ac fundamental constants
DESCRIPTION
AC Fundamental Constants. Savely G Karshenboim Pulkovo observatory (St. Petersburg) and Max-Planck-Institut f ür Quantenoptik (Garching). A strophysics, C locks and Fundamental Constants. Why astrophysics ? Cosmology: changing universe. Inflation: variation of constants. - PowerPoint PPT PresentationTRANSCRIPT
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AC Fundamental Constants
Savely G Karshenboim
Pulkovo observatory (St. Petersburg)and Max-Planck-Institut für Quantenoptik
(Garching)
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Astrophysics, Clocks andFundamental Constants
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Astrophysics, Clocks andFundamental ConstantsWhy 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.
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Astrophysics, Clocks andFundamental ConstantsWhy 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:But:everything related to astrophysics is everything related to astrophysics is model dependent and not transparent.model dependent and not transparent.
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[Optical] Atomic Clocks andFundamental ConstantsWhy atomic clocks?
Frequency measurements are most accurate up to date.
Different atomic and molecular transitions differently depend on fundamental constants (, 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 variation.
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Atomic Clocks andFundamental ConstantsWhy atomic clocks?
Frequency measurements are most accurate up to date.
Different atomic and molecular thansitions differently depend on fundamental constants (, 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 variation.
Up to now the optical measurements Up to now the optical measurements are the only source for accurate and are the only source for accurate and reliable model-independent constraints reliable model-independent constraints on a possible time variation of constants.on a possible time variation of constants.
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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
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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.
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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.
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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.
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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.
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Fundamental constants & various physical phenomenaFirst universal parameters appeared centuries ago.G and g entered a big number of various problems.
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Fundamental constants & various physical phenomenaFirst 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.
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Fundamental constants & various physical phenomenaFirst universal parameters appeared centuries ago.G and g entered a big number of various problems.G is still a constant,
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Fundamental constants & various physical phenomenaFirst universal parameters appeared centuries ago.G and g entered a big number of various problems.G is still a constant, g is not anymore.
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Fundamental constants & various physical phenomenaFirst 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
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Fundamental constants & various physical phenomenaFirst 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 ...)
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Fundamental constants & various physical phenomenaFirst 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
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Fundamental constants & various physical phenomenaFirst 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 – property of a universal interaction
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Fundamental constants & various physical phenomenaFirst 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 – property of a universal interaction Just in case:
is the fine structure constant:which is e2/40ħc.
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Fundamental constants & various physical phenomenaFirst 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 – property of a universal interaction me, mp – properties of individual elementary particles
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Fundamental constants & various physical phenomenaFirst 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 – property of a universal interaction me, mp – properties of individual elementary particles cesium HFS, carbon atomic mass – properties of specific
compound objects
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Lessons to learn:
A variation of certain constants already took place according to the inflation model.
is likely the most fundamental of phenomenological constants (the masses are not!) accessible with high accuracy.
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Lessons to learn:
A variation of certain constants already took place according to the inflation model.
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 `constant´is
a constant is to trace its origine and check.
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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).
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Fundamental constants & units for physical quantitiesEarly time: units are determined by humans (e.g. foot) Earth (e.g. g = 9.8 m/s, day) water (e.g. = 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.
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Fundamental constants & units for physical quantitiesEarly time: units are determined by humans (e.g. foot) Earth (e.g. g = 9.8 m/s, day) water (e.g. = 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 isRy ~ 13.6 eV
(or IH ~ 13.6 V) since all electric potentials were linked to atomic and molecular energy.
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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 a great illusion of SIillusion of SI.
The fundamental constants serve us both as natural units and as conversion factors.
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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 a great illusion of SIillusion 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.
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Constants & their numerical valuesWe have to distinguish clearly between fundamental
constants and their numerical values. The Rydberg constant is defined via e, h, me, 0 and c.It has no relation to cesium and its hyperfine structure
(nuclear magnetic moment).
While the numerical value of the Rydberg constant2 × {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.
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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.
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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.
Note: the progress is not necessaryan increase of accuracy,
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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.
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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.
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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.
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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.
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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.
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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.
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Optical frequency measurements & 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.
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What is the frequency comb? When an optical signal is
modulated by an rf, the results contains ffoptopt+nf+nfrfrf, 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 ffoffoff+nf+nfreprep.
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 ffoffoff in terms of ffreprep.
