A limitation of the geometric models of universe is that space locally is considered as a volume, whilst volume is a part of a selected system of inertia. Wouldn't it be more adequate to consider (the experienced) space as the set of all possible states of motion?
I know that there are experiments that speak against a discrete space, but are those experiments really that easy to size up?
Edit: It's only possible to observe space from the view of a system of inertia, but one can not ignore the possibility that space can be better described from an objective perspective. From the view of an observer, space seems to be a volume. But the volume is not system independent and even (e.g. magnetic) energies in the volumes depends on the observer.
The alternative is to start from the objective idea of states of possible particles in motion, independent of observers, look for the universal system independent laws and then statue correspondence principles, in analogy with quantum theories, to find the laws of the observable space.
Explanation: Forget atomic matter and light! What remains are particles apparently moving in our geometric framework. Our interpretation is that the movements are uniform on straight lines in a quasi isotropic flow and any particle is coequal apart from the type. How come that we must chose a system of inertia to describe that abstract world?
Suppose that space(s), just as surfaces and lines and points, only are geometrical ideas. What's left then, are particles in states (we observe as motion) and possibly other states without particles. Now, the uncertainty principle suggests that these states of possible motions are discrete and possibly are fermions and occur in a gigantic but finite number.
Somehow these states of motion, independent of observers, are the real reference points to describe our surrounding. Perhaps such a theory is impossible to formulate fully adequate with human mathematics (as geometry is the most of it) but the subject should be possible to discuss.
Is continuum a product of mathematical imagination?