Isaac Newton
Modern physics has abandoned the concept of absolute space and time of classical Newtonian physics. Relativistic theory demonstrated that space and time are relative. There are, apparently, no phrases repeated more often in works on the history of physics and philosophy. However, everything is not so simple, and such statements require certain clarifications (although quite linguistically). However, going back to the origins sometimes turns out to be very useful for understanding the current state of science.
Time, as we know, can be measured using a uniform periodic process. However, without time, how do we know that the processes uniform? Logical difficulties in defining such primary concepts are obvious. The uniformity of the clock must be postulated and called the uniform passage of time. For example, by defining time using uniform and linear motion, we thereby transform Newton's first law into a definition of the uniform passage of time. A clock runs uniformly if a body, which is not acted upon by forces, moves rectilinearly and uniformly (according to this clock). In this case, the movement is thought of relative to an inertial frame of reference, which for its definition also needs Newton’s first law and a uniformly running clock.
Another difficulty is related to the fact that two processes that are equally uniform at a given level of accuracy may turn out to be relatively uneven when measured more accurately. And we constantly find ourselves faced with the need to choose an increasingly reliable standard for the uniformity of the passage of time.
As already noted, the process is considered uniform and measuring time with its help is acceptable as long as all other phenomena are described as simply as possible. Obviously, a certain degree of abstraction is required when defining time in this way. The constant search for the right watch is associated with our belief in some objective property of time to have a uniform pace.
Newton was well aware of the existence of such difficulties. Moreover, in his “Principles” he introduced the concepts of absolute and relative time in order to emphasize the need for abstraction, determination on the basis of relative (ordinary, measured) time of his certain mathematical model - absolute time. AND in that his understanding of the essence of time does not differ from the modern one, although due to differences in terminology there was some confusion.
Let us turn to the “Mathematical Principles of Natural Philosophy” (1687). Abbreviated formulations of Newton's definition of absolute and relative time are as follows:
Absolute (mathematical) time flows uniformly without any relation to anything external. Relative (ordinary) time is a measure of duration, comprehended by the senses through any movement.The relationship between these two concepts and the need for them is clearly visible from the following explanation:
Absolute time is distinguished in astronomy from ordinary solar time by the equation of time. For the natural solar days, taken as equal in the ordinary measurement of time, are in fact unequal to each other. This inequality is corrected by astronomers in order to use more correct time when measuring the movements of celestial bodies. It is possible that there is no such uniform motion (in nature) by which time could be measured with perfect accuracy. All movements can accelerate or slow down, but the flow of absolute time cannot change.Newton's relative time is measured time, while absolute time is its mathematical model with properties derived from relative time through abstraction. In general, speaking about time, space and motion, Newton constantly emphasizes that they are comprehended by our senses and are thus ordinary (relative):
Relative quantities are not the same quantities whose names are usually given to them, but are only the results of measurements of the said quantities (true or false), comprehended by the senses and usually accepted as the quantities themselves.The need to build a model of these concepts requires the introduction of mathematical (absolute) objects, some ideal entities that do not depend on the inaccuracy of instruments. Newton's statement that “absolute time flows uniformly without any relation to anything external” is usually interpreted in the sense of the independence of time from motion. However, as can be seen from the above quotes, Newton speaks of the need to abstract from possible inaccuracies in the uniform running of any clock. For him, absolute and mathematical time are synonymous!
Newton nowhere discusses the issue that the speed of time may differ in different relative spaces (reference systems). Of course, classical mechanics implies the same uniformity of the passage of time for all reference systems. However, this property of time seems so obvious that Newton, very precise in his formulations, does not discuss it or formulate it as one of the definitions or laws of his mechanics. It is this property of time that was discarded by the theory of relativity. Absolute same time in Newton's understanding is still present in the paradigm of modern physics.
Let us now move on to Newton's physical space. If we understand by absolute space the existence of some selected, privileged frame of reference, then it is unnecessary to remind that it does not exist in classical mechanics. Galileo's brilliant description of the impossibility of determining the absolute motion of a ship is a prime example of this. Thus, the relativistic theory could not abandon what was missing in classical mechanics.
However, Newton’s question about the relationship between absolute and relative space is not clear enough. On the one hand, for both time and space, the term “relative” is used in the sense of “a measurable quantity” (comprehensible by our senses), and “absolute” in the sense of “its mathematical model”:
Absolute space, by its very essence, regardless of anything external, always remains the same and motionless. The relative is its measure or some limited moving part, which is determined by our senses by its position relative to certain bodies, and which in everyday life is accepted as motionless space.On the other hand, the text contains discussions about a sailor on a ship, which can also be interpreted as a description of the selected frame of reference:
If the Earth itself moves, then the true absolute motion of the body can be found from the true motion of the Earth in motionless space and from the relative motions of the ship in relation to the Earth and the body in the ship.Thus, the concept of absolute motion is introduced, which contradicts Galileo's principle of relativity. However, absolute space and motion are introduced in order to immediately cast doubt on their existence:
However, it is completely impossible to see or otherwise distinguish with the help of our senses the individual parts of this space from one another, and instead we have to turn to dimensions accessible to the senses. Based on the positions and distances of objects from any body taken as motionless, we determine places in general. It is also impossible to determine their (bodies') true peace by their relative position to each other.Perhaps the need to consider absolute space and absolute motion in it is associated with an analysis of the relationship between inertial and non-inertial reference systems. Discussing an experiment with a rotating bucket filled with water, Newton shows that the rotational motion is absolute in the sense that it can be determined, within the framework of the bucket-water system, by the shape of the concave surface of the water. In this respect, his point of view also coincides with the modern one. The misunderstanding expressed in the phrases given at the beginning of this section arose due to noticeable differences in the semantics of the use of the terms “absolute” and “relative” by Newton and modern physicists. Now, when we talk about absolute essence, we mean that it is described in the same way to different observers. Relative things may look different to different observers. Instead of “absolute space and time,” today we say “mathematical model of space and time.”
Therefore, those who interpret these words in it truly violate the meaning of Holy Scripture.
The mathematical structure of both classical mechanics and relativistic theory is well known. The properties that these theories impart to space and time follow unambiguously from this structure. Vague (philosophical) discussions about outdated “absoluteness” and revolutionary “relativity” are unlikely to bring us closer to solving the Main Mystery.
The Frenchman sitting next to him, Professor Vavier, continued this thought:
Moreover: upon returning to Earth, we will see time very realistically. Time from which we are now running at the speed of light. My two-year-old son will already be a thirty-two-year-old man. Who knows, maybe in a week I will become a grandfather.
John looked at his watch incredulously. They showed 15:11 on July 23, 1981. The third day of the flight, which was supposed to last a month for the astronauts and a whole thirty years for the rest of the earthlings and, most importantly, for Uncle Harvey, who was living out his days!
Japanese Okada, Chief Chronologist, noticed John's incredulous look and smiled:
I see you can’t understand these things with time and space...
“I once read Wells’ story “The Newest Accelerator,” Vavier intervened, “where time is also “shrinking”, like ours.
“And somehow I came across “Lost Horizon” by James Hilton,” added Professor Ivanov, “a story about a certain valley in Tibet, where time flowed more slowly. However, why go into such jungle in search of a “magnifying glass of time”? It is enough to watch a slow-motion film (as they usually say, which is completely wrong, everything is just the opposite - this is an accelerated film!) to see how, for example, a glass, dancing in the air, falls on the table for several minutes or a flower (that’s where It’s just a slow-motion movie) dissolves in a few seconds...
But the pioneer in this field was, perhaps, Andersen - the Dane Jansen would not have been a Dane if he had not said this. - You, of course, remember that fairy tale in which the princess, just before the wedding, somehow miraculously ended up in heaven, spent only three months there, and then returned to her lover. And during this time, so to speak, “in between,” many hundreds of years passed on Earth and the poor time traveler found in her capital only a very ancient monument to a certain princess, who unexpectedly disappeared just before the wedding...
The astronauts fell silent, John thought: “What will happen if our expedition is delayed a little and we return not in 2011, but, say, in 2100? Will the right of inheritance expire?” In order not to think about the likelihood of such sad circumstances, he spoke again:
You can accuse me of ignorance, but I just can’t understand all these different times. For me, time is always time. One time.
Is there really only one? - Professor Okada noted doubtfully. - You yourself don’t believe in it. How many times have you said and heard the following phrases: “What a time these days!”, “Hard times,” and so on. Hear: “times”, not “time”! Plural!
That's just what they say...
But that's how it is. Why the hell should there be only one time? Time is the form of existence of matter, the rhythm of this existence. Existence can be different, therefore, so can the rhythms. Even a barrel organ is able to change its rhythm depending on the speed at which we turn the handle. Even with the most pedantic musician, who constantly strikes the same key at equal intervals, even with him we will notice a change in rhythm, because it is impossible to maintain absolutely the same frequency and force of strikes. What then can be said about the symphonic super-orchestra that is the world! It is absolutely clear that for such a Methuselah as, for example, uranium with its long half-life, a thousand years is the same as an instant for us! And again, our human moment, lasting half a second, should seem like an astronomically large period of time to some Anti-Methuselah, for example, the pi-meson, which, as Dr. Glasser calculated back in 1961, “lives” for almost two ten-millionths of a billionth of a second!
