Physics
Scientific paper
May 1989
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989foph...19..607g&link_type=abstract
Foundations of Physics, Volume 19, Issue 5, pp.607-618
Physics
7
Scientific paper
A differential manifold (d-manifold, for short) can be defined as a pair (M, C), where M is any set and C is a family of real functions on M which is (i) closed with respect to localization and (ii) closed with respect to superposition with smooth Euclidean functions; one also assumes that (iii) M is locally diffeomorphic to Rn. These axioms have a straightforward physical interpretation. Axioms (i) and (ii) formalize certain “compatibility conditions” which usually are supposed to be assumed tacitly by physicists. Axiom (iii) may be though of as a (nonmetric) version of Einstein's equivalence principle. By dropping axiom (iii), one obtains a more general structure called a differential space (d-space). Every subset of Rn turns out to be a d-space. Nevertheless it is mathematically a workable structure. It might be expected that somewhere in the neighborhood of the Big Bang there is a domain in which space-time is not a d-manifold but still continues to be a d-space. In such a domain we would have a physics without the (usual form of the) equivalence principle. Simple examples of d-spaces which are not d-manifolds elucidate the principal characteristics the resulting physics would manifest.
Gruszczak Jacek
Heller Martin
Multarzynski Piotr
No associations
LandOfFree
Physics with and without the equivalence principle does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Physics with and without the equivalence principle, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Physics with and without the equivalence principle will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1874401