly improved and
  will be improved further.
• They allow a transparent model-independent
  interpretation in terms of a variation.

6
Atomic Clocks andFundamental Constants

• Why atomic clocks?
• Frequency measurements are most accurate up to
  date.
• Different atomic and molecular thansitions
  differently depend on fundamental constants (a,
  me/mp, gp etc).

• Why optical?
• Optical clocks have been greatly improved and
  will be improved further.
• They allow a transparent model-independent
  interpretation in terms of a variation.

Up to now the optical measurements are the only
source for accurate and reliable
model-independent constraints on a possible time
variation of constants.
7
Outline

• Are fundamental constants fundamental?
  constants?
• Various fundamental constants
• Origin of the constants in modern physics
• Measurements and fundamental constants
• Fundamental constants units of physical
  quantities
• Determination of fundamental constants
• Precision frequency measurements variation of
  constants
• Clocks for fundamental physics
• Advantages and disadvantages of laboratory
  searches
• Recent results in frequency metrology
• Current laboratory constraints

8
Introduction

• Physics is an experimental science and the
  measurements is the very base of physics.
  However, before we perform any measurements we
  have to agree on certain units.

9
Introduction

• Physics is an experimental science and the
  measurements is the very base of physics.
  However, before we perform any measurements we
  have to agree on certain units.
• Our way of understanding of Nature is a
  quantitive understanding, which takes a form of
  certain laws.

10
Introduction

• Physics is an experimental science and the
  measurements is the very base of physics.
  However, before we perform any measurements we
  have to agree on certain units.
• Our way of understanding of Nature is a
  quantitive understanding, which takes a form of
  certain laws.
• These laws themselves can provide no quantitive
  predictions. Certain quantitive parameters enter
  the expression of these laws. Some enter very
  different equations from various fields.

11
Introduction

• Physics is an experimental science and the
  measurements is the very base of physics.
  However, before we perform any measurements we
  have to agree on certain units.
• Our way of understanding of Nature is a
  quantitive understanding, which takes a form of
  certain laws.
• These laws themselves can provide no quantitive
  predictions. Certain quantitive parameters enter
  the expression of these laws. Some enter very
  different equations from various fields.
• Such universal parameters are recognized as
  fundamental physical constants. The fundamental
  constants are a kind of interface to apply these
  basic laws to a quantitive description of Nature.

12
Fundamental constants various physical phenomena

• First universal parameters appeared centuries
  ago.
• G and g entered a big number of various problems.

13
Fundamental constants various physical phenomena

• First universal parameters appeared centuries
  ago.
• G and g entered a big number of various problems.

Just in case G is the gravitaiton constant g
is acceleration of free fall.
14
Fundamental constants various physical phenomena

• First universal parameters appeared centuries
  ago.
• G and g entered a big number of various problems.
• G is still a constant,

15
Fundamental constants various physical phenomena

• First universal parameters appeared centuries
  ago.
• G and g entered a big number of various problems.
• G is still a constant, g is not anymore.

16
Fundamental constants various physical phenomena

• First universal parameters appeared centuries
  ago.
• G and g entered a big number of various problems.
• G is still a constant, g is not anymore.
• Universality
• theoretical point of view really fundamental
  ones are such as G, h, c

17
Fundamental constants various physical phenomena

• First universal parameters appeared centuries
  ago.
• G and g entered a big number of various problems.
• G is still a constant, g is not anymore.
• Universality
• theoretical point of view really fundamental
  ones are such as G, h, c
• practical point of view constants which are
  really necessary for various measurements (Bohr
  magneton, cesium HFS ...)

18
Fundamental constants various physical phenomena

• First universal parameters appeared centuries
  ago.
• G and g entered a big number of various problems.
• G is still a constant, g is not anymore.
• Universality
• theoretical point of view really fundamental
  ones are such as G, h, c
• practical point of view constants which are
  really necessary for various measurements (Bohr
  magneton, cesium HFS ...)
• Most fundamental constants in physics
• G, h, c properties of space-time

19
Fundamental constants various physical phenomena

• First universal parameters appeared centuries
  ago.
• G and g entered a big number of various problems.
• G is still a constant, g is not anymore.
• Universality
• theoretical point of view really fundamental
  ones are such as G, h, c
• practical point of view constants which are
  really necessary for various measurements (Bohr
  magneton, cesium HFS ...)
• Most fundamental constants in physics
• G, h, c properties of space-time
• a property of a universal interaction

