Would a pseudo Riemann manifold with Lorentz metric be obtained upon local rescaling of c?
Are you thinking of something like Weyl's theory?
Blagojević, Chapter 4
(In retrospect, I really should have put a large question mark in thread title.)
How do you come up with this stuff, atyy? More than once you've come up with a useful source or pdf that I've downloaded or marked.
But, I can't view the contents of Ch. 4, so I can't tell if the author discusses it. Care to clue me in?
There's probable some very simple explanation of why rescaling c doesn't work though.
Does this work any better (I think it's a link to Ch 4 directly)? http://books.google.com/books?id=N8JDSi_eNbwC&printsec=frontcover#PPA78,M1
Apparently if you impose allow a "scale" recalibration of the metric from point to point, only the curl of the scale is observable, which made Weyl think it could be the electromagnetic vector potential. According to this article, Einstein realised this would make clocks depend on their history, in contradiction to the existence of stable atomic spectra. Hmmm, is that really known to be true?
Early History of Gauge Theories and Kaluza-Klein Theories, with a Glance at Recent Developments
Lochlain O'Raifeartaigh, Norbert Straumann
Separate names with a comma.