Arithmetic operation on dimensionless mag units

Description

Not sure whether this is a bug or just a misunderstanding: I am wondering how dimensionless units work; especially the conversion to linear.

Expected behavior

I would expect that u.mag works equivalently to f.e. u.ABmag when it comes to conversion:

>>> import astropy.units as u
>>> m = 12 * u.ABmag
>>> print(m)
12.0 mag(AB)
>>> print(m.to(u.erg/u.s/u.m**2/u.Hz))
5.754399373371543e-21 erg / (Hz m2 s)
>>> flux = 1e-20 * u.erg/u.s/u.m**2/u.Hz
>>> print(flux.to(u.ABmag))
11.399999999999997 mag(AB)

i.e. u.mag should be convertible to and from a dimensionless unit.

Actual behavior

>>> import astropy.units as u
>>> m = 1 * u.mag
>>> print(m)
1.0 mag
>>> print(m.to(''))
Traceback (most recent call last):
[…]
  File "/usr/lib/python3/dist-packages/astropy/units/core.py", line 1027, in _apply_equivalencies
    raise UnitConversionError(
astropy.units.core.UnitConversionError: 'mag' and '' (dimensionless) are not convertible
>>> f = u.Quantity(10.0)
>>> print(f.to(u.mag))
Traceback (most recent call last):
[…]
  File "/usr/lib/python3/dist-packages/astropy/units/core.py", line 1027, in _apply_equivalencies
    raise UnitConversionError(
astropy.units.core.UnitConversionError: '' (dimensionless) and 'mag' are not convertible

Specific question: what is the “preferred” way to convert to copy to/from dimensionless magnitudes (except explicitly using -2.5*log10(f))?

Steps to Reproduce

See above

System Details

Astropy 5.0rc1

[pllim]

Maybe we should just stop using the magnitude system…

[olebole]

I think also with dex the calc is wrong. Normally, it is mag = -2.5*log10(f2/f1), which would for f2/f1=2 give -0.7526. Or, more explicit:

>>> m1 = 15*u.ABmag
>>> fac = 2.0
>>> m2 = (fac * m1.to('erg / (Hz m2 s)')).to(u.ABmag)
>>> print(m2)
14.247425010840047 mag(AB)