My work in electron fields is profound, and gets very funny. Steve Albers at last has great plots with colors showing field energy density. The electric field lines are radial spokes in the FAR. The plots are in our Cartesian space. The field is ruled by SPIN, and is flattened out. OUR USUAL SPACE IS, HERE, FLATTENED OUT. What used to be a ‘point’ and still looks like one to us, is no longer. It is a disk. I can plot it but we cannot just see it. I quipped to Burinskii, this doesn’t mean we can SEE this stuff!! X-ray vision??? I don’t know. Beyond 100 MEV maybe… to Steve:
DIV grad, remember you were asking about this? OH YEAH, and it is
business as usual with the Laplacian. Unless Albers is in the room. He will point out that curved spacetimes eliminate the unique integrability of some things… his fields have no divergence, and also no common potential… go figger !!!!!!!!!!!!!!!!!! Thus, no gradient per se is present. I MUST HAVE FIELDS, with no DIVERGENCE, but NOT LAPLACIANS. They are a limiting class of solutions.
Just like Einstein said, WE NEED NEW MATH TO WALK NEW PATHS.