Transcript Slide 1

AC Fundamental Constants
Savely G Karshenboim
Pulkovo observatory (St. Petersburg)
and Max-Planck-Institut für Quantenoptik (Garching)
Astrophysics, Clocks and
Fundamental Constants
Astrophysics, Clocks and
Fundamental 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.
Astrophysics, Clocks and
Fundamental Constants
Why astrophysics?
Why clocks?
Cosmology: changing
 Frequency: most
universe.
accurately measured.
 Inflation: variation of
 Different clocks:
But:
constants.
planetary motion,
everything
related to astrophysics
is
pulsars, atomic,
 Pulsars: astrophysical
molecular and nuclear
clocks.
model
dependent and not transparent.
clocks – different
 Quasars: light from a
dependence on the
very remote past.
fundamental constants.

[Optical] Atomic Clocks and
Fundamental 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 modelindependent
interpretation in terms
of a variation.
Atomic Clocks and
Fundamental Constants
Why atomic clocks?


Why optical?
 Optical clocks have
Frequency
Up
to now the optical
measurements
been greatly improved
measurements are most
are
theup
only
source forand
accurate
and
will be improved
accurate
to date.
further. constraints
reliable
model-independent
Different atomic
and
 They allow
a
on
a possible
time variation
of constants.
molecular
thansitions
differently depend on
fundamental constants
(a, me/mp, gp etc).
transparent modelindependent
interpretation in terms
of a variation.
Outline

Are fundamental constants: fundamental? constants?



Measurements and fundamental constants



Fundamental constants & units of physical quantities
Determination of fundamental constants
Precision frequency measurements & variation of
constants




Various fundamental constants
Origin of the constants in modern physics
Clocks for fundamental physics
Advantages and disadvantages of laboratory searches
Recent results in frequency metrology
Current laboratory constraints
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.
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.
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.
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.
Fundamental constants &
various physical phenomena
First universal parameters appeared centuries ago.
G and g entered a big number of various problems.
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.
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,
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.
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
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 ...)
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
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
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 e2/4pe0ħc.
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
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
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.
Lessons to learn:


A variation of certain constants already took place
according to the inflation model.
a is likely the most
The fundamental
only reasonoftophenomenological
be sure
constants (the masses
not!) `constant´is
accessible with high
that a are
certain
accuracy.
a constant is to trace its origine
and check.
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).
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.
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.
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.

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
the
constants
are changing the units
If we consider 1/f as a natural unit of time, and c as a natural unit
of are
velocity,
then theiras
numerical
values play role of conversion
changing
well.
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.

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 HFS}At.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.
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.
Progress in determination of
fundamental
Note: the progressconstants
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.
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.
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.
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.
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.
Optical frequency
measurements
Length measurements Clocks used to be
are related to optics
related to RF
Now: clocks enter optics and because of
since RF has too
because of accurate
morelarge
oscillations
in a givenfrequency
period they
wave lengths
for accuratemore accurate.
comparisons and
are potentially
measurements.
conventional
macroscopic and
electromagnetic
frequency range.
Optical frequency
measurements
Length measurements Clocks used to be
are related to optics
related to RF
Now: clocks enter optics and because of
since RF has too
because of accurate
more
oscillations
in a given
period they
large
wave lengths
That
is possible
because
of frequency
frequency
comb
for accurate
comparisons
and
which
precision
comparisons
aretechnology
potentially
moreoffers
accurate.
measurements.
conventional
optics
to optics and optics to
RF.
macroscopic and
electromagnetic
frequency range.
Optical frequency
measurements & a variations
Length measurements Clocks used to be
are related to optics
related to RF
Now: clocks enter optics and because of
since RF has too
because of accurate
more
oscillations
in a given
period they
large
wave lengths
That
is possible
because
of frequency
frequency
comb
for accurate
comparisons
and
which
precision
comparisons
aretechnology
potentially
moreoffers
accurate.
measurements.
conventional
optics
to optics
and optics
to
RF.
Meantime
comparing
various
optical
transitions
macroscopic
to cesium HFS we look for their
variationand
at the
level of a part in 1015 per a electromagnetic
year.
frequency range.
What is the frequency comb?




When an optical signal is
modulated by an rf, the
results contains fopt+nfrf,
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 foff+nfrep.




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 < 2×fmix.
That is achieved by using
special fibers.
With octave one can express
foff in terms of frep.
What is the frequency comb?




When an optical signal is
modulated by an rf, the
results contains fopt+nfrf,
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 foff+nfrep.




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 < 2×fmix.
That is achieved by using
special fibers.
With octave one can express
foff in terms of frep.
What is the frequency comb?




When an optical signal is
modulated by an rf, the
results contains fopt+nfrf,
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 foff+nfrep.




