We now come to Einstein’s special principle of relativity. It is an exact replica of the Newtonian principle, upholding the relativity of velocity and the absoluteness of acceleration.[36] The sole difference between the two principles is that in Einstein’s, the [Pg 105] elusiveness of absolute velocity through space is no longer restricted to mechanical experiments and to material systems; electromagnetic and optical experiments are now placed on exactly the same footing. While we are on the subject of the various principles of relativity, we may discuss two further types which play an important part in that extension of Einstein’s special theory known as the general theory of relativity. Here we are introduced to the General Principle of Relativity. This principle states that the mathematical expressions of the laws of nature must maintain the same form regardless of our choice of a frame of reference, be it Galilean (i.e., unaccelerated through empty space), accelerated, or even squirming like an octopus, while our clocks situated throughout the frame may beat at the most capricious rates. The classical principle of relativity conceded this invariance of natural laws in the case of Galilean frames, and synchronised clocks alone, and then only in the case of the laws of mechanics. The special principle recognised that this invariance held true even for the electromagnetic laws, but, as before, only for Galilean frames. The general principle of relativity, by extending the invariance of the laws of nature to all types of motions of the frame of reference, marks the starting point for the possible relativisation of acceleration, which had heretofore stood out as aloof and as distinctly absolute. The radical Mach-Einstein principle of relativity is the result of a natural desire to bring about the complete relativisation of all manner of motion, rotationary and accelerated, as well as uniform. This is achieved by ascribing all the dynamical effects which accompany the acceleration and rotation of material and electrodynamic systems, to motion with respect to the material universe as a whole. According to this principle, which is still highly speculative, there can exist no observable difference between the rotation of a body with respect to the universe of stars and the rotation of the stars round the body; exactly the same dynamical effects of centrifugal force would be set up in either case, so that no trace of absolute motion through empty space would be left. We see that Mach’s principle constitutes an attempt to vindicate the kinematical principle in spite of the difficulties of a dynamical nature which had been the cause of its rejection. It was in part with a view to satisfying Mach’s principle that Einstein elaborated the hypothesis of the cylindrical universe. The principle would fall if astronomical observation should prove this form for the universe to be unacceptable. [Pg 106] CHAPTER X