Traditionally, another reason most scientists dismiss the idea of ​​time travel is temporal paradoxes. For example, if you go back in time and kill your parents before the moment of your birth, then birth will become impossible. So, for starters, there's no way to go back in time and kill your parents. Not the best example, but it's important because science is based on logically consistent ideas; such a time paradox would be enough to throw off the idea of ​​time travel. These time paradoxes fall into several categories:
Grandpa's paradox. According to this paradox, it is possible to change the past in such a way that the existence of the present becomes impossible. For example, when traveling to the distant past to look at dinosaurs, one might accidentally step on a small furry creature that may have been the first ancestor of the human race. Having destroyed its ancestor, one's own existence is logically restored
impossible.

informational paradox. According to this paradox, information comes from the future, which means that it has no beginning. For example, you can imagine that some scientist created the same time machine and goes into the past to tell the secret of time travel to himself in early years. This secret will have no beginning, tk. the time machine that the scientist will create will not be invented by himself) - the secret of its design will be transferred to him by his senior incarnation.

Bilker's paradox. Suppose a person knows what his future will be like and does something that makes such a future impossible. For example, you create a time machine that can take a person into the future, and now he discovers that he is destined to marry a woman named Anna. However, in spite of fate, he decides to marry a woman named Galya, thus. making such a future impossible.

Sexual paradox. According to this paradox, you are your own father, which is biologically impossible. The hero of the story, written by the British philosopher D. Garrison, is not only his own father, but also eats himself. In the classic work by R. Heinlein “You are all zombies”, the hero is at the same time his own father, and mother, and daughter, and son - i.e. it embodies the entire family tree. Solving the mystery of the sexual paradox is actually quite difficult, since it requires knowledge of both the theory of time travel and the mechanics of DNA. But he still has the right to life - I advise you to read Heinlein and Harrison.

In "The End of Eternity" A. Azimov imagines the "temporary police", which is responsible for preventing such paradoxes. In the Terminator movie, the plot is based on an informational paradox - scientists study a microchip taken from a robot from the distant future, then they create a whole race of robots that are endowed with consciousness, and they conquer the whole world. In other words, the very design of these robots was not created by any inventor; it is simply taken from the wreckage of one of the robots of the distant future. In Back to the Future, J. Fox tries to avoid the "grandfather paradox" when he goes back in time and meets his teenage mother, who immediately falls in love with him. But if she rejects Father Fox's advances, then Michael's very existence will be in jeopardy.

Screenwriters willingly break the laws of physics, creating Hollywood blockbusters. But in the circle of physicists, such paradoxes are taken very seriously. Any solution to such paradoxes must be compatible with relativity and quantum theory. For example, to be consistent with the theory of relativity, the river of time must be infinite. AT general theory In relativity, time is represented as a smooth extended surface that cannot be broken and on which ripples cannot form. Its topology may change, but the river cannot just stop. This means that if you kill your parents before the moment of your own birth, then you cannot disappear. Such a scenario would be contrary to the laws of physics.

Physicists are currently divided into 2 groups, supporting 2 possible solutions to these time paradoxes. Russian cosmologist I. Novikov believes that we are forced to act in such a way as if paradoxes are inevitable. His approach is called the "school of consistency". If the river of time gently turns back and closes on itself again, creating a whirlpool, then, according to Novikov's assumptions, if we decide to go back in time, which would be fraught with the creation of a time paradox, then some "invisible hand" should intervene and prevent the jump into past. But there are problems with free will in Novikov's approach.. If we go back in time and meet our own parents, one might think that we are guided by our own will in our actions; Novikov believes that not yet open law physics forbids any action that would change the future (such as killing one's own parents or preventing one's own birth). He notes, "We can't send a time traveler to the Gardens of Eden to ask Eve not to
tear an apple from a tree.” What is this mysterious force that does not allow changing the past and creating a temporary paradox? “Such a pressure on our will is unusual and mysterious, but still it has its parallels,” writes
Novikov. - For example, I can express my will to walk on the ceiling without any special equipment. The law of gravity won't let me do that; I will fall to the floor if I try to do this, and therefore my free will is limited.”

But temporal paradoxes can also occur when inanimate matter (with no free will or power of intent at all) is thrown into the past. Suppose that before the battle of Alexander the Great with the Persian king Darius III in 330 BC. e. scientists send machine guns back in time with instructions in Old Persian on how to use them. All subsequent European history would change (and perhaps find that instead of one of European languages now speak some dialect of Persian).

