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 7 “At this point, I want to say that in general, it is not possible for the human mind to reveal the origin of its concepts, and it frequently finds itself tempted to believe that these concepts [space and time] are drawn from experience and that, owing to their importance, they ap- pear to have a higher rank. As for time, it appears that the following is a fact to our senses: everything that happens is called an event. Physical time, then, is a certain order of these events that seem to be given to our senses in an immediate way. This is Kant’s way of think- ing, and we could say that all those events are such that, taken two at a time, either one is earlier and the other later, or they are simultaneous. It appears to follow from this that time really exists in Nature without any restriction. Why do we believe this? We fix what we see with our senses, which give a temporal order that we apply unambiguously to events. One must distinguish between sensations and events. It is sufficient to say that one immediately believes the temporal order given by the nature of our mind, but it is easy to see that this is not certain. For the physicist it is necessary that there be a means to know whether a state- ment is true or not. Are the twinklings of two stars simultaneous? We don’t know how to proceed to dem- onstrate it, because the fact that a moving observer sees them as simultaneous does not mean anything.” After some reasoning, he poses the following definition: “Two events, for example, two lightning bolts, must be considered simultaneous when an observer located in a system of reference equidistant from the places in which they occur sees them at the same time.” Afterwards he says that there is no simultaneity when one takes another inertial system in uniform motion with respect to the first, that is, simultaneity is not absolute, and, there- fore, it is meaningless if the system it is referred to is not specified. This, together with the relativity of distance, makes us think that the difficulty is not a serious one and that the con- tradiction is only apparent, and can be resolved by attributing to each system a time of its own. This way, four numbers are assigned to each event, defining it with respect to a system k, numbers that will be the three coordinates x, y, z, and time t to the same event in another inertial system four other numbers, and are assigned, and, to complete our study of the phenomenon we must now only establish the relationship that joins the vari- ables x, y, z, t with and It is easy to demonstrate that if we require that the law of constancy of the velocity of light in space be valid in the system k and , the transformation will be univocal and will coincide with the so-called Lorentz transformation. From the study of this transformation we can immediately deduce several physical con- sequences, especially those relative to the behavior of solid bodies and clocks located at rest with respect to system and viewed from k we find that solid bodies undergo a contrac- tion in the direction of their movement, a contraction that increases with velocity, and that clocks are slowed down. This transformation, together with the principle of relativity, provides a means to obtain natural laws. I must note here an interesting analogy with thermodynamics: in it one seeks k′ x′, y′, z′, t′, x′, y′, z′, t′. k′ k′