Question

Are the dimensional measuring units such as meters in some way tensors? @Michele_Laino

Answer 1

The reason I ask is because they seem to have this tensor property, I can convert to different units and the number changes but the invariant quantity stays the same, simple example of what I mean is 2.54 cm = 1 inch. So it seems that we could probably find some Jacobian to transform from one measurement system to another.

Answer 2

I think that the introduction of a conversion factor, namely from cm to inches, can be viewed like a change of scale. The situation it is similar when Einstein introduced the \(light-time \;l\), namely he introduced an axis with the values of \(l=ct\) (and not \(t\) only), where, as usual, \(c\) is the light speed in vacuum. Of course the interval between two events, still remains an invariant in Minkowski space

Answer 3

The official SI brochure simply says that units have full algebraical value, and can be manipulated as such.