# 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 established around 1966 by the International Council for Science ( International Council for Science ).

## CODATA recommendations for physical constants

1969 CODATA Task Group on Fundamental Constants was established. The Secretariat of the Working Group is guided 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. The optimization is performed in principle by the least squares method on the basis of information available up to date internationally determined relevant measurements that are weighted to take account of their different accuracies with the inverse of the squares of their respective standard uncertainties. Since 1998, these recommendations are determined every four years ended December 31, through new measured values with significant influence more often if needed. The current current publication was edited by Peter J. Mohr, Barry N. Taylor and David Newell.

Total to date six records were published:

Since 1994, the CODATA recommendations available on the internet.

Details on the CODATA values as well as the underlying measurements and calculation methods are then published by the authors as a rule in the journal Reviews of Modern Physics. Thus, of Mohr and Taylor in 2000, the details of the CODATA 1998 values , the details about the values of CODATA 2002 and 2008, published in 2005 by CODATA 2006.

## Standard uncertainties of CODATA values

Values which are not determined exactly, the exact numerical value that is " estimated " or " unsafe" is, are always specified in the metrology together with an " uncertainty". This uncertainty describes according to VIM, the spread of possible estimates. CODATA values with a standard uncertainty (s: standard uncertainty ) specified. This means that this kind of uncertainty may be treated mathematically as a standard deviation. The uncertainty u is usually given rounded to 2 significant digits.

U can (also called coverage factor; s: coverage factor) with a coverage factor k> 1 be multiplied in order to increase the confidence interval. This product is referred to as expanded uncertainty U at a given expansion factor:

General expanded uncertainties are usually indicated with k = 2; in CODATA values k = 1, is generally

The uncertainties are determined in a statistical balancing account, keeping mostly to the guidelines issued by the Joint Committee for Guides in Metrology Guide to the Expression of Uncertainty in Measurement ( GUM). The CODATA used for its balancing accounting method the ( English ) term least-squares adjustment (LSA ).

In the CODATA tables, the ( absolute ) standard uncertainty is given in compact notation according to the SI recommendations for the representation of quantities in parentheses after the number. For example, the specification of the Avogadro constant by CODATA in 2010 is in the short form

Equivalent to the long spelling of the form

And indicates that the standard uncertainty is.

Hence the relative standard uncertainty as the ratio of absolute standard uncertainty and the amount of the appraised value of the variable. In the example above, is therefore

The relative standard uncertainty of CODATA 2010 data set move in the order of 10-12 (in the best case ) to 10-4 ( in the worst case). The best estimable fundamental constant is the Rydberg constant. This assumes, therefore, in the CODATA matching calculations the central role, so initially only their value - regardless of the uncertainties of all other constants - is determined. Other key roles in CODATA least-squares adjustment of Use have the fine structure constant α, the Planck constant h and the universal gas constant R, with

The worst estimable fundamental constant is the Newtonian gravitational constant with the high relative standard uncertainty of. This is therefore not included in CODATA least-squares adjustment with it.

## Dependencies between constants

The value and the standard uncertainty of many specified by the CODATA sizes calculated by mathematical- statistical conversion from other variables specified by the CODATA. Are all output variables independent of each other, the result is the standard uncertainty of a derived variable ( constant) according to the rules of the Gaussian error propagation law. With a dependency (correlation ) between two (or more), the constants of the law of error propagation covariance or correlation coefficient r has to be extended.

In general, the correlation between two sizes of at an amount of their correlation coefficient | 0.90 are considered as completely r | <0.10 as missing and | | r >. Most indicated by the CODATA correlation coefficient between two constants fall into one of these two categories.

While on the CODATA website is not a list of correlation coefficients to find, but it is possible the correlation coefficient ( en: correlation coefficient ) query between two arbitrary constants in accordance with the CODATA 2006 adjustment online.

### Two constants without correlation

If the absolute value | r | of the correlation coefficient between two sizes smaller than 0.10 as usually occurs on no correlation and r can usually be neglected for the calculation of the standard uncertainty.

For example, the correlation coefficient r ( KJ, RK ) between the Josephson constant KJ and von Klitzing constant RK

With

Specified. About the relationship

Is calculated according to the 2006 CODATA recommended estimate of the elementary charge e

With the specified standard uncertainty of 40 × 10-28 C, without taking into account the correlation coefficient.

The magnitudes of the correlation coefficients of the fine structure constant α and the Rydberg constant R ∞ to many other known constants are smaller than 0.10. So is the correlation coefficient between the Rydberg constant R ∞ and the universal gas constant R, and the Planck's constant h, the Josephson constant KJ, the elementary charge e, the Avogadro constant NA and the Faraday constant F exactly r ( R ∞, k ) = 0 the following table gives the corresponding correlation coefficient r of the fine structure constant α again.

### Two constants with perfect correlation

An example of a constant, the magnitudes of the correlation coefficients to many other known constant larger than 0.90, the NA Avogadro's number can be mentioned. An example of a perfect correlation ( | r | = 1) in CODATA model is the correlation between NA and the electron mass me. The following table gives the correlation coefficient r between the Avogadro constant NA and some other known constants again.

## Version differences of the CODATA recommendations

The recommended values for the same constant has been changed over the years. The following are the altered values of the Avogadro constant NA, the fine structure constant α are exemplary and the Rydberg constant R ∞ shown. Besides the absolute standard uncertainty and the relative standard uncertainty is given ( in its own column) in 10-9 (also called ppb), respectively.

A comparison of the relative standard uncertainties of the three selected variables shows that these are orders of magnitude apart, the Avogadro constant can be the worst and the Rydberg constant can be best appreciated.