2,500 years after Zeno of Elea, I came to the same conclusion as he, using the simple tools of logic: movement is impossible. Also, of course it is possible, since I go to work every morning and go home every afternoon, experience shows that there is movement and the world is in constant motion.
The more precise formulation is therefore that according to our experience there is movement, but with our ordinary concepts and the logic we use, it is inexplicable how it is possible and how it works. Something fundamental is missing from what we experience, feel and think about movement, something fundamental without which the whole thing has no meaning.
Towards the end of the working day, I thought it was time to go home, and guided by some inspiration, I formulated this by saying out loud, “Well, let’s port home.” Then, walking on the sidewalk in the rain, I said to myself: “Well, let’s teleport home.” And as I walked, taking one step after another, I imagined myself stepping on the atoms of space, and I realized that I was actually jumping on particles of space, teleporting from one to another in the void between two particles.
Movement is actually teleportation!
Zeno completely revealed all the problems related to movement with only the tools of logic, his paradoxes perfectly show why movement cannot be interpreted with the tools of human logic. And although many people have already tried to present the paradoxes as not real problem, in fact they are still unsolved to this day.
To a first approximation, the movement is simple: given two points in space, the starting point and the end point, and a body, in the simplest case a point of mass, which travels from the starting point to the end point in a finite time. The difficulties begin when we try to imagine the details of this process. The space between the two points can be continuous or made up of discrete points, we cannot currently imagine a third possibility.
Let’s look at the case of continuous space, in this case there is an infinite number of points between the starting point and the end point, which the body passes through during its movement, and which it touches during its movement. Zeno showed that motion is not only not possible, but also cannot begin, we cannot say which point is closest to the starting point, i.e. there is no point next to the starting point. So if we imagine the movement in such a way that the body touches the points between the start and end points in a row, then we are in trouble, since we cannot arrange the points in a row, because there is no point next to a point, no immediate neighbor, even from any point we believe that it is the next point, there will always be another point that is closer to the starting point. In the case of continuous space, we cannot describe the movement locally, i.e. we cannot break down the movement between the start and end points into smaller movements, because while we can identify the start and end points, we cannot identify the points through which the movement passes, we can only say that these points are between the start and end points. No matter how small we choose the distance between the two points, the problem remains the same, regardless of size.
Now let’s imagine that the space is discrete, i.e. there is a finite number of points between the starting point and the end point, we can assign a subsequent point to each point. Let’s now take two adjacent points, let the movement start from one and end at the other. Since the moving body also consists of field quanta, imagine a single field quantum moving between two adjacent field quanta. This takes time, if it didn’t, there would be motion at infinite speed. Moreover, the space quantum must have an extension, otherwise there could be no non-zero distance. But this is an extension in which you can’t move, we either jump through an entire quantum of space, or we stay where we are. And since we cannot be between two space quanta, the jump is momentary, time passes when we are in one space quantum.
On the other hand, the stadium paradox of Zeno clearly shows that discrete space does not solve the problem of movement either. If a body “A” moves to the left relative to “B” by one quantum of space during one quantum of time, and a body “C” moves to the right relative to “B” by the same amount, then “C” is moving to the right relative to “A” by two space quanta in one time quantum, which is impossible. For this reason, time cannot be quantized in the same way as space, and there cannot be a maximum speed, because this speed can always be exceeded due to relative motion.
There are two solutions, one is the special theory of relativity, the other, which I like more, is absolute space-time, because in this case we have to relate all movements to absolute space, and in comparison there can be a limit speed. In this case, however, two bodies can move relative to each other at a speed higher than the limit speed, without exceeding the limit speed in relation to absolute space. However, this is also a rather strange consequence.
So we see that neither the continuous nor the quantum nature of space explains how motion is possible locally. The real solution, therefore, looks like it cannot be grasped locally, but only globally, i.e. with logic alone we reached to the point where quantum mechanics reached with entanglement, the Bell inequality and the Aspect experiment. Reality is non-local.
Even more interesting is Zeno’s paradox of the arrow, where he asks about a flying arrow, how does the arrow actually know, that it flies. After all, at every moment of time it occupies the same part of space as in its state of rest, if we take a snapshot of a flying arrow, it will not differ in any way from a picture taken of a stationary arrow. Our first idea might be that the flying arrow still differs from the stationary arrow in something that we cannot see, but which is actually there in the arrow. It is impulse, which is actually velocity. The only problem with this is that the speed cannot be a property of the arrow, because the relative speed of two arrows flying in the same direction with the same speed relative to the surface is zero! So the two arrows cannot carry the velocity property, since each body moving in relation to them should show different information, for example exactly zero in relation to each other. And here the absolute movement arises again, because then each body carries with it the information of its speed relative to absolute space, and this information can be modified locally by movement relative to each other.
In relation to relative motion, it is not really the impulse that is interesting, but the kinetic energy. We would think that kinetic energy is the property of the moving body, but we can immediately understand that this is not the case if we examine the behavior of colliding bodies moving in different directions relative to each other. Two bodies colliding against each other can release enormous energy during the collision, while moving in the same direction at the same speed, they don’t even collide. How can the magnitude of the collision energy be so different, if kinetic energy is a property of moving bodies? We can say that the impulse is a vector quantity, so the direction is important, but the kinetic energy is a scalar, it has no direction. It seems that macroscopically and locally the movement cannot be explained in any way. We need quantum mechanics with its probability wave or guiding wave, we need the collapse of the wave function, irreversibility. And it is also necessary that the wave function extends to the entire Universe. And when the guiding wave collapses, teleportation actually takes place, the moving particle manifests at a single point, so that a moment later the guiding wave spreads out again to feel where and when the next collapse will occur. So there is no particle migrating from point to point, but a particle that disappears and reappears elsewhere and at a different time, which keeps the information about its movement in the global guiding wave, the relative movement is actually the interaction of the guiding waves.
Actually, we didn’t get very far. We are in the same place as Zeno, we can neither imagine nor explain the movement with our ordinary concepts. So here is something ordinary, which is locally inexplicable for now. Something that is, but that could not be. We cannot explain even the simplest phenomena in the world. We all move in space, but very few of us think about how it is possible, how it happens.
And at this moment, I don’t know of anyone who really understands what movement is.
English translation: Nyíregyháza, November 29, 2023