Complex "Para-Space" Model for Special Relativity Theory
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A dramatic simplification of the mathematical apparatus (no tensors) for Einstein's special relativity theory is presented. For this goal some simple application of complex numbers calculus is introduced in a specific manner, possibly overlooked in literature. This way of the proceeding was initiated by introducing a trigonometric representation of the Lorentz transformation. One more step from this representation yields complex (number) extension of the real Lorentz transform, so that the space-time Minkowski model M4 is extended to the complex and Euclidean model C4 and then the later is red...
A dramatic simplification of the mathematical apparatus (no tensors) for Einstein's special relativity theory is presented. For this goal some simple application of complex numbers calculus is introduced in a specific manner, possibly overlooked in literature. This way of the proceeding was initiated by introducing a trigonometric representation of the Lorentz transformation. One more step from this representation yields complex (number) extension of the real Lorentz transform, so that the space-time Minkowski model M4 is extended to the complex and Euclidean model C4 and then the later is reduced to the complex C3 time free "para-space" model. All the Einstein's special relativity facts are preserved with the models transition. However, in the new framework, many "difficult facts" of the relativity theory, between others time dilation, Lorentz contraction, universality of speed of light and other find their mathematical explanations. This was possible since nice (and exact !) relation between Einsteinian and Newtonian theories was exhibited in the new complex model.
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