L E C T U R E S A T T H E U N I V E R S I T Y O F M A D R I D 8 7 9 El Debate will give the most complete extract possible of the subsequent lectures, which will be more difficult to understand, as the lecturer indicated at the start, and will always attempt to remain on a level acceptable to the majority of readers. SECOND L ECTURE With the hall brimming with people, Professor Einstein punctually begins his second lecture, a natural continuation of the first and filled with interesting ideas, as the reader may judge. “Today I begin with the theory of general relativity. We have seen that the main idea of the special theory was the restricted principle of relativity, that is, the equivalence of all sys- tems of coordinates in uniform motion with respect to one another, that is, of all inertial systems. This can be expressed this way: There is no privileged state of motion. But it is necessary to note that it is true that there is not one privileged state but an infinitude: all inertial systems. It is thus natural to ask: Is it possible that Nature is such that it does not know such privileged states of motion? Can all systems, whatever their state of motion, be equally used for the expression of natural laws? At first glance this seems impossible, be- cause the first law of mechanics is not valid for all systems. Let k be a system with respect to which the law of inertia is valid. That is, in k a material point free of all exterior action will have rectilinear and uniform motion, but if we take a system in rotation, the move- ment of the point is no longer rectilinear but follows a curve. Then we can say that the law of inertia prefers a certain system and does not accept others. We will see that this argument has no value for the reason that the ordinary definition of an inertial system has a weak point. It is said that if there are no external forces, the point describes a straight line with uniform motion, but the nonexistence of external forces is recognized by the point’s de- scribing a straight line. There is a vicious circle here. On the other hand, there is an argument for the validity of the principle of general rela- tivity which seems to me of such force that I am convinced of the necessity of establishing such a principle. It is known to everyone: the equivalence between ponderable and inert masses. In mechanics there are two definitions of mass: one as a measure of inertia, that is, of the resistance that a material point reacts with to the change of its velocity the other, as a mea- sure of weight, that is, the force acting on a body in a gravitational field. It is almost a mir- acle for classical mechanics that these two measures, which are independent of each other, coincide. There are measurements whose precision reaches one part in ten million, demon- strating their equivalence. It is easy to see that if one accepts the hypothesis of general rel- ativity that all states of motion are equivalent for the formulation of natural laws, the equivalence of masses appears to be a natural thing. The law of the equivalence of ponder- able and inert masses can be stated this way: acceleration in a gravitational field does not depend on the physical or chemical state of a body, but only on the ratio of its inert and grav- itational masses. k′