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 necessity to deal with - the need to include into the Einstein equation the fictitious source density of the fictitious potential that derives from peculiar noninertial coordinates. The equivalence principle demands this inclusion. Awareness of artifacts while integrating from geometric boundary 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. [To be clear: the Einstein tensor term on the left of the famous equation may be as adaptable to peculiar coordinates as the term for mechanics on the right. And there are no more difficulties for geometry than mechanics after the correct metric is calculated. But this excludes any salvation for the cosmological constant term.]
Comments: 3 Pages. mburns92003@yahoo.com
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