Dear Ben,
I should like to add some important remarks to my to-day answer.
My changes of the physical theory concern only space-time properties, whereas corollaries of these changes concern cosmology and theory of elementary particles. It means that my changes are fundamental.
First about cosmology. There are two most fundamental problems in cosmology: dark matter and dark energy. The problem of dark matter is solved by introduction of the tachyon gas, as it is described in my essay.
The problem of dark energy is essentially the problem of absence of antigravitation in the contemporary cosmology. One tries to solve this problem by means of artificial introduction of negative pressure, or by lambda-term of corresponding sign. In the metric approach this problem is not yet solved, but there is a way to solution of this problem. In the non-Riemannian space-time geometry the gravitational equations of Einstein has another form (they a written for the world function, but not for the metric tensor). According to these equations inside the dust sphere of radius R appears a region of antigravitation, when R is close to the gravitational radius of the dust sphere. This antigravitation prevents from collapsing the dust sphere into a black hole. (Rylov Yu.A, Induced antigravitation in the extended general relativity . Gravitation and Cosmology, 2012, Vol. 18, No. 2, pp. 107-112,( 2012). DOI: 10.1134/S0202289312020089 ). It means, that antigravitation is possible in cosmology, and working in this direction, one may hope to solve problem of dark energy.
The problem of elementary particle theory looks as follows. The contemporary theory of elementary particles is a chemistry of elementary particle (but not a physics of elementary particles). I mean as follows. In the beginning of the twentieth century there are two theories (1) chemistry of chemical elements and (2) atomic physics (physics of chemical elements).
Chemistry of chemical elements was represented by the periodical system of chemical elements, which admits one to systematize chemical elements and their reactions and to predict new chemical elements. But the periodical system cannot say anything about arrangement of atoms, their electron envelopes etc.
The atomic physics (quantum mechanics) explains arrangement of atoms of different physical elements. But calculation of chemical reaction parameters from prime principles is very difficult just now.
Contemporary theory of elementary particles is an analog of the periodical system of chemical elements. It can predict new elementary particles, but it cannot say anything on arrangement of elementary particles. Contemporary theory of elementary particles is essentially a chemistry of elementary particles, where different elementary particles differ by their parameters (quantum numbers) but not by their arrangement. For instance, contemporary theory cannot say difference in arrangement of fermion and of boson. Detection of the Higgs boson cannot help us to understand arrangement of elementary particles.
On the contrary, theory of elementary particles founded on the discrete space time geometry admits one to understand the arrangement of elementary particles because in the discrete geometry the state of an elementary particle is described by the particle skeleton (but not by momentum and a set of quantum numbers). The particle skeleton is set of n+1, n=1,2,... space-time points, connected rigidly (Rylov Yu. A. Discrete space-time geometry and skeleton conception of particle dynamics International Journal of Theoretical Physics. Volume 51, Issue 6 (2012), Page 1847-1865, DOI: 10.1007/s10773-011-1061-y Available at http://arXiv.org/abs/1110.3399v1 ).
In particular, any fermion is a tachyon, having helical world line with timelike axis. Its skeleton consists of n+1 points, n>1. Boson has timelike world line.
Of course, it is only the first results, but it is important, that such a development of the elementary particle theory in a true direction (ascertainment of the elementary particle arrangement).
Best regards,
Yuri Rylov