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The constancy of light speed and relativistic effects can be established in Galilean kinematics by means of coordinate transformations. They generate different modified Galilean transformations, and one of them is mathematically identical with the Lorentz transformation. The usual physical interpretation of the Lorentz transformation requires the additional use of imaginary events, happening in imaginary worlds, and described by imaginary coordinate systems. The Lorentz-transformed time appears to be an imaginary physical quantity. Also the relativistic effects of special relativity are imaginary; they can be real only under special circumstances. The relativity principle of special relativity is not compatible with the constancy of light speed.

Special relativity is conceptually unable to describe reality in a satisfactory way when extended solid bodies are involved. For example, we consider two extended solid bodies gliding upon each other. When they occupy a certain relative position, there happen many local spatial coincidences between particles of the bodies, and all these events are equivalent in the domain of reality. Special relativity, however, describes only one of these events correctly. All the other meetings of real particles are described in ambiguous ways and by use of imaginary particle meetings. It follows that the classical synchronization of clocks on a reference frame is the only one compatible with our reality.