In fact, even the smallest intervention in the past can cause the most unexpected paradoxes in the present. For example, chaos theory uses the butterfly effect metaphor. At critical moments in the formation of the Earth's climate, the slightest flutter of a butterfly's wings is enough to send ripples through the water that can upset the balance of forces and cause a terrible thunderstorm. Even the smallest inanimate objects, being sent into the past, will inevitably change the past in the most unpredictable way, which will cause a time paradox.

The second way to resolve the temporal paradox is to have the river of time gently fork into two rivers, or branches, forming two different universes. In other words, if you go back in time and kill your parents before your own birth, then people who are not genetically different from their parents in an alternate universe would also die, one where the time traveler would never be born. But his parents in his native universe will remain alive.

The second hypothesis is called the "many worlds theory": its essence is that all possible multiple worlds can exist simultaneously. This eliminates the infinite number of discrepancies found by Hawking, pt.c. radiation will not pass through the portal over and over again, as in Misner space (see previous posts). If it gets through the portal, it will only happen once. Each time it passes through the portal, it will enter a new universe.

And this paradox goes back, perhaps, to a global question quantum theory: how can a cat be both alive and dead at the same time?

To answer this question, physicists had to take into account two shocking decisions: either there is a Cosmic Intelligence watching over all of us, or there is an infinite number of quantum universes.

Introduction. 2

1. The problem of formation. 3

2. The revival of the paradox of time. 3

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

4. Classical dynamics and chaos. 6

4.1 Theory of KAM... 6

4.2. Large Poincaré systems. eight

5. Solution of the paradox of time. nine

5.1. Laws of chaos. nine

5.2 Quantum chaos. ten

5.3 Chaos and the laws of physics. thirteen

6. The theory of unstable dynamical systems is the basis of cosmology. fourteen

7. Prospects for non-equilibrium physics. sixteen

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

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

Most important issue 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 justification for this problem by the authors 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 missing. According to Aristotle, living beings are not subject to any laws. Their activities are due to their own autonomous reasons. Every being strives to achieve its own truth. China was dominated by the views of the spontaneous harmony of the cosmos, a kind of statistical equilibrium, linking together nature, society and heaven.

The motivation for the authors to consider the issue of the time paradox was the fact that the time paradox does not exist on its own, 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 solve the paradox of time.

At the end of the 19th century, attention was paid to the formation of the paradox of time simultaneously from the natural scientific and philosophical points of view. In the works of the philosopher Henri Bergson, time plays leading role in condemning the interactions between man and nature, as well as the limits of science. For the Viennese physicist Ludwig Boltzmann, the introduction to physics of time as a concept associated with evolution was the goal of his whole life.

In the work of Henri Bergson creative evolution"The idea was expressed that science successfully developed only in those cases when it managed to reduce the processes occurring in nature to a 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 a new, she inevitably failed.

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

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

Unlike Bergson, the majority of scientists at present do not at all consider that a "different" science is needed to understand creative activity.

The book "Order out of chaos" outlined the history of 19th century physics in the center, which was the problem of time. So in the second half of the 19th century, two conceptions of time arose corresponding to opposite pictures of the physical world, one of them goes back to dynamics, the other to thermodynamics.

The last decades of the 20th century have witnessed a resurgence of the paradox of time. 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 the laws of nature, ignoring evolution and the creation of the new.

In fact, 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 ​​true evolution, which includes innovations that scientific point 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 of oscillation, which is gradually damped, or the Moon, the period of rotation of which around its own axis is decreasing more and more. Another example could be chemical reaction, whose velocity vanishes until equilibrium is reached. Such situations do not correspond to true evolutionary processes.

Second requirement– the need to introduce the concept of an event. By definition, events cannot be deduced from a deterministic law, whether reversible in time or not: an event, however one interprets it, means that what happens does not have to happen. Therefore, at best, one can hope to describe the event in terms of probabilities.

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

Darwin's theory of evolution is an excellent illustration of all three of the above requirements. 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 a startling event - the emergence of species, but Darwin described this event as the result of complex processes.

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

In contrast to the Darwinian approach, nineteenth-century thermodynamics focuses on equilibrium that meets only the first requirement, since it expresses non-symmetricality between the past and the future.

