Analysis of Correct Use of Time Transformation in Physics

Abstract

The paper deals with the analysis of mathematically correct use of time derivative in coordinate systems with time transformation. It combines the use of time derivative in different areas of physics with the results of this analysis. The results are used to verify the most well-known theories using time transformation. A general limit of the use of time transformation in physics is formulated and proved.
The analysis is supplemented by specific examples which illustrate the consequences of using a nonlinear (curved) time transformation. They show the formation of a resistor in the LC circuit as a result of time transformation, energy generation or loss, tilting of high rock walls, change in distance between the Earth's centre and the Earth's surface, twisting of Earth's axis, astronomical paradoxes, unknown acceleration properties. The internal consistency of both theories of relativity is also analysed, including the equivalence principle.
The result of the analysis shows that the use of a nonlinear (curved) time transformation is a dangerous tool of contemporary physics that decomposes its internal consistency. This also applies to the time transformations used in both theories of relativity.