Two trains are traveling side by side and at the same speed along parallel tracks. We areseated in one of the trains, and with us we have a special speedometer that measures theirrelative speed. Since the trains are traveling at the same speed, their relative speed is zero; thespeedometer therefore reads "0."
Suddenly the other train seems to start pulling ahead of ours. The speedometer shows areading of 10 miles per hour. The other train has apparently increased its speed. But can we beabsolutely certain of this increase?
If your answer is yes, you are wrong. You are wrong because all that we know is that therelative speed between the two trains changed from 0 mph to 10 mph. Nothing more. Thischange could have been brought about in one of two ways:
The other train increased its speed.
Our train decreased its speed.
There are thus two possible explanations to account for the change in speed, but we don'tknow which one is right. Furthermore, regardless of which explanation we choose, the endresult will be the same: the other train will arrive at the station first. So it makes no differencewhether we say that the other train increased its speed or that our train decreased its speed.
Since both explanations lead to the same result, you can choose either one. Whenever twothings are relative, you can choose either one of them. The converse is also true: wheneveryou have a choice between two things that are equally possible, then the things are relative.
There is no reason, except convenience, for choosing one explanation over the other. Therelative speed between the trains remains the same, 10 mph; and the end result will be thesame.
Now let's suppose that both trains are at the railroad station loading and unloading passengersand baggage. A half-hour passes. As we look at the other train through our window, we seethat our train seems to start moving, smoothly and slowly. For a minute or so, our train seemsto travel at a uniform speed. Our special speedometer shows that the relative speed betweenthe two trains is 20 mph. But as we look out our window, we suddenly see the last coach ofthe other train disappear from sight and notice the motionless station behind it. So we are notmoving after all. The other train has been moving!
This peculiar and often frustrating experience is an effect of relative motion. At the train stationwe cannot tell whether it was our train that changed its speed from 0 mph to 20 mph orwhether it was the other train that changed its speed from 0 mph to 20 mph. Only after theother train pulled out of the station could we see that it, and not our train, was moving.
Now let us again raise the question that was raised at the beginning of this article: can we beabsolutely certain that the other train did indeed increase its speed, and in this case pull outof the station?
If your answer is yes, then you are wrong again. All we can be certain of is that the relativespeed between the two trains changed.
These examples illustrate an important principle in the special theory of relativity. If A appearsto be moving at a steady speed relative to B, we cannot know for sure if it is A that is reallymoving. Perhaps A is standing still, and B is moving. Or perhaps both are moving. According torelativity, there is no experiment that can be devised to solve the problem. As there is no wayof deciding which of the two objects is moving, we can choose either one as the moving object.The reason is that their motion is relative, and relativity, as we have seen, means that we havea choice.
This principle - that if two objects are in uniform motion relative to each other, it isimpossible to decide which one is moving and which one is at rest - applies to all objectsmoving uniformly in a straight line through the universe.
In relativity you'll find that whenever you have a choice among things that are equally possible,you are dealing with relative things. For example, time, which is measured with clocks andwatches, is relative because it can be shown that there is more than one system of time. Allsystems of time are equally possible and you can choose any system you with.