# Wolfram Mathematica

## SI Units and Physical Constants

Beginning May 20, 2019, the seven SI base units (second, meter, kilogram, ampere, kelvin, mole and candela) are based on exact values of fundamental constants of physics. In addition to the already exact speed of light, on that date the Planck constant, the Boltzmann constant, the Avogadro constant and Millikan's constant (more often called elementary charge) now have exact values.

These defining physical constants have their own entity class in the "PhysicalConstant" domain.

Their new values can be summarized by retrieving the relevant properties.

To maintain relations between physical constants and the new SI unit values, physical constants that previously had uncertainties (e.g. the Josephson constant) now have exact values. Additionally, some physical constants that previously had exact values (such as the magnetic and electric constants and ) gained finite uncertainty. In particular, the uncertainty of these quantities is often determined from the uncertainty of powers of the fine-structure constant and the Rydberg constant .

To compute the uncertainties of a set of 10 important physical constants in the new SI, you can use the "EquivalentForms" property, which gives relations between constants that remain true in the new as well as the old SI.

In order to express all uncertainties in terms of the uncertainties of and , convert all forms into polynomial relations between the various physical constants.

For each constant, you can now use use Gröbner bases to reduce all equations to a minimal form involving only exact constants and and . This allows you to determine the leading contribution to uncertainties of the other constants in the list.

Here is the resulting overview of the old and new uncertainties of various constants so obtained.

Thus on May 20, 2019, the mass of an electron became specified with a 25 times smaller uncertainty than it was on May 19. Some constants will be known exactly, but and became uncertain, with relative uncertainties inherited from the fine-structure constant.