“Now I understand something,” John added guiltily, but Professor Okada waved his hand impatiently:
The person who says “now I understand” still understands very little about time! “Now” for a person is by no means objective modernity, but... the past! For example, when you look at the Sun from the Earth, you do not see it as it “now” is in your understanding, but perceive only what the retina of your eye has recorded at the moment, that is, a photograph of the Sun as it was for eight whole years minutes ago. This is exactly how long it takes light to travel from the Sun to the human eye. You don’t even see the expression on my face “now”, but only in the future, although close, namely in... one three-hundred-millionth of a second, since “now” I am at a distance of a meter from you.
And all this is because of Einstein,” Professor Ivanov sighed playfully. - Until the very beginning of our century, everything was simple over time. Newton, like many before and after him, argued; "Absolute time moves uniformly and independently of any object."
Even if I didn’t know about Einstein’s theory,” noted Professor Vavier, “I would still have guessed for myself that something was wrong with this uniformity and unity of time. Back in school, I noticed that an hour of playing football was significantly shorter than an hour of math, which I frankly hated.
Lord have mercy! - Professor Ivanov exclaimed, seriously frightened, - then by what miracle did you take the position of First Mathematician? If you mess up your calculations and “kick” our rocket like a soccer ball in a slightly different direction, then our match with time and space could end very badly! Can we even...
He didn’t finish, remembering that space ethics considers jokes about death in space to be a sign of bad taste, something like jokes about mother-in-law.
Questions of space and time have always interested human society. One of the concepts of these concepts comes from the ancient atomists - Democritus, Epicurus and others. They introduced the concept of empty space into scientific circulation and considered it as homogeneous and infinite.
In the process of creating a general picture of the universe, Isaac Newton (1642-1726), of course, also could not ignore the issue of the concept of space and time.
According to Newton, the world consists of matter, space and time. These three categories are independent of each other. Matter is located in infinite space. The movement of matter occurs in space and time. Newton divided space into absolute and relative. Absolute space is motionless, infinite. The relative is part of the absolute. He also classified time. By subabsolute, true (mathematical) time, he understood time that flows always and everywhere evenly, and relative time, according to Newton, is a measure of duration that exists in real life: second, minute, hour, day, month, year. For Newton, absolute time exists and lasts uniformly on its own, regardless of any events. Absolute space and absolute time represent the container of all material bodies and spaces and do not depend either on these bodies, or on these processes, or on each other.
Newton defines mass as the amount of matter and introduces the concept of “passive force” (force of inertia) and “active force” that creates the movement of bodies.
Having studied and identified the patterns of motion, Newton formulated its laws in this way:
1st law. Any body continues its state of rest or uniform rectilinear motion, since it is not forced by applied forces to change this state.
2nd law. The change in movement must be proportional to the applied driving force and occur in the direction of the straight line along which this force acts.
3rd law. An action always meets equal opposition, or the influence of two bodies on each other is equal to each other and directed in opposite directions.
Nowadays, the famous laws are formulated in a more convenient form:
> 1. Every material body maintains a state of rest or uniform rectilinear motion until the influence of other bodies forces it to change this state. The desire of a body to maintain a state of rest or uniform rectilinear motion is called inertia. Therefore, the first law is also called the law of inertia.
> 2. The acceleration acquired by a body is directly proportional to the force acting on the body and inversely proportional to the mass of the body.
> 3. The forces with which interacting bodies act on each other are equal in magnitude and opposite in direction.
Newton's second law is known to us as
F= m×a, or a= F/m
where the acceleration a received by a body under the influence of force F is inversely proportional to the mass of the body m. Magnitude m called inertial mass of the body, it characterizes the body’s ability to resist the acting (“active”) force, that is, to maintain a state of rest. Newton's second law is valid only in inertial frames of reference.
The first law can be obtained from the second, since in the absence of influence on the body from other forces, the acceleration is also zero. However, the first law is considered as an independent law, since it states the existence of inertial frames of reference.
>Inerial reference systems- these are systems in which the law of inertia is valid: a material point, when no forces act on it (or mutually balanced forces act on it), is in a state of rest or uniform linear motion.
Theoretically, there can be any number of equal inertial reference systems, and in all such systems the laws of physics are the same. This is stated by Galileo's principle of relativity (1636).
Scientific proof of the existence of universal gravitation and the mathematical expression of the law describing it became possible only on the basis of the laws of mechanics discovered by I. Newton. The law of universal gravitation was formulated by Newton in his work “Mathematical Principles of Natural Philosophy” (1687).
Newton formulated the law of universal gravitation in the following theses: “gravity exists for all bodies in general and is proportional to the mass of each of them,” “gravity towards individual equal particles of bodies is inversely proportional to the squares of the distances of places to particles.” This law is known as:
where m 1, w 2 are the masses of two particles, r- the distance between them, G- gravitational constant (in SI system G= 6.672 · 10 -11 m 2 /kg 2). The physical meaning of the gravitational constant is that it characterizes the force of attraction between two masses weighing 1 kg at a distance of 1 m.
Having discovered the law of universal gravitation, Newton was able to answer the question of why the Moon revolves around the Earth and why the planets move around the Sun. In each individual case he could calculate the force of gravity. But how the interaction between masses attracting each other is transmitted, what the nature of this force is, Newton could not explain.
In Newton's works, gravity is a force that acts over large distances and, as it were, without any material intermediary.
This led to the concept of "long-range action". Newton could not explain the nature of “action at a distance”. He thought about some kind of material “agent” with the help of which gravitational interaction is carried out, but he failed in solving this problem. Based on Newton's law of universal gravitation, celestial mechanics allows for the fundamental possibility of instantaneous transmission of signals, which contradicts modern physics (general relativity). Therefore, a literal understanding of Newton's law of gravitation is unacceptable from a modern point of view.
The Newtonian mechanistic paradigm in natural science dominated for more than 200 years, although it was criticized on a number of points, including in the understanding of space and time (Leibniz, Hegel, Berkeley, etc.). At the end of the 19th and beginning of the 20th centuries. Fundamentally new scientific ideas about the surrounding nature arose. New paradigms appeared: first relativistic and then quantum (see earlier). The concept of a field as a material environment that connects particles of matter and all physical objects of the material world has fully entered into the physical picture of the world. In modern physics, four types of interaction of material objects are known: electromagnetic, gravitational, strong and weak (see above). They are responsible for all interaction processes.
3.2. Conservation laws
Let's consider the most general laws of conservation, which govern the entire material world and which introduce a number of fundamental concepts into physics: energy, momentum (momentum), angular momentum, charge.
Law of conservation of momentum
As is known, the quantity of motion, or impulse, is the product of speed and the mass of a moving body: p = mv This physical quantity allows you to find the change in the movement of a body over a certain period of time. To solve this problem, one would have to apply Newton's second law countless times, at all intermediate moments of time. The law of conservation of momentum (momentum) can be obtained using Newton's second and third laws. If we consider two (or more) material points (bodies) interacting with each other and forming a system isolated from the action of external forces, then during the movement the impulses of each point (body) can change, but the total impulse of the system must remain unchanged:
m 1 v + m 1 v 2 = const.
Interacting bodies exchange impulses while maintaining the total impulse.
In the general case we get:
where P Σ is the total, total impulse of the system, m i v i- impulses of individual interacting parts of the system. Let us formulate the law of conservation of momentum:
> If the sum of external forces is zero, the momentum of the system of bodies remains constant during any processes occurring in it.
An example of the operation of the law of conservation of momentum can be considered in the process of interaction of a boat with a person, which has buried its nose in the shore, and the person in the boat quickly walks from stern to bow at a speed v 1 . In this case, the boat will move away from the shore at a speed v 2 :
A similar example can be given with a projectile that exploded in the air into several parts. The vector sum of the impulses of all fragments is equal to the impulse of the projectile before the explosion.
Law of conservation of angular momentum
It is convenient to characterize the rotation of rigid bodies by a physical quantity called angular momentum.
When a rigid body rotates around a fixed axis, each individual particle of the body moves in a circle with a radius r i at some linear speed v i. Speed v i and momentum p = m i v i perpendicular to the radius r i. Product of impulse p = m i v i per radius r i is called the angular momentum of the particle:
L i= m i v i r i= P i r i·
Whole body angular momentum:
If we replace the linear speed with the angular velocity (v i = ωr i), then
where J = mr 2 is the moment of inertia.
The angular momentum of a closed system does not change over time, that is L= const and Jω = const.
In this case, the angular momentum of individual particles of a rotating body can change as desired, but the total angular momentum (the sum of the angular momentum of individual parts of the body) remains constant. The law of conservation of angular momentum can be demonstrated by observing a skater spinning on skates with his arms extended to the sides and with his arms raised above his head. Since Jω = const, then in the second case the moment of inertia J decreases, which means that the angular velocity u must increase, since Jω = const.
