Paradoxes of the theory of relativity
Zeno.s Paradoxes
Suppose the swift Greek warrior Achilles is to run a race with a tortoise. Because the tortoise is the slower of the two, he is allowed to begin at a point some distance ahead. Once the race has started however, Achilles can never overtake his opponent.
For to do so, he must first reach the point from where the tortoise began. But by the time Achilles reaches that point, the tortoise will have advanced further yet. It is obvious, Zeno maintains, that the series is never ending: there will always be some distance, however small, between the two contestants. More specifically, it is impossible for Achilles to preform an infinite number of acts in a finite time.
It is not possible to complete any journey, because in order to do so, you must firstly travel half the distance to your goal, and then half the remaining distance, and again of what remains, and so on. However close you get to the place you want to go, there is always some distance left. Furthermore, it is not even possible to get started.
After all, before the second half of the distance can be travelled, one must cover the first half. But before that distance can be travelled, the first quarter must be completed, and before that can be done, one must traverse the first eight, and so on, and so on to infinitum.
A bouncing ball that reaches three quarters of its former height on each bounce, will bounce an infinite number of times, in the same way that distances and times decrease in the Dichotomy. The only difference is that Whitrow uses a factor of three-quarters where Zeno used one half.
It also doesn.t however matter what fraction is used. The only thing that would change if the balls initial velocity and the distance from the floor of the first bounce remained the same, would be the time in which an infinite numbers of bounces took place.
