The evolution of scientific thought from Newton to Einstein

by A. D'Abro

Quite apart from the negative experiments, Einstein lays special stress on another type of phenomenon. Thus, whether we displace a magnet before a closed circuit or the closed circuit before the magnet, the current induced in the wire is exactly the same in either case, so far as experiment can detect. That which appears relevant is the relative motion between magnet and circuit; the respective absolute velocities of magnet and circuit through the ether, which are of course different in both cases seem to be totally irrelevant.

In view of the importance of the question, let us mention another example. We remember that when discussing electrical phenomena in the first pages of the preceding chapter, we mentioned that an electrified body was surrounded by an electric field of force, whereas a current was surrounded by both an electric and a magnetic field. Subsequent experiments performed by Rowland confirmed the view that a charged body in motion generated the same electric and magnetic fields as a current flowing along a wire, so that we had to agree that a charged body in motion developed a magnetic field by the sole virtue of its motion.

Now here again we are in a quandary to understand what is to be meant by motion. Classical science assumed that motion in this case meant motion with respect to the stagnant ether, and that an electric current was constituted by the rushing of electrons through the ether. Numerous difficulties beset this view. Owing to the earth’s motion through the ether, every charged body on the earth’s surface would constitute an electric current; so that around every electrically charged body a magnetic field should be present. Yet experiment failed to detect this magnetic field. Was it due to the crudeness of our experiments? This solution was scarcely possible; for if we displaced our charged body before a magnetised needle (Rowland’s experiment), the needle was deflected, proving that experiments were perfectly able to detect the magnetic field when it was truly produced. It appeared as though the type of velocity that constituted a current was not velocity through the ether at all, but velocity relative to the recording instrument or, more generally, to the observer. Once again, the only type of velocity which appeared to have any significance in nature was relative velocity, and never velocity through the stagnant ether or absolute space.

Hence, Einstein postulated his special principle of relativity, according to which Galilean motion through the ether or space is meaningless. This principle is, as we see, merely an extension of the Newtonian mechanical principle to the case of the ether, or in other words to electromagnetic and optical experiments.

What is called the special theory of relativity concerns the rational consequences that must follow from the special principle. These consequences may be anticipated as follows: If Galilean motion through the ether is meaningless, the laws of electrodynamics must remain invariant in form when we change our Galilean system of reference. But this implies that the space and time transformations which the co-ordinates of all points undergo, when we change systems, must be given by the Lorentz transformations.

In Einstein’s theory, however, the significance of the transformations is entirely different. It will be remembered that in ordinary language these transformations implied the FitzGerald contraction and the slowing down of time. In Lorentz’s theory these modifications arose as a result of a real velocity through the ether; and though it was impossible for the observer in the moving frame to detect their presence, yet in spite of all they were physically real. In Einstein’s theory, on the other hand, velocity through the ether being meaningless, the modifications arise only as a result of the relative motion of one frame with respect to the other, and are thus due to conditions of observation and not to any intrinsic change. For instance, if in any two Galilean frames originally at relative rest, two identical clocks and two identical cubes are placed, and if then the two frames are set in relative motion, either observer would discover as a result of his measurements that the other man’s clock had slowed down and that his cube had become flattened in the direction of the relative motion. Nothing would have happened to the cubes and clocks; only the conditions of observation would have been changed.

Expressed mathematically, this means that the variable

which enters into the Lorentz transformations now stands for the relative velocity of one frame with respect to the other, and no longer for velocity through the ether. In this measure the transformations of Einstein’s theory, though identical in appearance with those of Lorentz’s, are far different in meaning. To avoid confusion, the appellation Einstein-Lorentz or Lorentz-Einstein transformations is accordingly often made use of.[45]

There is still a further difference, a most important one, distinguishing the implications of the transformations in the two theories. In Lorentz’s theory there was a privileged observer situated in the frame at rest in the ether. In Einstein’s theory there is no such privileged observer; for since a privileged state of rest in the ether is meaningless, all observers in Galilean frames are on the same footing. Hence, Lorentz’s distinction between the true time of the frame at rest and the distorted, local or electromagnetic times of the frames in motion through the ether loses its significance. Henceforth, all these so-called local times given by the Lorentz transformations constitute the true times lived, sensed and experienced by the respective observers in their respective Galilean frames.