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Dipping creation is a fantastic element of paradox. How to travel in time: all the methods and paradoxes. Kant's understanding of space and time

Dipping creation is a fantastic element of paradox. How to travel in time: all the methods and paradoxes. Kant's understanding of space and time

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Article topic:	Time paradox
Rubric (thematic category)	Philosophy

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Space-time theory of relativity

Kant's understanding of space and time

The problem of the infinity of the world

The problem of the infinity of the world is connected with discussions about space (even the expression arose: horror infinity(lat.) - horror of the infinite).

The world either has boundaries or not, that is, it is infinite.

But accepting either of the two possible answers is impossible. Just as it is impossible to imagine an infinite space, it is also impossible to imagine a limited universe, the question arises: what is beyond this boundary? In the latter case, if there is something beyond the border, then this something must be included by us within the boundaries of the world, which means that if we pointed to the border separating something from something, then we did not indicate the border of the world, but only the border of some of its parts. Beyond the borders of the world the world must end - there must be nothing.

So, it is impossible to imagine the infinity of space and it is impossible to imagine nothingness. Dead end

While most philosophers tried to understand time and space as something external to man, Immanuel Kant believed that space and time do not exist independently of man, but are our forms of perception of the world. In other words, space and time do not belong to the world, but belong to man.

“...space is nothing more than the form of all external phenomena, in which alone objects of sense are given to us.” (I. Kant. Prolegomena to any future metaphysics).

Time “is not inherent in the objects themselves, but only in the subject who contemplates them.” (I. Kant. Critique of Pure Reason).

In the theory of relativity, time and space are considered inseparable from each other and form the so-called four-dimensional space-time.

To describe the so-called events four coordinates are used.

One of the recognized philosopher-geniuses of the 20th century, Ludwig Wittgenstein, believed that philosophical problems are riddles generated by the use of words (language).

ʼʼThis kind of error is repeated again and again in philosophy; for example, when we are puzzled by the nature of time, when time seems to us mysterious thing. We have a strong tendency to think that there is something hidden here, something that we can see from the outside, but which we cannot see inside. In reality there is nothing like it. We want to learn not new facts about time. All the facts that interest us are open to our attention. But we are misled by the use of the noun “time” (Wittgenstein L. The Blue Book).

Consider, as an example, the question: “What is time?”, as asked by St. Augustine and others. At first glance, this is a question about definition, but then the question immediately arises: “What will we achieve with a definition, since it will only lead us to other undefined terms?” And why should one be confused by the lack of a definition of time, rather than the lack of, say, a “chair”? Why shouldn't we be confused in all cases where we cannot give a definition? So, the definition often makes it clear grammar words. In fact, it is the grammar of the word “time” that confuses us. We are simply expressing this confusion by asking a slightly misleading question - the question "What is...? "...

St. Augustine was confused by the following “contradiction” in his discussions of time: How is it possible to measure time? For the past cannot be measured because it has already passed; the future cannot be measured because it has not yet arrived. The present should not be measured, since it has no extension.

The contradiction that seems to arise here is what might be called a conflict between two different uses of the word, in in this case the words ʼʼmeasureʼʼ. We can say that Augustine reflects on the process of measurement lengths: say, the distance between two marks on a conveyor belt, the belt of which moves in front of us, and we can only see a small part of it (present tense). The solution to this puzzle will be to compare what we mean by ʼʼmeasurementʼʼ (the grammar of the word ʼʼmeasurementʼʼ) applied to distance on a conveyor belt with the grammar of the word applied to timeʼʼ (Ibid.).

Here Wittgenstein does not give a detailed explanation of how he himself solves the paradox of time, but only indicates the method of solution.

He offers the example of a conveyor belt.

We see only a small piece (representing the present time), which is very small and moves - we cannot measure it (we do not have time). How to take a measurement? Accordingly, Augustine believes that time also eludes us. (True, in the time of Augustine there were no conveyor belts).

But Wittgenstein calls us to pay attention to the grammar of the word ʼʼmeasurementʼʼ (its use in language) applied to time. In other words, pay attention to how we measure time, implying that it is done differently, in life we do not have mysterious problems with measuring time.

