TOWARD A NEW ELECTROMAGNETICS
PART III:  CLARIFYING THE VECTOR CONCEPT

(MECHANIC'S VECTOR)

Figure 2.  Chargeless mass system vector.

CHARGELESS MASS SYSTEM VECTOR
-- (Figure 2) --

This type of vector actually is the essential vector of mechanics, involving mass-motion (momentum), force (mass-motion change), etc.  The fundamental difference between this type of vector and the geometer's vector is the presence of smeared mass existing in time (i.e., mass-time), welded together with a geometer's vector, but with no seam in the middle, into a new kind of "vector" AS A SYSTEM.  The vector is the SYSTEM EXISTING IN TIME .
To illustrate:
"Momentum" is more properly referred to as "mass-motion" rather than "mass in motion."  That is, at the fundamental level, the mass is NOT "separate" from its motion.  It is NOT separated from the time in which the smearing occurs.  The idea of momentum, however, is really to express the time-density of the mass-smeared-through-length.  It is, in other words, the time rate of length-smearing of mass.  Now in our minds we have conceived that

 (1)

where, by the symbol we mean "coupled to";  but we actually have

 (2)

where we are not allowed to separate (even in thought) m and .  Quantum mechanics agrees with this essentially, because is a canonical variable linked to length, in any observable physical change.  (The REASON p is canonically linked to ΔL is because is the time-rate of length-smearing of m.  If there is no length, there is no length-smearing of m to have a time rate OF in the first place.)
Note that, not only is

 (3)

but also

 (4)

which is a much stronger and quite different statement.  That is, is IDENTICALLY  , not just calculably EQUAL TO (m)().  This means that is a SYSTEM that is COMPRISED of mass-motion.

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