On Interpretation of Special Relativity: a complement to Covariant   Harmonic Oscillator Picture
  In 1971 Feynman, Kislinger and Ravndal [1] proposed Lorentz-invariant differential equation capable to describe relativistic particle with mass and internal space-time structure. By making use of new variables that differentiate between space-time particle position and its space-time separations, one finds this wave equation to become separable and providing the two kinds of solutions endowed with different physical meanings. The first kind constitutes the running waves that represent Klein-Gordon-like particle. The second kind, widely discussed by Kim and Noz [4], constitutes standing waves which are normalizable space-time wave functions. To fully appreciate how valuable theses solutions are it seems necessarily, however, to verify a general outlook on relativity issue that (still) is in force. It was explained [5] that Lorentz symmetry should be perceived rather as the symmetry of preferred frame quantum description (based on the freedom of choice of comparison scale) than classical Galilean idea realized in a generalized form. Currently we point to some basic consequences that relate to solutions of Feynman equation framed in the new approach. In particular (i) Lorentz symmetry group appears to describe energy-dependent geometry of extended quantum objects instead of relativity of space and time measure, (ii) a new picture of particle-wave duality involving running and standing waves emerges, (iii) space-time localized quantum states are shown to provide a new way of description of particle kinematics, and (iv) proposed by Witten [14] generalized form of Heisenberg uncertainty relation is derived and shown be the integral part of overall non-orthodox approach. 
Paul Korbel