# Notes

## Section 13: Space, Time and Relativity

History of relativity

(See also page 1028.) The idea that mechanical processes should work the same regardless of how fast one is moving was expressed by Galileo in the early 1600s, particularly in connection with the motion of the Earth—and was incorporated in the laws of mechanics formulated by Isaac Newton in 1687. But when the wave theory of light finally became popular in the mid-1800s it seemed to imply that no similar principle could be true for light. For it was generally assumed that waves of light must correspond to explicit disturbances in a medium or ether that fills space. And it was thus expected that for example the apparent speed of light would depend on how fast one was moving with respect to this ether. And indeed in particular this was what the equations for electromagnetism developed by James Maxwell in the 1860s seemed to suggest. But in 1881 an experiment by Albert Michelson (repeated more accurately in 1887 as the Michelson–Morley experiment and now done to the 10-20 level) showed that in fact this was not correct. Already in 1882 George FitzGerald and Hendrik Lorentz noted that if there was a contraction in length by a factor Sqrt[1 - v2/c2] in any object moving at speed v (with c being the speed of light) then this would explain the result. And in 1904 Lorentz pointed out that Maxwell's equations are formally invariant under a so-called Lorentz transformation of space and time coordinates (see note below). Then in 1905 Albert Einstein proposed his so-called special theory of relativity—which took as its basic postulates not only that the laws of mechanics and electrodynamics are independent of how fast one is moving, but that this is also true of the speed of light. And while at first these postulates might seem incompatible, what Einstein showed was that they are not—at least if modifications are made to the basic laws of mechanics. In the few years that followed, various formulations of this result were given, with Hermann Minkowski in 1908 showing that it could be derived if one just assumes that space and time enter all physical laws together in a certain kind of 4D vector. In the late 1800s Ernst Mach had emphasized the idea of formulating science and particularly mechanics in terms only of concepts that can actually be measured by observers. And in this framework Einstein and others gave what seemed to be almost purely deductive arguments for relativity theory—with the result that it generally came to be assumed that there was no meaningful sense in which one could ever imagine deriving relativity from anything more fundamental. Yet as I discussed earlier in the chapter, if a complete theory of physics is to be as simple as possible, then most things like relativity theory must in effect be derived from more basic features of the theory—as I start to try to do in the main text of this section.

From Stephen Wolfram: A New Kind of Science [citation]