Page 14 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 2
terms of time and the speed of light, so it follows automatically that every observer will measure light to have
the same speed (by definition, 1 meter per 0.000000003335640952 second). There is no need to introduce the
idea of an ether, whose presence anyway cannot be detected, as the Michelson-Morley experiment showed.
The theory of relativity does, however, force us to change fundamentally our ideas of space and time. We must
accept that time is not completely separate from and independent of space, but is combined with it to form an
object called space-time.

It is a matter of common experience that one can describe the position of a point in space by three numbers, or
coordinates. For instance, one can say that a point in a room is seven feet from one wall, three feet from
another, and five feet above the floor. Or one could specify that a point was at a certain latitude and longitude
and a certain height above sea level. One is free to use any three suitable coordinates, although they have only
a limited range of validity. One would not specify the position of the moon in terms of miles north and miles
west of Piccadilly Circus and feet above sea level. Instead, one might describe it in terms of distance from the
sun, distance from the plane of the orbits of the planets, and the angle between the line joining the moon to the
sun and the line joining the sun to a nearby star such as Alpha Centauri. Even these coordinates would not be
of much use in describing the position of the sun in our galaxy or the position of our galaxy in the local group of
galaxies. In fact, one may describe the whole universe in terms of a collection of overlapping patches. In each
patch, one can use a different set of three coordinates to specify the position of a point.

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 Figure
2:1.)

file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/a.html (5 of 12) [2/20/2001 3:14:16 AM]