OK, so here’s an update on where I am with my thinking right now. It looks as though a three-dimensional universe can be defined numerically using quartets of coprime non-negative integers. The physical realization of this is that each quartet defines an element in a system of Ford hyperspheres over the rational points of a unit tetrahedron in a three dimensional space. The network of hyperspheres defines the space-time of this universe, and each hypersphere can be regarded as a “bubble” in its “quantum froth”.
A reminder: the elements in a system of Ford hyperspheres (or spheres, or circles) touch but they don’t overlap; each one’s diameter is a rational number; and the coordinates of its center are also rational numbers in an appropriate coordinate system consisting of three (or two, or one) spatial dimensions, plus one time dimension. Each point of this space with rational coordinates has exactly one hypersphere centered “above” it, at a “time” that corresponds to the inverse of its diameter.
As this spacetime structure is currently defined, it is not expanding but rather, it is becoming more detailed as time progresses. Of course, the inhabitants of such a universe (if they existed) would perceive it differently. Being creatures of this system, they would presumably regard themselves as staying the same size and their universe as expanding. However, the difference is merely one of scale and can be resolved by applying a scaling factor which varies over time.
Note that I’m saying that SOME universe can be defined in this way, not necessarily OUR universe. Many details remain to be worked out. The problems I want to tackle next are those of symmetry and scaling, then it’ll be time to look for evidence of matter and energy in this spacetime froth.
[...] coincidence of time? A follow-up to the article that I posted earlier today. The system of hyperspheres I described contains elements that are [...]