Law of energy conservation
Energy is a universal measure of various forms of movement and interaction. The energy given by one body to another is always equal to the energy received by the other body. To quantify the process of energy exchange between interacting bodies, mechanics introduces the concept of the work of a force that causes movement.
The kinetic energy of a mechanical system is the energy of mechanical motion of that system. The force causing the movement of a body does work, and the energy of a moving body increases by the amount of work expended. As is known, a body of mass m, moving at speed v, has kinetic energy E= mv 2 /2.
Potential energy is the mechanical energy of a system of bodies that interact through force fields, for example through gravitational forces. The work done by these forces when moving a body from one position to another does not depend on the trajectory of movement, but depends only on the initial and final position of the body in the force field.
Such force fields are called potential, and the forces acting in them are called conservative. Gravitational forces are conservative forces, and the potential energy of a body of mass m, raised to a height h above the Earth's surface is equal to
E sweat = mgh,
Where g- acceleration of gravity.
Total mechanical energy is equal to the sum of kinetic and potential energy:
E= E kin + E sweat
Law of conservation of mechanical energy(1686, Leibniz) states that in a system of bodies between which only conservative forces act, the total mechanical energy remains unchanged in time. In this case, transformations of kinetic energy into potential energy and vice versa can occur in equivalent quantities.
There is another type of system in which mechanical energy can be reduced by conversion into other forms of energy. For example, when a system moves with friction, part of the mechanical energy is reduced due to friction. Such systems are called dissipative, that is, systems that dissipate mechanical energy. In such systems, the law of conservation of total mechanical energy is not valid. However, when mechanical energy decreases, an amount of energy of a different type always appears equivalent to this decrease. Thus, energy never disappears or reappears, it only changes from one type to another. Here the property of indestructibility of matter and its movement is manifested.
Law of conservation of charge
Electric charges are sources of electromagnetic fields. The entire set of electrical phenomena is a manifestation of the existence of movement and interaction of electric charges.
At the end of the 19th century. The English physicist Thomson discovered the electron - the carrier of a negative elementary electric charge (-1.6 · 10 -19 C), and at the beginning of the 20th century. Rutherford discovered the proton, which has the same elementary positive charge. Since each particle is characterized by a certain inherent electric charge, the law of charge conservation can be considered as a consequence of the conservation of the number of particles, if interconversion of particles does not occur.
When physical bodies are electrified, the number of charged particles does not change, but only their redistribution in space occurs. In general, the law of conservation of charge can be formulated as follows:
> in a closed system, the algebraic sum of the charges of the system remains unchanged in time, no matter what processes occur within this closed system.
This concept has existed in physics for a long time, and in 1843 M. Faraday experimentally confirmed this law. Like other conservation laws, law of conservation of charge valid at all structural levels of the material world.
The law of conservation of charge, together with the law of conservation of energy, characterizes the stability of the electron. It cannot spontaneously transform into a heavier particle or a lighter one.
In the first case, this is not allowed by the law of conservation of energy, and in the second, by the law of conservation of charge.
3.3. Principles of modern physics
Principle of symmetry
Symmetry is understood as homogeneity, proportionality, harmony of some material objects. Asymmetry is the opposite concept. Any physical object contains elements of symmetry and asymmetry. Let's consider symmetries in physics, chemistry and biology.
In physics, symmetry is defined as follows: if physical laws do not change under certain transformations to which a system (physical object) can be subjected, then these laws are considered to have symmetry (or are invariant) with respect to these transformations.
Symmetries are divided into spatiotemporal And internal, the latter relate only to the microcosm.
Among the spatio-temporal ones, we will consider the main ones.
1. Time shift. Changing the origin does not change physical laws. Time is uniform throughout space.
2. Shift of the spatial coordinate reference system. This operation does not change physical laws. All points in space have equal rights, and space is homogeneous.
3. Rotating the spatial coordinate reference system also keeps physical laws unchanged - which means space is isotropic.
4. Classic Galileo's principle of relativity establishes symmetry between rest and uniform linear motion.
5. Reversal of the sign of the times does not change the fundamental laws in the macrocosm, that is, the processes of the macrocosm can also be described by reversing the sign of time. At the level of the macrocosm, the irreversibility of processes is observed, since they are associated with the nonequilibrium state of the Universe.
In chemistry, symmetries are manifested in the geometric configuration of molecules. This determines both the chemical and physical properties of molecules. Most simple molecules have axes of symmetry, planes of symmetry. For example, the ammonia molecule NH 3 is a regular triangular pyramid, the methane molecule CH 4 is a regular tetrahedron. Concepts of symmetry are very useful in the theoretical analysis of the structure of complex compounds, their properties and behavior.
In biology, symmetries have long been studied by specialists. Of greatest interest is the structural symmetry of biological objects. It manifests itself in the form of one or another regular repetition. At the lower stages of the development of living nature, representatives of all classes of point symmetry (regular polyhedra, balls) are found. At higher stages of evolution, plants and animals are found mainly with axial and actinomorphic symmetry. Biological objects with axial symmetry are characterized by an axis of symmetry (jellyfish, phlox flower), and with actinomorphic ones - an axis of symmetry and planes intersecting on this axis (for example, a butterfly with bilateral symmetry).
The symmetry of crystals is widely known. This property of crystals seems to combine with themselves in various positions through rotations, reflections, and parallel transfers. The symmetry of the external shape of crystals is determined by the symmetry of their atomic structure.
All this is due to the symmetry of the physical properties of crystals.
Symmetry and conservation laws
In 1918, German mathematician Emmy Noether proved a fundamental theorem establishing a connection between the properties of symmetry and conservation laws. The essence of the theorem is that continuous transformations in space-time, leaving the action invariant, are: shift in time, shift in space, three-dimensional spatial rotation, four-dimensional rotations in space-time. According to Noether's theorem, the law of conservation of energy follows from invariance with respect to time shift; from invariance with respect to spatial shifts - the law of conservation of momentum; from invariance with respect to spatial rotation - the law of conservation of angular momentum; invariance under Lorentz transformations (four-dimensional rotations in space-time) - a generalized law of motion of the center of mass: the center of mass of a relativistic system moves uniformly and rectilinearly. Noether's theorem applies not only to space-time symmetries, but also to internal ones. For example, during all transformations of elementary particles, the sum of the electrical charges of the particles remains unchanged.
The law of conservation of charge in macrosystems was confirmed experimentally long before Noether, in 1843 by M. Faraday. There is no strict scientific explanation of the reasons for the fulfillment of the law of conservation of charge.
The principle of complementarity
The principle of complementarity is fundamental in modern physics. The concept of complementarity was introduced into science by N. Bohr in 1928. This was the time of the formation of quantum mechanics. It is difficult to overestimate the importance of the principle of complementarity for the development of our ideas about the world and the knowledge of various patterns. We almost always operate on the principle of complementarity. Thus, to characterize many physical processes, two quantities are used simultaneously. For example, when assessing the movement of a material point - the coordinate of the point and its speed. One value seems to complement the other. This is typical for almost any moving material objects. This is how the principle of complementarity works in practice.
The principle of complementarity appears especially clearly in the microcosm. All microparticles have a dualistic particle-wave nature. Instrumental methods made it possible to detect this duality of microparticles, first in the photon, then in the electron and other microparticles. Any device for detecting microparticles registers them as something whole, localized in a very small area of space. On the other hand, one can observe diffraction and interference of these same microparticles on crystal lattices or artificially created obstacles during their movement, that is, microparticles have pronounced wave properties.
However, when assessing the phenomena of the world around us, we are captive of our macroscopic concepts. Therefore, an observer, assessing microprocesses, must, without a doubt accepting microparticles as localized objects (particles or corpuscles), at the same time “speculate” their wave properties. The observer must apply two complementary concepts. Only in combination with these two sets of concepts will information about microprocesses be reliable.
Thus, one characteristic can reflect only part of the truth, and by collecting the contradictory characteristics of one object, you can get a complete picture of this object. In general form, the principle of complementarity can be formulated as follows:
> In the field of quantum phenomena, the most general physical properties of any system must be expressed in terms of complementary pairs of independent variables, each of which can be better defined only by correspondingly reducing the degree of certainty of the other.
Heisenberg Uncertainty Principle
The uncertainty principle is a fundamental law of the microworld. It can be considered a particular expression of the principle of complementarity.
In classical mechanics, a particle moves along a certain trajectory, and at any moment in time it is possible to accurately determine its coordinates and its momentum. Regarding microparticles, this idea is incorrect. A microparticle does not have a clearly defined trajectory; it has both the properties of a particle and the properties of a wave (wave-particle duality). In this case, the concept of “wavelength at a given point” has no physical meaning, and since the momentum of a microparticle is expressed through the wavelength - p= To/ l, then it follows that a microparticle with a certain momentum has a completely uncertain coordinate, and vice versa.
