Events and Space-Time: The Basic Building Blocks

The notion of an event is the basic building block of the theory. It will dominate all that follows.

By an event we mean an idealized occurrence in the physical world having extension in neither space nor time. For example, "the explosion of a firecracker" or "the snapping of one's fingers" would represent an event. (By contrast, "a particle" would not represent an event, for it has "extension in time"; "a long piece of rope" has "extension in space.") By "occurrence in the physical world" we mean that an event is to be regarded as a part of the world in which we live, not as a construct in some theory. Of course, there are many events around: some occurred long ago, some are occurring now, and others will (presumably) occur in the future. What is meant by "idealized ... having extension in neither space nor time" requires more explanation. Consider the explosion of a firecracker. The explosion lasts for some finite time (say, one-tenth of a second), and so this occurrence has extension in time; the explosion takes place over some finite region of space (say, one-quarter of an inch), so it has extension in space. If, however, we used a smaller and faster-burning firecracker, these "extensions" would be smaller. An event is to be an idealization of this situation in the limit of a "very small, very fast-burning" firecracker. (The situation is similar to that which would arise from the statement: "A point on the blackboard is an idealized chalk mark having extension neither up-down nor right-left." This analogy goes a little deeper: events will shortly become "points" of an appropriate space.)

We regard two events as being "the same" if they coincide, that is, if they "occur at the same place at the same time." That is to say, we are not now concerned with how an event is marked — by firecracker or finger-snap — but only with the thing itself.

Is one to regard events as "existing" even if there is nobody there to mark them with finger-snap or otherwise (for example, in a dark, empty closet at 3 A.M.)? It is part of what we wish to mean by an event that the answer is to be yes. Perhaps it would have been better to say originally "An event is an idealized potential occurrence...." As a general rule, failure in physics to attribute "existence" to things not directly perceived leads to various difficulties of the "If a tree falls in the forest and nobody is there to hear it, does it still make a sound?" variety. Failure to do so in the present case would, as far as I can see, make further development of the theory virtually impossible. This is not to say that such questions are uninteresting or unimportant. Rather, it has become the custom in physics to relegate them to others by the practice of being liberal in bestowing "existence."

Are events real? What are they really like? These questions are dealt with (more accurately, avoided) by means of another custom. Physics does not, at least in my opinion, deal with what is "real" or with what something is "really like." The reason, I suppose, is some combination of (1) One does not know how to effectively attack such questions. (2) One does not know what sort of thing would represent an answer. (3) These questions are too hard. In any case, one conventionally deals with relationships between things which one does not (or perhaps cannot) understand on a deeper level. One does, of course, sometimes come to understand some basic concept more deeply. (For example, space and time were basic concepts in Newtonian gravitation. With general relativity, one does feel a sense of deeper understanding.) Perhaps it is true to say that one has found from experience that deeper insight into the basic concepts of a theory comes most often, not from a frontal attack on those concepts, but rather from working upward into the theory itself.

Relationships between events — that is what we are after. Virtually everything we say hereafter can be resolved, directly or indirectly, into some statement of such a relationship.

We wish to discover the "correct" theory of the relationship between events. It is instructive to arrive at the final theory indirectly, through a sequence of preliminary attempts. We begin then with the rather naive view of everyday experience, a view which will subsequently be found to be inappropriate.

According to the Aristotelian view, an event is naturally characterized by giving its position in space together with the time of its occurrence.

We can make this view more explicit. Let there be set up, within a room, a Cartesian coordinate system x, y, z. That is to say, each position in space is to be described by three real numbers: the value of x, the value of y, and the value of z. For example, the "value of x" might be the distance of that position from one side wall, the "value of y" the distance from the front wall, and the "value of z" the distance from the floor. Our coordinate system permits, then, "numerical location of positions." The position described by x = 12, y = 3, z = 9 is that located 12 feet from the side wall, 3 feet from the front wall, and 9 feet from the floor. Now let the room be filled solidly — wall to wall, floor to ceiling — with people. Each person always maintains his same position within the room. Each person can describe his fixed position, then, by giving the appropriate values of x, y, and z. Let those values be printed on a small badge which each person wears. Next let there be distributed, to each of our subjects, an accurate watch. These watches are all synchronized (for example, by having another person communicate with each person and compare his watch with theirs).

Imagine, then, the arrangement sketched above. We use this arrangement to characterize events as follows. Let some event be chosen, marked, say, by the explosion of a firecracker. Since our subjects are packed solidly, one of them will be in the immediate vicinity of the explosion. Let that person write on a slip of paper the three numbers (x, y, and z values) which appear on his badge, and also a fourth number, the time, according to his watch, at which the explosion was experienced. This slip of paper is then passed forward to a moderator desirous of knowing our characterization of this particular event.

Of what does our characterization consist? Of four numbers, the values of x, y, z, and t (time). The first three numbers give the "position of the event in space"; the fourth gives the "time of its occurrence." We are here characterizing events, then, according to the Aristotelian view.

Why did we go on and on, taking the trouble to be so explicit and so careful about such a simple idea? There are several reasons. The characterization of physical...