9 4 6 A P P E N D I X F relativistic possibilities mentioned earlier, a physical base is required. We already have that physical base: the two fundamental postulates. The problem is reduced to determining them (the relationships) so that, assuming the speed of light is constant, “the natural laws that move relatively with rectilinear and uniform motion will turn out to be identical.” For example, the length of a bar located in a system M, according to an observer in the same system, must be equal to the length obtained when it is transported to another system N that moves relative to the first one in the manner indicated and by having it measured by another observer located in that system (in N) if a flash of light emanates from any point, the wave must appear equally spherical for observers at M and for those at N. Lorentz’s Equations [Einstein] then mathematically deduced those relationships, that is, the Lorentz transfor- mation equations, demonstrating that they contain the relativity of distances and durations assumed to be possible. If an observer at rest with respect to the system measures the dura- tion of a unit of time, another observer that moves relative to him at a certain velocity ob- serves a duration that is the square root of one minus the square of the ratio of this velocity to the speed of light. That is, instead of obtaining the same time between the two occurrenc- es, a lesser time is obtained. Something analogous happens with lengths, which accounts for the contraction that, as an effect of movement, Fitzgerald and Lorentz attributed to the bodies in order to explain Michelson’s results. These equations, he said, are simply relationships through which an observer can infer the knowledge that another moving observer can possess relative to him in the manner in- dicated. It is important to emphasize that, despite the relativity of distances and durations, there is a science of the universe, since the laws are of the same form for all observers that move relatively, as mentioned. We can, the sage continued, explain the surprising result of Fizeau’s experiment. In order to do so it is necessary for us to show, he said, that the principle of the superposition of the velocities of classical mechanics is invalid. In it, he added, if a body moves above the Earth at velocity V and above it another body moves in the same direction at velocity v, with re- gard to the first, the velocity of this second body with respect to the Earth is V+ v. In the theory of relativity, on the other hand, it has a lesser value. In Fizeau’s experiment, the velocities are: that of light with respect to an observer that moves with the water, and that of the water with respect to the apparatus. The velocity of the waves with respect to the apparatus, that is, with respect to the tubes, is less than sum of both of those. Through this result, he demonstrated how one can deduce simply the in- crement of the velocity of the light at a fraction proportional to a factor that depends of the refractive index of the liquid. This is an increment identical to the one established empiri- cally by Fizeau. I am going to conclude my lecture, he said, by showing that with those transformation equations, the form of the laws of phenomena is the same for two systems that move in the form we have already repeated so many times that is, that they are independent of the observer.