W. Heisenberg (1927), taking into account the dual nature of microparticles, came to the conclusion that it is impossible to simultaneously characterize a microparticle with both coordinates and momentum with any predetermined accuracy.
The following inequalities are called Heisenberg uncertainty relations:
Δx Δ p x ≥ h,Δ yΔp y ≥ h,Δ zΔp z ≥ h.
Here Δx, Δy, Δz mean coordinate intervals in which a microparticle can be localized (these intervals are coordinate uncertainties), Δ p x ,Δ p y,Δ p z mean the intervals of pulse projections onto the coordinate axes x, y, z, h- Planck's constant. According to the uncertainty principle, the more accurately the impulse is recorded, the greater the uncertainty in the coordinate will be, and vice versa.
Principle of correspondence
As science develops and accumulated knowledge deepens, new theories become more accurate. New theories cover ever wider horizons of the material world and penetrate into previously unexplored depths. Dynamic theories are replaced by static ones.
Each fundamental theory has certain limits of applicability. Therefore, the emergence of a new theory does not mean a complete negation of the old one. Thus, the movement of bodies in the macrocosm with speeds significantly lower than the speed of light will always be described by classical Newtonian mechanics. However, at speeds comparable to the speed of light (relativistic speeds), Newtonian mechanics is not applicable.
Objectively, there is continuity of fundamental physical theories. This is the principle of correspondence, which can be formulated as follows: no new theory can be valid unless it contains as a limiting case the old theory relating to the same phenomena, since the old theory has already proven itself in its field.
3.4. The concept of the state of the system. Laplace determinism
In classical physics, a system is understood as a collection of some parts connected to each other in a certain way. These parts (elements) of the system can influence each other, and it is assumed that their interaction can always be assessed from the standpoint of cause-and-effect relationships between the interacting elements of the system.
The philosophical doctrine of the objectivity of the natural relationship and interdependence of phenomena of the material and spiritual world is called determinism. The central concept of determinism is the existence causality; Causality occurs when one phenomenon gives rise to another phenomenon (effect).
Classical physics stands on the position of rigid determinism, which is called Laplaceian; it was Pierre Simon Laplace who proclaimed the principle of causality as a fundamental law of nature. Laplace believed that if the location of the elements (some bodies) of a system and the forces acting in it are known, then it is possible to predict with complete certainty how each body of this system will move now and in the future. He wrote: “We must consider the present state of the Universe as the consequence of the previous state and as the cause of the subsequent one. A mind which at a given moment knew all the forces operating in nature, and the relative positions of all its constituent entities, if it were still so vast as to take into account all these data, would embrace in one and the same formula the movements of the largest bodies of the Universe and the lightest atoms. Nothing would be uncertain for him, and the future, like the past, would stand before his eyes.” Traditionally, this hypothetical creature, which could (according to Laplace) predict the development of the Universe, is called in science “Laplace’s demon.”
In the classical period of the development of natural science, the idea was affirmed that only dynamic laws fully characterize causality in nature.
Laplace tried to explain the whole world, including physiological, psychological, and social phenomena from the point of view of mechanistic determinism, which he considered as a methodological principle for constructing any science. Laplace saw an example of the form of scientific knowledge in celestial mechanics. Thus, Laplacean determinism denies the objective nature of chance, the concept of the probability of an event.
Further development of natural science led to new ideas of cause and effect. For some natural processes, it is difficult to determine the cause - for example, radioactive decay occurs randomly. It is impossible to unambiguously relate the time of “escape” of an α- or β-particle from the nucleus and the value of its energy. Such processes are objectively random. There are especially many such examples in biology. In modern natural science, modern determinism offers various, objectively existing forms of interconnection of processes and phenomena, many of which are expressed in the form of relationships that do not have pronounced causal connections, that is, do not contain moments of generation of one by another. These are space-time connections, relations of symmetry and certain functional dependencies, probabilistic relationships, etc. However, all forms of real interactions of phenomena are formed on the basis of universal active causality, outside of which not a single phenomenon of reality exists, including the so-called random phenomena, in the aggregate of which static laws are manifested.
Science continues to develop and is enriched with new concepts, laws, and principles, which indicates the limitations of Laplacean determinism. However, classical physics, in particular classical mechanics, still has its niche of application today. Its laws are quite applicable for relatively slow movements, the speed of which is significantly less than the speed of light. The importance of classical physics in the modern period was well defined by one of the creators of quantum mechanics, Niels Bohr: “No matter how far the phenomena go beyond the classical physical explanation, all experimental data must be described using classical concepts. The rationale for this is simply to state the precise meaning of the word “experiment.” With the word "experiment" we indicate a situation where we can tell others exactly what we have done and what exactly we have learned. Therefore, the experimental setup and observational results must be described unambiguously in the language of classical physics.”
3.5. Special theory of relativity (STR)
Introduction to service station
We become acquainted with the theory of relativity in high school. This theory explains to us the phenomena of the surrounding world in such a way that it contradicts “common sense.” True, the same A. Einstein once remarked: “Common sense is prejudices that develop before the age of eighteen.”
Back in the 18th century. scientists tried to answer questions about how gravitational interaction is transmitted and how light (later, any electromagnetic waves) propagates. The search for answers to these questions was the reason for the development of the theory of relativity.
In the 19th century physicists were convinced that there was a so-called ether (world ether, luminiferous ether). According to the ideas of past centuries, this is a kind of all-pervading, all-filling environment. Development of physics in the second half of the 19th century. required scientists to concretize their ideas about the ether as much as possible. If we assume that the ether is like a gas, then only longitudinal waves could propagate in it, and electromagnetic waves could propagate transversely. It is not clear how celestial bodies could move in such an ether. There were other serious objections to the broadcast. At the same time, Scottish physicist James Maxwell (1831-1879) created the theory of the electromagnetic field, from which, in particular, it followed that the final speed of propagation of this field in space was 300,000 km/s. The German physicist Heinrich Hertz (1857-1894) experimentally proved the identity of light, heat rays and electromagnetic “wave motion”. He determined that the electromagnetic force acts at a speed of 300,000 km/s. Moreover, Hertz established that “electric forces can be separated from weighty bodies and continue to exist independently as a state or change in space.” However, the situation with the ether raised many questions, and a direct experiment was required to abolish this concept. The idea was formulated by Maxwell, who proposed using the Earth as a moving body, which moves in orbit at a speed of 30 km/s. This experience required extremely high measurement accuracy. This most difficult problem was solved in 1881 by American physicists A. Michelson and E. Morley. According to the "stationary ether" hypothesis, one can observe the "etheric wind" as the Earth moves through the "ether", and the speed of light in relation to the Earth should depend on the direction of the light ray relative to the direction of the Earth's movement in the ether (that is, light is directed along the movement of the Earth and against ). The speeds in the presence of ether had to be different. But they turned out to be unchanged. This showed that there was no air. This negative result confirmed the theory of relativity. The experiment of Michelson and Morley to determine the speed of light was repeated several times later, in 1885-1887, with the same result.
In 1904, at a scientific congress, the French mathematician Henri Poincaré (1854-1912) expressed the opinion that in nature there cannot be speeds greater than the speed of light. At the same time, A. Poincaré formulated the principle of relativity as a universal law of nature. In 1905 he wrote: “The impossibility of proving by experiment the absolute motion of the Earth is obviously a general law of nature.” Here he points out the Lorentz transformations and the general connection between spatial and temporal coordinates.
Albert Einstein (1879-1955), when creating the special theory of relativity, did not yet know about Poincaré’s results. Einstein would later write: “I absolutely do not understand why I am extolled as the creator of the theory of relativity. If it weren’t for me, Poincaré would have done it in a year, Minkowski would have done it in two years, after all, more than half of this business belongs to Lorentz. My merits are exaggerated." However, Lorentz, for his part, wrote in 1912: “Einstein’s merit lies in the fact that he was the first to express the principle of relativity in the form of a universal, strict law.”
Two postulates of Einstein in SRT
To describe physical phenomena, Galileo introduced the concept of an inertial frame. In such a system, a body that is not acted upon by any force is at rest or in a state of uniform linear motion. The laws describing mechanical motion are equally valid in different inertial systems, that is, they do not change when moving from one coordinate system to another. For example, if a passenger is walking in a moving train carriage in the direction of its movement at a speed v 1 = 4 km/h, and the train is moving at speed v 2 = 46 km/h, then the speed of the passenger relative to the railway track will be vΣ= v 1 +v 2 = 50 km/h, that is, there is an addition of speeds. According to “common sense” this is an unshakable fact:
v Σ= v 1 +v 2
However, in the world of high speeds, comparable to the speed of light, the specified formula for adding speeds is simply incorrect. In nature, light travels at speed With= 300,000 km/s, regardless of which direction the light source is moving relative to the observer.
In 1905, 26-year-old Albert Einstein published an article “On the electrodynamics of moving bodies” in the German scientific journal “Annals of Physics.” In this article, he formulated two famous postulates that formed the basis of the partial, or special, theory of relativity (SRT), which changed the classical ideas about space and time.
