Properties of the 5-Dimensional Extended Space Model with Variable Photons Mass and Size

We propose the generalization of Einsteins special theory of relativity (STR). In our model we use the (1+4)-dimensional space G, which is the extension of the (1+3)-dimensional Minkowski space M(T;X,Y,Z). As a fifth additional coordinate the intervals is used. The physical meaning of the fifth coordinate is Action. This value is constant under the usual Lorentz transformations in M, but it changes when the transformations in the extended space G(T, X, Y, Z, S) are used. We call this model the Extended space model (ESM). From a physical point of view our expansion means that processes in which the rest mass of the particles changes are acceptable now. Lorentz transformations in the 4D Minkowski space M(T; X, Y, Z) in the planes (T, X), (T, Y), (T, Z) allow changing the energy and momentum of a particle in the conjugate space of the expanded 4D energy-momentum space M*(E; Px, Py, Pz). In the new 5D space G(T, X, Y, Z, S) in comparison with the Minkowski space M(1, 3), in addition to Lorentz rotations new types of hyperbolic rotations (T, S) and (T,X) have a clear physical meaning in the 5D energy-momentum-mass space G*(E, Px, Py, Pz, M). This space is ad- joint to the space G(T, X, Y, Z, S). Namely in the space G*(E, Px, Py, Pz, M) the rotation (T, S) changes the energy and mass of the particle in a consistent way, and rotation (X, S) changes the momentum and mass of the particles in a consistent way. In the ESM gravity and electromagnetism are combined in one field, and it is possible to construct a 5x5 Energy-Momentum-Mass tensor. In the ESM a photon can have a nonzero variable mass and this mass can be either positive or negative. It is also possible to establish in the frame of ESM connection between mass of a particle and its size.