On the CODATA Recommended Values of the Fundamental Physical Constants: V3.2(1998) & V4.0(2002)

Abstract

With the help of special program package PAREVAL designed in {\sl Mathematica} system we reproduce values of basic fundamental physical constants obtained by NIST and recommended by CODATA for international usage since 1998. In our adjustment we use the input data and methods published by NIST in 1998. It is shown, that the detected earlier inaccuracy of published by NIST correlations (that made the NIST 1998&2002 results doubtful) are, most probably, due to inadmissible independent rounding. The simple estimate of the critical numbers of decimal digits in the independently rounded correlation coefficients is obtained. Further independent rounding of ``critically rounded'' correlations can lead to the non positive semi definite correlation matrices and hence is inadmissable. It is demonstrated by a few examples that the poor presentation of the correlated random quantities in the scientific literature is a common bad practice and is argued (once again) that the common standard for presentation numerical values of correlated quantities in publications and sites is urgently and badly needed.