20
Fundamental constants various physical phenomena

• First universal parameters appeared centuries
  ago.
• G and g entered a big number of various problems.
• G is still a constant, g is not anymore.
• Universality
• theoretical point of view really fundamental
  ones are such as G, h, c
• practical point of view constants which are
  really necessary for various measurements (Bohr
  magneton, cesium HFS ...)
• Most fundamental constants in physics
• G, h, c properties of space-time
• a property of a universal interaction

Just in case a is the fine structure
constant which is e2/4pe0hc.
21
Fundamental constants various physical phenomena

• First universal parameters appeared centuries
  ago.
• G and g entered a big number of various problems.
• G is still a constant, g is not anymore.
• Universality
• theoretical point of view really fundamental
  ones are such as G, h, c
• practical point of view constants which are
  really necessary for various measurements (Bohr
  magneton, cesium HFS ...)
• Most fundamental constants in physics
• G, h, c properties of space-time
• a property of a universal interaction
• me, mp properties of individual elementary
  particles

22
Fundamental constants various physical phenomena

• First universal parameters appeared centuries
  ago.
• G and g entered a big number of various problems.
• G is still a constant, g is not anymore.
• Universality
• theoretical point of view really fundamental
  ones are such as G, h, c
• practical point of view constants which are
  really necessary for various measurements (Bohr
  magneton, cesium HFS ...)
• Most fundamental constants in physics
• G, h, c properties of space-time
• a property of a universal interaction
• me, mp properties of individual elementary
  particles
• cesium HFS, carbon atomic mass properties of
  specific compound objects

23
Lessons to learn

• A variation of certain constants already took
  place according to the inflation model.
• a is likely the most fundamental of
  phenomenological constants (the masses are not!)
  accessible with high accuracy.

24
Lessons to learn

• A variation of certain constants already took
  place according to the inflation model.
• a is likely the most fundamental of
  phenomenological constants (the masses are not!)
  accessible with high accuracy.

The only reason to be sure that a certain
constantis a constant is to trace its origine
and check.
25
Units

• Physics is based on measurements and a
  measurement is always a comparison.
• Still there is a substantial difference between
• a relative measurement (when we take advantage of
  some relations between two values we like to
  compare) and
• an absolute measurements (when a value to compare
  with has been fixed by an agreement e.g. SI).

26
Fundamental constants units for physical
quantities

• Early time units are determined by
• humans (e.g. foot)
• Earth (e.g. g 9.8 m/s, day)
• water (e.g. r 1 g/cm3 Celsius temperature
  scale)
• Sun (year)
• Now we change most of our definitions but keep
  size of the units!
• The fundamental scale is with atoms and particles
  and most of constants are 1 or 1.

27
Fundamental constants units for physical
quantities

• Early time units are determined by
• humans (e.g. foot)
• Earth (e.g. g 9.8 m/s, day)
• water (e.g. r 1 g/cm3 Celsius temperature
  scale)
• Sun (year)
• Now we change most of our definitions but keep
  size of the units!
• The fundamental scale is with atoms and particles
  and most of constants are 1 or 1.
• An only constant 1 is
• Ry 13.6 eV
• (or IH 13.6 V) since all electric potentials
  were linked to atomic and molecular energy.

28
Towards natural units

• Kilogram is defined via an old-fashion way an
  artifact.
• Second is defined via a fixed value of cesium HFS
• f 9 192 631 770 Hz (Hz 1/s).
• Metre is defined via a fixed value of speed of
  light
• c 299 792 458 m/s .
• If we consider 1/f as a natural unit of time, and
  c as a natural unit of velocity, then their
  numerical values play role of conversion factors
• 1 s 9 192 631 770 1/f,
• 1 m/s (1/299 792 458) c.
• Those numerical factors are needed to keep the
  values as they were introduced a century ago what
  is a great illusion of SI.
• The fundamental constants serve us both as
  natural units and as conversion factors.

29
Towards natural units

• Kilogram is defined via an old-fashion way an
  artifact.
• Second is defined via a fixed value of cesium HFS
• f 9 192 631 770 Hz (Hz 1/s).
• Metre is defined via a fixed value of speed of
  light
• c 299 792 458 m/s .
• If we consider 1/f as a natural unit of time, and
  c as a natural unit of velocity, then their
  numerical values play role of conversion factors
• 1 s 9 192 631 770 1/f,
• 1 m/s (1/299 792 458) c.
• Those numerical factors are needed to keep the
  values as they were introduced a century ago what
  is a great illusion of SI.
• The fundamental constants serve us both as
  natural units and as conversion factors.

