SLIDE 10.
PHYSICAL VECTORS

In quantum mechanics, as
we approach the quantum level, we find that the notions of a particle
(static concept) and a wave become inseparable.
That is, any particle becomes a "smear" in length and time,
and it becomes inseparable from its smear. At the quantum level,
there is no separate energy, length, mass, momentum, energy, or time 
all are welded together inextricably into a quantity called
"action," having the units of angular momentum. So at the fundamental quantum level, a moving point becomes a smear, and a vector represents a physical, undifferentiated entity. To go quickly, we now define a vector as consisting of a smeared particle. That is, the particle is smeared in both time and length, and it is not differentiated from time or length. There are four kinds of particles in physics which can be smeared to form vectors. First, there is a point in space or spacetime. This point may be approximated as massless and chargeless. At least that is the way the geometers of old conceived it in the abstract, and so the idea of a "point" in space assumes it to be chargeless and massless. Second, there is a tiny particle of mass, often abstracted to be a "pointmass," but visualized as having no charge. This is the mechanic's particle. Third, there is a tiny charged mass, such as an electron, and this is the electrician's particle. Again, it is often abstracted as a charged pointmass. Fourth, there is a charged point, having no mass, and this is the advanced electrician's particle, which he uses to form the idea of potentials and fields. Smearing these four particles at the fundamental quantum level produces four different kinds of physical vectors: the geometer's, the mechanic's, the electrician's and the advanced electrician's vectors. They are all different. 