Discussing the problematic and “almost mystical” aspect of the ideas of past, future and present, Wittgenstein says:

“What this aspect is and how it happens that it arises can be illustrated by the classic question: “Where does the present go when it becomes the past, and where is the past?” Under what circumstances does this question seem attractive to us? For under certain circumstances it does not seem so, and we eliminate it as meaningless.

It is clear that this question arises most easily in cases where things float past us - for example, logs floating down a river. In this case, we can say that the logs that passed by us are located at the bottom left, and the logs that will pass by us are at the top right. We then use this situation as a comparison for everything that happens in time, and even embody this comparison in our language when we say that “the present event is passing” (the log is passing), “the future event is about to come” (the log is to come). We are talking about the flow of events; but also about the passage of time - the river along which the log moves.

Here is one of the richest sources of philosophical confusion: we are talking about the future event of something appearing in my room, as well as the future occurrence of that event.

We are speaking Something will happen, as well as: “Something is approaching me”; we indicate the log as “something”, but also the approach of the log to me.

It may happen that we will not be able to get rid of the consequences of our symbolism, which seems to admit of questions like: “Where does the flame of a candle go when it is extinguished?”, “Where does the light go?”, “Where does the past go?” Our symbolism begins to haunt us. - We can say that we are led to confusion by an analogy that irresistibly pulls us along. - This also happens when the meaning of the word “now” appears to us in a mystical light (Wittgenstein L. The Brown Book).

Time paradox - concept and types. Classification and features of the category "Time Paradox" 2017, 2018.

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One of the topics of long-term debate is the possibility of travel in space and time. This is a tempting and beautiful theory about the possibility of changing your past, looking into the future, finding out what you did wrong in the past and correcting it again... looking into the future again, finding out the mistake of the past...

A strong psychological basis for the dream of almost every person is the opportunity to return to the past of one’s life and correct something there for the better. Of course, it would be a sin not to take advantage of the opportunities and not to look into the future - to find out how the descendants settled there, what they achieved and whether they completely destroyed this world.

It is difficult to say how serious the proposal to build a working time machine device may be. Currently, there is not even a hypothetical technology for how a time machine mechanism could be constructed. And except for science fiction writers, no one else knows how the distortion of the structure of space will occur.

Time paradoxes.

At the same time, the time machine, generated by science fiction writers - but not yet born by science - has already given rise to a lot of hypotheses about time paradoxes, including in the scientific community. Writer Ray Bradbury spoke about one of the popular and subsequently filmed hypotheses, promulgating the theory of a crushed butterfly in the past, and how it ends for the whole world in the present.

However, it is not a fact that events can develop according to the option predicted by Bradbury. Let's say the Universe can be imagined as a certain system of equations, which already includes the possibility of traveling in space and time. Also, based on this, it is not difficult to conclude something else - a crushed butterfly will remain just a crushed butterfly and nothing more.

And even if you carry it on the sole of a shoe after a hundred thousand years, it will not break the chain of entropy, and in no way will it destroy the processes of the universe. Since the probability of this is already included at the level of error in the equation of events, during time travel through several measurement systems.

Science does not deny the possibility of time travel, however, it is sure that if it is still possible to get to the future, then it is impossible to travel to the past, this is anti-scientific. However, there are many options for the development of time paradoxes, of course, except for a time traveler, no one can say which of them is correct.

Traveling into the past is impossible, so paradoxes are not worth a damn; Professor Stephen Hawking speaks about the impossibility of this kind of travel.

If time travel to the past is possible, it is travel to alternatively evolving realities. And then, this is the structure of the Universe already known to us, where no solutions to probabilities cause paradoxes - that is, actions committed by someone in the past will not cause any disturbances in reality, and accordingly the probability of a paradox will be zero.

Protecting the Universe from fools.

No matter what efforts the traveler made in the past to change his present reality of his time, everything will be meaningless. It is likely that a distortion of reality around an object plunged into the past will still occur. But reality, distorted by the presence of the traveler and his actions, will be distorted only in the “cloud” of time surrounding him.