If the constants are changing the units are
changing as well.
30
Constants their numerical values

• We have to distinguish clearly between
  fundamental constants and their numerical values.
• The Rydberg constant is defined via e, h, me, e0
  and c.
• It has no relation to cesium and its hyperfine
  structure (nuclear magnetic moment).
• While the numerical value of the Rydberg constant
• 2 Ry 9 192 631 770 / Cs HFSAt.un.
• is related to cesium and SI, but not to Ry.
• If e.g. we look for variation of constants
  suggesting a variation of cesium magnetic moment,
  the numerical value of Ry will vary, while the
  constant itself will not.

31
Progress in determination of fundamental constants

• This is the progress for over 30 years.
  Impressive for some of constants (Ry, me/mp) and
  moderate for others.

32
Progress in determination of fundamental constants
Note the progress is not necessary an increase
of accuracy,

• This is the progress for over 30 years.
  Impressive for some of constants (Ry, me/mp) and
  moderate for others.

33
Progress in determination of fundamental constants

• This is the progress for over 30 years.
  Impressive for some of constants (Ry, me/mp) and
  moderate for others.

34
Lessons to learn

• If fundamental constants are changing, the units
  are changing as well.
• Variation of a dimensional quantity can in
  principle be detected.
• However, it is easier to deal with dimensionless
  quantities, or numerical values in well-defined
  units.

35
Lessons to learn

• Fundamental constants have been measured not so
  accurately as we need.
• We have to look for consequenses of their
  variations for most precision measured
  quantities.
• One can note from accuracy of the Rydberg
  constant those are frequencies.

36
Optical frequency measurements

• Length measurements are related to optics since
  RF has too large wave lengths for accurate
  measurements.

• Clocks used to be related to RF because of
  accurate frequency comparisons and conventional
  macroscopic and electromagnetic frequency range.

37
Optical frequency measurements

• Length measurements are related to optics since
  RF has too large wave lengths for accurate
  measurements.

• Clocks used to be related to RF because of
  accurate frequency comparisons and conventional
  macroscopic and electromagnetic frequency range.

Now clocks enter optics and because of more
oscillations in a given period they are
potentially more accurate.
38
Optical frequency measurements

• Length measurements are related to optics since
  RF has too large wave lengths for accurate
  measurements.

• Clocks used to be related to RF because of
  accurate frequency comparisons and conventional
  macroscopic and electromagnetic frequency range.

Now clocks enter optics and because of more
oscillations in a given period they are
potentially more accurate.
That is possible because of frequency comb
technology which offers precision comparisons
optics to optics and optics to RF.
39
Optical frequency measurements a variations

• Length measurements are related to optics since
  RF has too large wave lengths for accurate
  measurements.

• Clocks used to be related to RF because of
  accurate frequency comparisons and conventional
  macroscopic and electromagnetic frequency range.

Now clocks enter optics and because of more
oscillations in a given period they are
potentially more accurate.
That is possible because of frequency comb
technology which offers precision comparisons
optics to optics and optics to RF.
Meantime comparing various optical transitions
to cesium HFS we look for their variation at the
level of a part in 1015 per a year.
40
What is the frequency comb?

• When an optical signal is modulated by an rf, the
  results contains foptnfrf, where n 0, 1, 2
  ...
• When the rf signal is very unharmonic, n can be
  really large.
• For the comb one starts with femtosecond pulses.
• Each comd line can be presented as foffnfrep.

• A measurement is a comparison of an optical
  frequency f with a comb line, determining their
  differnce which is in rf domain.
• An important issue is an octave, i.e. a spectrum
  where fmax lt 2fmix.
• That is achieved by using special fibers.
• With octave one can express foff in terms of frep.

41
What is the frequency comb?

• When an optical signal is modulated by an rf, the
  results contains foptnfrf, where n 0, 1, 2
  ...
• When the rf signal is very unharmonic, n can be
  really large.
• For the comb one starts with femtosecond pulses.
• Each comd line can be presented as foffnfrep.

• A measurement is a comparison of an optical
  frequency f with a comb line, determining their
  differnce which is in rf domain.
• An important issue is an octave, i.e. a spectrum
  where fmax lt 2fmix.
• That is achieved by using special fibers.
• With octave one can express foff in terms of frep.

42
What is the frequency comb?

• When an optical signal is modulated by an rf, the
  results contains foptnfrf, where n 0, 1, 2
  ...
• When the rf signal is very unharmonic, n can be
  really large.
• For the comb one starts with femtosecond pulses.
• Each comd line can be presented as foffnfrep.

