15-2 The Lorentz transforrnation When the failure of the equations of physics in the above case came to the first thought that occurred was that the trouble must lie in the new maxwell equations of electrodynamics, which were only 20 years old at the time. It seemed almost obvious that these equations must be wrong, so the thing to do was to change them in such a way that under the Galilean transformation the principle of relativity would be satisfied. When this was tried, the new terms that had to be put into the equations led to predictions of new electrical phenomena that did not exist at all when tested experimentally, so this attempt had to be abandoned Then it gradually became apparent that Maxwell's laws of electrodynamics were correct, and the trouble must be sought elsewhere. In the meantime, H. A. Lorentz noticed a remarkable and curious thing when he made the following substitutions in the Maxwell equations namely, Maxwell's equations remain in the same form when this transformation is applied to them! Equations(15.3)are known as a Lorentz transformation Einstein, following a suggestion originally made by Poincare, then proposed that all the physical laws should be of such a kind that they remain unchanged under a Lorentz transformation. In other words, we should change not the laws of electro dynamics, but the laws of mechanics, How shall we change Newton,s laws so that they will remain unchanged by the Lorentz transformation? If this goal is set, we then have to rewrite Newtons equations in such a way that the conditions we have imposed are satisfied. As it turned out, the only requirement is that the mass m in Newton's equations must be replaced by the form shown in Eq.(15.1). When this change is made, Newton's laws and the laws of electrod- namics will harmonize. Then If we use the Lorentz transformation in comparing Moe's measurements with Joes, we shall never be able to detect whether either is moving, because the form of all the equations will be the same in both coordinate It is interesting to discuss what it means that we replace the old transformation between the coordinates and time with a new one, because the old one(Gallean) seems to be self-evident, and the new one(Lorentz) looks peculiar. We wish to know whether it is logically and experimentally possible that the new, and not the old, transformation can be correct. To find that out, it is not enough to study the laws of mechanics but, as Einstein did, we too must analyze our ideas of space and time in order to understand this transformation. We shall have to discuss these ideas and their implications for mechanics at some length, so we say in in phase advance that the effort will be justified, since the results agree with experiment 15-3 The Michelson-Morley experiment Fig. 15-2. Schematic diagram of the As mentioned above, attempts were made to determine the absolute velocity Michelson-Morley experiment of the earth through the hypothetical"ether"that was supposed to pervade all space. The most famous of these experiments is one performed by Michelson and Morley in 1887. It was 18 years later before the negative results of the experi ment were finally explained, by Einstein The Michelson-Morley experiment was performed with an apparatus like that shown schematically in Fig. 15-2. This apparatus is essentially comprised of a light source A, a partially silvered glass plate B, and two mirrors C and E, all mounted on a rigid base. The mirrors are placed at equal distances L from B The plate B splits an oncoming beam of light, and the two resulting beams con- 15-3