For example: having accidentally led to the death of your grandfather in the past (they were run over by a car, or killed because of their grandmother in a duel), nothing will happen to the descendants of the deceased, and they will not disappear. Since the change will occur locally, in the very cloud of entropy created around the traveler, which represents a kind of protection of the Universe from the “fool”.

The universe's mockery is not your grandfather.

If the example with the butterfly and grandfather, although banal, is quite indicative of how a local field (cloud) of entropy can work around a time traveler into the past, and thereby respond to the tasks created by him of changing the future reality - then that’s not all.

For example, how will the protection mechanism work if: a traveler from the future to the past performs a simple action, opens a deposit on behalf of his grandfather for his grandson - the sly man himself has not yet been born, so he will have to persuade the grandfather. However, what path will the situation take?

The past is unchanged and the contribution will never exist,

Or will it be the universe's mockery? solve your problems with its help, the grandfather will suddenly turn out to be someone else’s grandfather, and the investment will go into other hands.

Perhaps the most correct thought that reflects the attitude to the problem of a time machine as a device is that such a device is not even worth generating time paradoxes because of it. And moreover, from the point of view of entropy and the Universe, in order not to create problems of interference in destinies, it would be best not to allow the existence of a time machine at all.

look at essays similar to "Time Paradox"

Plan
Introduction 2
1. Problem of becoming 3
2. Rebirth of the Time Paradox 3
3. Basic problems and concepts of the time paradox 5
4. Classical dynamics and chaos 6

4.1 KAM theory 6

4.2. Large Poincaré systems 8
5. Solution to the time paradox 9

5.1.Laws of chaos 9

5.2.Quantum chaos 10

5.3.Chaos and the laws of physics 13
6. The theory of unstable dynamic systems - the basis of cosmology 14
7. Prospects for nonequilibrium physics 16
Conclusion 19

Introduction

Space and time are the main forms of existence of matter. There is no space and time separated from matter, from material processes. Space and time outside of matter are nothing more than an empty abstraction.

In the interpretation of Ilya Romanovich Prigogine and Isabella Stengers, time is a fundamental dimension of our existence.

Most important issue The topic of my essay is the problem of the laws of nature. This problem is “brought to the fore by the paradox of time.” The authors' justification for this problem is that people are so accustomed to the concept of "law of nature" that it is taken for granted. Although in other views of the world such a concept of “laws of nature” is absent. According to Aristotle, living beings are not subject to any laws. Their activities are determined by their own autonomous reasons. Every being strives to achieve its own truth. In China, the dominant view was about the spontaneous harmony of the cosmos, a kind of statistical equilibrium linking nature, society and the heavens together.

The motivation for the authors to consider the issue of the time paradox was the fact that the time paradox does not exist in itself; two other paradoxes are closely related to it: the “quantum paradox”, the “cosmological paradox” and the concept of chaos, which ultimately can lead to to solving the time paradox.

1. The problem of becoming

Attention was drawn to the formation of the paradox of time simultaneously from the natural science and philosophical points of view in late XIX century. In the works of philosopher Henri Bergson, time plays a major role in judging the interactions between man and nature, as well as the limits of science. For the Viennese physicist Ludwig Boltzmann, introducing time into physics as a concept associated with evolution was the goal of his entire life.

In Henri Bergson's work “Creative Evolution,” the idea was expressed that science developed successfully only in those cases when it was able to reduce the processes occurring in nature to monotonous repetition, which can be illustrated by the deterministic laws of nature. But whenever science tried to describe the creative power of time, the emergence of something new, it inevitably failed.

Bergson's conclusions were perceived as an attack on science.

One of the goals that Bergson pursued when writing his work
"Creative evolution" was "the intention of showing that the whole is of the same nature as myself."

Most scientists currently do not believe, unlike
Bergson that to understand creative activity we need a “different” science.

Order Out of Chaos was a history of 19th century physics centered on the problem of time. Thus, in the second half of the 19th century, two concepts of time arose corresponding to opposite pictures physical world, one of them goes back to dynamics, the other to thermodynamics.