• A measurement is a comparison of an optical
  frequency F with a comb line, determining their
  differnce which is in rf domain.
• An important issue is an octave, i.e. a spectrum
  where fmax lt 2fmix.
• That is achieved by using special fibers.
• With octave one can express foff in terms of frep.

43
What is the frequency comb?

• When an optical signal is modulated by an rf, the
  results contains foptnfrf, where n 0, 1, 2
  ...
• When the rf signal is very unharmonic, n can be
  really large.
• For the comb one starts with femtosecond pulses.
• Each comd line can be presented as foffnfrep.

• A measurement is a comparison of an optical
  frequency F with a comb line, determining their
  differnce which is in rf domain.
• An important issue is an octave, i.e. a spectrum
  where fmax lt 2fmix.
• That is achieved by using special fibers.
• With octave one can express foff in terms of frep.

Presence of regular reference lines, distance
between which is in rf domain, across all the
visible spectrum (and a substantial paft of IR
and UV) allows a comparison of two opical
lines, or an optical againts a radio frequency.
44
Optical frequency measurements a variations

• Length measurements are related to optics since
  RF has too large wave lengths for accurate
  measurements.

• Clocks used to be related to RF because of
  accurate frequency comparisons and conventional
  macroscopic and electromagnetic frequency range.

Now clocks enter optics and because of more
oscillations in a given period they are
potentially more accurate.
I regret to inform you that the result for the
variations is negative.
That is possible because of frequency comb
technology which offers precision comparisons
optics to optics and optics to RF.
Meantime comparing various optical transitions
to cesium HFS we look for their variation at the
level of a part in 1015 per a year.
45
Optical frequency measurements a variations

• Length measurements are related to optics since
  RF has too large wave lengths for accurate
  measurements.

• Clocks used to be related to RF because of
  accurate frequency comparisons and conventional
  macroscopic and electromagnetic frequency range.

Now clocks enter optics and because of more
oscillations in a given period they are
potentially more accurate.
I regret to inform you that the result for the
variations is negative.
That is possible because of frequency comb
technology which offers precision comparisons
optics to optics and optics to RF.
Meantime comparing various optical transitions
to cesium HFS we look for their variation at the
level of few parts in 1015 per a year.
I am sorry!
46
Optical frequency measurements a variations

• Length measurements are related to optics since
  RF has too large wave lengths for accurate
  measurements.

• Clocks used to be related to RF because of
  accurate frequency comparisons and conventional
  macroscopic and electromagnetic frequency range.

Now clocks enter optics and because of more
oscillations in a given period they are
potentially more accurate.
I regret to inform you that the result for the
variations is negative.
That is possible because of frequency comb
technology which offers precision comparisons
optics to optics and optics to RF.
Meantime comparing various optical transitions
to cesium HFS we look for their variation at the
level of few parts in 1015 per a year.
I am really sorry!
47
Atomic Clocks andFundamental Constants

• Clocks
• Atomic and molecular transitions
• their scaling with a, me/mp etc.
• Advantages and disadvantages of clocks to search
  the variations.
• Recent progress.

48
Atomic Clocks

• Caesium clock
• Primary standard
• Locked to an unperturbed atomic frequency.
• All corrections are under control.

49
Atomic Clocks

• Caesium clock
• Primary standard
• Locked to an unperturbed atomic frequency.
• All corrections are under control.

Clock frequency atomic frequency
50
Atomic Clocks

• Caesium clock
• Primary standard
• Locked to an unperturbed atomic frequency.
• All corrections are under control.

• Hydrogen maser
• An artificial device designed for a purpose.
• The corrections (wall shift) are not under
  control.
• Unpredictable drift bad long term stability.

Clock frequency atomic frequency
51
Atomic Clocks

• Caesium clock
• Primary standard
• Locked to an unperturbed atomic frequency.
• All corrections are under control.

• Hydrogen maser
• An artificial device designed for a purpose.
• The corrections (wall shift) are not under
  control.
• Unpredictable drift bad long term stability.

Clock frequency atomic frequency
Clock frequency ? atomic frequency
52
Atomic Clocks

• Caesium clock
• Primary standard
• Locked to an unperturbed atomic frequency.
• All corrections are under control.

• Hydrogen maser
• An artificial device designed for a purpose.
• The corrections (wall shift) are not under
  control.
• Unpredictable drift bad long term stability.

