A very simple, fundamental physical explanation is presented of time dilation and length contraction. This explanation is obtained from a classical model of physics that is Galilean. It assumes the existence of a medium (ether) that acts as an absolute reference in accordance with Mach’s principle. Time and space are conventional, i.e., a three-dimensional space independent of time. In addition, the explanation relies on the assumption that all physics, including matter such as clocks and measuring rods, has a scalar wave structure. Matter is assumed to consist of locally stable scalar wave structures, specifically scalar standing wave structures. The scalar waves are just variations in space and time of medium density. Also, an element of special relativity is used, namely, the one taking into account the finite velocity of light.
Van Willigenburg, L. G., & De Koning, W. L. (2018). Wave structure of matter causing time dilation and length contraction in classical physics. Physics Essays, 31(4), 434-440. https://doi.org/10.4006/0836-1398-31.4.434