Page 15 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 2

Figure 2:2

For example, in Figure 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 Figure 2:3.

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