8 7 8 A P P E N D I X H the form of natural laws in such a way that a “perpetuum mobile” not be possible. We find something similar in relativity: natural laws must be such that their expression not vary from a system k to another . If for k and the natural law is not the same, then the principle of relativity has been violated and one could establish a privileged system or state of motion that could be deter- mined by the Lorentz transformation. If we express a natural law mathematically in a sys- tem k using the four coordinates x, y, z, t, applying the Lorentz transformation and by an analytical process of elimination, we obtain the mathematical expression of the law in a sys- tem with the variables If the two expressions for k and are not identical, the principle of relativity is not fulfilled and the expression of the law is not acceptable. On the contrary, if the two expressions in the systems k and are identical, the law is well formulated. Minkowski gave a very elegant method for finding the form of the laws without the transformation the method he employed is very similar to the vectorial one used in classi- cal physics. In it [classical physics], one tries to find equations that do not vary as the posi- tion of the system of coordinates changes. This condition only affects space, not time. One can easily explain why one speaks of a space of four dimensions in relativistic phys- ics, but not in classical physics. In classical physics, even when phenomena are defined by four variables, these are of a very different nature, since three refer to space and the fourth to time, the last being common to all systems of coordinates. In relativistic physics, the four variables have an identical meaning, insofar as they are dependent on the system of coordi- nates. Important physical consequences of special relativity: the electrodynamics of Max- well-Lorentz preserves the form of its equations because they satisfy the conditions expressed above. On the other hand, Newton’s dynamics is not preserved and must be mod- ified in the sense that there be no body whose velocity is superior to that of light in vacuo. The resistance of a body to receiving ever higher velocities grows as these velocities in- crease and it becomes infinite when the velocity equals that of light, or, in other words, the velocity of the propagation of light in space is an unattainable upper limit. This result has been confirmed experimentally in the theory of electrons, in which enormous velocities are found. The most important consequence refers to the principle of the conservation of energy, which is found to be valid for all systems. The inertia of a body increases with the energy communicated to it, and so it comes about that the inert mass of a body is energy, thus fus- ing the two classical principles of the conservation of mass and the conservation of energy into only one [principle] of conservation of energy. This principle is very important for the general theory. At this point Professor Einstein sums up his beautiful and attractive discourse with the following sentence: “All we have said today is no more than an immediate consequence of two principles: that of special relativity and that of the constancy of the velocity of light in vacuo.” As we said before, in this first lecture Einstein remains on elementary terrain, and one can complete the ideas expounded here by reading his popularizing volume, translated into almost all European languages. k′ k′ k′ x′, y′, z′, t′. k′ k′