In its concept of the zero vector, vector mathematics discards zero-vector summations of active systems of vectors. It replaces such a summation with a zero vector. This is fine for mathematics as an abstract system, but it is in error when applied to real electromagnetic force fields of nature. In the abstract mathematics, a vector zero summation is made the "absence of all finite vectors". Further, all vector zeros are made equal. No concept of the "internal stress" of the zero vector exists in abstract vector mathematics. However, physically the zero summation or "balancing" of vector
forces in a medium represents Obviously, in the physical case vector zero summations may materially differ,
both in the pattern of stress and the magnitude of stress. They cannot all be
equated. Further, they are not the In the physical case, several changes to the axioms of abstract vector
mathematics are required. (1) the "potential" of a vector zero must be
taken into account, such as is represented by the sum of the squares of the
magnitudes of its vector components. (2) the specific deterministic pattern of
the vector components comprising the zero must be taken into account. (3) The
dynamic variation in both the deterministic directions and deterministic
magnitudes of the components and of the overall pattern must be taken into
account. (4) Frequencies of the changes in the direction, magnitude, and actual
makeup of the vector zero must now be accounted for. That is, This leads to a system of "vectors nested inside vectors" ad
infinitum. In other words, it leads to an infinite-dimensional system, and the
"opening" of every finite closed vector system For application to physical electrogravitational systems, at least 5 dimensions are required, four of space and one of time. Here we still are considering only a special case where all vector zero
summations represent EM force field energy locked in a gravitational potential,
or gravitational force field energy locked inside the EM potentials. That is, we are prescribing a system where the only
(See T. E. Bearden |