9 4 8 A P P E N D I X F ordinary sense, but rather a “variant in which Nature is simultaneously afforded a place in its continuous evolution.” That we are not accustomed to considering the world (in the sense that is commonly giv- en to that concept) as a continuum of those four dimensions—he went on to say—comes from the fact that in physics, prior to the theory of relativity, time played a role that was independent of the coordinates. It formed a continuum in and of itself, since it was indepen- dent of place and of the state of movement. On the other hand, in the theory of relativity, he added, time depends on spatial coordi- nates, since in Lorentz’s equation, which connects the time of two systems, coordinates also appear. The time elapsed between two events with respect to a system is not invalidated when it occurs in relation to another system that moves relative to the first. Two events that appear simultaneous to an observer, that is, events that are separated only spatially, appear to be separated by an interval of time to another observer moving relative to the first one, Next he explained mathematically the symbolic representation of Minkowski’s events (we will allow ourselves to use this term), pointing out that the path chosen by Minkowski was such that his universe might be considered a Euclidean continuum in four dimensions, since the “distance” between two different points appeared connected to the four dimen- sions in the same way that spatial distance was connected to the coordinates pertaining to space. He then went on to give a demonstration of such different points for two coordinates of space and time, using the foundation of Lorentz’s equations, of course. The objective was to demonstrate that, fundamentally, the knowledge that observer B has of the world of another observer A, with B moving relative to A, is inferior in a graphic sense. A takes his spatial and temporal axes, at right angles to one another for convenience’s sake, and represents the events in his system. Each point provides the place and time of an event. He immediately inquires, using Lorentz’s equations, which axes he should use in or- der to discover what knowledge B possesses of his world, and once discovered, he deter- mines through the fundamental invariance connecting distances and durations, as specified above, the units of longitude and of time he must use in order to construct his world as B sees it. Professor Einstein then demonstrated that Lorentz’s equations are meaningless if the ve- locity of one of the systems becomes equal to that of light, which is interpreted by saying that the velocity of light is a terminal velocity, that is, the maximum velocity that can be observed. He showed that the axis of time which A must use to infer the knowledge that B possesses of his world is more inclined with regard to the axis of nature itself, the greater the relative velocity, growing indefinitely closer to a 45o angle as the latter increases, which corresponds to the maximum velocity we mentioned a moment ago. If, as we have assumed up to now—he said—the origins of A’s axes coincide with those A uses to denote the vision of his world as perceived by B, it is clear that we can represent them with widely varying angles, but the time axes, in any case, can never form an angle greater than 45o, as stated above. No matter how often this is repeated, the limiting positions of the axes by which A can determine what aspect of his world all observers perceive will obviously form a cone. The spatial axes are outside this cone.