Physical meaning of transformation equations between two reference frames

When time is an independent variable, the time is physical time, which is defined by physics; when time is a dependent variable, the time is mathematical time, which is defined by an equation. When a frame is selected as reference frame, the frame is a stationary frame, and other frames are moving frames. The two-frame setup we usually use for transformation is only for one-dimensional motion. Above three points is what we discussed in this paper since they are easily confused.    

 In this paper, we state the necessary and sufficient conditions to verify the correctness of transformation equations between two reference frames. This criterion is based on the concept and physical meaning of transformation between two reference frames. It is important to clarify the physical meaning of transformation and verify whether a transformation equation is correct; otherwise, it will lead to various surprising conclusions due to misconception.    

This paper also explains why Galilean transformation does not apply to electromagnetic motion, the physical meaning of Lorentz covariance and the relationship between Lorentz covariance and the principle of relativity. This paper is a preparation for our next three papers.