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. 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 andFundamental Constants

4. 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 andFundamental Constants But: everything related to astrophysics is model dependent and not transparent.

5. 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. [Optical] Atomic Clocks andFundamental Constants

6. 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. Atomic Clocks andFundamental Constants 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 resultsin 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. Gis 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 e2/4pe0ħc.

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 `constant´is 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 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.

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. 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

37. 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 Now: clocks enter optics and because of more oscillations in a given period they are potentially more accurate.

38. 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 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. 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 & a variations 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. 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?

41. 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?

42. 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?

43. 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? 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. 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 & a variations 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. 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 & a variations 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. 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 & a variations 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. Caesium clock Primary standard: Locked to an unperturbed atomic frequency. All corrections are under control. Atomic Clocks

49. Caesium clock Primary standard: Locked to an unperturbed atomic frequency. All corrections are under control. Atomic Clocks Clock frequency = atomic frequency

50. 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. Atomic Clocks Clock frequency = atomic frequency