Clock frequency atomic frequency
Clock frequency ? atomic frequency
If we like to look for a variation of natural
constants we have to deal with standards
similar to caesium clock.
53
Atomic Clocks

• Caesium clock
• Primary standard
• Locked to an unperturbed atomic frequency.
• All corrections are under control.

• Hydrogen maser
• An articitial device designed for a purpose.
• The corrections (wall shift) are not under
  control.
• Unpredictable drift bad long term stability.

Clock frequency atomic frequency
Clock frequency ? atomic frequency
To work with such a near primary clock is the
same as to measure an atomic frequency in SI or
other appropriate units.
If we like to look for a variation of natural
constants we have to deal with standards
similar to caesium clock.
54
Scaling of atomic transitions

Gross structure Ry
Fine structure a2 Ry
HFS structure a2 mNucl/mB Ry
Relativistic corrections F(a)
55
Scaling of atomic transitions

Gross structure Ry
Fine structure a2 Ry
HFS structure a2 mNucl/mB Ry
Relativistic corrections F(a)
That is what one can easily derive for
hydrogen. More complicated atoms lead to more
complicated calculation of numerical factors.
56
Scaling of atomic transitions

Gross structure Ry
Fine structure a2 Ry
HFS structure a2 mNucl/mB Ry
Relativistic corrections F(a)
Characteristic electron velocity in an atom is
ac/n.
57
Scaling of molecular transitions

Electronic transitions Ry
Vibrational transitions (me/mp)1/2 Ry
Non-harmonic corrections F ((me/mp)1/4)
Rotational transitions me/mp Ry
Relativistic corrections F(a)
58
Scaling of atomic and molecular transitions

• Atomic transitions
• Gross structure
• Fine structure
• HFS structure
• Relativistic corrections

• Molecular transitions
• Electronic transitions
• Vibrational transitions
• Rotational transitions
• Relativistic corrections

59
Scaling of atomic and molecular transitions

• Atomic transitions
• Gross structure
• Fine structure
• HFS structure
• Relativistic corrections

• Molecular transitions
• Electronic transitions
• Non-harmonic corrections
• Rotational transitions
• Relativistic corrections

Up to date the most accurate results have been
obtained for atomic transitions related to gross
and HFS structure. Others are not competitive.
60
Scaling of atomic and molecular transitions

• Atomic transitions
• Gross structure
• Fine structure
• HFS structure
• Relativistic corrections

• Molecular transitions
• Electronic transitions
• Non-harmonic corrections
• Rotational transitions
• Relativistic corrections

That is not so bad because the relativistic
corrections are large. Sometimes really
large. They are (Za)2.
Up to date the most accurate results have been
obtained for atomic transitions related to gross
and HFS structure. Others are not competitive.
61
Scaling of atomic and molecular transitions

• Neutral atom (Rb, Cs)

• Nucleus
• charge Ze
• Electron core
• charge -(Z-1)e
• charge of nucleus electron core e
• Valent electron
• partly penetrates into core
• v/c a (outside core)
• v/c Za (inside core)

62
Scaling of atomic and molecular transitions

• Atomic transitions
• Gross structure
• Fine structure
• HFS structure
• Relativistic corrections

• Molecular transitions
• Electronic transitions
• Non-harmonic corrections
• Rotational transitions
• Relativistic corrections

That is not so bad because the relativistic
corrections are large. Sometimes really
large. They are (Za)2.
Up to date the most accurate results have been
obtained for atomic transitions related to gross
and HFS structure. Others are not competitive.
63
Best data from frequency measurements
Atom Frequency GHz df/f 10-15 Df/Dt Hz/yr _at_
H, Opt 2466061 14 -816 MPQ
Ca, Opt 455986 13 -45 PTB
Rb, HFS 6.8 1 (05)10-6 LPTF
Yb, Opt 688359 9 -13 PTB
Yb, HFS 12.6 73 (44) 10-4 NML
Hg, Opt 1064721 9 07 NIST
64
Best data from frequency measurements
65
Best data from frequency measurements
66
More even better data from frequency measurements
67
More even better data from frequency measurements
68
More even better data from frequency measurements

• NIST quantum logics direct comparison between
  two optical clocks

69
More even better data from frequency measurements

• 1D optical lattice

70
Best data from frequency measurements
71
A direct measurement
72
Progress in a variations since the 1st ACFC
meeting (June 2003)

• Method
• f C0 c Ry F(a)

73
Progress in a variations since the 1st ACFC
meeting (June 2003)

• Method
• f C0 c Ry F(a)
• and thus
• d lnf/dt d lncRy/dt
• A d lna/dt.

