Theoretical Accuracy of Fundamental Constants

by David Bradley

from the Royal Society

NIST's Dr Peter Mohr, who works with Barry Taylor on the CODATA adjustment of the fundamental constants explains further how the best values of basic constants and conversion factors for science are "derived" using a least-squares analysis. This approach involves finding the best fit to a set of data by reducing the sum of the squares of the differences (the so-called residuals) between the mathematical functions of the constants and the experimental data. In applying this approach, the CODATA adjustment takes into account all of the latest relevant experimental and theoretical information in a consistent framework, explained Mohr.

Theory, he added, has a crucial role to play in the ongoing re-evaluation of the physical constants. Indeed, the fundamental constants appear as parameters in theoretical expressions, and so theory itself is involved with their values at a basic level; without the theoretical expressions the fundamental constants would not have a context.

Usually, to test a theory, one evaluates a theoretical expression, takes out a reference book to find the constants and plugs in the appropriate values to see if the prediction agrees with the experiment. That, explained Mohr, is the standard procedure of science. However, he and his colleagues are undertaking essentially the inverse task: to create the book of numbers. This then involves taking theory and experiment and checking to see how well they agree with another. So, the scientists have to assume that the theory is valid in order to obtain the best values of the constants, and to understand which if any theoretical assumptions might be wrong and so be forewarned of potential problems with the increasing precision of the constants.

New experimental data are compared with their predicted values based on the best theoretical models at the time, which are themselves sophisticated mathematical formulae which are functions of the fundamental constants. The best values of the constants, which are published by CODATA, are then taken to be those that give the best agreement between the available experimental data and the theoretical predictions within the least-squares framework.

Mohr's exposition of the assumptions made in the theoretical framework not only provides a better understanding of the role of theory in defining the fundamental constants, but reveals insights about the fundamentals of these values themselves. For example, the direct link between Avogadro's number, which defines the number of particles in a mole of stuff, and the quantum-defining Planck constant provides information on their relationship in physics and chemistry.

Read on... Changing constants