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

The paradox of time "puts 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 activity is conditioned by their own autonomous internal causes. Every being strives to achieve its own truth. China was dominated by views of the spontaneous harmony of the cosmos, a kind of statistical equilibrium that binds together nature, society and heaven.

Not unimportant role was played by Christian ideas about God as establishing laws for all living things.

For God, everything is a given. New, choice or spontaneous action is relative from a human point of view. Such theological views seemed to be fully supported by the discovery of the dynamic laws of motion. Theology and science 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 to classical dynamics.

The paradox of time 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 responsibility for the collapse lies with the observer and his observations. 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, it is necessary to note the third paradox - the cosmological paradox. Modern cosmology ascribes age to our universe. The universe was born in a big bang about 15 billion years ago. years ago. It is clear that this was an event. But events are not included in the traditional formulation of the concepts of the laws of nature. This put physics on the brink of the greatest crisis. Hawking wrote about the Universe like this: "... it just has to be, and that's it!".

With the advent of the works of Kolmogorov, continued by Arnold and Moser - the so-called KAM theory - the problem of non-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.

The 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 ​​taken 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 the dynamical system there is a 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 is reduced to the statement that the measure 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 perturbations, resonances lead to periodic motion (the so-called resonant tori), while in general case we have a quasi-periodic motion (nonresonant 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 resonant tori will change dramatically (according to the Poincaré theorem), while the quasi-periodic motion will change insignificantly, at least for a small perturbation parameter (the KAM theory requires that additional conditions which we will not consider here). The main result of the KAM theory is that we now have two completely different types of trajectories: slightly changed quasi-periodic trajectories and stochastic j trajectories that have arisen during the destruction of resonant tori.

The most important result of the KAM theory - the appearance of stochastic trajectories - is confirmed by numerical experiments. Consider a system with two degrees of freedom. Its phase space contains two coordinates q 1, q 2 and two pulses p1, p2. Calculations are made at a given energy value H ( q 1, q 2, p 1, p 2), and so only three independent variables remain. To avoid building trajectories in three-dimensional space, we agree to consider only the intersection of trajectories with the plane q 2 p 2. To simplify the picture even more, we will build only half of these intersections, namely, we will take into account only those points at which the trajectory “pierces” the section plane from bottom to top. This technique was used by Poincare, and it is called the Poincaré section (or the Poincaré mapping). The Poincare 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, i.e. limited by the surface of the torus, then successive intersection points fill on the plane q 2 p 2 closed curve. If the motion is stochastic, then the trajectory randomly wanders in some regions of the phase space, and the points of its intersection also randomly fill a certain region on the q2p2 plane.

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

The diffusion equations have broken symmetry in time. They describe an approximation 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 dynamical chaos theory. Its main contribution lies elsewhere: the KAM theory showed that for small values ​​of the coupling parameter we have an intermediate regime in which two types of trajectories 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 (BSPs). We now turn to their consideration.

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 relations between frequencies. However, the situation changes radically on going to BSP: resonances play the main role in BSP.

Consider as an example the interaction between some particle and a field. The field can be viewed as a superposition of oscillators with a continuum of frequencies wk . In contrast to the field, the particle oscillates with one fixed frequency w 1 . We have before us an example of a non-integrable Poincaré system. Resonances will occur whenever wk =w 1 . It is shown in all physics textbooks that the emission of radiation is due precisely to 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 a continuous index function k , corresponding to the wavelengths of the field oscillators. This is the specific feature large systems Poincare, i.e., chaotic systems that do not have regular trajectories coexisting with stochastic trajectories. Large systems Poincare (BSP) correspond to important physical situations, in fact, to most of the situations that we encounter in nature. But BSP also allow exclude Poincaré divergences, i.e., to remove the main obstacle on the way to the integration of the equations of motion. This result, which significantly increases the power of the dynamical description, destroys the identification of Newtonian or Hamiltonian mechanics and time-reversible determinism, since the equations for the BSP generally lead to fundamentally probabilistic evolution with broken symmetry in time.

Let's turn now to quantum mechanics. There is an analogy between the problems that we face in classical and quantum theory, since the classification of systems proposed by Poincare, into integrable and non-integrable, remains valid for quantum systems.