74
Progress in a variations since the 1st ACFC
meeting (June 2003)

• Method
• f C0 c Ry F(a)
• d lnf/dt d lncRy/dt
• A d lna/dt.
• Measurements
• Optical transitions in Hg (NIST), H (MPQ), Ca
  (PTB), Yb (PTB) versus Cs HFS
• Calcium (NIST), aluminum ion (NIST), strontium
  ion (NPL) and neutral strontium (Tokyo, JILA,
  LNE-SYRTE) and mercury (LNE-SYRTE) and octupole
  Yb (NPL) are coming.

75
Progress in a variations since the 1st ACFC
meeting (June 2003)

• Method
• f C0 c Ry F(a)
• d lnf/dt d lncRy/dt
• A d lna/dt.
• Measurements
• Optical transitions in Hg (NIST), H (MPQ), Ca,
  Yb (PTB) versus Cs HFS
• Calculation of relativistic corrections
  (Flambaum, Dzuba)
• A d lnF(a)/d lna

76
Progress in a variations since the 1st ACFC
meeting (June 2003)

• (MPQ), Ca, Yb (PTB) versus Cs HFS.
• Calculation of relativistic corrections
  (Flambaum, Dzuba)
• A d lnF(a)/d lna

• Method
• d lnf/dt d lncRy/dt
• A d lna/dt.
• Measurements of optical transitions in Hg
  (NIST), H

77
Progress in a variations since the 1st ACFC
meeting (June 2003)

• Method
• f C0 c Ry F(a)
• d lnf/dt d lncRy/dt
• A d lna/dt.
• Measurements
• Optical transitions in Hg (NIST), H (MPQ), Yb
  (PTB) versus Cs HFS
• Ca, Sr, Sr, Hg, Al and octupole Yb are coming
• Calculation of relativistic corrections
  (Flambaum, Dzuba)
• A d lnF(a)/da

78
Progress in a variations since the 1st ACFC
meeting (June 2003)

• Method
• f C0 c Ry F(a)
• d lnf/dt d lncRy/dt
• A d lna/dt.
• Measurements
• Optical transitions in Hg (NIST), H (MPQ), Yb
  (PTB) versus Cs HFS
• Ca, Sr, Sr, Hg, Al and octupole Yb are coming
• Calculation of relativistic corrections
  (Flambaum, Dzuba)
• A d lnF(a)/da

Hg

Sr, Sr, Ca, Al
octupole Yb
79
Progress in a variations since the 1st ACFC
meeting (June 2003)

• Method
• f C0 c Ry F(a)
• d lnf/dt d lncRy/dt
• A d lna/dt.
• Measurements
• Optical transitions in Hg (NIST), H (MPQ), Yb
  (PTB) versus Cs HFS
• Ca, Sr, Sr, Hg, Al and octupole Yb are coming
• Calculation of relativistic corrections
  (Flambaum, Dzuba)
• A d lnF(a)/da

80
Progress in a variations since the 1st ACFC
meeting (June 2003)

• Method
• f C0 c Ry F(a)
• d lnf/dt d lncRy/dt
• A d lna/dt.
• Measurements
• Optical transitions in Hg (NIST), H (MPQ), Yb
  (PTB) versus Cs HFS
• Ca, Sr, Sr, Hg, Al and octupole Yb are coming
• Calculation of relativistic corrections
  (Flambaum, Dzuba)
• A d lnF(a)/da

81
Progress in a variations since the 1st ACFC
meeting (June 2003)

• Method
• f C0 c Ry F(a)
• d lnf/dt d lncRy/dt
• A d lna/dt.
• Measurements
• Optical transitions in Hg (NIST), H (MPQ), Yb
  (PTB) versus Cs HFS
• Ca, Sr, Sr, Hg, Al and octupole Yb are coming
• Calculation of relativistic corrections
  (Flambaum, Dzuba)
• A d lnF(a)/da

82
Further constraints

• Model independent constraints can be reached for
  variations of a, Ry, and certain nuclear
  magnetic moments in units the Bohr magneton.

83
Further constraints

• Model independent constraints can be reached for
  variations of a, Ry, and certain nuclear
  magnetic moments in units the Bohr magneton.
• Those are not fundamental.

84
Further constraints

• Model independent constraints can be reached for
  variations of a, Ry, and certain nuclear
  magnetic moments in units the Bohr magneton.
• Those are not fundamental.

• However, we badly need a universal presentation
  of all data for a cross check.

