What is a space-time diagram? Roughly speaking, it is a graphic representation of a physical phenomenon, such as motion, in four dimensions. Why four dimensions? Well, because we have three dimensions of space plus one dimension of time. Now, of course, you canít really draw diagrams and pictures in four dimensions. So we usually suppress one or two spatial dimensions, that is, consider an idealized situation of motion along a line or motion on a plane. It is important, however, to always keep a temporal dimension, not to suppress it, because it is the presence of time in these diagrams, along with space, that paves the way to understanding relativity.

Here is a simple example. Suppose you take a trip from your house to a store and back. One way to represent your trip is to sketch a series of purely spatial "snapshots" (courtesy of Peter Bokulich):

Another way is to employ a space-time diagram, as below:

The difference between (a) and (b) is that (a) represents motion "dynamically," by providing a series of pictures as it develops in time, whereas (b) incorporates time "inside" a diagram, makes it part of a representation. This is all very simple but extremely important. In this course, you will learn how to represent various motions in this spatio-temporal fashion. The significance of this procedure lies in the fact (to be dule appreciated by every student of Special Relativity) that our world is a world of space-time, not just a world of space "developing" in time. Time is part of the structure of a certain four-dimensional space called "space-time." All events of the physical world--past, present, and future--are embedded in this four-dimensional space-time. Think of this space-time as a set of points each characterized by four numbers, their coordinates, three spatial and one temporal.

A diagram below represents the following events:

• A: The fall of Constantinople
• B: The accession of Elizabeth I
• C: Columbusí voyage to America in 1492

[Courtesy: Storrs McCall, A Model of the Universe, Oxford, 1994]

Now that you get an idea, try to draw an (x,t) space-time diagram representing (in one dimension, i.e. along the x axis only) the following situation: Car A overtakes and passes car B on a straight highway.