It is difficult to talk about the "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 incomputability. The situation changes dramatically when we turn 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. In order to include the breaking of symmetry in time in the description, we must leave the usual Hilbert space. In the simple examples considered by them here, irreversible processes were determined only by the Lyapunov time, but all the above considerations can be generalized to more complex mappings that describe irreversible! processes of another type, such as diffusion.

The probabilistic description we have 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 new, more general definitions of chaos. In classical dynamics, chaos is defined by the "exponential divergence" of trajectories, but such a definition of chaos does not allow generalization to quantum theory. In quantum theory, there is no "exponential divergence" of wave functions and, therefore, there is no sensitivity to initial conditions in the usual sense. Nevertheless, 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 in relation 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 pure state from mixed states. Even if we choose a pure state as the initial one, 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 we talk 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 of the modern concept of the laws of nature.

Quantum chaos is identified with the existence of an irreducible probabilistic representation. In the case of BSPs, 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 pass from the amplitudes |φ i + > to the probabilities |φ i + ><φ i + |. Фундаментальное уравнение в данном случае записывается в терминах вероятности. Даже если начать с чистого состояния ρ=|ψ> <ψ|, оно разрушится в ходе движения системы к равновесию.

The destruction of the state can be associated with the destruction of the wave function. In this case, the evolution of the "collapse" is so important that it makes sense to follow it with an example.

Let there be a wave function ψ(0) at some initial time t=0. The Schrödinger equation transforms it into ψ(t)=

e - itH ψ(0). Whenever one has to deal with irreducible representations, the expression ρ=ψψ must lose its meaning, otherwise it would be possible to pass from ρ to ψ and vice versa.

This is precisely what happens to nonvanishing interactions in potential scattering.

Figure 1 shows the graphs of the dependence of sin(ώt)/ώ on ώ

fig.1 Schematic plot of sin(ώt)/ώ

Given the wave function, we can calculate the density matrix

.

This expression is ill-defined, but combined with trial functions, both ill-defined expressions make sense:

Consider the diagonal elements of the density matrix:

The graph of this function is shown in Fig. 2

rice. 2 schematic plot of magnitude

In combination with the trial function f(ω), it is required to calculate

Conversely, the amplitude of the wave in combination with the trial function remains constant in time, since

.

The reason for such a different behavior of the functions becomes clear if we compare the graphs of the functions shown in Figs. 1 and 2: the sinωt/ω function takes both positive and negative values, while the function takes only positive values ​​and makes a "greater contribution to the integral."

The conclusions obtained can be confirmed by modeling the probability P as a function of k with increasing values ​​of t. Graphs are shown in Fig.5.

Now it can be noted that the collapse propagates in space causally, in accordance with the general requirements of the theory of relativity, excluding effects propagating instantly.

rice. 3 modeling the probability P as a function of k with increasing values ​​of t.

In addition, in order to achieve equilibrium in a finite time, the scattering must be repeated many times, i.e. systems of N bodies with incessant interactions are needed.

Chaos has been repeatedly defined through the existence of irreducible probabilistic representations. Such a definition makes it possible to cover a much wider area than the founders of the modern dynamical theory of chaos, in particular, A. N. Kolmogorov and Ya. G. Sinai, originally assumed. Chaos is due to sensitivity to initial conditions and, consequently, exponential divergence of trajectories. This leads to irreducible probabilistic representations. Description in terms of trajectories has given way to a probabilistic description. Therefore, one can take this fundamental property as a distinctive feature of chaos. An instability develops that forces us to abandon the description in terms of individual trajectories or individual wave functions.

There is a fundamental difference between classical chaos and quantum chaos. Quantum theory is directly related to wave properties. Planck's constant leads to additional coherence compared to the classical behavior. As a result, the conditions for quantum chaos become more limited than those for classical chaos. Classical chaos arises even in small systems, for example, in mapped and systems studied by the KAM theory. The quantum analogue of such small systems has a quasi-periodic behavior. Many authors have come to the conclusion that quantum chaos does not exist at all. But it's not. First, it is required that the spectrum be continuous (i.e., that quantum systems were"large"). Secondly, quantum chaos is defined as being associated with the emergence of irreducible probabilistic representations.

Traditional quantum theory has a large number of weaknesses. The formulation of this theory continues the tradition of classical theory - in the sense that it follows the ideal of timeless description. For simple dynamical systems, such as a harmonic oscillator, this is quite natural. But even in this case, is it possible to describe such systems in isolation? They cannot be observed apart from the field leading to quantum transitions and emission of signals (photons).

