A brief history of time - Stephen Hawking [12]
An event is something that happens at a particular point in space and at a particular time. So one can specify it by four numbers or coordinates. Again, the choice of coordinates is arbitrary; one can use any three well-defined spatial coordinates and any measure of time. In relativity, there is no real distinction between the space and time coordinates, just as there is no real difference between any two space coordinates. One could choose a new set of coordinates in which, say, the first space coordinate was a combination of the old first and second space coordinates. For instance, instead of measuring the position of a point on the earth in miles north of Piccadilly and miles west of Piccadilly, one could use miles northeast of Piccadilly, and miles north-west of Piccadilly. Similarly, in relativity, one could use a new time coordinate that was the old time (in seconds) plus the distance (in light-seconds) north of Piccadilly.
It is often helpful to think of the four coordinates of an event as specifying its position in a four-dimensional space called space-time. It is impossible to imagine a four-dimensional space. I personally find it hard enough to visualize three-dimensional space! However, it is easy to draw diagrams of two-dimensional spaces, such as the surface of the earth. (The surface of the earth is two-dimensional because the position of a point can be specified by two coordinates, latitude and longitude.) I shall generally use diagrams in which time increases upward and one of the spatial dimensions is shown horizontally. The other two spatial dimensions are ignored or, sometimes, one of them is indicated by perspective. (These are called space-time diagrams, like Fig. 2.1.) For example, in Fig. 2.2 time is measured upward in years and the distance along the line from the sun to Alpha Centauri is measured horizontally in miles. The paths of the sun and of Alpha Centauri through space-time are shown as the vertical lines on the left and right of the diagram. A ray of light from the sun follows the diagonal line, and takes four years to get from the sun to Alpha Centauri.
As we have seen, Maxwell’s equations predicted that the speed of light should be the same whatever the speed of the source, and this has been confirmed by accurate measurements. It follows from this that if a pulse of light is emitted at a particular time at a particular point in space, then as time goes on it will spread out as a sphere of light whose size and position are independent of the speed of the source. After one millionth of a second the light will have spread out to form a sphere with a radius of 300 meters; after two millionths of a second, the radius will be 600 meters; and so on. It will be like the ripples that spread out on the surface of a pond when a stone is thrown in. The ripples spread out as a circle that gets bigger as time goes on. If one stacks snapshots of the ripples at different times one above the other, the expanding circle of ripples will mark out a cone whose tip is at the place and time at which the stone hit the water (Fig. 2.3). Similarly, the light spreading out from an event forms a (three-dimensional) cone in (the four-dimensional) space-time. This cone is called the future light cone of the event. In the same way we can draw another cone, called the past light cone, which is the set of events from which a pulse of light is able to reach the given event (Fig. 2.4).
Given an event P, one can divide the other events in the universe into three classes. Those events that can be reached from the event P by a particle or wave traveling at or below the speed of light are said to be in the future of P. They will lie within or on the expanding sphere of light emitted from the event P. Thus they will lie within or on the future light cone of P in the space-time diagram.