2. Revival of the time paradox

The last decade of the 20th century witnessed the revival of the time paradox. Most of the problems discussed by Newton and Leibniz are still relevant. In particular, the problem of novelty. Jacques Monod was the first to draw attention to the conflict between the concept of natural laws that ignore evolution and the creation of new things.

In reality, the scope of the problem is even wider. The very existence of our universe defies the second law of thermodynamics.

Like the origin of life for Jacques Monod, the birth of the universe is perceived by Asimov as an everyday event.

The laws of nature are no longer opposed to the idea of the truth of evolution, which includes innovations that are scientifically defined by three minimum requirements.

The first requirement is irreversibility, expressed in breaking the symmetry between past and future. But this is not enough. If we consider a pendulum whose oscillations are gradually fading or the Moon, whose period of rotation around own axis are increasingly decreasing. Another example could be chemical reaction, the speed of which becomes zero before reaching equilibrium. Such situations do not correspond to truly evolutionary processes.

The second requirement is the need to introduce the concept of event. By their definition, events cannot be derived from a deterministic law, be it time-reversible or irreversible: an event, no matter how it is interpreted, means that what happens does not necessarily have to happen.
Therefore, at best one can hope to describe the event in terms of probabilities.

This leads to the third requirement that must be introduced.
Some events must have the ability to change the course of evolution, i.e. evolution must not be stable, i.e. characterized by a mechanism capable of making certain events the starting point of a new development.

Darwin's theory of evolution serves as an excellent illustration of all three requirements formulated above. Irreversibility is obvious: it exists at all levels from new ecological niches, which in turn open up new possibilities for biological evolution. Darwin's theory was supposed to explain the amazing event - the emergence of species, but Darwin described this event as the result complex processes.

The Darwinian approach provides only a model. But every evolutionary model must contain the irreversibility of events and the possibility for some events to become the starting point for a new order.

In contrast to the Darwinian approach, thermodynamics of the 19th century focuses on equilibrium that meets only the first requirement, because it expresses the non-symmetrical relationship between past and future.

However, thermodynamics has undergone significant changes over the past 20 years. The second law of thermodynamics is no longer limited to describing the equalization of differences that accompanies the approach to equilibrium.

3. Basic problems and concepts of the time paradox

The time paradox "poses before us the problem of the laws of nature."
This problem requires more detailed consideration. According to Aristotle, living beings are not subject to any laws. Their activities are determined by their own autonomous internal reasons. Every being strives to achieve its own truth. In China, the dominant view was about the spontaneous harmony of the cosmos, a kind of statistical equilibrium linking nature, society and the heavens together.

Christian ideas about God as setting laws for all living things also played an important role.

For God, everything is a given. Newness, choice or spontaneous actions are relative from a human point of view. Such theological views seemed to be fully supported by the discovery of dynamic laws of motion.
Theology and science have reached agreement.

The concept of chaos is introduced because chaos allows the paradox of time to be resolved and leads to the inclusion of the arrow of time in the fundamental dynamic description. But chaos does something more. It brings probability into classical dynamics.

The time paradox does not exist by itself. Two other paradoxes are closely related to it: the “quantum paradox” and the “cosmological paradox.”

There is a close analogy between the time paradox and the quantum paradox. The essence of the quantum paradox is that the observer and the observations he makes are responsible for the collapse.
Therefore, the analogy between the two paradoxes is that man is responsible for all the features associated with becoming and events in our physical description.

Now, we should note the third paradox - the cosmological paradox.
Modern cosmology ascribes age to our universe. The universe was born as a result big bang about 15mld. years ago. Clearly this was an event. But events are not included in the traditional formulation of the concepts of natural laws. This brought physics to the brink of its greatest crisis.
Hawking wrote about the Universe this way: “...it just has to be, that’s all!”

4. Classical dynamics and chaos

4.1 KAM theory

With the advent of Kolmogorov's work, continued by Arnold and Moser - the so-called KAM theory - the problem of integrability was no longer considered as a manifestation of nature's resistance to progress, but began to be considered as a new starting point for the further development of dynamics.

