Are the dimensional measuring units such as meters in some way tensors? @Michele_Laino
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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.
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
The official SI brochure simply says that units have full algebraical value, and can be manipulated as such.