85
Further constraints

• Model independent constraints can be reached for
  variations of a, Ry, and certain nuclear
  magnetic moments in units the Bohr magneton.
• Those are not fundamental.

• However, we badly need a universal presentation
  of all data for a cross check.
• The next step can be done with the help of the
  Schmidt model.

86
Further constraints

• Model independent constraints can be reached for
  variations of a, Ry, and certain nuclear
  magnetic moments in units the Bohr magneton.
• Those are not fundamental.

• We badly need a universal presentation of all
  data for a cross check.
• The next step can be done with the help of the
  Schmidt model.
• The model is not quite reliable and the
  constraints are model dependent.

87
Further constraints

• Model independent constraints can be reached for
  variations of a, Ry, and certain nuclear
  magnetic moments in units the Bohr magneton.
• Those are not fundamental.

• We badly need a universal presentation of all
  data for a cross check.
• The next step can be done with the help of the
  Schmidt model.
• The model is not quite reliable and the
  constraints are model dependent.

However Nothing is better!
88
Current laboratory constraints on variations of
constants
X Variation d lnX/dt Model
a ( 0.32.0)10-15 yr -1 --
c Ry ( 2.13.1)10-15 yr -1 --
me/mp (2.96.2)10-15 yr -1 Schmidt model
mp/me (2.95.8)10-15 yr -1 Schmidt model
gp ( 0.10.5)10-15 yr -1 Schmidt model
gn (33) 10-14 yr -1 Schmidt model
89
Current laboratory constraints on variations of
constants
X Variation d lnX/dt Model
a ( 0.32.0)10-15 yr -1 --
c Ry ( 2.13.1)10-15 yr -1 --
me/mp (2.96.2)10-15 yr -1 Schmidt model
mp/me (2.95.8)10-15 yr -1 Schmidt model
gp ( 0.10.5)10-15 yr -1 Schmidt model
gn (33) 10-14 yr -1 Schmidt model
At present dlnX/dt for a and c Ry are
improved substantially
90
From talk by Ekkehard Peik at Leiden-2009 workshop
91
From talk by Ekkehard Peik at Leiden-2009 workshop
92
Current laboratory constraints on variations of
constants
X Variation d lnX/dt Model
a ( 0.32.0)10-15 yr -1 --
c Ry ( 2.13.1)10-15 yr -1 --
me/mp (2.96.2)10-15 yr -1 Schmidt model
mp/me (2.95.8)10-15 yr -1 Schmidt model
gp ( 0.10.5)10-15 yr -1 Schmidt model
gn (33) 10-14 yr -1 Schmidt model
93
Various constraints
Astrophysics contradictions at level of 1 part in 1015 per a year a non-transperant statistical evaluation of the data time separation 1010 yr.

94
What are astrophysical data from?

• Quasars produce light from very remote past.
• Travelling to us the light cross delute clouds.
• We study absorbsion lines.
• The lines are redshifted.
• To identify lines we compare various ratios they
  should match the laboratory values.

• The ratios are sensitive to value of a, me/mp and
  me/mp in different ways.
• Small departures from the present-day laboratory
  results are analized as a possible systematic
  effect due to a variation of fundamental
  constant.

95
What are astrophysical data from?

• Quasars produce light from very remote past.
• Travelling to us the light cross delute clouds.
• We study absorbsion lines.
• The lines are redshifted.
• To identify lines we compare various ratios they
  should match the laboratory values.

• The ratios are sensitive to value of a, me/mp and
  me/mp in different ways.
• Small departures from the present-day laboratory
  results are analized as a possible systematic
  effect due to a variation of fundamental
  constant.

96
Julian A. King et al., arXiv1202.4758
97
Consequences for atomic clocks (from
Victor Flambaum)

• Sun moves 369 km/s relative to CMB cos (f) 0.1
  towards area with larger a
• This gives average laboratory variation
• Da/a 1.5 10 -18 cos(f) per year
• Earth moves 30 km/s relative to Sun-
• 1.6 10 -20 cos(wt) annual modulation

98
Various constraints
Astrophysics contradictions at level of 1 part in 1015 per a year a non-transperant statistical evaluation of the data time separation 1010 yr. Geochemistry (Oklo Co) a model-dependent evaluation of data based on a single element (Oklo) a simplified interpretation in terms of a contradictions at level of 110-17 per a year separation 109 yr.

99
What is Oklo?

• Some time ago French comission for atomic energy
  reported on reduction of amount of U-235 the
  U-deposites (1972) in Oklo (Gabon, West Africa)
  contains 0.705 instead of 0.712.
• The interpretation was a fossil natural nuclear
  reactor.