KAM theory considers the influence of resonances on trajectories. It should be noted that the simple case of a harmonic oscillator with a constant frequency independent of the action variable J is an exception: the frequencies depend on the values accepted by the action variables J. At different points in the phase space, the phases are different. This leads to the fact that at some points of the phase space of a dynamic system there is resonance, while at other points there is no resonance. As is known, resonances correspond to rational relationships between frequencies. The classical result of number theory comes down to the statement that the measure rational numbers compared to measure irrational numbers equal to zero. This means that resonances are rare: most points in phase space non-resonant. Moreover, in the absence of disturbances, resonances lead to periodic motion (so-called resonant tori), whereas in the general case we have quasiperiodic motion (non-resonant tori).
We can say briefly: periodic movements are not the rule, but the exception.

Thus, we have the right to expect that with the introduction of perturbations, the nature of the motion on the resonant tori will change sharply (according to Poincaré’s theorem), while the quasiperiodic motion will change insignificantly, at least for a small perturbation parameter (KAM theory requires additional conditions, which we will not consider here). The main result of the KAM theory is that we now have two completely various types trajectories: slightly changed quasiperiodic trajectories and stochastic j trajectories that arose during the destruction of resonant tori.

The most important result of the KAM theory - the appearance of stochastic trajectories - is confirmed by numerical experiments. Let's consider a system with two degrees of freedom. Its phase space contains two coordinates q1, q2 and two momenta p1, p2. The calculations are carried out at a given energy value H(q1,q2,p1,p2), and therefore only three independent variables remain. To avoid constructing trajectories in three-dimensional space, we agree to consider only the intersection of trajectories with the plane q2p2.
To further simplify the picture, we will construct only half of these intersections, namely, take into account only those points at which the trajectory
“pierces” the section plane from bottom to top. I have also used this technique
Poincaré, and it is called the Poincaré section (or Poincaré map). The Poincaré section clearly shows the qualitative difference between periodic and stochastic trajectories.

If the motion is periodic, then the trajectory intersects the q2p2 plane at one point. If the motion is quasi-periodic, that is, limited to the surface of the torus, then successive intersection points fill a closed curve on the q2p2 plane. If the motion is stochastic, then the trajectory randomly wanders in some regions of the phase space, and its intersection points also randomly fill a certain region on the q2р2 plane.

Another important result of the KAM theory is that by increasing the coupling parameter, we thereby increase the regions in which stochasticity predominates. At a certain critical value of the coupling parameter, chaos arises: in this case we have a positive Lyapunov exponent, corresponding to the exponential divergence over time of any two close trajectories. Moreover, in the case of fully developed chaos, the cloud of intersection points generated by the trajectory satisfies equations like the diffusion equation.

The diffusion equations have broken symmetry in time. They describe the approach to a uniform distribution in the future (i.e. at t
-> +?). Therefore, it is very interesting that in a computer experiment, based on a program compiled on the basis of classical dynamics, we obtain evolution with broken symmetry in time.

It should be emphasized that the KAM theory does not lead to a dynamic theory of chaos. Its main contribution lies elsewhere: the KAM theory showed that for small values of the coupling parameter we have an intermediate regime in which trajectories of two types coexist - regular and stochastic. On the other hand, we are mainly interested in what happens in the limiting case, when again only one type of trajectories remains. This situation corresponds to the so-called large Poincaré systems (LPS). We now turn to their consideration.

4.2. Large Poincaré systems

When considering the classification of dynamical systems into integrable and non-integrable proposed by Poincaré, we noted that resonances are rare, since they arise in the case of rational relationships between frequencies. But with the transition to BSP the situation changes radically: in
BSP resonances play a major role.

Let us consider, as an example, the interaction between a particle and a field. The field can be considered as a superposition of oscillators with a continuum of frequencies wk. Unlike the field, the particle oscillates with one fixed frequency w1. Here is an example of a non-integrable system
Poincare. Resonances will occur whenever wk =w1. All physics textbooks show that the emission of radiation is caused by precisely such resonances between a charged particle and a field. The emission of radiation is an irreversible process associated with Poincaré resonances.

