Derivation and application of three-dimensional logical transformation
Mingke Yuan · Zenodo (CERN European Organization for Nuclear Research) · 2019
The misconception of time and space causes various interpretations and outcomes. In order to restore the true physical meaning of time, this paper emphasizes the definitions of mathematical time and physical time. In this paper, we derived the three-dimensional logical transformation according to the principle of invariance of light speed and three-dimensional setup of two reference frames. The logical transformation is for replacing Lorentz transformation and Galilean transformation. The Lorentz speed transformation given by Einstein is correct. From the speed transformation, Einstein derived the famous mass-speed equation and mass-energy equation. However, the Lorentz factor is superfluous, and it was eliminated when deriving the Lorentz speed transformation. Without Lorentz factor, the Lorentz transformation becomes one-dimensional logical transformation. That is why the one-dimensional logical speed transformation is exactly the same as the Lorentz speed transformation. Since Lorentz transformation is based on one-dimensional setup of two reference frames, the Lorentz transformation is not applicable for particles moves in three-dimensional space. That is why the three-dimensional Lorentz transformations of physical quantities are contradictory and problematic. According to the logical transformation and the principle of invariance of relative velocity, we also derived a series of three-dimensional physical formulas and physical quantity transformations. We believe these equations will be useful for high-energy physics, quantum mechanics, and clock correction of GPS. These equations may be also useful for astrophysics.