In the first postulate, Einstein developed Galileo's classical principle of relativity. He showed that this principle is universal, including for electrodynamics (and not just for mechanical systems). This position was not unambiguous, since it was necessary to abandon Newtonian long-range action.
Einstein's generalized principle of relativity states that no physical experiments (mechanical and electromagnetic) within a given frame of reference can establish whether this system is moving uniformly or is at rest. At the same time, space and time are connected with each other, dependent on each other (for Galileo and Newton, space and time are independent of each other).
Einstein proposed the second postulate of the special theory of relativity after analyzing Maxwell's electrodynamics - this is the principle of the constancy of the speed of light in a vacuum, which is approximately equal to 300,000 km/s.
The speed of light is the fastest speed in our Universe. There cannot be a speed greater than 300,000 km/s in the world around us.
In modern accelerators, microparticles are accelerated to enormous speeds. For example, an electron accelerates to a speed v e = 0.9999999 C, where v e, C are the speeds of electron and light, respectively. In this case, from the point of view of the observer, the mass of the electron increases by 2500 times:
Here m e0 is the rest mass of the electron, m e- electron mass at speed v e .
An electron cannot reach the speed of light. However, there are microparticles that have the speed of light, they are called “luxons”.
These include photons and neutrinos. They have practically no rest mass, they cannot be slowed down, they always move at the speed of light With. All other microparticles (tardyons) move at speeds less than the speed of light. Microparticles whose movement speed could be greater than the speed of light are called tachyons. There are no such particles in our real world.
An extremely important result of the theory of relativity is the identification of the connection between energy and mass of a body. At low speeds
Where E = m 0 c 2 - rest energy of a particle with rest mass m 0 ,a E K- kinetic energy of a moving particle.
A huge achievement of the theory of relativity is the fact that it established the equivalence of mass and energy (E = m 0 c 2). However, we are not talking about the transformation of mass into energy and vice versa, but rather that the transformation of energy from one type to another corresponds to the transition of mass from one form to another. Energy cannot be replaced by mass, since energy characterizes the ability of a body to do work, and mass is a measure of inertia.
At relativistic speeds close to the speed of light:
Where E- energy, m- particle mass, m- rest mass of the particle, With- speed of light in vacuum.
From the above formula it is clear that in order to achieve the speed of light, an infinitely large amount of energy must be imparted to the particle. For photons and neutrinos this formula is not fair, since they have v= c.
Relativistic effects
In the theory of relativity, relativistic effects mean changes in the space-time characteristics of bodies at speeds comparable to the speed of light.
As an example, a spacecraft such as a photon rocket is usually considered, which flies in space at a speed commensurate with the speed of light. In this case, a stationary observer can notice three relativistic effects:
1. Increase in mass compared to rest mass. As speed increases, so does mass. If a body could move at the speed of light, then its mass would increase to infinity, which is impossible. Einstein proved that the mass of a body is a measure of the energy it contains (E= mc 2 ). It is impossible to impart infinite energy to the body.
2. Reduction of the linear dimensions of the body in the direction of its movement. The greater the speed of a spaceship flying past a stationary observer, and the closer it is to the speed of light, the smaller the size of this ship will be for a stationary observer. When the ship reaches the speed of light, its observed length will be zero, which cannot be. On the ship itself, the astronauts will not observe these changes. 3. Time dilation. In a spacecraft moving at close to the speed of light, time passes more slowly than for a stationary observer.
The effect of time dilation would affect not only the clock inside the ship, but also all the processes occurring on it, as well as the biological rhythms of the astronauts. However, a photon rocket cannot be considered as an inertial system, because during acceleration and deceleration it moves with acceleration (and not uniformly and rectilinearly).
The theory of relativity offers fundamentally new estimates of space-time relationships between physical objects. In classical physics, when moving from one inertial system (No. 1) to another (No. 2), the time remains the same - t 2 = t L and the spatial coordinate changes according to the equation x 2 = x 1 -vt. The theory of relativity uses the so-called Lorentz transformations:
From the relationships it is clear that spatial and temporal coordinates depend on each other. As for the reduction in length in the direction of movement, then
and the passage of time slows down:
In 1971, an experiment was carried out in the USA to determine time dilation. They made two absolutely identical exact watches. Some watches remained on the ground, while others were placed in a plane that flew around the Earth. An airplane flying in a circular path around the Earth moves with some acceleration, which means that the clock on board the airplane is in a different situation compared to a clock resting on the ground. In accordance with the laws of relativity, the traveling clock should have lagged behind the resting clock by 184 ns, but in fact the lag was 203 ns. There were other experiments that tested the effect of time dilation, and they all confirmed the fact of slowing down. Thus, the different flow of time in coordinate systems moving uniformly and rectilinearly relative to each other is an immutable experimentally established fact.
General theory of relativity
After the publication of the special theory of relativity in 1905, A. Einstein turned to the modern concept of gravity. In 1916, he published the general theory of relativity (GTR), which explains the theory of gravity from a modern point of view. It is based on two postulates of the special theory of relativity and formulates the third postulate - the principle of equivalence of inertial and gravitational masses. The most important conclusion of General Relativity is the position about changes in geometric (spatial) and temporal characteristics in gravitational fields (and not only when moving at high speeds). This conclusion connects GTR with geometry, that is, in GTR the geometrization of gravity is observed. Classical Euclidian geometry was not suitable for this. New geometry appeared in the 19th century. in the works of the Russian mathematician N.I. Lobachevsky, the German - B. Riemann, the Hungarian - J. Bolyai.
The geometry of our space turned out to be non-Euclidean.
General relativity is a physical theory based on a number of experimental facts. Let's look at some of them. The gravitational field affects the movement of not only massive bodies, but also light. A ray of light is deflected into the field of the Sun. Measurements carried out in 1922 by the English astronomer A. Eddington during a solar eclipse confirmed this prediction of Einstein.
In general relativity, the orbits of planets are not closed. A small effect of this kind can be described as a rotation of the perihelion of an elliptical orbit. Perihelion is the point of the orbit of a celestial body closest to the Sun, which moves around the Sun in an ellipse, parabola or hyperbola. Astronomers know that the perihelion of Mercury’s orbit rotates by about 6,000 per century.” This is explained by gravitational disturbances from other planets. At the same time, there remained an irremovable remainder of about 40” per century. In 1915, Einstein explained this discrepancy within the framework of general relativity.
There are objects in which the effects of general relativity play a decisive role. These include “black holes”. A “black hole” occurs when a star is compressed so much that the existing gravitational field does not even release light into outer space. Therefore, no information comes from such a star. Numerous astronomical observations indicate the real existence of such objects. General Relativity provides a clear explanation for this fact.
In 1918, Einstein predicted, based on general relativity, the existence of gravitational waves: massive bodies moving with acceleration emit gravitational waves. Gravitational waves must travel at the same speed as electromagnetic waves, that is, at the speed of light. By analogy with electromagnetic field quanta, it is customary to speak of gravitons as gravitational field quanta. Currently, a new field of science is being formed - gravitational wave astronomy. There is hope that gravitational experiments will yield new results.
Based on the equations of the theory of relativity, the domestic mathematician and physicist A. Friedman in 1922 found a new cosmological solution to the equations of general relativity. This solution indicates that our Universe is not stationary, it is continuously expanding. Friedman found two options for solving Einstein’s equations, that is, two options for the possible development of the Universe. Depending on the density of matter, the Universe will either continue to expand, or after some time it will begin to contract.
In 1929, American astronomer E. Hubble experimentally established a law that determines the speed of expansion of galaxies depending on the distance to our galaxy. The further away the galaxy is, the greater its speed of expansion. Hubble used the Doppler effect, according to which a light source moving away from the observer increases its wavelength, that is, shifts to the red end of the spectrum (reddens).
Thus, all known scientific facts confirm the validity of the general theory of relativity, which is the modern theory of gravity.
3.6. The beginnings of thermodynamics. Ideas about entropy
General information about thermodynamics
>Thermodynamics is the science of the most general properties of macroscopic bodies and systems in a state of thermodynamic equilibrium, and of the processes of transition from one state to another.
Classical thermodynamics studies physical objects of the material world only in a state of thermodynamic equilibrium. Here we mean a state into which a system comes over time, being under certain constant external conditions and a certain constant ambient temperature. For such equilibrium states, the concept of time is unimportant. Therefore, time is not used explicitly as a parameter in thermodynamics. In its original form, this discipline was called “mechanical theory of heat.” The term “thermodynamics” was introduced into the scientific literature in 1854 by W. Thomson. Equilibrium processes of classical thermodynamics also make it possible to judge the patterns of processes occurring during the establishment of equilibrium, that is, it considers the ways to establish thermodynamic equilibrium.
At the same time, thermodynamics considers the conditions for the existence of irreversible processes. For example, the spread of gas molecules (the law of diffusion) ultimately leads to an equilibrium state, and thermodynamics prohibits the reverse transition of such a system to the original state.