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What is the frequency comb? When an optical signal is
modulated by an rf, the results contains ffoptopt+nf+nfrfrf, 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 ffoffoff+nf+nfreprep.
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 ffoffoff in terms of ffreprep.
![Page 42: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/42.jpg)
What is the frequency comb? When an optical signal is
modulated by an rf, the results contains ffoptopt+nf+nfrfrf, 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 ffoffoff+nf+nfreprep.
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 ffoffoff in terms of ffreprep.
![Page 43: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/43.jpg)
What is the frequency comb? When an optical signal is
modulated by an rf, the results contains ffoptopt+nf+nfrfrf, 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 ffoffoff+nf+nfreprep.
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 ffoffoff in terms of ffreprep.
Presence of regular reference lines,Presence of regular reference lines,distance between which is in rf domain,distance between which is in rf domain,
across all the visible spectrumacross all the visible spectrum(and a substantial paft of IR and UV)(and a substantial paft of IR and UV)
allows a comparison of two opical lines,allows a comparison of two opical lines,or an optical againts a radio frequency.or an optical againts a radio frequency.
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Optical frequency measurements & 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.
I regret to inform you that the result for the variations is negative.
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Optical frequency measurements & 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 few parts in 1015 per a year.
I regret to inform you that the result for the variations is negative.
I am sorry!
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Optical frequency measurements & 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 few parts in 1015 per a year.
I regret to inform you that the result for the variations is negative.
I am really sorry!
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Atomic Clocks andFundamental Constants
Clocks Atomic and molecular transitions:
their scaling with , me/mp etc. Advantages and disadvantages of
clocks to search the variations. Recent progress.
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Atomic Clocks
Caesium clock
Primary standard:
Locked to an unperturbed atomic frequency.
All corrections are under control.
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Atomic Clocks
Caesium clock
Primary standard:
Locked to an unperturbed atomic frequency.
All corrections are under control.
Clock frequency = atomic frequency
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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
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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
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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 variationof natural constants we have to deal with standards similarto caesium clock.
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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
If we like to look for a variationof natural constants we have to deal with standards similarto caesium clock.
To work with such a near primary clock is the same as to measure an atomic frequency in SI or other appropriate units.
![Page 54: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/54.jpg)
Scaling of atomic transitions
Gross structure Ry
Fine structure 2 × Ry
HFS structure 2 × Nucl/B × Ry
Relativistic corrections
× F()
![Page 55: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/55.jpg)
Scaling of atomic transitions
Gross structure Ry
Fine structure 2 × Ry
HFS structure 2 × Nucl/B × Ry
Relativistic corrections
× F()
That is what one can easily derive for hydrogen.That is what one can easily derive for hydrogen.
More complicated atoms lead to More complicated atoms lead to more complicated calculation of numerical factors.more complicated calculation of numerical factors.
![Page 56: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/56.jpg)
Scaling of atomic transitions
Gross structure Ry
Fine structure 2 × Ry
HFS structure 2 × Nucl/B × Ry
Relativistic corrections
× F()
Characteristic electron velocity in an atom is Characteristic electron velocity in an atom is c/n. c/n.
![Page 57: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/57.jpg)
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()
![Page 58: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/58.jpg)
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
![Page 59: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/59.jpg)
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 resultshave been obtained for atomic transitionsrelated to gross and HFS structure.
Others are not competitive.
![Page 60: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/60.jpg)
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 resultshave been obtained for atomic transitionsrelated to gross and HFS structure.
Others are not competitive.
That is not so bad because That is not so bad because the relativistic correctionsthe relativistic correctionsareare large. large.
Sometimes – reallySometimes – really largelarge..
They are ~ (They are ~ (ZZ))22..
![Page 61: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/61.jpg)
Scaling of atomic and molecular transitionsNeutral 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 ~ (outside core) v/c ~ Z(inside core)
![Page 62: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/62.jpg)
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 resultshave been obtained for atomic transitionsrelated to gross and HFS structure.
Others are not competitive.
That is not so bad because That is not so bad because the relativistic correctionsthe relativistic correctionsareare large. large.
Sometimes – reallySometimes – really largelarge..
They are ~ (They are ~ (ZZ))22..
