Paradoxes of movement

Movement of the body - what could be easier? But what is the physical meaning of the word "moves"? It seems that everything is obvious - the body at a certain point in time is in one place and the same moment of time leaves this place and is transferred to another. Are not the paradoxes of movement hidden in such an explanation?

Are not the paradoxes of movement hidden in such an explanation?

The concept of movement was also considered by ancient Greek thinkers. And they pointed out the ambiguity of his explanation. For the first time on the paradoxes of the movement, the ancient Greek philosopher Zenon of Eleus, who lived in the 5th century BC, pointed out in his famous aporias. On the motion he wrote four aporias - "Dichotomy", "Achilles and Turtle", "Arrow", "Stages".

The most famous aporia is Achilles and the Turtle. It says that the famous hero of the war between Greece and Troy will never be able to catch up with the turtle. The course of thought was as follows. Let Achilles be at a certain distance from the turtle. While he runs through it, the turtle will creep forward a little more. Further he must run this distance. But the turtle will again creep forward a little. And so on ad infinitum. In addition, the fact that Achilles can not catch up with the turtle is indicated by the aporia "Dichotomy". After all, he first needs to travel half the distance to the turtle, and before that - half the distance, and so on to infinity.

Such paradoxes lead to one conclusion - there is no movement! But in fact it is a really existing fact and can not be described from the standpoint of infinite length, infinite time, infinite divisibility. And here more than two and a half millennia attempts are made to explain the paradoxes of movement on the basis of logic, physics, mathematics. These issues were dedicated to their works by more than one generation of scientists - from Democritus and Aristotle, to modern philosophers.

Which of us could not bring an obvious experimental fact - a rapidly running person is catching up slowly with a runner. But evidence is not a proof of truth. For example, the Sun rises in the east, and sets in the west, but our planet moves around the Sun, and not, as it seems - obviously, the Sun around the Earth. And in general - if everything was obvious, then a scientific search would not be necessary.

Let us still introduce some physical parameters to explain the paradoxes of motion, for example, in describing the movements of Achilles and the tortoise. Let Achilles be at a distance l from the turtle and run at a speed V, and it creeps at a speed V1. We'll try to find the time for which he will catch up with her. Achilles in time t1 = l/V runs through the distance that separates him from the turtle. It will creep within this time the distance V1t1. This distance will run through the time t2 = V1l/V2, and it will creep further V12l/V2, which he will run during the time t2 = V12l/V3, and so on. Summarizing all the intervals, you can find the time for which Achilles will catch up with the turtle. It turns out that this will be a geometric progression whose sum of terms is equal to t = l/(V - V1). Thus, the introduction of the concept of velocity makes it possible to solve mathematically the paradoxes of motion.

True, it should be taken into account that the refutation of the conclusions of aporias is possible only if we take into account the fact that our calculations are based on the correct assumption. In other words - that our logic is true. And here again we come to the paradoxes of the movement. From Zeno's aporias one can see a very difficult question: how much infinitely can we separate and reduce the distance and intervals of time. And, as it turns out, this issue is not solved in the modern science of the microworld. Modern physics to overcome difficulties in explaining the motion of elementary particles offers the idea of quantization of space, that is, proposes to introduce the concept of elementary length, which is not further divided. In addition to this idea, there is the idea of the regenerative motion of elementary particles, according to which elementary particles move in space, disappearing at one point and arising in the other. This process is explained on the basis of the properties of the physical vacuum. So quantum teleportation is a scientific theory, not fiction.

Thus, after examining seemingly obvious paradoxes of the movement outlined in Zeno's aporias, we came to the conclusion that not everything is so unambiguous and obvious in our world, as it seems to us. And the concept of motion, especially of elementary particles, is extremely complex and to this day is not fully understoo.

Tools