DOC: constants: explain `0.0` uncertainty

[davidhansen314]

The CODATA2018 website (https://physics.nist.gov/cuu/Constants/) sometimes rounds an "exact" physical constant. This may occur when a constant is derived from other exact constants. For example, Boltzmann constant in eV/K is rounded to 8.617 333 262... x 10-5 eV K-1, but the website lists it as "exact" because it is the ratio of two exact constants: Boltzmann constant / elementary charge.

In scipy/constants/codata.py, lines 1504 and 1516, the uncertainty is set equal to 0 if the quantity is "exact." This is appropriate for quantities like "elementary charge" (no rounding), but it is NOT appropriate for quantities like
"Boltzmann constant in eV/K" because this quantity has been rounded.

I'm not sure what the best solution is. The CODATA2018 website does not give the uncertainty for rounded values of "exact" constants, so the uncertainty is unknown. Perhaps the uncertainty values in codata.py should be set to reflect this. A better (but more difficult) solution to implement would be to define the derived constants relative to the more fundamental constants. For example, the "Boltzmann constant in eV/K" would be defined as "Boltzmann constant" / "elementary charge". Documentation for this second solution is probably more difficult compared to the current implementation of pointing to the CODATA website for all numerical values.

[jakobjakobson13]

@pv has already put a lot of work in this topic by gh-11345.

[mdhaber]

@davidhansen314 You suggested:

A better (but more difficult) solution to implement would be to define the derived constants relative to the more fundamental constants. For example, the "Boltzmann constant in eV/K" would be defined as "Boltzmann constant" / "elementary charge".

gh-11345 implements this, but the uncertainty is still reported as 0.0. Does e351d2f do an OK job of documenting what is happening?

The CODATA database uses ellipses to indicate that a value is defined
(exactly) in terms of others but cannot be represented exactly with the
allocated number of digits. In these cases, SciPy calculates the derived
value and reports it to the full precision of a Python float. Although
physical_constants lists the uncertainty as 0.0 to indicate that
the CODATA value is exact, the value in physical_constants is still
subject to the truncation error inherent in double-precision representation.