Committee on Data for Science and Technology

The Committee on Data for Science and Technology (CODATA) is a Paris- based organization with the goal of improving the quality, reliability and accessibility of interesting data from all fields of science and technology. CODATA was around 1966 by the International Council for Science ( International Council for Science founded).

CODATA recommendations for physical constants

In 1969 the CODATA Task Group on Fundamental Constants was founded. The working group's secretariat is held in the Fundamental Constants Data Center of the National Institute of Standards and Technology . Your goal is the periodic publication of an optimally estimated set of values ​​of physical constants and the associated standard uncertainties. In principle, optimization is carried out using the least squares method on the basis of the internationally determined relevant measured values ​​available up to the reference date, which are weighted with the reciprocal of the squares of their respective standard uncertainties to take into account their different accuracies. Since 1998, these recommendations have been determined every four years with a reference date of December 31, and more often if necessary with new measured values ​​with a significant influence.

The current publication was edited by Eite Tiesinga, Peter J. Mohr, David B. Newell and Barry N. Taylor.

A total of eight data sets have been published to date (see also literature list):

1. CODATA 1973, E. Richard Cohen, Barry N. Taylor
2. CODATA 1986 (Web Version 1.0 1994-10-06), E. Richard Cohen, Barry N. Taylor
3. CODATA 1998 (Web Version 3.0 1999-07-23), Peter J. Mohr, Barry N. Taylor
4. CODATA 2002 (Web Version 4.0 2003-12-09), Peter J. Mohr, Barry N. Taylor
5. CODATA 2006 (Web Version 5.0 2007-03-07), Peter J. Mohr, Barry N. Taylor, David B. Newell
6. CODATA 2010 (Web Version 6.0 2011-06-02), Peter J. Mohr, Barry N. Taylor, David B. Newell
7. CODATA 2014 (Web Version 7.0 2015-06-25), Peter J. Mohr, David B. Newell, Barry N. Taylor
8. CODATA 2018 (Web Version 8.0 2019-05-20), Eite Tiesinga, Peter J. Mohr, David B. Newell, and Barry N. Taylor

There was the special publication "CODATA 2017 special fundamental constants adjustment" on the occasion of the redefinition of the SI units .

The publication of CODATA 2018 took place on May 20, 2019, the day of measurement , as the new SI definitions came into force on this day. The next regular release according to the four-year cycle will then be CODATA 2022.

The CODATA recommendations have been available on the Internet since 1994. The databases were developed by J. Baker, M. Douma and S. Kotochigova.

Details on the CODATA values ​​as well as the underlying measured values ​​and calculation methods are then usually published by the authors in the journal Reviews of Modern Physics . Mohr and Taylor published the details of the CODATA 1998 values ​​in 2000, the details of the CODATA 2002 values ​​in 2005 and those of CODATA 2006 in 2008.

Standard uncertainties of CODATA values

Values ​​that are not defined with a specific numerical value, ie whose numerical value is "estimated" or "uncertain", are always given in metrology together with an "uncertainty". According to VIM, this uncertainty describes the range of possible estimates. CODATA are tested at a standard uncertainty (s: standard uncertainty ) specified. This means that this type of uncertainty can be treated computationally like a standard deviation. The uncertainty u is usually given rounded to 2 significant digits.

The uncertainties are determined in a statistical equalization calculation, largely following the guidelines of the Guide to the Expression of Uncertainty in Measurement  (GUM) published by the Joint Committee for Guides in Metrology . CODATA uses the term least-squares adjustment (LSA) for its adjustment procedure .

In the CODATA tables, the (absolute) standard uncertainty is given in compact notation in accordance with the SI recommendations for the representation of quantities in brackets after the numerical value.

Examples from CODATA 2010

The following examples are from the publication by CODATA 2010 ( PJ Mohr, BN Taylor, DB Newell: CODATA recommended values ​​of the fundamental physical constants: 2010. In: Rev. Mod. Phys. 84 (4). 2012, p. 1527– 1605 , accessed on June 16, 2019 (in particular Table XL on page 1586).  ). For some of the values ​​mentioned, the uncertainties have now become smaller, or the values ​​have even become exact values due to the SI redefinitions of May 20, 2019 .