• It happens because 2 Gyr ago the uranium was
  enriched.
• That was so-called water-water reactor.
• The operation lasts from 0.5 to 1.5 Myr.
• The fission produces Sm isotopes and Sm-149 has a
  neutron-capture resonance at 97.3 meV.

100
What is Oklo?

• Some time ago French comission for atomic energy
  reported on reduction of amount of U-235 the
  U-deposites (1972) in Oklo (Gabon, West Africa)
  contains 0.705 instead of 0.712.
• The interpretation was a fossil natural nuclear
  reactor.

• It happens because 2 Gyr ago the uranium was
  enriched.
• That was so-called water-water reactor.
• The operation lasts from 0.5 to 1.5 Myr.
• The fission produces Sm isotopes and Sm-149 has a
  neutron-capture resonance at 97.3 meV.

101
What is Oklo?

• Some time ago French comission for atomic energy
  reported on reduction of amount of U-235 the
  U-deposites (1972) in Oklo (Gabon, West Africa)
  contains 0.705 instead of 0.712.
• The interpretation was a fossil natural nuclear
  reactor.

• It happens because 2 Gyr ago the uranium was
  enriched.
• That was so-called water-water reactor.
• The operation lasts from 0.5 to 1.5 Myr.
• The fission produces Sm isotopes and Sm-149 has a
  neutron-capture resonance at 97.3 meV.

102
What is Oklo?

• Some time ago French comission for atomic energy
  reported on reduction of amount of U-235 the
  U-deposites (1972) in Oklo (Gabon, West Africa)
  contains 0.705 instead of 0.712.
• The interpretation was a fossil natural nuclear
  reactor.

• It happens because 2 Gyr ago the uranium was
  enriched.
• That was so-called water-water reactor.
• The operation lasts from 0.5 to 1.5 Myr.
• The fission produces Sm isotopes and Sm-149 has a
  neutron-capture resonance at 97.3 meV.

Just in case Myr mega-year Gyr giga-year
meV milli-electron-volt
103
What is Oklo?

• Some time ago French comission for atomic energy
  reported on reduction of amount of U-235 the
  U-deposites (1972) in Oklo (Gabon, West Africa)
  contains 0.705 instead of 0.712.
• The interpretation was a fossil natural nuclear
  reactor.

• It happens because 2 Gyr ago the uranium was
  enriched.
• That was so-called water-water reactor.
• The operation lasts from 0.5 to 1.5 Myr.
• The fission produces Sm isotopes and Sm-149 has a
  neutron-capture resonance at 97.3 meV.

104
What is Oklo?

• Some time ago French comission for atomic energy
  reported on reduction of amount of U-235 the
  U-deposites (1972) in Oklo (Gabon, West Africa)
  contains 0.705 instead of 0.712.
• The interpretation was a fossil natural nuclear
  reactor.

• It happens because 2 Gyr ago the uranium was
  enriched.
• That was so-called water-water reactor.
• The operation lasts from 0.5 to 1.5 Myr.
• The fission produces Sm isotopes and Sm-149 a
  neutron-capture resonance at 97.3 meV.

• In 1976 Shlyachter suggested
• to examine Sm isotopes to test
• variation of the constants.

105
Various constraints
Astrophysics contradictions at level of 1 part in 1015 per a year a non-transperant statistical evaluation of the data time separation 1010 yr. Geochemistry (Oklo Co) a model-dependent evaluation of data based on a single element (Oklo) a simplified interpretation in terms of a contradictions at level of 110-17 per a year separation 109 yr.
Laboratory (HFS incl.) particular experiments which may be checked recent and continuing progress involvment of the Schmidt model access to gn time separation 10 yr.
106
Various constraints
Astrophysics contradictions at level of 1 part in 1015 per a year a non-transperant statistical evaluation of the data time separation 1010 yr. Geochemistry (Oklo Co) a model-dependent evaluation of data based on a single element (Oklo) a simplified interpretation in terms of a contradictions at level of 110-17 per a year separation 109 yr.
Laboratory (HFS incl.) particular experiments which may be checked recent and continuing progress involvment of the Schmidt model access to gn time separation 10 yr. Laboratory (opt. Cs) particular experiments which may be checked recent and continuing progress model-independence access only to a and cRy reliability time separation 1-3-10 yr.
107
Acknowledgments

• No fundamental constants have been hurt during
  preparation of this talk. Neither their
  variations in the Earth area have been reported
  to any scientific authority.