Metric in Reference System Transformation

In the past physics the assumption in the Principle of Relativity that the metrics for the reference systems are completely equivalent always exists, i.e. the statement of metric in reference system transformation had an absolute significance, which are irrelevant to the motion state of the reference systems. Through the experiment of the wave motion on the water surface caused by translating the uniform falling water drops the author finds that the wave motion velocity is mutually independent and constant energy release velocity, not related to the motion state of the uniform falling water drops parallel to the water surface. If the uniform falling water drops are regarded as wave sources or clocks, the wavelengths or periods of relatively moving wave sources or clocks differ for different motion velocities and directions. Here we show that the metrics for the relatively moving reference systems vary in different motion states if the wave sources or clocks are regarded as reference systems, with each reference system having its own metric. The metrics in reference system are of no practical significance unless the metrics for the reference system are specified. Therefore, the universality of the assumption in the Principle of Relativity that the metrics for the reference systems are completely equivalent is insufficient for describing the natural phenomena. The conflict between the Principle of Light Propagation and the Principle of Relativity will disappear only if the assumption is abandoned.