![Page 63: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/63.jpg)
Best data from frequency measurements
Atom Frequency
[GHz]
f/f[10-15]
f/t[Hz/yr]
@
H, Opt 2466061
14 -8±16 MPQ
Ca, Opt 455986
13 -4±5 PTB
Rb, HFS 6.8
1 (0±5)×10-
6
LPTF
Yb+, Opt
688359
9 -1±3 PTB
Yb+, HFS
12.6
73 (4±4) ×10-4
NML
Hg+, Opt
1064721
9 0±7 NIST
![Page 64: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/64.jpg)
Best data from frequency measurements
![Page 65: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/65.jpg)
Best data from frequency measurements
![Page 66: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/66.jpg)
More even better data from frequency measurements
![Page 67: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/67.jpg)
More even better data from frequency measurements
![Page 68: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/68.jpg)
More even better data from frequency measurements
NIST: quantum logics & direct comparison NIST: quantum logics & direct comparison between two optical clocks between two optical clocks
![Page 69: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/69.jpg)
More even better data from frequency measurements
1D optical lattice
![Page 70: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/70.jpg)
Best data from frequency measurements
![Page 71: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/71.jpg)
A `direct’ measurement
![Page 72: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/72.jpg)
Progress in variations since the 1st ACFC meeting (June 2003) Method:
f = C0 × c Ry × F()
![Page 73: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/73.jpg)
Progress in variations since the 1st ACFC meeting (June 2003) Method:
f = C0 × c Ry × F()
and thusd ln{f}/dt = d ln{cRy}/dt
+ A × d ln/dt.
![Page 74: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/74.jpg)
Progress in variations since the 1st ACFC meeting (June 2003) Method:
f = C0 × c Ry × F() d ln{f}/dt = d ln{cRy}/dt
+ A × d ln/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.
![Page 75: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/75.jpg)
Progress in variations since the 1st ACFC meeting (June 2003) Method:
f = C0 × c Ry × F() d ln{f}/dt = d ln{cRy}/dt
+ A × d ln/dt. Measurements: Optical transitions in Hg+ (NIST),
H (MPQ), Ca, Yb+ (PTB) versus Cs HFS;
Calculation of relativistic corrections (Flambaum, Dzuba):
A = d lnF()/d ln
![Page 76: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/76.jpg)
Progress in variations since the 1st ACFC meeting (June 2003) Method:
d ln{f}/dt = d ln{cRy}/dt + A × d
ln/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()/d ln
![Page 77: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/77.jpg)
Progress in variations since the 1st ACFC meeting (June 2003) Method:
f = C0 × c Ry × F() d ln{f}/dt = d ln{cRy}/dt
+ A × d ln/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()/d
![Page 78: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/78.jpg)
Progress in variations since the 1st ACFC meeting (June 2003) Method:
f = C0 × c Ry × F() d ln{f}/dt = d ln{cRy}/dt
+ A × d ln/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()/d
Sr+, Sr, Ca, Al+octupol
e Yb+
Hg
![Page 79: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/79.jpg)
Progress in variations since the 1st ACFC meeting (June 2003) Method:
f = C0 × c Ry × F() d ln{f}/dt = d ln{cRy}/dt
+ A × d ln/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()/d
![Page 80: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/80.jpg)
Progress in variations since the 1st ACFC meeting (June 2003) Method:
f = C0 × c Ry × F() d ln{f}/dt = d ln{cRy}/dt
+ A × d ln/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()/d
![Page 81: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/81.jpg)
Progress in variations since the 1st ACFC meeting (June 2003) Method:
f = C0 × c Ry × F() d ln{f}/dt = d ln{cRy}/dt
+ A × d ln/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()/d
![Page 82: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/82.jpg)
Further constraints
Model independent constraints can be reached for variations of , {Ry}, and certain nuclear magnetic moments in units the Bohr magneton.
![Page 83: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/83.jpg)
Further constraints
Model independent constraints can be reached for variations of , {Ry}, and certain nuclear magnetic moments in units the Bohr magneton.
Those are not fundamental.
![Page 84: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/84.jpg)
Further constraints
Model independent constraints can be reached for variations of , {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.
![Page 85: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/85.jpg)
Further constraints
Model independent constraints can be reached for variations of , {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.
![Page 86: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/86.jpg)
Further constraints
Model independent constraints can be reached for variations of , {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.
![Page 87: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/87.jpg)
Further constraints
Model independent constraints can be reached for variations of , {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 However: Nothing is better!better!
