Wikipedia:Reference desk/Archives/Science/2024 December 9

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December 9

I'm collecting examples of a purely "physical property of a physical property" (of a body).

By (purely) physical property, I mean any measured property whose measurement depends on (purely) physical [dimensions usually measured by physical] units. A few examples of physical properties include: momentum, energy, electric charge, magnetic charge, velocity, and the like (actually the elementary particles carry plenty of purely physical properties).

However, by purely (physical property), I mean that it's not also a mathematical or geometric property, i.e. excluding: numeric value (size) of a physical property, density of energy ("density" is also a mathematical concept - e.g. in density of primes), center of mass ("center" is also a geometric concept), and the like. But I do consider velocity to be a purely physical property, because its description invloves (e.g.) the temporal dimension (which actually "flows" - whereas the way time "flows" can't be described by any mathematical equation. Anyway this "flow" is another issue I don't want to discuss in this thread).

So, for finding a purely "physical property of a physical property" (of a body), I've thought about one example so far: the physical units dimensions of any physical property.

I'll be glad for any additional examples. 2A06:C701:746D:AE00:ACFC:490:74C3:660 (talk) 11:22, 9 December 2024 (UTC)

The physical units in which physical quantities are expressed (such as erg, eV, foe, joule, therm) are somewhat arbitrary social constructions. The dimension of a physical quantity is a much more purely physical property. It is a point in an abstract vector space. One may argue that there is some arbitrariness in the choice of the basis of this space. The SI standard uses time (${\mathsf {T}}$), length (${\mathsf {L}}$), mass (${\mathsf {M}}$), electric current (${\mathsf {I}}$), absolute temperature (${\mathsf {\Theta }}$), amount of substance (${\mathsf {N}}$) and luminous intensity (${\mathsf {J}}$) as the basis, but other choices for the base physical dimensions span the same vector space.  --Lambiam 12:42, 9 December 2024 (UTC)

Yes, I really meant "dimensions" of a physical property, thank you. 2A06:C701:746D:AE00:ACFC:490:74C3:660 (talk) 14:24, 9 December 2024 (UTC)