Authors: Michael J. Burns
Tensor ranks are not relative. Each tensor type and symmetry denotes its own class of geometric objects, that are not really interpretable as members of another class. Coordinate free geometry is the real theory, so tensor notation with coordinates can only be taken as a distant translation. But there is a perverse tradition in academia to the contrary. Vectors are used to portray physical objects that are plainly nothing of the sort. This only adds confusion to the study of mechanics and electromagnetism. Even in cosmology the wrong tensor ranks and operators are used, invoking a system of compensating errors that eventually go uncompensated on the edge. The two Bianchi identities, with the exterior derivative as the operator, are the correct foundation for the theory. These identities are geometric in their essence, not based in coordinate algebra. By contrast, the cosmological constant is simply a mathematical error. And there is an analytic blunder to deal with - the failure to include (into the cosmological equation) the fictitious source density of the fictitious potential that derives from the noninertial Friedmann coordinates. The equivalence principle demands this inclusion. Awareness of artifacts while integrating from geometric initial conditions on the two Bianchi identities is the method to bypass these errors. Coordinate artifacts are a superset of real curvature, and form a background condition that cannot be handled completely at the dynamical equations.
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