On Jun 24, 2:54 pm, stevendaryl3...@yahoo.com (Daryl McCullough) wrote: > Steve Bell says...
> >By the "curvature of space" I mean the determinant of the > >3x3 space part of the Riemann-Christoffel curvature tensor evaluated at that > >point. > > The separation of spacetime into a spatial part plus a time > part is coordinate-dependent. Different coordinates will make > that separation differently. > > Yes, if you fix a particular coordinate system, then > you can talk about the spatial curvature tensor, but > you must first decide on a coordinate system (or at > least, you have to decide on your time axis).
there are essential properties that can be extracted common to all such theories and it is possible to in essence "quotient them out"
the arnowitt-deser-misner (adm) decomposition takes full advantage of this to provide a foliation of spacetime giving 3+1 field equations that are useful to exploring quantisation schemas that don't suffer certain classes of contradictions
it's this kind of decomposition on which is built the wheeler-dewitt equation and theories like bohmian gravity or the acoustic gravity theory of unruh