The task of the thermodynamics of irreversible processes was first to study nonequilibrium processes for states that do not differ too much from the equilibrium state. The emergence of the thermodynamics of irreversible processes dates back to the 50s. last century. It was formed on the basis of classical thermodynamics, which arose in the second half of the 19th century. In the development of classical thermodynamics, an outstanding role was played by the works of N. Carnot, B. Clapeyron, R. Clausius and others. A relatively long time passed before it became clear that classical thermodynamics is essentially thermostatics, and the fundamental equations of Fourier-Ohm-Fick and Navier —Stokes represent the elements of future thermodynamics. Here we should name one of the pioneers of the new direction in thermodynamics - the American physicist L. Onsager (Nobel Prize 1968), as well as the Dutch-Belgian school of I. Prigogine, S. de Groot, P. Mazur. In 1977, the Belgian physicist and physical chemist of Russian origin, Ilya Romanovich Prigogine, was awarded the Nobel Prize in Chemistry “for his contributions to the theory of nonequilibrium thermodynamics, in particular to the theory of dissipative structures, and for its applications in chemistry and biology.”
Thermodynamics as a function of state
The equality of temperatures at all points of some systems or parts of one system is a condition of equilibrium.
The state of homogeneous liquids or gases is completely fixed by specifying any two of three quantities: temperature G, volume V, pressure p. The connection between p, V And T called the equation of state. French physicist B. Clapeyron in 1934 derived the equation of state for an ideal gas, combining the Boyle-Mariotte and Gay-Lusac laws. D.I. Mendeleev combined Clapeyron's equations with Avogadro's law. According to Avogadro's law, at equal pressures R and temperature G moles of all gases occupy the same molar volume V m, therefore, for all gases there is a molar gas constant R. Then the Clapeyron–Mendeleev Equation can be written as:
pV m= RT.
Numerical value of the molar gas constant R= 8.31 J/mol K.
First law of thermodynamics
The first law, or the first law of thermodynamics, or the law of conservation of energy for thermal systems, can be conveniently considered using the example of the operation of a heat engine. The heat engine contains a heat source Q 1 , a working fluid, for example a cylinder with a piston, under which the gas can be heated (ΔQ 1) or cooled by a refrigerator that removes heat ΔQ 2 from the working fluid. In this case, work Δ can be performed A and the internal energy Δ changes U.
The energy of thermal motion can be converted into the energy of mechanical motion, and vice versa. During these transformations, the law of conservation and transformation of energy is observed. In relation to thermodynamic processes, this is the first law of thermodynamics, established as a result of generalization of centuries-old experimental data. Experience shows that the change in internal energy ΔU is determined by the difference between the amount of heat Q 1 , obtained by the system, and work A:
ΔU= Q 1 - A
Q 1 = A 1 + ΔU.
In differential form:
dQ= dA+ dU.
The first law of thermodynamics determines the second state function - energy, more precisely, internal energy U, which represents the energy of the chaotic movement of all molecules, atoms, ions, etc., as well as the energy of interaction of these microparticles. If the system does not exchange energy or matter with the environment (isolated system), then dU= 0, a U= const in accordance with the law of conservation of energy. It follows that work A equal to the amount of heat Q, that is, a periodically operating engine (heat engine) cannot perform more work than the energy imparted to it from the outside, which means that it is impossible to create an engine that, through some transformation of energy, can increase its total amount.
Circular processes (cycles). Reversible and irreversible processes
>By circular process(cycle) is a process in which a system passes through a series of states and returns to its original state. Such a cycle can be represented as a closed curve in the axes P, V, Where P- pressure in the system, and V- its volume. A closed curve consists of sections where volume increases (expansion) and sections where volume decreases (contraction).
In this case, the work done per cycle is determined by the area covered by the closed curve. The cycle that proceeds through expansion and then compression is called direct; it is used in heat engines - periodically operating engines that perform work using heat received from outside. The cycle, which proceeds through compression and then expansion, is called reverse and is used in refrigeration machines - periodically operating installations in which, due to the work of external forces, heat is transferred from one body to another. As a result of a circular process, the system returns to its original state:
ΔU=0, Q= A
The system can both receive heat and give it away. If the system receives Q 1 warmth, but gives off Q 2 , then the thermal efficiency for the circular process
Reversible processes can occur in both forward and reverse directions
In the ideal case, if the process occurs first in the forward and then in the reverse direction and the system returns to its original state, then no changes occur in the environment. Reversible processes are an idealization of real processes in which some energy loss always occurs (for friction, thermal conductivity, etc.)
The concept of a reversible circular process was introduced into physics in 1834 by the French scientist B. Clapeyron
Ideal cycle of a Carnot heat engine
When we talk about the reversibility of processes, it should be borne in mind that this is some kind of idealization. All real processes are irreversible, therefore the cycles in which heat engines operate are also irreversible, and therefore nonequilibrium. However, to simplify quantitative assessments of such cycles, it is necessary to consider them equilibrium, that is, as if they consisted only of equilibrium processes. This is required by a well-developed apparatus of classical thermodynamics.
The famous ideal Carnot engine cycle is considered an equilibrium reverse circular process. In real conditions, any cycle cannot be ideal, since there are losses. It occurs between two heat sources with constant temperatures at the heat sink T 1 and heat sink T 2, as well as the working fluid, which is taken to be an ideal gas (Fig. 3.1).
Rice. 3.1. Heat Engine Cycle
We believe that T 1 > T 2 and heat removal from the heat sink and heat supply to the heat sink do not affect their temperatures, T 1 And T 2 remain constant. Let us denote the gas parameters at the left extreme position of the heat engine piston: pressure - R 1 volume - V 1 , temperature T 1 . This is point 1 on the graph on the axes P-V. At this moment, the gas (working fluid) interacts with the heat sink, the temperature of which is also T 1 . As the piston moves to the right, the gas pressure in the cylinder decreases and the volume increases. This will continue until the piston reaches the position determined by point 2, where the parameters of the working fluid (gas) take on the values P 2 , V 2 , T 2 . The temperature at this point remains unchanged, since the temperature of the gas and the heat sink are the same during the transition of the piston from point 1 to point 2 (expansion). A process in which T does not change, is called isothermal, and curve 1-2 is called an isotherm. In this process, heat passes from the heat transmitter to the working fluid Q 1 .
At point 2, the cylinder is completely isolated from the external environment (there is no heat exchange) and with further movement of the piston to the right, a decrease in pressure and an increase in volume occurs along curve 2-3, which is called adiabatic(process without heat exchange with the external environment). When the piston moves to the extreme right position (point 3), the expansion process will end and the parameters will have the values P 3, V 3, and the temperature will become equal to the temperature of the heat sink T 2. With this position of the piston, the insulation of the working fluid is reduced and it interacts with the heat sink. If we now increase the pressure on the piston, it will move to the left at a constant temperature T 2(compression). This means that this compression process will be isothermal. In this process the heat Q 2 will pass from the working fluid to the heat sink. The piston, moving to the left, will come to point 4 with the parameters P 4 , V 4 and T 2, where the working fluid is again isolated from the external environment. Further compression occurs along an adiabatic 4-1 with increasing temperature. At point 1, compression ends at the working fluid parameters P 1 , V 1 , T 1 . The piston returned to its original state. At point 1, the isolation of the working fluid from the external environment is removed and the cycle repeats.
Efficiency of an ideal Carnot engine:
Analysis of the expression for the efficiency of the Carnot cycle allows us to draw the following conclusions:
1) The higher the efficiency, the higher the T 1 and the less T 2 ;
2) efficiency is always less than unity;
3) Efficiency is zero at T 1 = T 2.
The Carnot cycle makes the best use of heat, but, as stated above, it is idealized and is not feasible in real conditions. However, its significance is great. It allows you to determine the highest efficiency value of a heat engine.
Second law of thermodynamics. Entropy
The second law of thermodynamics is associated with the names of N. Carnot, W. Thomson (Kelvin), R. Clausius, L. Boltzmann, W. Nernst.
The second law of thermodynamics introduces a new state function - entropy. The term “entropy”, proposed by R. Clausius, is derived from the Greek. entropia and means "transformation".
It would be appropriate to present the concept of “entropy” in the formulation of A. Sommerfeld: “Every thermodynamic system has a state function called entropy. Entropy is calculated as follows. The system is transferred from an arbitrarily chosen initial state to the corresponding final state through a sequence of equilibrium states; all portions of heat dQ conducted to the system are calculated and each is divided by its corresponding absolute temperature T, and all values thus obtained are summed up (the first part of the second law of thermodynamics). During real (non-ideal) processes, the entropy of an isolated system increases (the second part of the second law of thermodynamics).”
Accounting and storing the amount of energy is not yet enough to judge the possibility of a particular process. Energy should be characterized not only by quantity, but also by quality. It is important that energy of a certain quality can spontaneously transform only into energy of a lower quality. The quantity that determines the quality of energy is entropy.
