MUCH of the difficulty which philosophers and laymen experience in understanding Einstein’s theory arises from a confusion between the different meanings that may be attributed to the concepts “relativity of space and motion.” For the student who already possesses some knowledge of classical science, confusions of this type, of course, are not to be feared. But in view of the general misconceptions on the subject we will mention briefly the various principles, elucidating them further as we come across them in the course of this book. We must name here: 1. The primordial mathematical relativity of space and time. 2. The kinematical or visual principle of relativity. 3. The dynamical or classical Galilean and Newtonian principle of relativity. 4. Einstein’s special principle of relativity. 5. Einstein’s general principle of relativity. 6. The radical Mach-Einstein principle of relativity. Let us consider these various principles in their order. The mathematical type of relativity is the one we have already had occasion to mention when discussing mathematical space and time. It implies that a distance in space, even after the space has been referred to the observer’s frame, has a purely relative magnitude; so that two distances in space may be congruent or unequal according to our measuring conventions. Even after we have decided upon our measuring conventions, the magnitude of a spatial distance can only be expressed by the magnitude of our measuring rod; and if during the night all lengths were to contract in the same way, no difference could be detected when we awoke on the following day. Similar conclusions would apply to time. Now, this mathematical aspect of the relativity of space and time would appear to be in conflict with everyday experience; for if during the night all things were to move twice as fast, there is not the slightest doubt that certain very apparent physical changes would be manifest. For instance, a rapidly rotating flywheel might burst under the tremendous strain of centrifugal stresses. However, it must be remembered that the mathematician is discussing pure amorphous mathematical space; and even though Weyl’s theory throws a new light on the relativity of magnitude by referring it to the radius of the universe as a whole, the entire question is still somewhat obscure. We need lose no more time over these purely mathematical conceptions, but shall concern ourselves with the principles of relativity which [Pg 104] relate to the real universe of physics, to real space, together with its metrical field.