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Subject: Most of differential geometry is excess baggage
There is no such thing as a bare manifold, for example, in physics.
All we have in physics for good measurements in Einstein's GR are tiny detectors in close proximity measuring the same external fields, computing their invariants, and comparing their numbers. When their numbers match, then they know they each made a good measurement.
All the theorems of differential geometry and other branches of math are excess baggage, they are opiates, Sirens luring you to the rocks. Of course, I have no objection to using the pure mathematics as a tool, but it should always be the slave not the master - and used with extreme caution like any powerful narcotic.
On Dec 3, 2010, at 6:45 PM, JACK SARFATTI wrote:
PS I don't demand a "direct connection" to experiment either, but there must be some connection or it's bad and bogus.
Also clearly wrong statements like Z's assertion g = -m/r^2 is a "first order tensor invariant" in Einstein's GR are not acceptable. Z's ":" covariant derivative connection is ill-posed both mathematically and physically. The formal trick of putting more than a single connection on a manifold is bad and bogus physics even if it is correct mathematics.
I mean, of course connections that are not-gauge equivalent - unless there is some kind of topological obstruction so that there are topologically inequivalent connections each of which will lead to a distinct observable effect, e.g. magnetic vortices in a superconductor with different numbers of quanta of magnetic flux, different winding numbers.
On Dec 3, 2010, at 6:28 PM, Paul Zielinski  aka Z wrote:
Please note the distinction I am making between operationalism *per se*, and naive operationalism.