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 < 2fmix.
That is achieved by using
special fibers.
With octave one can express
foff in terms of frep.
What is the frequency comb?





A measurement is a
When an optical signal is
comparison of an optical
modulated by an rf, the
frequency F with a comb
results contains fopt+nfrf,
line, determining their
where n = 0, ±1, ± 2 ...
differnce which is in rf
When the rf signal is very
domain.
unharmonic, n can be really

An important issue is an
large.
octave, i.e. a spectrum
where fmax < 2fmix.
For the comb one starts with
Presence
of
regular
reference
femtosecond pulses.

That
is achieved
by lines,
using
distance between
is in rf domain,
specialwhich
fibers.
Each comd line can be
across
all
theoctave
visible one
spectrum

With
can express
presented as foff+nfrep.
(and a substantial
paft of
foff in terms
of IR
frepand
. UV)
allows a comparison of two opical lines,
or an optical againts a radio frequency.
Optical frequency
measurements & a variations
Length measurements Clocks used to be
are related to optics
related to RF
Now: clocks enter optics and because of
since RF has too
because of accurate
I
regret
to
inform
you
more
oscillations
in
a
given
period
they
large
wave
lengths
frequency
That is possible because of frequency
comb
that
theoffers
result
for the
for accurate
comparisons
and
which
precision
comparisons
aretechnology
potentially
more
accurate.
Meantime
comparing
various
optical
transitions
measurements.
conventional
optics
to optics
and optics
to
RF.
variations
is negative.
to cesium HFS we look for their
variationand
at the
macroscopic
level of a part in 1015 per a electromagnetic
year.
frequency range.
Optical frequency
measurements & a variations
Length measurements Clocks used to be
are related to optics
related to RF
Now: clocks enter optics and because of
since RF has too
because of accurate
I
regret
to
inform
you
more
oscillations
in
a
given
period
they
large
wave
lengths
frequency
That is possible because of frequency
comb
that
theoffers
result
for the
for accurate
comparisons
and
which
precision
comparisons
aretechnology
potentially
more
accurate.
Meantime
comparing
various
optical
transitions
measurements.
conventional
optics
to optics
and optics
to
RF.
variations
is negative.
to cesium HFS we look for their
variationand
at the
macroscopic
level of few parts in 1015 perelectromagnetic
a year.
I am sorry!
frequency range.
Optical frequency
measurements & a variations
Length measurements Clocks used to be
are related to optics
related to RF
Now: clocks enter optics and because of
since RF has too
because of accurate
I
regret
to
inform
you
more
oscillations
in
a
given
period
they
large
wave
lengths
frequency
That is possible because of frequency
comb
that
theoffers
result
for the
for accurate
comparisons
and
which
precision
comparisons
aretechnology
potentially
more
accurate.
Meantime
comparing
various
optical
transitions
measurements.
conventional
optics
to optics
and optics
to
RF.
variations
is negative.
to cesium HFS we look for their
variationand
at the
macroscopic
level of few parts in 1015 perelectromagnetic
a year.
I am really
sorry!
frequency
range.
Atomic Clocks and
Fundamental Constants




Clocks
Atomic and molecular transitions:
their scaling with a, me/mp etc.
Advantages and disadvantages of clocks
to search the variations.
Recent progress.
Atomic Clocks
Caesium clock

Primary standard:


Locked to an
unperturbed atomic
frequency.
All corrections are
under control.
Atomic Clocks
Caesium clock
Primary standard:
Clock frequency =
atomic frequency



Locked to an
unperturbed atomic
frequency.
All corrections are
under control.
Atomic Clocks
Caesium clock
Primary standard:
Clock frequency =
atomic frequency



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.
Atomic Clocks
Caesium clock
Primary standard:
Clock frequency =
atomic frequency



Locked to an
unperturbed atomic
frequency.
All corrections are
under control.
Hydrogen maser

An artificial device
designed for a
Clock
frequency 
purpose.
atomic
frequency(wall
 The corrections

shift) are not under
control.
Unpredictable drift –
bad long term
stability.
Atomic Clocks
Caesium clock
An artificial device
designed for a
Clock
frequency 
purpose.
Locked to an
atomic
frequency(wall
 The corrections
unperturbed atomic
shift)
are not under
If we like to look for
a variation
frequency.
control.
of natural constants
we
have
 Unpredictable drift –
All corrections are
to deal with standards
similar
bad long
term
under control.
to caesium clock. stability.
Primary standard:
Clock frequency =
atomic frequency



Hydrogen maser

Atomic Clocks
Caesium clock
Hydrogen maser
An articitial device
 Primary standard:
designed for a
Clock frequency =
purpose.
Clock
frequency 
atomic frequency
To work with such atomic
anear
primary
The corrections
 Locked to an
frequency(wall
clock is the
same as toshift)
measure
are not under
unperturbed
atomic
If we like
to lookinfor
aor
variation
control.
an
atomic
frequency
SI
other
frequency.
of
natural
constants
we
have
 Unpredictable
drift –
appropriate
 All corrections
areunits.
bad long
term
to deal with standards
similar
under control.
to caesium clock. stability.

