Wolfram Language

Uncertainty in Physical Constants

The "PhysicalConstant" entity domain contains an extensive tabulation of physical constants, including many fundamental constants of nature.

A comprehensive set of properties is also available for physical constants.

Central among these properties are the best measured value and uncertainty. This example shows how different physical constants are known to have very different uncertainties.

Consider the gravitational constant appearing in the law of universal gravitation.

Here is a list of the best current value together with its associated uncertainty.

To aid in computation, the value of a constant may be returned with uncertainty included in a number of different forms, as illustrated below for .

To examine the relative uncertainties of physicals constants, first retrieve the values for all constants, then remove constants with exact values, unknown uncertainties and the constants corresponding to atomic and natural units.

Construct a new list of data in which relative uncertainties are converted to precisions. Also single out a few important constants to ensure they are labeled in the resulting plot using the LabelVisibility option.

Now plot the sorted precisions of tabulated constants.

This plot instantly reveals the tremendous differences in the precision to which various constants are known. For example, the gravitational constant is the least well known of the core set of fundamental constants of nature (to only 4.6 decimal digits), while the electron factor is known to an amazing 12.7 digits.

The precisions to which physical constants are known can also be nicely viewed as a word cloud, where symbols are shown with size weighted by the precision to which they are known (and where the precision has been scaled by cubing it to better emphasize the variations).

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