For example, the redefinition of the meanwhile exact value of the Avogadro constant in CODATA 2010 in the short form

${\displaystyle N_{\mathrm {A} }=6{,}022\,141\,29(27)\cdot 10^{23}\ \mathrm {mol} ^{-1}}$

indicated what is equivalent to the long spelling of the form

${\displaystyle N_{\mathrm {A} }=6{,}022\,141\,29\cdot 10^{23}\ \mathrm {mol} ^{-1}}$; ${\displaystyle u(N_{\mathrm {A} })=0{,}000\,000\,27\cdot 10^{23}\ \mathrm {mol} ^{-1}}$

and stated that the standard uncertainty was. ${\displaystyle u(N_{\mathrm {A} })=27\cdot 10^{15}\ \mathrm {mol} ^{-1}}$

This resulted in the relative  standard uncertainty as the quotient of the absolute standard uncertainty and the amount of the estimated value of the quantity. In the example mentioned, it was ${\displaystyle u_{r}}$

${\displaystyle u_{r}(N_{\mathrm {A} })={\frac {0{,}000\,000\,27}{6{,}022\,141\,29}}=4{,}4\cdot 10^{-8}=44\cdot 10^{-9}\ .}$

The relative standard uncertainties of the CODATA 2010 data set ranged from 10 ⁻¹² (in the best case) to 10 ⁻⁴ (in the worst case). The fundamental constant that can best be estimated at that time was the Rydberg constant . This therefore plays the central role in the CODATA adjustment calculations, so that initially only its value is determined - regardless of the uncertainties of all other constants. Further key roles in CODATA's least-squares adjustment at that time were played by the fine structure constant α , Planck's quantum of action h and the universal gas constant R , with : ${\displaystyle R_{\infty }}$ ${\textstyle u_{r}(R_{\infty })\ll u_{r}(\alpha )\ll u_{r}(h)\ll u_{r}(R)}$

${\displaystyle u_{r}(R_{\infty })=5{,}0\cdot 10^{-12}}$

${\displaystyle u_{r}(\alpha )=3{,}2\cdot 10^{-10}}$

${\displaystyle u_{r}(h)=4{,}4\cdot 10^{-8}}$

${\displaystyle u_{r}(R)=9{,}1\cdot 10^{-7}}$

As already mentioned, some things have changed in this inequality: In 2019, and . h is now exact, as is R as the product of two exact values . At NIST, the value of R is abbreviated after the tenth valid digit and specified as 8.314 462 618 ... J mol ^-1  K ^-1 . ${\textstyle u_{r}(R_{\infty })=1{,}0\cdot 10^{-12}}$ ${\textstyle u_{r}(\alpha )=1{,}5\cdot 10^{-10}}$ ${\textstyle R=N_{\mathrm {A} }\,k}$

The fundamental constant that is hardest to estimate is Newton's gravitational constant with the high standard relative uncertainty of . This is therefore not included in CODATA's least-squares adjustment. ${\displaystyle G}$ ${\displaystyle 1{,}2\cdot 10^{-4}}$

Dependencies between constants

The value and the standard uncertainty of many of the variables specified by CODATA is obtained by mathematical-statistical conversion from other variables specified by CODATA. If all output quantities are independent of one another, the standard uncertainty of a derived quantity (constant) results according to the rules of the Gaussian law of error propagation . In the case of a dependency (correlation) between two (or more) constants, the error propagation law must be extended by the covariances or the correlation coefficients r .

In general, the correlation between two quantities can have an absolute value of their correlation coefficient of | r  | <0.10 as missing and with | r  | > 0.90 can be considered perfect. Most of the correlation coefficients between two constants given by the CODATA fall into one of these two categories.

The CODATA website does not have a list of correlation coefficients, but it is possible to query the correlation coefficient between any two constants according to the CODATA 2006 adjustment online.