In order to include evolutionary elements in the picture, it is necessary to proceed to the formulation of the laws of nature in terms of an irreducible probabilistic description.

Cosmology should be based on the theory of unstable dynamical systems. To some extent, this is just a program, but, on the other hand, within the framework of physical theory, it exists at the present time.

In addition, the introduction of probability at a fundamental level removes some of the obstacles to the construction of a consistent theory of gravity. In their paper, Unruh and Wald wrote that this difficulty can be traced directly to the conflict between the role of time in quantum theory and the nature of time in general relativity. In quantum mechanics, all measurements are made at "moments of time": only quantities related to the instantaneous state of the system have physical meaning. On the other hand, in general relativity, only the space-time geometry is measurable. Indeed, as we have seen, quantum measurement theory corresponds to instantaneous, acausal processes. From the point of view of the authors, this circumstance is a strong argument against the "naive combination" of quantum theory and the general theory of relativity, which also includes such a concept as the "wave function of the Universe." However, this approach avoids the paradoxes associated with quantum measurements.

The birth of our Universe is the most obvious example of instability leading to irreversibility. What is the fate of our universe at the present time? The Standard Model predicts that in the end, our Universe is doomed to death either as a result of continuous expansion (thermal death) or as a result of subsequent contraction (a “terrible crack”). For the Universe, which has merged under the sign of instability from the Minkowski vacuum, this is no longer the case. Nothing now prevents us from assuming the possibility of repeated instabilities. These instabilities can develop on different scales.

Modern field theory considers that in addition to particles (with positive energy), there are completely filled states with negative energy. Under certain conditions, for example, in strong fields, pairs of particles pass from vacuum to states with positive energy. The process of birth of a pair of particles from vacuum is irreversible . Subsequent transformations leave the particles in states with positive energy. Thus, the Universe (considered as a set of particles with positive energy) is not closed. Therefore, the formulation of the second law proposed by Clausius is inapplicable! Even the universe as a whole is an open system.

It is in the cosmological context that the formulation of the laws of nature as irreducible probabilistic representations entails the most striking consequences. Many physicists believe that progress in physics should lead to a unified theory. Heisenberg called it the "Urgleichung" ("proto-equation"), but it is now more commonly referred to as the "theory of everything." If such a universal theory is ever to be formulated, it will have to include dynamical instability and thus take into account time symmetry breaking, irreversibility and probability. And then the hope of constructing such a "theory of everything", from which it would be possible to derive a complete description of physical reality, will have to be abandoned. Instead of premises for deductive inference, one can hope to find principles of coherent "narration" from which not only laws, but also events would follow, which would give meaning to the probabilistic emergence of new forms, both regular behavior and instability. In this regard, one can draw similar conclusions from Walter Thirring: “The proto-equation (if such a thing exists at all) must potentially contain all possible paths that the Universe could take, and therefore many 'delay lines'. With such an equation, physics found itself in a situation similar to that created in mathematics. near 1930, when Gödel showed that mathematical constructions can be consistent and still contain true statements. Similarly, the "proto-equation" will not contradict experience, otherwise it would have to be modified, but it will far from determine everything. As the universe evolves, "circumstances create their own laws." It is precisely this idea of ​​the Universe developing according to its own internal laws that we arrive at on the basis of an irreducible formulation of the laws of nature.

The physics of non-equilibrium processes is a science penetrating into all spheres of life. It is impossible to imagine life in a world devoid of interconnections, created by irreversible processes. Irreversibility plays an essential constructive role. It leads to many phenomena such as the formation of vortices, laser radiation, fluctuations in a chemical reaction.

In 1989, the Nobel Conference took place at Gustav Adolf College (St. Peter, Minnesota). It was entitled "The End of Science", but the meaning and content of these words were not optimistic. The organizers of the conference issued a statement: "... We have come to the end of science, that science as a kind of universal, objective kind of human activity has ended" . The physical reality described today is temporary. It covers laws and events, certainties and probabilities. The invasion of time into physics does not at all indicate a loss of objectivity or "intelligibility". On the contrary, it opens the way for new forms of objective knowability.

The transition from a Newtonian description in terms of a trajectory or a Schrödinger description in terms of wave functions to a description in terms of ensembles does not entail a loss of information. On the contrary, such an approach makes it possible to include new essential properties in the fundamental description of unstable chaotic systems. The properties of dissipative systems cease to be only phenomenological, but become properties that cannot be reduced to certain features of individual trajectories or a wave function.

