MATHEMATICS of DIVERGENCE…

“We can establish a vector field by parallel displacment of an arbitrary vector, to all points in a neighborhood in the Riemann space, if and only if the Riemann tensor of the space is identically zero. We refer to such a space as an integrable space.” Yessssssssssssss, my ABS text, Intro to Drain Plumbing. We’ll see if anyone’s awake. DOING ELECTROMAGNETISM, if we start with a statement of a scalar potential field, we take its gradient in calculus, as the field. To reverse this, we would INTEGRATE, ahah !!!!!!!!! DO YOU SEE WHAT I SAW?? The Kerr particle near-field is certainly not flat, in Riemann curvature. Again, from page 160, “The vector at a nearby point is independent of path if and only if the Riemann tensor is identically zero.” PATH DEPENDENCE, YES. This is how we get twin paradoxes, for real. We also get new rules for the divergence operator. . . . . THE GRADIENT OPERATOR is a straightforward differentiation by each variable in turn, producing a field component in that direction. If this is how your electric field is produced yes, each one could be integrated back, BY THAT VARIABLE, to the same common potential form !!!  The new rules of divergence solution spaces, mean there are other possible solutions for zero-divergence fields, which cannot be traced back to a common potential form. I don’t need to care.

 

 

 

 

 

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