We propose a spacetime scheme representing the union of the real and non-real spacetime as a possible geometrical framework for Caldirola’s idea, that the bradyonic motion can be regarded as a light-like motion in an additional extra space. The playground of all physical processes is the union space. However, the physical processes in union space are differently projected on the real and non-real spacetime. The waves linked with luxons in union space are projected on the real spacetime so that they propagate here always with the velocity of light. The waves linked with bradyons in union space are projected on the non-real spacetime so that they propagate here with the velocity of light. The wave linked with a bradyon in union space, which is projected on the real spacetime, is here described by the Schroedinger and Dirac equations. There is proposed a symmetry which demands that the physical world is in its law the same whether it is seen from real or non-real spacetime. We discuss some consequences of this symmetry in the theory of elementary particles.