![Page 88: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/88.jpg)
Current laboratory constraints on variations of constants
X Variation d lnX/dt Model
(– 0.3(– 0.3±±2.0)2.0)××1010-15-15 yr yr -1-1 ----
{c Ry}{c Ry} (– 2.1(– 2.1±±3.1)3.1)××1010-15-15 yr yr -1-1 ----
mmee/m/mpp (2.9(2.9±±6.2)6.2)××1010-15-15 yr yr -1-1 Schmidt
model
pp//ee (2.9(2.9±±5.8)5.8)××1010-15-15 yr yr -1-1 Schmidt
model
ggpp (– 0.1(– 0.1±±0.5)0.5)××1010-15-15 yr yr -1-1 Schmidt
model
ggnn (3(3±±3) 3) ××1010-14-14 yr yr -1-1 Schmidt
model
![Page 89: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/89.jpg)
Current laboratory constraints on variations of constants
X Variation d lnX/dt Model
(– 0.3(– 0.3±±2.0)2.0)××1010-15-15 yr yr -1-1 ----
{c Ry}{c Ry} (– 2.1(– 2.1±±3.1)3.1)××1010-15-15 yr yr -1-1 ----
mmee/m/mpp (2.9(2.9±±6.2)6.2)××1010-15-15 yr yr -1-1 Schmidt
model
pp//ee (2.9(2.9±±5.8)5.8)××1010-15-15 yr yr -1-1 Schmidt
model
ggpp (– 0.1(– 0.1±±0.5)0.5)××1010-15-15 yr yr -1-1 Schmidt
model
ggnn (3(3±±3) 3) ××1010-14-14 yr yr -1-1 Schmidt
model
At present: dlnX/dt for and {c Ry}{c Ry}
are improved substantially:
![Page 90: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/90.jpg)
From talk by Ekkehard Peik at Leiden-2009 workshop
![Page 91: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/91.jpg)
From talk by Ekkehard Peik at Leiden-2009 workshop
![Page 92: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/92.jpg)
Current laboratory constraints on variations of constants
X Variation d lnX/dt Model
(– 0.3(– 0.3±±2.0)2.0)××1010-15-15 yr yr -1-1 ----
{c Ry}{c Ry} (– 2.1(– 2.1±±3.1)3.1)××1010-15-15 yr yr -1-1 ----
mmee/m/mpp (2.9(2.9±±6.2)6.2)××1010-15-15 yr yr -1-1 Schmidt
model
pp//ee (2.9(2.9±±5.8)5.8)××1010-15-15 yr yr -1-1 Schmidt
model
ggpp (– 0.1(– 0.1±±0.5)0.5)××1010-15-15 yr yr -1-1 Schmidt
model
ggnn (3(3±±3) 3) ××1010-14-14 yr yr -1-1 Schmidt
model
![Page 93: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/93.jpg)
Various constraintsAstrophysics:contradictions at level of 1 part in 1015 per a year; a non-transperant statistical evaluation of the data; time separation: 1010 yr.
![Page 94: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/94.jpg)
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 e/p 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.
![Page 95: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/95.jpg)
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 e/p 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.
![Page 96: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/96.jpg)
Julian A. King et al., arXiv:1202.4758
![Page 97: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/97.jpg)
Consequences for atomic clocks (from Victor Flambaum)
Sun moves 369 km/s relative to CMB cos towards area with larger
This gives average laboratory variation cosper year
Earth moves 30 km/s relative to Sun- 1.6 10 -20cos(tannual modulation
![Page 98: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/98.jpg)
Various constraintsAstrophysics: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 ;contradictions at level of 1×10-17 per a year; separation: 109 yr.
![Page 99: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/99.jpg)
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.
![Page 100: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/100.jpg)
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.
![Page 101: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/101.jpg)
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.
![Page 102: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/102.jpg)
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-yearMyr = mega-year
Gyr = giga-year Gyr = giga-year
meV = milli-electron-voltmeV = milli-electron-volt
![Page 103: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/103.jpg)
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.
![Page 104: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/104.jpg)
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 In 1976 Shlyachter suggested to examine Sm isotopes to test to examine Sm isotopes to test
variation of the constants.variation of the constants.
![Page 105: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/105.jpg)
Various constraintsAstrophysics: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 ;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.
![Page 106: AC Fundamental Constants](https://reader036.vdocuments.site/reader036/viewer/2022062305/5681473b550346895db47976/html5/thumbnails/106.jpg)
Various constraintsAstrophysics: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 ;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; model-independence; access only to and {cRy}; reliability; time separation ~ 1-3-10 yr.
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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.