Scaling
of atomic transitions
Gross structure
Ry
Fine structure
a2 × Ry
HFS structure
a2 × mNucl/mB × Ry
Relativistic corrections
× F(a)
Scaling
of atomic transitions
Gross structure
Ry
Fine structure
a2 × Ry
HFS structure
a2 × mNucl/mB × Ry
corrections
a)
That isRelativistic
what one can
easily derive ×
forF(
hydrogen.
More complicated atoms lead to
more complicated calculation of numerical factors.
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.
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)
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
Scaling of atomic and
molecular transitions
Atomic transitions
Molecular transitions
 Gross structure
 Electronic transitions
date the most accurate
results
 Up
Finetostructure
 Non-harmonic
have been obtained forcorrections
atomic transitions
 HFS structure
related to gross and HFS
structure.
Rotational
 Relativistic
transitions
corrections
Others are not competitive.
 Relativistic
corrections
Scaling of atomic and
molecular transitions
Atomic transitions
Molecular transitions
structure
ThatisGross
not so
bad because Electronic transitions
date
the most accurate
results
 Up
Finetostructure
 Non-harmonic
the relativistic
corrections
have been obtained forcorrections
atomic transitions
are large.
 HFS structure
related to gross and HFS
structure.
Rotational
 Relativistic
transitions
corrections
Sometimes
really
large.
Others –
are
not competitive.
 Relativistic
corrections
They are ~ (Za)2.
Scaling of atomic and
molecular transitions
Neutral atom (Rb, Cs)

Nucleus


Electron core



charge: +Ze
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)
Scaling of atomic and
molecular transitions
Atomic transitions
Molecular transitions
structure
ThatisGross
not so
bad because Electronic transitions
date
the most accurate
results
 Up
Finetostructure
 Non-harmonic
the relativistic
corrections
have been obtained forcorrections
atomic transitions
are large.
 HFS structure
related to gross and HFS
structure.
Rotational
 Relativistic
transitions
corrections
Sometimes
really
large.
Others –
are
not competitive.
 Relativistic
corrections
They are ~ (Za)2.
Best data from frequency
measurements
Atom
H, Opt
Ca, Opt
Rb, HFS
df/f
[GHz] [10-15]
2466061
14
Df/Dt
[Hz/yr]
-8±16
MPQ
13
-4±5
PTB
1
(0±5)×10-6
LPTF
Frequency
455986
6.8
@
Yb+, Opt
688359
9
-1±3
PTB
Yb+, HFS
12.6
73
(4±4) ×10-4
NML
Hg+, Opt 1064721
9
0±7
NIST
Best data from frequency
measurements
Best data from frequency
measurements
More even better data from
frequency measurements
More even better data from
frequency measurements
More even better data from
frequency measurements
NIST: quantum logics & direct comparison
between two optical clocks
More even better data from
frequency measurements
1D optical lattice
Best data from frequency
measurements
A `direct’ measurement
Progress in a variations since the
1st ACFC meeting (June 2003)

Method:
f = C0 × c Ry × F(a)
Progress in a variations since the 1st
ACFC meeting (June 2003)

Method:
f = C0 × c Ry × F(a)
and thus
d ln{f}/dt = d ln{cRy}/dt
+ A × d lna/dt.
Progress in a variations since the
1st ACFC meeting (June 2003)
Method:
f = C0 × c Ry × F(a)
d ln{f}/dt = d ln{cRy}/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 (LNESYRTE) and octupole Yb+ (NPL)
are coming.

Progress in a variations since the
1st ACFC meeting (June 2003)

Method:
f = C0 × c Ry × F(a)
d ln{f}/dt = d ln{cRy}/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
Progress in a variations since the
1st ACFC meeting (June 2003)


Method:
d ln{f}/dt = d ln{cRy}/dt
+ A × d lna/dt.
Measurements of 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
Progress in a variations since the
1st ACFC meeting (June 2003)

Method:
f = C0 × c Ry × F(a)
d ln{f}/dt = d ln{cRy}/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
Progress in a variations since the
1st ACFC meeting (June 2003)

Method:
f = C0 × c Ry × F(a)
d ln{f}/dt = d ln{cRy}/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
octupole
Yb+
Sr+, Sr, Ca, Al+
Progress in a variations since the
1st ACFC meeting (June 2003)

