5-Dimensional Extended Space Model
  We put forward an idea that physical phenomena have to be treated in 5-dimensional space where the fifth coordinate is the interval S. Thus, we considered the (1+4) extended space G(T;X,Y,Z,S). In addition to Lorentz transformations (T;X), (T;Y), (T;Z) which are in (1+3)-dimensional Minkowski space, in the proposed (1+4)d extended space two other types of transformations exist in planes (T,S); (X,S), (Y,S), (Z,S) that converts massive particles into massless and vice versa. We also consider energy-momentum-mass 5-d space which is conjugated to the time-coordinates-interval (T;X,Y,Z,S) space. The mass in above mentioned 5-d energy-momentum-mass space corresponds to the interval S in 5-d space (T,X,Y,Z,S). Well known energy-momentum 4-vector P(1+3)=(E/c; px,py,pz) in the Minkowski (T;X,Y,Z) space is transformed to the the 5-vector - P(1+4)=(E/c; px,py,pz,mc) in the extended space G(T;X,Y,Z,S) and becomes isotropic for 5-vectors of the massive as well as for the massless particles. 
D.Yu.Tsipenyuk (1), V.A.Andreev (2) ((1) General Physics Institute of   the Russian Academy of Sciences,(2) Lebedev Physics ...