пятница, 15 июня 2012 г.

THE PARADOX OF ZENON ABOUT AHILL AND THE SPECIAL THEORY OF RELATIVITY (fragment)




In the article the explanation of Zenon’s paradox about Ahill and is offered to a turtle, without connection with the representation of infinite number of pieces. And the analogy between this paradox and some positions of the special theory of relativity is shown, too.






We shall consider the paradox of Zenon about Ahill and a turtle. Ahill can easily get to the point, where was a turtle, but for this time it will move to another point. So it can proceed infinitely long and Ahill will never catch up a reptile.
The majority of people see in this paradox only an artful focus because the runner will easily catch up and overtake the sluggish rival. It is considered to be an error conclusion about unattainability of a turtle is caused by absence of knowledge of operations with infinitesimal sizes. Thus one can argue as follows: each piece on which Ahill catches up a turtle less than the previous, therefore its length comes to zero, but the sum of these infinitesimal pieces will be equal to any final distance. However we shall consider the last infinitesimal piece on which Ahill should overtake a turtle. As though it would be small, it is necessary to spend certain time for which the turtle all the same will creep any distance for its passage. And so on each piece it will not depend on its length. That is the reference to infinitesimal sizes does not allow to solve the given paradox.
Let's imagine the artist who aspires to draw continuously varying landscape. At first he looks at a landscape surrounding it, then addresses to an easel and embodies the seen. But, when he compares the drawn with the nature, it appears that the landscape has changed. He takes again a brush and a paint in hands and so he can repeat infinitely. He will never achieve the exact similarity because of variability of the object of the image. Ahill behaves in similar way. He looks where there is a turtle at present and aspires to this point. Having reached it he is convinced that the reptile has crept in another point, and so it will be indefinitely. That is impossible to overtake the object if you do not know where he will be in future, or you behave so as if you do not know this.

If Ahill has no no assumptions of how the turtle will move, he will have to act according to the algoritm offered in paradox, and it will never be caught up. Besides, the turtle can really move in an unpredictable way. It can disappear in one point and unexpectedly appear in another. In this case, even if the speed of a turtle will be insignificant, Ahill will not be able to catch up with it. He can appear only in those points where she was before. If the object of prosecution moves vaguely, it is only possible to overtake it casually.
The most surprising is that Ahill, following the given algoritm of prosecution of a turtle, does not change the speed. That is for the detached onlooker the turtle moves quite definitely and the speed of Ahill's movement decreases to the speed of this reptile. But for the runner himself the movement of a turtle is unpredictable, and its own speed remains the former. It is possible to say that from the point of view of the detached onlooker Ahill's time began to go more slowly. The analogy to the theory of a relativity is obvious. The more is the speed of the "cosmonaut" to the speed of light, the less is his own time.

Let's assume that the movement of a turtle consists of a set of chaotic micro-movements in different directions and with different speed. However, summing up, they form the movement with constant speed and in certain direction. The detached onlooker is not able to distinguish fine and uncertain movements of a turtle, he considers, that it moves rectilinearly and in regular intervals. Therefore the observer does not see the reasons for which it is impossible to catch up and overtake a reptile. Ahill tries to catch up with a turtle at a microlevel. For him it is imperceptible and unpredictable, therefore he cannot catch up with it. If one continues the analogy of the special theory of relativity at a macrolevel, the speed of light is constant, and the direction is definite. Therefore we do not see the reasons for which it would be impossible to exceed this speed and to "overtake" a ray of light. But physics is caused by the processes occurring at a microlevel. And the movement of light is unpredictable at a microlevel. Mayby therefore this speed is unattainable for material bodies? Probably the weight is a unit of definiteness, and a particle of light of zero weight at rest possess the maximal uncertainty that makes them inaccessible, as the turtle is inaccessible for Ahill.

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