In Einstein’s theory, however, the significance of the transformations is entirely different. It will be remembered that in ordinary language these transformations implied the FitzGerald contraction [Pg 145] and the slowing down of time. In Lorentz’s theory these modifications arose as a result of a real velocity through the ether; and though it was impossible for the observer in the moving frame to detect their presence, yet in spite of all they were physically real. In Einstein’s theory, on the other hand, velocity through the ether being meaningless, the modifications arise only as a result of the relative motion of one frame with respect to the other, and are thus due to conditions of observation and not to any intrinsic change. For instance, if in any two Galilean frames originally at relative rest, two identical clocks and two identical cubes are placed, and if then the two frames are set in relative motion, either observer would discover as a result of his measurements that the other man’s clock had slowed down and that his cube had become flattened in the direction of the relative motion. Nothing would have happened to the cubes and clocks; only the conditions of observation would have been changed. Expressed mathematically, this means that the variable which enters into the Lorentz transformations now stands for the relative velocity of one frame with respect to the other, and no longer for velocity through the ether. In this measure the transformations of Einstein’s theory, though identical in appearance with those of Lorentz’s, are far different in meaning. To avoid confusion, the appellation Einstein-Lorentz or Lorentz-Einstein transformations is accordingly often made use of.[45] There is still a further difference, a most important one, distinguishing the implications of the transformations in the two theories. In Lorentz’s theory there was a privileged observer situated in the frame at rest in the ether. In Einstein’s theory there is no such privileged observer; for since a privileged state of rest in the ether is meaningless, all observers in Galilean frames are on the same footing. Hence, Lorentz’s distinction between the true time of the frame at rest and the distorted, local or electromagnetic times of the frames in motion through the ether loses its significance. Henceforth, all these so-called local times given by the Lorentz transformations constitute the true times lived, sensed and experienced by the respective observers in their respective Galilean frames.