The new formulation of the laws of dynamics also makes it possible to solve some technical problems. Due to the fact that even simple situations lead to non-integrated Poincaré systems. Therefore, physicists turned to the S-matrix theory, i.e. idealization of scattering occurring within a limited time. However, this simplification applies only to simple systems.

The described approach leads to a more consistent and uniform description of nature. There was a gap between the fundamental knowledge of physics and all levels of description, including chemistry, biology, and the humanities. The new perspective creates a deep connection between the sciences. Time ceases to be an illusion that relates human experience to some subjectivity that lies outside of nature.

The following question arises: if chaos plays a unified role from classical mechanics to quantum physics and cosmology, then is it possible to construct a "theory of everything in the world" (TVS)? Such a theory cannot be built. This idea claims to comprehend the plans of God, i.e. to reach a fundamental level, from which it is possible to derive deterministically all phenomena. Chaos theory has a different unification. TVS, containing chaos, could not come to a timeless description. Higher levels would be allowed by the fundamental levels, but would not follow from them.

The main goal of the proposed method - the search for "a narrow path, lost somewhere between two concepts, ..." - a clear illustration of the creative approach in science. The role of creativity in science has often been underestimated. Science is a collective matter. The solution to a scientific problem, in order to be acceptable, must satisfy precise criteria and requirements. However, these restrictions do not exclude creativity, on the contrary, they challenge it.

Laying the path, it turned out that a significant part of the concrete world around us has so far "eluded the cells of the scientific network" (according to Whitehead). New horizons have opened before us, new questions have arisen, new situations have arisen, fraught with danger and risk.

The central problem posed by I. Prigogine and I. Stengers was the problem of the "laws of nature", which follows from the paradox of time. Therefore, its solution provides an answer to the paradox of time.

Prigogine I. and Stengers I. connect their solution to the paradox of time with the fact that the discovery of dynamic instability led to the fact that individual trajectories had to be abandoned. Therefore, chaos turned into a tool of physics, which gave a solution to the paradox of time, as it was said at the beginning of the work, the paradox of time depends on chaos, and dynamic chaos underlies all sciences.

The concept of the "arrow of time" was introduced in 1928 by Eddington in his book The Nature of the Physical World.

Kolmogorov–Arnold–Moser theory

Mathematical notation of the density matrix

Parameter name	Meaning
Article subject:	The paradox of time
Rubric (thematic category)	Philosophy

Answers

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 reasoning about space (there was even an expression: horror infinity(lat.) - the 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 not possible to imagine an infinite space, so it is not possible to imagine a limited universe, the question arises: what is beyond this boundary? In the latter case, if there is something outside the border, then this something must be included by us within the limits of the world, which means that if we indicated 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 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

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

ʼʼ ... space is nothing but the form of all external phenomena, in which only sense objects are given to us ʼʼ. (I.Kant. Prolegomena to any future metaphysics).

Time ʼʼis not inherent in the objects themselves, but only in the subject who contemplates themʼʼ. (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 genius philosophers of the 20th century, Ludwig Wittgenstein, believed that philosophical problems are riddles generated by the use of words (language).

ʼʼAn error of this kind is repeated again and again in philosophy; for example, when we are puzzled by the nature of time, when time seems to us enigmatic thing. We have a strong tendency to believe that there is something hidden here, something that we can see from the outside, but which we cannot look inside. In fact, there is nothing like it. We want to know 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 ʼʼtimeʼʼʼʼ (Wittgenstein L. The Blue Book).

Consider, as an example, the question: ʼʼWhat is time?ʼʼ, as asked by St. Augustine and others. At first glance, this is a question of definition, but then the question immediately arises: ʼʼWhat will we achieve with a definition, because it will only lead us to other indefinite terms?ʼʼ. And why should one be confused by the lack of a definition of time, and not the absence of, say, a "chair"? Why don't we get confused whenever we can't define it? So the definition often clarifies grammar the words. In fact, it is the grammar of the word ʼʼtimeʼʼ that confuses us. We just express this confusion by asking a slightly misleading question - the question ʼʼWhat is... ?ʼʼ...

St. Augustine in his discussion of time was confused by the following ʼʼcontradictionʼʼ: 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, on the other hand, should not be measured, because it has no extension.