The new feature is that the frequency wk is continuous function index k, corresponding to the wavelengths of the field oscillators. This is a specific feature of large Poincaré systems, i.e. chaotic systems that do not have regular trajectories coexisting with stochastic trajectories. Large Poincaré systems (LPS) correspond to important physical situations, in fact to most situations we encounter in nature. But BSPs also make it possible to eliminate Poincaré divergences, i.e., eliminate the main obstacle to the integration of the equations of motion. This result, which significantly increases the power of the dynamic description, destroys the identification of Newtonian or Hamiltonian mechanics and time-reversible determinism, since the equations for the BSP in the general case lead to a fundamentally probabilistic evolution with broken symmetry in time.

Let us now turn to quantum mechanics. Between the problems we face in classical and quantum theory, there is an analogy, since the classification of systems proposed by Poincaré into integrable and non-integrable remains valid for quantum systems.

5. Solution to the time paradox

5.1.Laws of chaos

It is difficult to talk about “laws of chaos” while we are considering individual trajectories. We are dealing with the negative aspects of chaos, such as exponential divergence of trajectories and non-computability. The situation changes dramatically when we move to a probabilistic description. The description in terms of probabilities remains valid at all times. Therefore, the laws of dynamics should be formulated at the probabilistic level. But this is not enough.
To include time symmetry breaking in the description, we must leave ordinary Hilbert space. In the simple examples they considered here, irreversible processes were determined only by Lyapunov time, but all the above considerations can be generalized to more complex mappings that describe irreversible processes! other types of processes, for example, diffusion.

The probabilistic description we obtained is irreducible: this is an inevitable consequence of the fact that eigenfunctions belong to the class of generalized functions. As already mentioned, this fact can be used as a starting point for a new, more general definition chaos. In classical dynamics, chaos is determined by the “exponential divergence” of trajectories, but this definition of chaos does not allow generalization to quantum theory. In quantum theory there is no "exponential decay" of wave functions and therefore no sensitivity to initial conditions in the usual sense. However, there are quantum systems characterized by irreducible probabilistic descriptions. Among other things, such systems are of fundamental importance for our description of nature.
As before, the fundamental laws of physics as applied to such systems are formulated in the form of probabilistic statements (rather than in terms of wave functions). It can be said that such systems do not allow one to distinguish a pure state from mixed states. Even if we choose a pure state as the initial state, it will eventually turn into a mixed state.

The study of the mappings described in this chapter is of great interest. These simple examples allow us to visualize what we mean when talking about the third, irreducible formulation of the laws of nature. However, mappings are nothing more than abstract geometric models. Now we turn to dynamical systems based on the Hamiltonian description - the foundation modern concept laws of nature.

5.2.Quantum chaos

Quantum chaos is identified with the existence of an irreducible probabilistic representation. In the case of BSP, this representation is based on Poincaré resonances.

Consequently, quantum chaos is associated with the destruction of the invariant of motion due to Poincaré resonances. This indicates that in the case of BSP it is impossible to move from amplitudes |?i+> to probabilities |?i+>

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Introduction. 2

1. The problem of formation. 3

2. Revival of the time paradox. 3

3. Basic problems and concepts of the time paradox. 5

4. Classical dynamics and chaos. 6

4.1 KAM theory... 6

4.2. Large Poincaré systems. 8

5. Solution to the time paradox. 9

5.1. Laws of chaos. 9

5.2. Quantum chaos. 10

5.3.Chaos and the laws of physics. 13

6. The theory of unstable dynamic systems is the basis of cosmology. 14

7. Prospects for nonequilibrium physics. 16

In the interpretation of Ilya Romanovich Prigogine and Isabella Stengers, time is a fundamental dimension of our existence.

The most important problem on the topic of my essay is the problem of the laws of nature. This problem is “brought to the fore by the paradox of time.” The authors' justification for this problem is that people are so accustomed to the concept of "law of nature" that it is taken for granted. Although in other views of the world such a concept of “laws of nature” is absent. According to Aristotle, living beings are not subject to any laws. Their activities are determined by their own autonomous reasons. Every being strives to achieve its own truth. In China, the dominant view was about the spontaneous harmony of the cosmos, a kind of statistical equilibrium linking nature, society and the heavens together.

