Points, Lines, Planes, Cubes ... these are all mathematical descriptions of "something", right?
Are they, by themselves, real? Can a point (whether you use is as a first "dimension" building block in constructing a series of dimensions, or as a "zero-dimension" "point", exist? As a zero-dimension object, the concept is nutzo - something with no dimensions has no existence. It lacks ANY dimensions. However, if we use it as a starting point, assigning it a "dimension" of 1, it has at least 1 dimension of existence. It is self-consistent, and self-contained.
Of course, to have it interact in our universe, we could give it position coordinates, time coordinates, and probability coordinates. Let's take an electron. We can describe its' orbit to a certain degree of probability and time. If we add more time, we can describe more probabilities, to the point where, if we have enough time (duration), we can, to a "good enough degree" predict the chemical properties of the atom it orbits.
We'll never be 100% right 100% of the time, because the underlying graininess of the universe doesn't permit that, just like we can never describe any real object 100% of the time with 100% accuracy. Doesn't that sound exactly like what we see with such things as the two-slit experiment - we cannot make an arbitrary, linear prediction as to which of the two slits a photon will go through, and photons "interfere" with photons that have passed through before and after, IF they are observed. A grainy universe in all dimensions (time, probability, as well as space) allows for the graininess of time that would allow individual photons to interfere with others that "aren't there at the same time".
Now I don't know about you, but I've never been happy with the "collapse of the wave function" and "superposition of states", nor with the "branching universes." While they're allowed under this model, they're not required. More importantly, normal interactions would appear to have superpositions of states under certain circumstances, so we don't have to resort to the voodoo of the copenhagen crowd. Schrodinger's cat never is really both dead and alive, but can, until we open the box, be described as being in that state - or not. (okay, those last 2 words are a bad pun).
It also explains "spooky effects at a distance" without having to get into "quantum entanglement", provided we allow for conservation of probability, which seems a reasonable assumption - it just becomes a natural part of our universe, and by definition, not spooky. Heck, it becomes required, which means we can have our quantum cryptography being based on fundamental physical properties of the universe