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Consider the Scalar quantity of Temperature. There is absolute zero, but there is also a scale that sets zero at the freezing point of water. The conversion between the two requires a translation of the zero point. The unit degree also changes and is accounted for a scaling factor. There are no rotations in 1-D, but there is orientation and an interval on a temperature scale can be positive or negative. It appears to be a space with 1-D vectors defined as temperature changes from each point on the scale (formally: a vector space over the field of reals) and meet the definition of a 1-D affine space.

Now consider mass. Mass doesn't have any standard scales whose zero point is offset from absolute zero mass. But wait, what if I rent a scale to weigh my gold and the proprietor sets the reading to zero for the first two grams as payment for my using his scale. It's not standard, but my take home gold after certifying its weight is 2 grams less (because I pay it to him). The conversion process is now the same as for the temperature scales: a translation is involved. Furthermore, he could use grams while I use ounces which I must account for with a scale factor. Does the potential for arbitrarily changing the zero on the mass scale mean that mass is also an affine space? Here we may also define a mass gain or loss as a 1-D vector quantity as we have done with temperature.

I believe we can apply the same logic to potential energy (zero relative to local minimum), luminous intensity (zero is the point of detectability by the human eye), charge (set zero as the amount needed to make my hair stand on end). Sounds silly, but zero on the scales for these quantities is arbitrary. Does this make each more properly modeled as a variable that represents any member of an affine space, rather than just thinking of them naively as Reals (formally a Field with additional axioms in place to guarantee ordering among the members of the space)?

Please be as mathematical as you want with your answers.