Each observer could use radar to say where and when an event took place by sending out a pulse of light or radio waves. Part of the pulse is reflected back at the event and the observer measures the time at which he receives the echo. The time of the event is then said to be the time halfway between when the pulse was sent and the time when the reflection was received back: the distance of the event is half the time taken for this round trip, multiplied by the speed of light. (An event, in this sense, is something that takes place at a single point in space, at a specified point in time.) This idea is shown here, which is an example of a space-time diagram…
Figure 2:1
Using this procedure, observers who are moving relative to each other will assign different times and positions to the same event. No particular observer’s measurements are any more correct than any other observer’s, but all the measurements are related. Any observer can work out precisely what time and position any other observer will assign to an event, provided he knows the other observer’s relative velocity.
Nowadays we use just this method to measure distances precisely, because we can measure time more accurately than length. In effect, the meter is defined to be the distance traveled by light in 0.000000003335640952 second, as measured by a cesium clock. (The reason for that particular number is that it corresponds to the historical definition of the meter – in terms of two marks on a particular platinum bar kept in Paris.) Equally, we can use a more convenient, new unit of length called a light-second. This is simply defined as the distance that light travels in one second. In the theory of relativity, we now define distance in 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.