V.5 No 2 39 On basic formalism of special theory of relativity
 Conclusions In the carried out study, we have revealed that Lorentz transformations are the group of automorphisms only for the operation of coordinate transformation, not for the secondary transformations of speeds and accelerations. As the result, in transformations between mutually moving reference frames, the law of vectors summation and the invariance of law describing the accelerated motion of bodies are invalid. In particular, the time-constant acceleration in relation to a stationary reference frame, in transition to a moving inertial reference frame, becomes dependent on the momentary speed of body. In its turn, this non-single-valued nature of transformation of vectors makes the operation of differentiation and integration in limits of both SR and GR illegal. We showed that the attempts of relativists to form the 4-D vector of acceleration as a derivative over intrinsic time are illegal - on one hand because of discrepancy between the concept of intrinsic reference frame and accelerated motion of body, and on the other because of paradoxical solutions that violate the laws describing the motion of bodies in inertial reference frames. We also have established that the system of transformation, basing on which relativists conclude space-time transformation real, does not match with Lorentz transformation. Due to which they are not invariant and do not satisfy the conditions of self-consistence of the group of transformations. This proves the statement of real reduction of space-time to be wrong. Besides, we showed that SR illegally joins the conceptions of invariant and 4-D interval; this happened because of Poincare’s mistake in determining of 4-D interval in the complex space; Minkowski and Einstein copied this mistake to SR. Thereupon the 4-D interval gains a paradoxical property to lessen with growing speed of body in measurements in the stationary inertial reference frame. When we correct this mistake, the interval takes natural properties inherent to the concept of interval, but stops to be invariant, and we may not consider Lorentz transformations as the rotation of coordinate system by some imaginary angle. Also, with it Einstein’s invariant may not be used as an interval in the law of least action. In amount, yielded results give us the grounds to state full disability of relativistic conception to solve the problems of kinematic and dynamics. September 8, 2005 Supplement 1. On reality of space-time reduction in SR: / 1 / 2 / References: 1. Karavashkin, S.B. and Karavashkina, O.N. Notes on physical absolute. SELF Transactions, 3 (2003), 1- 8 2. Karavashkin, S.B. and Karavashkina, O.N. On transverse Doppler effect in classical formalism. SELF Transactions, 5 (2005), 46- 56 3. Karavashkin, S.B. and Karavashkina, O.N.On reality of black holes.  SELF Transactions, 5 (2005), 2, 1- 17 4. Karavashkin, S.B. and Karavashkina, O.N. On light aberration. SELF Transactions, 5 (2005), 2, 18- 28 5. Ilyin, V.A. and Poznyak, E.H. Fundamentals of mathematical analysis, part 1. Nauka, Moscow, 1971 (Russian) 6. Pauli, W. Theory of relativity. GITTL, Moscow- Leningrad, 1947 (Russian) 7. Levich, V.G. The course of theoretical physics, vol. 1. Physmathgiz, Moscow, 1962 (Russian) 8. Sedov, L.I. Mechanics of continuum, vol. 1. Nauka, Moscow, 1973 (Russian) 9. Einstein, A. Theory of relativity. - In: Collection of scientific works, vol. 1, p. 175- 186. Nauka, Moscow, 1965 (Russian) 10. Companeetz, A.S. The course of theoretical physics, vol. 1. Prosveccenie, Moscow, 1972 (Russian) 11. Born, M. Einstein’s theory of relativity. Dover Publications, New York, 1962 (Cited after Russian edition) 12. Marder, L. Time and the space-traveller. George Allen and Unwin ltd., London, 1971. Cited after Russian edition: Marder, L. The clock paradox. Mir, Moscow, 1974 13. Konoplyova, R.P. and Sokolik, G.A. The problem of identity and relativity principles. - In: Einstein’s collection 1967, p. 348- 370. Nauka, Moscow, 1967 (Russian) 14. Petrov, A.Z. Einstein’s spaces. Physmathgiz, Moscow, 1961 (Russian) 15. Einstein, A. The principle of relativity and its corollaries. - In: Collection of scientific works, vol. 1, p. 138- 164. Nauka, Moscow, 1965 (Russian) 16. Denisov, A.A. Myths of theory of relativity. Vilnius, 1989 (Russian) 17. Einstein, A. The dialogue on objections against the theory of relativity. - In: Collection of scientific works, vol. 1, p. 616- 625. Nauka, Moscow, 1965 (Russian) 18. Einstein, A. On the electrodynamics of moving bodies. - In: Collection of scientific works, vol. 1, p. 7. Nauka, Moscow, 1965 (Russian) 19. Einstein, A. The relativity principle and its corollaries in modern physics. - In: Collection of scientific works, vol. 1, p. 138- 164. Nauka, Moscow, 1965 (Russian) 20. Einstein, A. The project of general theory of relativity and gravitation theory (with M. Grossmann). - In: Collection of scientific works, vol. 1, p. 227- 266. Nauka, Moscow, 1965 (Russian) 21. Sudakov, V.V. Four-dimensional interval. - In: Physical encyclopedia, vol. 2, p. 287. Sovetskaya encyclopedia, 1962 (Russian) 22. Modenov, P.S. Analytical geometry. Moscow University Press, 1969 (Russian) 23. Bakelman, I. Ya. Higher geometry. Prosveccenie, Moscow, 1967 (Russian) 24. Poincare, A. On dynamics of electron. - In: Selected works, vol. 3, p. 433- 486. Nauka, Moscow, 1974 (Russian) 25. Lavrentiev, M.A. and Shabat, B.V. Methods of theory of complex variable. Nauka, Moscow, 1973 (Russian)

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