Special and general relativity theories are critically evaluated regarding their contemporary role as a foundation for a cosmological world picture. It is argued that the rest frame, where all physical processes take place, is more important in this role than the various relativistic distortions of these processes seen by different remote observers. This idea was previously formulated quantitatively with numerical examples from the Bohr atom, quantum physics and astrophysical observations. The theory identifies an observer on one local spatial dimension via Lorentz transformations connected with a space-like separated perpendicular observer who is non-local and only measures time. It was shown that this geometrical construction, where each unit local length comes with a line increment, is relevant both to the atom and to the universe. For example, the Planck length obtained from the Bohr atom could be expressed in terms of the apparent local Hubble expansion rate and the latter substituted into the Schroedinger equation to yield a circular current surrounding a magnetic pole. The distant non-local observer sees the radius Lorentz-contracted at relativistic speeds ultimately so much as to be able to contribute dynamics to the local frame, which was exemplified numerically by the CMBR. Evidence was also presented indicating that the oscillating line increment is capable of contributing mass from vacuum via the resonance particles. Elaborating on the latter idea indicates energy contributions of around 80, 90 and 125 GeV embedded in a robustly defined geometrical framework that has relevance (and even precedence) also in classical physics. The apparent transition from one to several spatial dimensions is exemplified by reinterpreting Compton scattering. The emergence of additional spatial dimensions and tangible locality are also discussed in terms of the number pi which appears by applying the Wallis product to the 1-D universe. The presence of the number pi thus indicates the presence of local particles as further exemplified by the CMBR and Compton scattering. The mass of the 1-D universe is obtained by considering local as well as non-local contributions as prescribed on the basis of the geometry. This yields corrections to the ‘classical’ geometrised mass such that the universe’s baryon particle density visible on the local axis is close to its electron density. Several unrelated numerical approaches guided by the proposed geometry indicate that the particle density of a primordial universe is roughly 1/m^3 (1/m^2).