Built-in way to handle uncertainty in measurment and physical constants?

Question

Is there a built-in or fairly elegant way to handle uncertainties in measurement data and/or physical constants?

For instance, the 2010 CODATA for the elementary charge is given as $\mathsf{1.602 176 565(35) \times 10^{19}}\textrm{ C}$, where the $(35)$ represents uncertainly of $\mathsf{0.000 000 035 \times 10^{19}}\textrm{ C}$. Or, in my case the D2 transition in $^9Be^+$ $\nu = \mathsf{31928.7436(40) \times 10^{19}}\textrm{ cm}^{-1}$.

I want to not only specify the uncertainty, but carry it through equations and calculate resultant uncertainties. I don't want to recreate my own system of doing this if there are already functions and notation for doing this.

Sadly, no. There is this post (Expression of uncertainty in measurement.) but my answer is old, ugly and not full. — Kuba, Apr 30 '15 at 10:38
Maybe Interval will handle your needs on this? Also this might be useful. Same coauthor has these as well, that might give a few ideas either from the basic principles or the underlying code. — Daniel Lichtblau, Apr 30 '15 at 13:54

score 8 · Accepted Answer · answered Apr 18 '19 at 02:07

Since Mathematica 12, you can use the new Around function to deal with uncertainties and error propagation. You can even retrieve uncertainties in physical constants, like elementary charge:

Around@@Entity["PhysicalConstant", "ElementaryCharge"][{"Value","StandardUncertainty"}]

Outputting:

$1.60217663 (4 \pm 8 )\times 10^{-19}\text{C}$

Or you can define your own value such as the D2 line in your example:

\[Nu] = Around[31928.7436/Quantity[1, "Centimeters"], 
   0.0040/Quantity[1, "Centimeters"]]*10^19

Built-in way to handle uncertainty in measurment and physical constants?

1 Answers1