Standing Waves as Frames of Reference: a Classical Model of the Relativistic Space-Time
We consider free vibrations of an inﬁnite ideal homogeneous string, that described in the laboratory reference by the equation u <sub>tt</sub> = a <sup>2</sup>u <sub>xx</sub>. We propose a model in which the role of frames is performed by the standing waves. The concept of motion in the model is analyzed. It is shown that there exist an inﬁnite number of equivalent frames of reference moving relative to each other. Distances, intervals of time, speeds obey the formulas of special theory of relativity, in which the role of invariant speed is performed by the constant a.