At the end of the 19th century, attention was drawn to the emergence of the time paradox from both natural science and philosophical points of view. In the works of philosopher Henri Bergson, time plays a major role in judging the interactions between man and nature, as well as the limits of science. For the Viennese physicist Ludwig Boltzmann, introducing time into physics as a concept associated with evolution was the goal of his entire life.

Bergson's conclusions were perceived as an attack on science.

One of Bergson's goals in writing Creative Evolution was "to show that the whole is of the same nature as myself."

Most scientists today do not at all believe, unlike Bergson, that “another” science is needed to understand creative activity.

The book "Order Out of Chaos" outlined the history of 19th century physics, which centered on the problem of time. Thus, in the second half of the 19th century, two concepts of time arose corresponding to opposite pictures of the physical world, one of them goes back to dynamics, the other to thermodynamics.

In reality, the scope of the problem is even wider. The very existence of our universe defies the second law of thermodynamics.

Like the emergence of life for Jacques Monod, the birth of the universe is perceived by Asimov as an everyday event.

The laws of nature are no longer opposed to the idea of the truth of evolution, which includes innovations that are scientifically defined by three minimum requirements.

First requirement– irreversibility, expressed in the violation of symmetry between the past and the future. But this is not enough. If we consider a pendulum whose oscillations are gradually fading, or the Moon, whose period of rotation around its own axis is increasingly decreasing. Another example could be a chemical reaction, the rate of which becomes zero before reaching equilibrium. Such situations do not correspond to truly evolutionary processes.

Second requirement– the need to introduce the concept of event. By their definition, events cannot be derived from a deterministic law, be it time-reversible or irreversible: an event, no matter how it is interpreted, means that what happens does not necessarily have to happen. Therefore, at best one can hope to describe the event in terms of probabilities.

this implies third requirement, which must be entered. Some events must have the ability to change the course of evolution, i.e. evolution must not be stable, i.e. characterized by a mechanism capable of making certain events the starting point of a new development.

Darwin's theory of evolution serves as an excellent illustration of all three requirements formulated above. Irreversibility is obvious: it exists at all levels from new ecological niches, which in turn open up new opportunities for biological evolution. Darwin's theory was supposed to explain the astonishing event of the emergence of species, but Darwin described this event as the result of complex processes.

The Darwinian approach provides only a model. But every evolutionary model must contain the irreversibility of events and the possibility for some events to become the starting point for a new order.

The time paradox "poses before us the problem of the laws of nature." This problem requires more detailed consideration. According to Aristotle, living beings are not subject to any laws. Their activities are determined by their own autonomous internal causes. Every being strives to achieve its own truth. In China, the dominant view was about the spontaneous harmony of the cosmos, a kind of statistical equilibrium linking nature, society and the heavens together.

Christian ideas about God as setting laws for all living things also played an important role.

The time paradox does not exist by itself. Two other paradoxes are closely related to it: the “quantum paradox” and the “cosmological paradox.”

There is a close analogy between the time paradox and the quantum paradox. The essence of the quantum paradox is that the observer and the observations he makes are responsible for the collapse. Therefore, the analogy between the two paradoxes is that man is responsible for all the features associated with becoming and events in our physical description.

KAM theory considers the influence of resonances on trajectories. It should be noted that the simple case of a harmonic oscillator with a constant frequency independent of the action variable J is an exception: the frequencies depend on the values accepted by the action variables J. At different points in the phase space, the phases are different. This leads to the fact that at some points of the phase space of a dynamic system there is resonance, while at other points there is no resonance. As is known, resonances correspond to rational relationships between frequencies. The classic result of number theory boils down to the statement that the measure of rational numbers compared to the measure of irrational numbers is equal to zero. This means that resonances are rare: most points in phase space are non-resonant. In addition, in the absence of disturbances, resonances lead to periodic motion (the so-called resonant tori), whereas in the general case we have quasiperiodic motion (non-resonant tori). We can say briefly: periodic movements are not the rule, but the exception.