Processes in living and nonliving matter generally proceed in such a way that entropy in closed isolated systems increases, and the quality of energy decreases. This is the meaning of the second law of thermodynamics.
If we denote entropy by S, then
which corresponds to the first part of the second law according to Sommerfeld.
You can substitute the expression for entropy into the equation of the first law of thermodynamics:
dU= T×dS - dU.
This formula is known in the literature as the Gibbs ratio. This fundamental equation combines the first and second laws of thermodynamics and essentially defines all equilibrium thermodynamics.
The second principle establishes a certain direction for the flow of processes in nature, that is, the “arrow of time.”
The most profound meaning of entropy is revealed in the static assessment of entropy. In accordance with Boltzmann's principle, entropy is related to the probability of the state of the system by the known relation
S= K × LnW,
Where W- thermodynamic probability, and TO- Boltzmann constant.
The thermodynamic probability, or static weight, is understood as the number of different distributions of particles along coordinates and velocities corresponding to a given thermodynamic state. For any process that occurs in an isolated system and transfers it from state 1 to state 2, the change Δ W thermodynamic probability is positive or equal to zero:
ΔW = W 2 - W 1 ≥ 0
In the case of a reversible process, ΔW = 0, that is, the thermodynamic probability, is constant. If an irreversible process occurs, then Δ W> 0 and W increases. This means that an irreversible process transfers the system from a less probable state to a more probable one. The second law of thermodynamics is a statistical law; it describes the patterns of chaotic movement of a large number of particles that make up a closed system, that is, entropy characterizes the measure of disorder, randomness of particles in the system.
R. Clausius defined the second law of thermodynamics as follows:
> a circular process is impossible, the only result of which is the transfer of heat from a less heated body to a more heated one (1850).
In connection with this formulation, in the middle of the 19th century. the problem of the so-called thermal death of the Universe was identified. Considering the Universe as a closed system, R. Clausius, relying on the second law of thermodynamics, argued that sooner or later the entropy of the Universe must reach its maximum. The transition of heat from more heated bodies to less heated ones will lead to the fact that the temperature of all bodies in the Universe will be the same, complete thermal equilibrium will occur and all processes in the Universe will stop - the thermal death of the Universe will occur.
The fallacy of the conclusion about the thermal death of the Universe lies in the fact that it is impossible to apply the second law of thermodynamics to a system that is not a closed system, but an endlessly developing system. The Universe is expanding, galaxies are scattering at speeds that are increasing. The universe is not stationary.
The formulation of the second law of thermodynamics is based on postulates that are the result of centuries of human experience. In addition to the above-mentioned postulate of Clausius, the most famous is the postulate of Thomson (Kelvin), which speaks of the impossibility of constructing an eternal heat engine of the second kind (perpetuum mobile), that is, an engine that completely converts heat into work. According to this postulate, of all the heat received from a heat source with a high temperature - a heat sink, only a part can be converted into work. The rest must be diverted to a heat sink with a relatively low temperature, that is, at least two heat sources of different temperatures are required for the operation of a heat engine.
This explains the reason why it is impossible to convert the heat of the atmosphere around us or the heat of the seas and oceans into work in the absence of the same large-scale sources of heat with a lower temperature.
The third law of thermodynamics, or Nernst's thermal theory
Among the status functions other than temperature T, internal energy U and entropy S, there are also those that contain the product T·S. For example, when studying chemical reactions, state functions such as free energy play an important role F= U - T S or Gibbs potential Ф = U+ pV- TS. These state functions include the product T·S. However, the magnitude S is determined only up to an arbitrary constant S 0, since entropy is determined through its differential dS. Consequently, without specifying S 0, the application of state functions becomes uncertain. The question arises about the absolute value of entropy.
Nernst's thermal theory answers this question. In Planck’s formulation, it boils down to the statement: the entropy of all bodies in a state of equilibrium tends to zero as the temperature approaches zero Kelvin:
Since entropy is determined up to an additive constant S 0 , then it is convenient to take this constant equal to zero.
The thermal theorem was formulated by Nerst at the beginning of the 20th century. (Nobel Prize in Physics in 1920). It does not follow from the first two principles, therefore, due to its generality, it can rightfully be considered as a new law of nature - the third law of thermodynamics.
Nonequilibrium thermodynamics
Nonequilibrium systems are characterized not only by thermodynamic parameters, but also by the rate of their change in time and space, which determines flows (transfer processes) and thermodynamic forces (temperature gradient, concentration gradient, etc.).
The appearance of flows in the system disrupts the statistical equilibrium. In any physical system, processes always occur that try to return the system to a state of equilibrium. There is, as it were, a confrontation between the transference processes that disrupt the balance, and the internal processes that try to restore it.
Processes in nonequilibrium systems have the following three properties:
1. Processes that bring a system to thermodynamic equilibrium (recovery) occur when there are no special factors maintaining a nonequilibrium state within the system itself. If the initial state is strongly nonequilibrium, and against the background of the general tendency of the system towards equilibrium, subsystems of great interest are born in which entropy locally decreases, then local subsystems arise where orderliness increases. Moreover, the total increase for the entire system is many times greater. In an isolated system, the local decrease in entropy is, of course, temporary. In an open system, through which powerful flows flow for a long time, reducing entropy, some ordered subsystems may arise. They can exist, changing and developing, for a very long time (until the flows feeding them stop).
2. The birth of local states with low entropy leads to an acceleration of the overall growth of entropy of the entire system. Thanks to the ordered subsystems, the entire system as a whole moves faster towards increasingly disordered states, towards thermodynamic equilibrium.
The presence of an ordered subsystem can speed up the exit of the entire system from a “safe” metastable state by millions or more times. In nature, nothing is given “for free”.
3. Ordered states are dissipative structures that require a large influx of energy for their formation. Such systems react to small changes in external conditions more sensitively and more diversely than the thermodynamic equilibrium state. They can easily collapse or transform into new ordered structures.
The emergence of dissipative structures is of a threshold nature. Nonequilibrium thermodynamics related the threshold character to instability. A new structure is always the result of instability and arises from fluctuation.
The outstanding merit of nonequilibrium thermodynamics is the establishment of the fact that self-organization is inherent not only in “living systems.” The ability to self-organize is a common property of all open systems that can exchange energy with the environment. In this case, it is disequilibrium that serves as the source of order.
This conclusion is the main thesis for the range of ideas of I. Prigogine’s group.
The compatibility of the second law of thermodynamics with the ability of systems to self-organize is one of the largest achievements of modern nonequilibrium thermodynamics.
Entropy and matter. Entropy change in chemical reactions
As the temperature increases, the speed of various types of particle movement increases. Hence the number of microstates of particles, and, accordingly, the thermodynamic probability W, and the entropy of matter increase. When a substance transitions from a solid to a liquid state, the disorder of particles and, accordingly, entropy (ΔS melt) increases. Disorder and, accordingly, entropy increase especially sharply during the transition of a substance from a liquid to a gaseous state (AS boiling). Entropy increases when a crystalline substance transforms into an amorphous one. The higher the hardness of a substance, the lower its entropy. An increase in atoms in a molecule and the complexity of molecules leads to an increase in entropy. Entropy is measured in Cal/mol·K (entropy unit) and in J/mol·K. In calculations, entropy values in the so-called standard state are used, that is, at 298.15 K (25 °C). Then entropy is denoted S 0 298 . For example, the entropy of oxygen 0 3 - S 0 298 = 238.8 units. e., and 0 2 - S 0 298 = 205 units. e.
The absolute entropy values of many substances are tabulated and given in reference books. For example:
N 2 0(f) = 70.8; H 2 0(g) = 188.7; CO(g) = 197.54;
CH 4 (r) = 186.19; H 2 (g) = 130.58; NS1(g) = 186.69; HCl(p) = 56.5;
CH 3 0H(l) = 126.8; Ca(k) = 41.4; Ca(OH) 2 (k) = 83.4; C(diamond) = 2.38;
C(graphite) = 5.74, etc.
Note: g - liquid, g - gas, j - crystals; p - solution.
Change in entropy of the system as a result of a chemical reaction (Δ S) equal to the sum of the entropies of the reaction products minus the entropies of the starting substances. For example:
CH 4 +H 2 0(g) = C0 + 3H 2 - here Δ S 0 298 = S 0 co.298 + 3 S 0 H2.298 - S 0 H4.298 - S 0 H2.298 =
197.54 = 3 130.58 - 188.19 - 188.7 = 214.39 J/mol K.
As a result of the reaction, entropy increased (A S> 0), the number of moles of gaseous substances increased.
Information entropy. Entropy in biology
Information entropy serves as a measure of message uncertainty. Messages are described by many quantities x 1 , x 2 x n, which could be, for example, the words: p 1 , p 2 …, p n. Information entropy is denoted by S n or H u. For a certain discrete statistical probability distribution P i use the following expression:
given that:
Meaning S n= 0 if any probability P i= 1, and the remaining probabilities of the appearance of other quantities are equal to zero. In this case, the information is reliable, that is, there is no uncertainty in the information. Information entropy takes on its greatest value when P i are equal to each other and the uncertainty in the information is maximum.