The contradiction, ĸᴏᴛᴏᴩᴏᴇ, seems to arise here, might be called a conflict between two different uses of the word, in this case the word ʼʼmeasureʼʼ. We can say that Augustine is thinking about the process of measurement lengths: say the distance between two marks on a conveyor belt whose belt is moving in front of us and we can only see a small piece of it (present tense). The solution to this puzzle will be to compare what we mean by ʼʼmeasureʼʼ (the grammar of the word ʼʼmeasureʼʼ) applied to distance on a conveyor belt with the grammar of that 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 an example with a conveyor belt.

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

But Wittgenstein urges us to pay attention to the grammar of the word ʼʼmeasureʼʼ (its usage in language) applied to time. In other words, paying attention to how we measure time, meaning that it is done differently, in life we ​​do not have mysterious problems with measuring time.

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

ʼʼWhat this aspect is and how it happens that it arises can be illustrated by the classic question: ʼʼWhere does the present go when it becomes the past, and where is the past?ʼʼ. 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 are floating past us - for example, logs being floated down the river. In this case, we can say that the logs that passed by us, are at the bottom left, and the logs that will pass by us are at the top right. Then we use this situation as a comparison for everything that happens in time, and even embody this comparison in our language when we say that ʼʼthe present event passesʼʼ (the log passes), ʼʼthe future event must comeʼʼ (the log must come). We are talking about the course of events; but also about the flow 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 this event.

We are speaking Something will happenʼʼ, and also: ʼʼSomething is approaching meʼʼ; we point to the log as ʼʼsomethingʼʼ, but also to the approach of the log towards me.

It may happen that we will not be able to get rid of the consequences of our symbolism, which seems to allow questions like: ʼʼWhere does the flame of a candle go when it is extinguished?ʼʼ, ʼʼWhere does the light go?ʼʼ, ʼʼWhere does the past go?ʼʼ. We are beginning to be haunted by our symbolism. - We can say that we are confused by an analogy that irresistibly pulls us along. - This also happens when the meaning of the word ʼʼnowʼʼ is presented to us in a mystical lightʼʼ (Wittgenstein L. Brown Book).

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

TIME PARADOX

TIME PARADOX

(twin paradox, relativity theory when finding time intervals shown by two clocks BUT and AT, of which watches . everything was at rest in an inertial frame of reference, and the clock AT flew away from BUT, made a trip and returned to BUT. A contradiction arises when . And a period of time has passed t, then by moving with post. v hours AT a period of time will pass

I. D. Novikov.

Physical encyclopedia. In 5 volumes. - M.: Soviet Encyclopedia. Editor-in-Chief A. M. Prokhorov. 1988 .

See what the "PARADOX OF TIME" is in other dictionaries:

time paradox

This page needs a major overhaul. It may need to be wikified, expanded, or rewritten. Explanation of the reasons and discussion on the Wikipedia page: For improvement / November 7, 2012. Date of setting for improvement November 7, 2012 ... Wikipedia

twin paradox- laiko paradoksas statusas T sritis fizika atitikmenys: engl. clock paradox; twin paradox vok. Uhrenparadoxon, n; Zwillingsparadoxon, n rus. twin paradox, m; time paradox, m; clock paradox, m pranc. paradoxe de l'horloge, m; paradoxe… … Fizikos terminų žodynas

clock paradox- laiko paradoksas statusas T sritis fizika atitikmenys: engl. clock paradox; twin paradox vok. Uhrenparadoxon, n; Zwillingsparadoxon, n rus. twin paradox, m; time paradox, m; clock paradox, m pranc. paradoxe de l'horloge, m; paradoxe… … Fizikos terminų žodynas

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Thought experiment considering a disk rotating at near-light speed. In the modern sense, it shows the incompatibility of some concepts of classical mechanics with the special theory of relativity, as well as the possibility of different ... ... Wikipedia

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The Einstein Podolsky Rosen paradox (EPR paradox) is an attempt to indicate the incompleteness of quantum mechanics using a thought experiment, which consists in measuring the parameters of a micro-object indirectly, without affecting this object ... ... Wikipedia

Books

• Svarga. Paradox of time, Marina Zagorodskaya. Humanity is increasingly thinking about time travel. But what will be the consequences? Will this affect the development of civilization as a whole? What awaits the time traveler in the past?…