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James McLean wrote:The term "flux" seems to be well established, so I would be surprised if mathematicians did not use it. Of course, they may have generalized the concept in some way - I wouldn't know.
This whole discussion is a microcosm of the more general fact that all fluxes are signed quantities that depend on a choice of positive direction, but are not vectors.
Help me out here. We have something that is not a scalar. It has
magnitude *and direction*. But is not a vector. So, what is it?
Do mathematicians have a name for this type of non-scalar non-vector
quantity?
So current is a signed quantity, and properly dealing with it requires defining a positive direction on each circuit segment. Why not just say that, instead of trying to make it a vector? In fact, even here the vector model defeats the point: one of the salient properties of vectors is that only a single coordinate system choice is required to solve a problem; but for a circuit, you often want to pick a *different* positive direction for each segment.
I don't see much merit in that argument. I can imagine lots of
mechanics problems where I might decide that this force is a multiple
of this unit vector, and that force is a multiple of that unit vector,
with lots of different unit vectors. A spaceship with N thrusters
for maneuvering springs to mind.