The basic ideas of an unconventional physical model of creation of the observed physical space and ultimate particles from a finite set of special discrete objects (byuons) are presented and discussed. The qualitative distinctions between the theory of byuons and previous physical theories are discussed. Predictions of theory of byuons are proposed: the existence of the cosmological vectorial potential Ag, a novel fundamental vectorial constant defining the global anisotropy of physical space and a new non-gauge force of nature. The results of experimental investigations of new non-gauge interaction (using high current magnets, torsion and piezoresonance balances, the rate changes of β-decay of radioactive elements, etc.) and astrophysical observations are described. It was shown the construction of electric generator using the byuon energy and the new non-gauge force for obtaining of the electricity.