After the redefinition of 2019 , a number of constants have become exact. The associated correlations disappeared as a result. Non-trivial correlations exist e.g. B. still between the following constants:

Long form	Constant k	r  ( k , α)	r  ( k , m e )	r  ( k , R ⚭ )	r  ( k , μ 0 )
Fine structure constant	α	1	-0.99998	0.00207	1.00000
Electron mass	m e	-0.99998	1	0.00436	-0.99998
Rydberg's constant	R ∞	0.00207	0.00436	1	0.00207
Magnetic field constant	μ 0	1.00000	-0.99998	0.00207	1

Version differences of the CODATA recommendations

The recommended values ​​for the same constant have changed over the years. In the following, the changed values ​​of the Avogadro constant N _A , the fine structure constant α and the Rydberg constant R _∞ are shown as examples . In addition to the absolute standard uncertainty, the relative standard uncertainty u (in a separate column) is also given in 10 ⁻¹² .

publication	N A in 10 23  mol −1	u of N A  / 10 −12	α in 10 −3	u of α  / 10 −12	R ∞ in m −1	u from R ∞  / 10 −12
CODATA 1973	6.022 045  000(31)	5,148,000	7.297 350 6 00 00(60)	822,000	10,973,731.77 0 000(83)	76,000
CODATA 1986	6.022 136 7 00(36)	598,000	7,297 353 08 0 00(33)	45,000	10 973 731,534  000(13)	1,200
CODATA 1998	6.022 141 99 0(47)	78,000	7,297 352 533  00(27)	3,700	10 973 731,568 549 (83)	7.6
CODATA 2002	6.022 141 5 00(10)	166,000	7,297 352 568  00(24)	3,300	10 973 731,568 525 (73)	6.6
CODATA 2006	6.022 141 79 0(30)	50,000	7,297 352 537 6 0(50)	680	10 973 731,568 527 (73)	6.6
CODATA 2010	6.022 141 29 0(27)	44,000	7,297 352 569 8 0(24)	320	10 973 731,568 539 (55)	5.0
CODATA 2014	6.022 140 857 (74)	12,000	7,297 352 566 48 (17)	230	10 973 731,568 508 (65)	5.9
CODATA 2018	6.022 140 76 0(exact)	0	7,297 352 569 3 0(11)	137	10 973 731,568 160 (21)	1.9

A comparison of the relative standard uncertainties of the three selected quantities shows that they are orders of magnitude apart. Before the redefinition in 2019 , the Avogadro constant could be the worst and the Rydberg constant the best; because of the redefinition, Avogadro's constant is now an exact constant.

literature

1969

BN Taylor, WH Parker, DN Langenberg:
Determination of e / h, Using Macroscopic Quantum Phase Coherence in Superconductors: Implications for Quantum Electrodynamics and the Fundamental Physical Constants.
Reviews of Modern Physics, Vol. 41, No. 3 (July 1969), 375-496, doi : 10.1103 / RevModPhys.41.375 (Paywall),
Erratum Rev. Mod. Phys. Vol. 45, No. 1 (January 1973), 109 doi : 10.1103 / RevModPhys.45.109 (open access)

1973

ER Cohen, BN Taylor:
The 1973 Least-Squares Adjustment of the Fundamental Constants.
Journal of Physical and Chemical Reference Data, Vol. 2, No. 4 (1973), 663–734, doi : 10.1063 / 1.3253130 (Paywall)
( PDF from CiteSeer, 6.73 MB , PDF from SemanticScholar, 6.73 MB )

1986

ER Cohen, BN Taylor:
The 1986 CODATA Recommended Values ​​of the Fundamental Physical Constants.
Journal of Research of the National Bureau of Standards, Vol. 92, No. 2 (March – April 1987), 85–95,
( PDF from NIST, 684 KB )

ER Cohen, BN Taylor:
The 1986 CODATA Recommended Values ​​of the Fundamental Physical Constants.
Journal of Physical and Chemical Reference Data, Vol. 17 (1988), 1795–1803, doi : 10.1063 / 1.555817 (Paywall),
( PDF from NIST, 1.07 MB )

1998

PJ Mohr, BN Taylor:
CODATA recommended values ​​of the fundamental physical constants: 1998.
Reviews of Modern Physics, Vol. 72, no. 2 (April 2000), 351–495, doi : 10.1103 / RevModPhys.72.351 (Paywall)

PJ Mohr, BN Taylor:
CODATA recommended values ​​of the fundamental physical constants: 1998.
Journal of Physical and Chemical Reference Data, Vol. 28, No. 6 (1999), 1713-1852, doi : 10.1063 / 1.556049 (Paywall),
( PDF from NIST, 1.85 MB )

