L E C T U R E S A T U N I V E R S I T Y O F B U E N O S A I R E S 9 4 5 ometry into an objective science, into a branch of physics, and we might then ask and de- termine if the laws of that geometry, thus interpreted, correspond to real objects. Let us now consider time. In classical science the simultaneity of two events is an abso- lute fact that does not depend at all on the observer regarding it. The simultaneity that is mentally attributed to two events lacks meaning for the outside world. In that world we can establish simultaneity only through physical measurement. Let’s see how this is possible. The occurrence of events at any point A can be recorded by placing a clock at that point and noting the positions of the hands in the instants during which they occur. Another observer can do the same at another point, B and so on in other places. One would then have records corresponding to the different sites, but no correspondence between the instants when the occurrences took place at those points. The problem is reduced to determining how it is pos- sible to arrive at an understanding of the simultaneity of any two of them. In this way, one might establish a correspondence between the times observed at A and those observed at B. Thus one would have a single time “in each system.” There is only one way—he said—to resolve that problem and it is by taking advantage of any physical phenomenon that is propagated from one point to another. It doesn’t neces- sarily have to be light, but we tend to fall back on that because, apart from the ease with which we can do so, it is in the study of its phenomena where we have found difficulties. We could, for example, recognize the simultaneity of events that take place at A and at B by placing ourselves at midpoint on the line that connects them and observing them by using mirrors from there. Here the hypothesis that light takes the same amount of time to cover distances between the midpoint and those two locations is introduced. Thus we could syn- chronize the clocks placed at those points and successively at other locations. In that way we could have a definition of time, he continued, with respect to a system, that system in relation to which the clocks are at rest. It is uncertain a priori that this defi- nition could be adapted to another system that moves relative to it. That is, it is possible for an observer, moving at a certain velocity, to pass through the midpoint between A and B at the moment when he sees two occurrences taking place, not to see them, like this one, si- multaneously. This means presupposing the possibility of relative time. The same thing happens with distances. The length of a train car in motion can be measured practically by an observer riding inside, in the ordinary way: by determining how many times and fractions thereof a ruler can fit in it. But how could its length be measured from outside, from the rails? In this one way alone: by placing observers at rest along the rails, provided with clocks that have been synchronized in the aforementioned manner, and by making them mark the positions occupied by its extremes at a given moment. It would then suffice to measure, with a ruler identical to the one used before, the distance between those marks. With this way of mea- suring, though, time intervenes, and a priori one must accept the possibility that the length determined might be different from that obtained through the first measurement. This is a probable hypothesis. In order to find the relationships that connect distances and times measured by an ob- server and those accessible to another observer that moves relative to the first, assuming the