A universe of a finite but increasing number of states of motion?

Question

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?

Answer 1

I am not sure what specific experiments you are referring when "there are experiments that speak against a discrete space". There many not disproved physical theories that assume that space is digital. There are many variations, but for a more detailed account see Digital Physics. Regarding your claim that "space as the set of all possible states of motion", it sound vague and unclear for a reader not inside your mind. I am not aware of any theory resembling something like that. If you could put it in a mathematical form, it would be much more clear what you mean by that. But that would not be enough, even if your theory could explain and predict current physical phenomenon, it has to do it in a simpler way than current models to be considered "more convenient". Physics is pretty advanced at this point and vague ideas without predictive power will not be considered serious. Of course, you start with the idea, but that is not enough. An additional problem with your idea is that is really unclear what you are proposing, as if using technical words but with nonstandard meanings. That is probably why your question has not received the attention you claim.

Answer 2

I join the comments of Julian Fernandez.

Just some hints for some of your ideas:

Spacetime is relative i.e. observer-depending. It seems that behind relative spacetime there is a system of absolute time (= proper time) and absolute space (=space without considering time dilation and length contraction which are relative) where spacetime is "mixing up" space and time according to the laws of relativity. Absolutely spoken, spacetime, time dilation and even length contraction seem to be exclusively a time issue (= relativity of simultaneity), with very little impact on absolute space. So I would encourage your attempt to consider space as absolute.

However, when you are looking for absolute space, filtering away every relative (spacetime) element it is certain that you can no longer consider any phenomena which are due to spacetime (such as magnetism). Physics are generally based on a relative spacetime view, thus if you are taking an absolute point of view, you have to check for each physical law if it is still valid under this condition. You cannot just suppose that there is absolute space and continue applying spacetime logics.

I cannot see any room for an analogy with quantum theories. These are working within a small, elementary scale free of quantum decoherence, and they are vanishing when we consider composed large scale phenomena.