2002

PJ Mohr, BN Taylor:
CODATA recommended values ​​of the fundamental physical constants: 2002.
Reviews of Modern Physics, Vol. 77, No. 1 (January – March 2005), 1–107, doi : 10.1103 / RevModPhys.77.1 (Paywall),
( PDF from NIST, 855 KB )

2006

PJ Mohr, BN Taylor, DB Newell:
CODATA recommended values ​​of the fundamental physical constants: 2006.
Reviews of Modern Physics, Vol. 80, No. 2 (April-June 2008), 633-730, doi : 10.1103 / RevModPhys.80.633 (Paywall),
( Arxiv Preprint, PDF 1.14 MB )

PJ Mohr, BN Taylor, DB Newell:
CODATA recommended values ​​of the fundamental physical constants: 2006.
Journal of Physical and Chemical Reference Data, Vol. 37, No. 3 (2008), 1187–1284, doi : 10.1063 / 1.2844785 (Paywall ),
( PDF from NIST, 1.81 MB )

2010

PJ Mohr, BN Taylor, DB Newell:
CODATA recommended values ​​of the fundamental physical constants: 2010.
Reviews of Modern Physics, Vol. 84, (October – December 2012) 1527–1605, doi : 10.1103 / RevModPhys.84.1527 (Paywall),
( ArXiv Preprint, PDF 1.02 MB )

PJ Mohr, BN Taylor, DB Newell:
CODATA Recommended Values ​​of the Fundamental Physical Constants: 2010.
Journal of Physical and Chemical Reference Data, Vol. 41, No. 4 (2012), 043109, doi : 10.1063 / 1.4724320 (Paywall),
( PDF from NIST, 2.21 MB )

2014

PJ Mohr, DB Newell, BN Taylor:
CODATA recommended values ​​of the fundamental physical constants: 2014.
Reviews of Modern Physics, Vol. 88, No. 3 (July – September 2016), 035009, doi : 10.1103 / RevModPhys.88.035009 (Paywall ),
( Arxiv preprint, PDF 146 KB )

PJ Mohr, DB Newell, BN Taylor:
CODATA Recommended Values ​​of the Fundamental Physical Constants: 2014.
Journal of Physical and Chemical Reference Data, Vol. 45, (2016), 043102, doi : 10.1063 / 1.4954402 (Paywall),
( PDF from NIST, 2.40 MB )

2017

DB Newell et al .:
The CODATA 2017 values ​​of h, e, k, and N _A for the revision of the SI.
Metrologia, Vol. 55, No. 1 (2018), L13 – L16, doi : 10.1088 / 1681-7575 / aa950a (open access)

PJ Mohr, DB Newell, BN Taylor, E. Tiesinga:
Data and analysis for the CODATA 2017 special fundamental constants adjustment.
Metrologia, Vol. 55, No. 1 (2018), 125–146, doi : 10.1088 / 1681-7575 / aa99bc (open access)

2018

CODATA Recommended Values ​​of the Fundamental Physical Constants: 2018
( Table, PDF from NIST, 61 KB )

Web links

• www.codata.org - Homepage of CODATA
• Homepage of the CODATA Committee on Fundamental Physical Constants
• Homepage of CODATA-Germany eV

