The Newtonian or Galilean or classical or dynamical principle of relativity expresses this elusiveness of absolute velocity or Galilean motion through space so far as mechanical experiments are concerned, while it stresses by contrast the physical significance of absolute acceleration and rotation. As is well known, it was this absoluteness or physical significance of acceleration and rotation which compelled Newton to recognise that space could not be relative. That the Newtonian principle of relativity will considerably restrict the scope of the visual principle can be gathered easily from the following example:
If a body were moving with respect to our frame of reference with a relative velocity, but with no relative acceleration, we should be justified according to the Newtonian principle in maintaining that it would be impossible to decide by mechanical experiments whether it was we who were moving towards the body or the body that was moving towards us. To this extent the visual principle is satisfied. But, on the other hand, if a relative acceleration of rotation existed as between ourselves and the body, mechanical experiments would enable us to ascertain what fraction of the relative acceleration or rotation was due to our own absolute acceleration or rotation in empty space, hence also what fraction was due to the body’s motion.
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 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.
CHAPTER X
CLASSICAL MECHANICS AND THE NEWTONIAN PRINCIPLE OF RELATIVITY
WE mentioned, when discussing amorphous mathematical space, that position and hence motion could have no meaning other than that of expressing conditions with respect to some particular frame of reference. In short, the visual principle of relativity would have to be adhered to.
We will accordingly select some arbitrary system of reference, which we will assume to be defined by three mutually perpendicular planes meeting at a common point
. The instantaneous position of a body will henceforth be defined when we have measured with rigid rods its distances from the three planes of our frame; and the only type of position and of motion of the body which we can define in an unambiguous way will be its position and motion as referred to our frame.