I recently realized something about the way my models could exhibit gravity-like phenomena. If you recall, the models give a “space” that is constantly subdividing into ever-smaller granules as the “time” evolves. (We then multiply by a scaling factor to keep the size of the newest granules constant, which produces an expanding model universe.) The physical model can also be viewed as a “space” defined by an expanding graph of connected points, with new points continually appearing in between the existing ones.
If, however, this “space” does not subdivide where it is occupied by “matter” (or, more generally, if the regions of “space” that contain the most “matter” are the regions which subdivide the most slowly), then, when we apply the scaling factor, space would appear to expand fastest in those regions that contain the least matter. Equivalently, the regions that contain matter would appear to be “pulling” on the rest of space, in proportion to the amount of matter they contain.
This could help explain why gravity is so weak in relation to the other fundamental forces of physics–it’s because the Universe is so old and has expanded so much during its long existence, that the gravitational effect is now greatly diluted in comparison to what it was in the Universe’s early stages, whereas the shorter-range forces are not.
Now since the subdivision of space and the passage of time are one and the same thing in my model, this means that when we measure time passing in a particular location, we are also monitoring the subdividing of space there. So if I’m right in thinking that “occupied” space tends not to subdivide as much as “unoccupied” space, this would also imply that clocks run slower in regions that contain more matter–which is of course what we observe in our Universe, and what General Relativity describes.
To put it in a nutshell, “Matter eats Space and slows Time.” And although I haven’t yet specified how “matter” occurs in my model, I’m thinking that maybe I should be looking for it where there’s the least amount of subdivision going on at any given “time.” If I find it there, that would help explain how small-scale “quantum” processes can produce large-scale “relativistic” effects.
(Note: no apples were harmed in the conception of this blog post.)