Individual evidence

1. ^ NIST: Fundamental Constants Data Center. Homepage. Retrieved June 29, 2019 . 
2. ↑ ^{a b} Peter Mohr, Barry Taylor: CODATA recommended values ​​of the fundamental physical constants: 1998 . In: Reviews of Modern Physics . tape 72 , no. 2 , April 2000, p. 351–495 , doi : 10.1103 / RevModPhys.72.351 (English, usm.uni-muenchen.de [PDF; 1,2 MB ; accessed on June 29, 2019] can be downloaded from the University Observatory in Munich, Faculty of Physics at the Ludwig Maximilians University).
3. ↑ NIST: Eite Tiesinga. Retrieved June 16, 2019 . 
4. ↑ NIST: Peter J. Mohr. Retrieved June 16, 2019 . 
5. ↑ NIST: David B. Newell. Retrieved June 16, 2019 . 
6. ↑ NIST: Barry N. Taylor. Retrieved June 16, 2019 . 
7. ↑ NIST: Version history of CODATA recommended values. Retrieved June 29, 2019 . 
8. ^ E. Richard Cohen, Barry N. Taylor: The 1973 Least-Squares Adjustment of the Fundamental Constants . In: Journal of Physical and Chemical Reference Data . tape 2 , no. 4 , 1973, p. 663–734 , doi : 10.1063 / 1.3253130 (English, downloadable from the NIST reprint page via SRD as a PDF [accessed on June 29, 2019]).
9. ^ NIST Reference on Constants, Units and Uncertainty: Older values ​​of the constants. 1986 values. Retrieved June 29, 2019 . 
10. ^ NIST Reference on Constants, Units and Uncertainty: Older values ​​of the constants. 1998 values. Retrieved June 29, 2019 . 
11. ^ NIST Reference on Constants, Units and Uncertainty: Older values ​​of the constants. 2002 values. Retrieved June 29, 2019 . 
12. ^ NIST Reference on Constants, Units and Uncertainty: Older values ​​of the constants. 2006 values. Retrieved June 29, 2019 . 
13. ^ NIST Reference on Constants, Units and Uncertainty: Older values ​​of the constants. 2010 values. Retrieved June 29, 2019 . 
14. ^ NIST Reference on Constants, Units and Uncertainty: Older values ​​of the constants. 2014 values. Retrieved June 29, 2019 . 
15. ↑ Peter J. Mohr, David B. Newell, Barry N. Taylor: CODATA Recommended Values ​​of the Fundamental Physical Constants: 2014 . In: Zenodo . 2015, doi : 10.5281 / zenodo.22826 , arxiv : 1507.07956 .
16. ↑ Eite Tiesinga, Peter J. Mohr, David B. Newell, and Barry N. Taylor: CODATA Recommended Values of the Fundamental Physical Constants: 2018 . 2019. Available on the National Institute of Standards and Technology website
17. ↑ Peter J Mohr, David B Newell, Barry N Taylor and Eite Tiesinga: Data and analysis for the CODATA 2017 special fundamental constants adjustment . Retrieved April 26, 2019
18. ↑ NIST on CODATA 2018.
19. ↑ CODATA Internationally recommended values ​​of the Fundamental Physical Constants
20. ↑ Peter Mohr, Barry Taylor: CODATA recommended values ​​of the fundamental physical constants: 2002 (PDF; 884 kB). In: Reviews of Modern Physics 77 (2005), No. 1, pp. 1-107.
21. ^ Mohr, Taylor, Newell 2008: CODATA recommended values ​​of the fundamental physical constants: 2006 In Reviews of Modern Physics. Volume 80, 2008-04 ( physics.nist.gov PDF; 2.1 MB).
22. ↑ ISO 1995: Guide to the Expression of Uncertainty in Measurement
23. ↑ ^{a b c d e} National Institute of Standards and Technology (NIST): CODATA recommended Values ​​of the Fundamental Physical Constants: 2018. (PDF) NIST SP 961 May 2019, accessed on June 16, 2019 (a current version is always available physics.nist.gov downloadable). 
24. ^ Online query of the correlation coefficient between two constants on the CODATA website
25. ^ NIST Reference on CUU: Correlation coefficient between two constants. fine-structure constant α versus electron mass m _e . Retrieved June 30, 2019 . 
26. ^ NIST Reference on CUU: Correlation coefficient between two constants. fine-structure constant α versus Rydberg constant R _⚭ . Retrieved June 30, 2019 . 
27. ^ NIST Reference on CUU: Correlation coefficient between two constants. fine-structure constant α versus vacuum magnetic permeability μ ₀ . Retrieved June 30, 2019 . 
28. ^ NIST Reference on CUU: Correlation coefficient between two constants. electron mass m _e versus Rydberg constant R _⚭ . Retrieved June 30, 2019 . 
29. ^ NIST Reference on CUU: Correlation coefficient between two constants. electron mass m _e versus vacuum magnetic permeability μ ₀ . Retrieved June 30, 2019 . 
30. ^ NIST Reference on CUU: Correlation coefficient between two constants. Rydberg constant R _⚭ versus vacuum magnetic permeability μ ₀ . Retrieved June 30, 2019 .