Consider a train moving with constant speed along a straight course; obviously there is no trace of acceleration in the train’s motion, since no forces of inertia are felt in its interior. In common practice, we should speak of the train as having a definite speed of so many miles per second. But if we reflect we shall see that this constant speed is computed with respect to the earth’s surface, considered as defining a Galilean frame of reference. Were the earth suddenly to become invisible, we should have no physical means of determining the exact speed of the train through space. But suppose, now, that the train were slowing down, speeding up or rounding a curve. In this case, even if the earth were invisible, the train would still possess at each instant a definite acceleration and this acceleration would still be perceptible, and would be measured by the forces of inertia pulling and pushing the passengers about in the train. We see, then, that acceleration has an existence per se and that, in contrast to velocity, it is determinate even in the absence of a frame of reference. Now, it follows from the classical principle of relativity that, absolute velocity being meaningless (at least so far as mechanics is concerned), the only type of uniform translationary motion which can be detected by mechanical means reduces to relative uniform translationary motion of matter with respect to matter; that is, motion with respect to something observable. The magnitude of this relative motion depends essentially on the Galilean frame we may select. Relative uniform translationary motion can, of course, be detected visually, but it can be detected also in a number of other ways. Thus the relative motion of a razor blade on a strop causes heat due to friction. The relative displacement of a knife between the two poles of an electromagnet produces induced currents which manifest themselves by rendering it difficult to cut through the lines of force of the field. The relative motion of an incandescent atom produces a shift in the [Pg 113] spectral lines (Doppler effect), and it is thanks to this shift that astronomers are able to determine the radial velocities of the stars with respect to the earth. In other words, though absolute velocity can never be detected by mechanical experiments and is therefore meaningless in mechanics, yet relative velocity of matter with respect to matter can be detected in a number of ways; so that this relative type of velocity is the only one that has any physical significance, or at least any mechanical significance.