  What if physics is just the way we perceive geometry? That is, what if
geometry and physics will one day become one and the same discipline? I believe
that will mean we will at last really understand physics, without postulates
other than those defining the particular space where the physics play is
performed. In this paper I use 5-dimensional spacetime as a point of departure
and make a very peculiar assignment between coordinates and physical distances
and time. I assume there is an hyperspherical symmetry which is made apparent
by assigning the hypersphere radius to proper time and distances on the
hypersphere to usual 3-dimensional distances. Time, or Compton time to
distinguish from cosmic time is the 0th coordinate and I am able to project
everything into 4-dimensions by imposing a null displacement condition.
Surprisingly nothing else is needed to explain Hubble's expansion law without
any appeal to dark matter; an empty Universe will expand naturally at a flat
rate in this way. I then discuss the perturbative effects of a small mass
density in the expansion rate in a qualitative way; quantitative results call
for the solution of equations that sometimes have not even been clearly
formulated and so are deferred to later work. A brief outlook of the
consequences an hyperspherical symmetry has for galaxy dynamics allows the
derivation of constant rotation velocity curves, again without appealing to
dark matter. An appendix explains how electromagnetism is made consistent with
this geometric approach and justifies the fact that photons must travel on
hypersphere circles, to be normal to proper time.