Method:
f = C0 × c Ry × F(a)
d ln{f}/dt = d ln{cRy}/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
Progress in a variations since the
1st ACFC meeting (June 2003)

Method:
f = C0 × c Ry × F(a)
d ln{f}/dt = d ln{cRy}/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
Progress in a variations since the
1st ACFC meeting (June 2003)

Method:
f = C0 × c Ry × F(a)
d ln{f}/dt = d ln{cRy}/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
Further constraints
Model independent
constraints can be
reached for
variations of a,
{Ry}, and certain
nuclear magnetic
moments in units
the Bohr magneton.
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.
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.
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.
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.
Further constraints
We badly need a universal
Model independent
presentation of all data
constraints can be
for a cross check.
reached for
The next step can be done
variations of a,
with the help of the
{Ry}, and certain
Schmidt model.
nuclear magnetic
The model is not quite
moments in units
reliable and the
the Bohr magneton.
However: Nothing is better!
constraints are model
Those are not
dependent.
fundamental.
Current laboratory constraints
on variations of constants
X
Variation d lnX/dt
Model
a
(– 0.3±2.0)×10-15 yr -1
--
{c Ry}
(– 2.1±3.1)×10-15 yr -1
--
me/mp
(2.9±6.2)×10-15 yr -1
Schmidt model
mp/me
(2.9±5.8)×10-15 yr -1
Schmidt model
gp
(– 0.1±0.5)×10-15 yr -1
Schmidt model
gn
(3±3) ×10-14 yr -1
Schmidt model
Current laboratory constraints
on variations of constants
X
Variation d lnX/dt
a
mp/me
(– 0.3±2.0)×10-15 yr -1
-At present:
-15 yr -1
(– 2.1±3.1)×10
-dlnX/dt for a and {c Ry}
-15 yr -1
(2.9±6.2)×10
Schmidt model
are improved substantially:
(2.9±5.8)×10-15 yr -1
Schmidt model
gp
(– 0.1±0.5)×10-15 yr -1
Schmidt model
gn
(3±3) ×10-14 yr -1
Schmidt model
{c Ry}
me/mp
Model
From talk by Ekkehard Peik at Leiden-2009 workshop
From talk by Ekkehard Peik at Leiden-2009 workshop
Current laboratory constraints
on variations of constants
X
Variation d lnX/dt
Model
a
(– 0.3±2.0)×10-15 yr -1
--
{c Ry}
(– 2.1±3.1)×10-15 yr -1
--
me/mp
(2.9±6.2)×10-15 yr -1
Schmidt model
mp/me
(2.9±5.8)×10-15 yr -1
Schmidt model
gp
(– 0.1±0.5)×10-15 yr -1
Schmidt model
gn
(3±3) ×10-14 yr -1
Schmidt model
Various constraints
Astrophysics:
contradictions at level of 1 part
in 1015 per a year; a nontransperant statistical evaluation
of the data; time separation:
1010 yr.
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.
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.
Julian A. King et al., arXiv:1202.4758
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 Sun1.6 10 -20 cos(wt) annual modulation
Various constraints
Astrophysics:
contradictions at level of 1 part
in 1015 per a year; a nontransperant 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 1×10-17
per a year; separation: 109 yr.
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.
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.
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.
What is `Oklo´?


Some time ago French
comission for atomic
energy reported on
reduction
of
Justof
in amount
case:
U-235: the U-deposites
Myr
mega-year
(1972)
in=Oklo
(Gabon,
West Africa)
contains
Gyr = giga-year
0.705% instead of
0.712%.
meV = milli-electron-volt
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.
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.
What is `Oklo´?


Some time ago French
 It happens because 2
comission for atomic
Gyr ago the uranium
energy reported on
was `enriched´.
reduction
of amount
of suggested
In 1976
Shlyachter
 That was so-called
U-235:tothe
U-deposites
reactor.
examine
Sm isotopeswater-water
to test
(1972) in Oklo (Gabon,
 The operation lasts
variation
of the constants.
West Africa)
contains
from 0.5 to 1.5 Myr.
0.705% instead of
 The fission produces Sm
0.712%.
isotopes and Sm-149 a
The interpretation was
neutron-capture
a fossil natural nuclear
resonance at 97.3 meV.
reactor.
Various constraints
Astrophysics:
contradictions at level of 1 part
in 1015 per a year; a nontransperant statistical evaluation
of the data; time separation:
1010 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.
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 1×10-17
per a year; separation: 109 yr.
Various constraints
Astrophysics:
contradictions at level of 1 part
in 1015 per a year; a nontransperant 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 1×10-17
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; modelindependence; access only to a
and {cRy}; reliability; time
separation ~ 1-3-10 yr.
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.