The evolution of scientific thought from Newton to Einstein

by A. D'Abro

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 relate to the real universe of physics, to real space, together with its metrical field.

The kinematical or visual principle of relativity, which is at least as old as the Greeks, states that a body can be considered in motion only when referred to some other body. For instance, if we consider the particular case of the earth and sun, we would conclude, according to whether we referred motion to the earth or sun, either that the sun was rotating round the earth every twenty-four hours, or else that the earth was rotating on its axis.

The two methods of presentation would be equivalent. Again, it would be impossible for us to state whether a body was approaching us faster and faster with some accelerated motion or whether it was we who were travelling with accelerated motion towards the body, visual appearances being the same in either case. Obviously this kinematical or visual principle would connote the complete relativity of all motion and rest, hence the complete relativity of space.

But a closer study of the dynamics of material systems proves the visual principle to be untenable. It was found that the behaviour of material systems, and thus the results of mechanical experiments, were influenced by absolute acceleration and rotation through space, although they remained totally unaffected by absolute velocity.