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The several considerations on Galilean and Lorenz T ransformations

The several considerations on Galilean and Lorenz T ransformations . By Aleksandr Tsybin. The Galilean Transformation . The Galilean Transformations was first mention in the work of P. Frank in 1909 First consider equations of motion for a material object where

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The several considerations on Galilean and Lorenz T ransformations

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  1. The several considerations on Galilean and Lorenz Transformations By AleksandrTsybin

  2. The Galilean Transformation The Galilean Transformations was first mention in the work of P. Frank in 1909 First consider equations of motion for a material object where The formula for the Galilean Transformation is:

  3. Lorenz’s Transformation We now consider Maxwell’s Electrodynamics equations in vector equation representation there are four equations: • Gauss’s Law for Electric field • Gauss’s Law for magnetic field • The Faraday’s Law • Ampere’ Law

  4. If we let Than Maxwell’s equation have the view: Derived from them are three differential equations. For example the first one is: (1)

  5. New Cartesian axes transfer with constant velocity with respect to the former Cartesian axes . We will look for this transformations in the form: (2) If where Then (3)

  6. If we get : (4) Therefore Eq.(1) is invariant to the transformations: (5) These are the Lorenz Transformation equations , derived without presumptions about a finite speed of interaction in Nature

  7. Let us consider a wave equation that describes the propagation of sound in medium: (6) For this equation instead the Lorentz’s transformations we have analogous transformation:

  8. Conclusion The Galilean and Lorentz transformations are so connected with Special Relativity that, as a rule, their interpretation is possible only within the limits of this theory. In this work I demonstrated that these transformations can be developed without the use of Einstein postulates. The above derivation can account for a well-known Effects of Special Relativity: • The mass of particles increases with an increase in their velocity, and • The equation can be obtained by other means.

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