Metaphysics of space and time

In the mathematical abstractions of space time I described that I think that space and time can be specified by the mathematical concepts of metric and order. These are mathematical abstractions of our physical concepts of space and time. When space and time are separated from their physical meaning in this way, then they take on a metaphysical meaning.

When considering different metaphysical possibilities, like the notion of a two dimensional flat world like space structure, a space with more dimensions, or something like an automata whose only notion of space is a graph and whose time is merely a discrete total order, quite obviously we are already divorcing the concepts of space and time from their actual physical meaning.

As space and time can be considered both metaphysically as well physically, I would would feel remiss without talking at least a little about the nature of physical space and time. There are two important sources of realizations about physical space and time (1) special relativity and (2) general relativity. Special relativity at least tells us that the type of order that we will use for time must be a partial order rather then a total order. Many of these models mentioned before like automata tend to have absolute time which makes them a bad match for reality. The partial order underlying spacetime, could even be the fundamental structure of the universe as described by causal sets.

Then there is the issue of general relativity and the whole issue of the curvature of spacetime. There are two aspects to the curvature of spacetime (1) the local curvature (2) the global curvature. The global curvature appears to be mostly flat, so the curvature is largely caused by local phenomena in spacetime. The curvature is very much localized, because the gravitational force follows the inverse square law. It is localized both in space and time because the curvature can change over time, which means there is not a constant geometry of the universe. This means that you cannot simply use a separate concept like a metric to describe space separate from time. Nonetheless, it is often useful to consider metrics as a separate concept as described earlier.