Time dilation. There is, however, another distortion that material objects undergo as a function of their absolute motion. That is a slowing down of clocks (and physical processes generally) at the same rate as the length contractions, or the so-called “time dilation,” which took somewhat longer for Lorentz to discover.
The Galilean transformation for time in Newtonian physics is simply t = t’ , because Newtonian physics assumes that time is the same everywhere. But by using transformation equations to describe the distortions in material objects, Lorentz found that he had to introduce a special equation for transforming time: t’ = t – vx/c2 (Goldberg, p. 94). The new factor in the transformation equation, vx/c2, implied that time on the moving frame varies with location in that frame. Lorentz called it “local time,” but he did not attribute any physical significance to it. “Local time” is not compatible with the belief in absolute space and time, and Lorentz described it as “no more than an auxiliary mathematical quantity” (Torretti, p. 45, 85), insisting that his transformation equations were merely “an aid to calculation” (Goldberg, p. 96).
The slowing down of physical processes is called “time dilation.” Lorentz discovered this distortion by tinkering with various ways of calculating the coordinates used on inertial reference frames in relative motion. Thus, it is natural to describe time dilation as the slowing down of clocks on the moving reference frame. It was included in the final version of Lorentz’s explanation, now called the “Lorentz transformation equations.” (Lorentz 1904) Those equations contained not only the length contraction and transformation for “local time”, but also the implication that clocks on moving frames are slowed down at the same rate as lengths are contracted (that is, ). The final Lorentz equation for time transformation included both the variation in local time and time dilation: .
Though Lorentz took the distortions that he discovered in fast-moving material objects to be laws of nature, he did not think that they were basic. He thought they were effects of motion on the interactions between electrons and the ether which could be explained by his electronic theory of matter, and he saw explaining this effect as the the main challenge to Newtonian physics. The transformation equations themselves never seemed puzzling to Lorentz, because he never took them to more than just a mathematical aid to calculation.