The total entropy of several messages is equal to the sum of the entropies of individual messages (additivity property).
American mathematician Claude Shannon, one of the creators of mathematical information theory, used the concept of entropy to determine the critical speed of information transmission and to create “noise-resistant codes.” This approach (using the probabilistic entropy function from statistical thermodynamics) turned out to be fruitful in other areas of natural science.
The concept of entropy, as shown for the first time by E. Schrödinger (1944), and then by L. Brillouin and others, is essential for understanding many phenomena of life and even human activity.
It is now clear that with the help of the probabilistic entropy function it is possible to analyze all stages of the transition of a system from a state of complete chaos, which corresponds to equal probabilities and the maximum value of entropy, to a state of the maximum possible order, which corresponds to the only possible state of the elements of the system.
A living organism, from the point of view of the physical and chemical processes occurring in it, can be considered as a complex open system located in a nonequilibrium, non-stationary state. Living organisms are characterized by a balance of metabolic processes leading to a decrease in entropy. Of course, entropy cannot be used to characterize life as a whole, since life cannot be reduced to a simple set of physical and chemical processes. It is characterized by other complex processes of self-regulation.
Self-test questions
1. Formulate Newton’s laws of motion.
2. List the basic laws of conservation.
3. Name the general conditions for the validity of conservation laws.
4. Explain the essence of the symmetry principle and the connection of this principle with conservation laws.
5. Formulate the principle of complementarity and the Heisenberg uncertainty principle.
6. What is the “collapse” of Laplacean determinism?
7. How are Einstein’s postulates formulated in STR?
8. Name and explain relativistic effects.
9. What is the essence of GTR?
10. Why is a perpetual motion machine of the first kind impossible?
11. Explain the concept of a circular process in thermodynamics and the ideal Carnot cycle.
12. Explain the concept of entropy as a function of the state of the system.
13. Formulate the second law of thermodynamics.
14. Explain the essence of the concept of “nonequilibrium thermodynamics”.
15. How is the change in entropy during chemical reactions determined qualitatively?
The current absolute time value (time of day, wall time, time of day) is defined in the kernel/timer. with the following.
struct timespec xtime;
The timespe c data structure is defined in the file
struct timespec(
time_t tv_sec; /* seconds */
long tv_nsec; /* nanoseconds */
1970 (UTC, Universal Coordinated Time). The specified date is called epoch(beginning of an era). In most Unix-like operating systems, time is counted from the beginning of the epoch. The xtime.tv_nse c field stores the number of nanoseconds that have passed in the last second.
Reading or writing the xtime variable requires acquiring the xtime_lock lock. This is a lock - not a regular spinlock, but sequential locking, which is discussed in Chapter 9, "Kernel Synchronization Features."
To update the value of the xtime variable, you need to acquire a sequential write lock as follows.
write_seqlock(&xtime_lock);
/* update the value of the xtime variable ... */
write_sequnlock(&xtime_lock);
Reading the value of the xtim e variable requires the use of the read _ functions
seqbegin() and read_seqretr y() as follows.
unsigned long lost;
seq = read_seqbegin(&xtime_lock);
usec = timer->get_offset(); lost = jiffies wall_jiffies; if (lost)
usec += lost * (1000000 / HZ);
sec = xtime.tv_sec;
usec += (xtime.tv_nsec / 1000);
) while (read_seqretry(&xtime_lock, seq));
This cycle is repeated until it is guaranteed that no data was written while the data was being read. If a timer interrupt occurs while the loop is running and the xtime variable is updated while the loop is running, the sequence number returned will be incorrect and the loop will repeat again.
The main user interface for retrieving the absolute time value is the gettimeofda y() system call, which is implemented as the sys_gettimeofday() function as follows.
asmlinkage long sys_gettimeofday(struct timeval *tv, struct timezone *tz)
if (likely(tv !=NULL)) ( struct timeval_ktv; do_gettimeofday(&ktv);
if (copy_to_userftv, &ktv, sizeof(ktv))
if (unlikely(tz !=NULL)) (
if (copy_to_user(tz, &sys_tz, sizeof(sys_tz)))
If a non-zero value for the tv parameter is passed from user space, then the hardware-dependent function do_gettimeofday() is called. This function basically performs the xtime variable read loop that was just discussed. Likewise, if the tz parameter is non-zero, the user is returned the time zone in which the operating system is located. This setting is stored in the sys_tz variable. If errors occur when copying an absolute time or time zone value into user space, the function returns -EFAULT. If successful, a null value is returned.
The kernel provides the time() system call 6 , but the gettimeofday() system call completely overrides its functionality. The C function library also provides other functions related to absolute time, such as ftime() and ctirae().
The settimeofday() system call allows you to set the absolute time to a specified value. In order to execute it, the process must be able to use CAP_SYS_TIME.
Apart from updating the xtime variable, the kernel does not use absolute time as much as user space. One important exception is file system code that stores file access times in file indexes.
Timers
Timers(timers), or, as they are sometimes called, dynamic timers, or kernel timers, necessary to control the passage of time in the kernel. Kernel code often needs to defer certain functions to a later time. A vague concept has been deliberately chosen here. "Later". The purpose of the mechanism of the lower halves is not detain execution, and don't do the work right now. In this regard, a tool is needed that allows you to delay the execution of work for a certain period of time. If this time interval is not very small, but also not very large, then the solution to the problem is kernel timers.
6 For some hardware platforms function sys_time() is not implemented, but instead it is emulated by the C library of functions based on the call gettimeofday().
Timers are very easy to use. You need to do some initial work, specify the time at which the wait will end, specify a function to be executed when the timeout interval ends, and activate the timer. The specified function will be executed when the timer interval expires. Timers are not cyclical. When the timeout interval ends, the timer is eliminated. This is one of the reasons why timers are called dynamic 7. Timers are constantly created and destroyed, and there is no limit to the number of timers. The use of timers is very popular in all parts of the kernel.
Using Timers
Timers are represented using time r list structures, which are defined in the file
struct tier_list(
struct list_head entry; /* timers are stored in a linked list */
unsigned long expires; /* timeout expiration time in system timer pulses (jiffies) */
spinlock_t lock; /* lock to protect this timer */
void (*function) (unsigned long); /*timer handler function*/ unsigned long data; /* single handler argument */ struct tvec_t_base_s *base; /*internal timer data, do not touch! */
Fortunately, using timers does not require a deep understanding of the purpose of the fields in this structure. In fact, it is highly discouraged to misuse the fields of this structure in order to maintain compatibility with possible future code changes. The kernel provides a family of timer interfaces to make this job easier. All necessary definitions are in the file
The first step in creating a timer is to declare it as follows.
struct timer_list my_timer;
Next, the fields of the structure, which are intended for internal use, must be initialized. This is done using a helper function before calling any functions that operate on the timer.
my_timer.expire s = jiffie s + delay ; /* timer time interval will end after delay pulses */
7 Another reason is that in older kernels (before 2.3) there were static timers. These timers were created at compile time, not at run time. He had limited opportunities and no one is upset about their absence now.
my_timer.data = 0; /* a parameter equal to zero is passed to the Sudet handler function */
my_timer.function = my_function; /* function to be executed
when the timer interval expires */
The value of the my_timer.expire s field indicates the waiting time in system timer pulses (the absolute number of pulses must be specified). When the current value of the jiffie s variable becomes greater than or equal to the value of the my_time r field. expires , the handler function my_timer.functiio n is called with the parameter my_timer.data . As can be seen from the description of the timer_list structure, the handler function must conform to the following prototype.
void my_timer_function(unsigned long data);
The dat a parameter allows you to register multiple timers with one handler and distinguish between timers with different values for this parameter. If the argument is not needed, then you can simply specify zero (or any other) value.
The last operation is to activate the timer.
add_timer(&my_timer);
And the timer starts! You should pay attention to the importance of the expired field value. The kernel executes the handler when the current value of the system timer pulse counter more, than the specified timer response time, or equal to him. Although the kernel guarantees that no timer handler will execute before the timer expires, there may still be delays in the execution of the timer handler. Typically, timer handlers are executed at a time close to the firing time, but they can be delayed until the next system timer tick. Therefore, timers cannot be used for hard real-time operation.
Sometimes you may need to change the timing of a timer that is already active. The kernel implements the mod_time r() function, which allows you to change the time at which the active timer is triggered.
mod_timer(&my_timer, jiffies + new_delay); /* setting a new response time*/
The mod_time r() function also allows you to work with a timer that is initialized but not active. If the timer is not active, then the mod_timer() function will activate it. This function returns 0 if the timer was inactive and 1 if the timer was active. In either case, before mod_time r() returns, the timer will be activated and its firing time will be set to the specified value.
In order to deactivate the timer before it fires, you must use the del_time r() function as follows.
del_timer(&my_timer);
This function works with both active and inactive timers. If the timer is already inactive, then the function returns the value 0, otherwise it returns the value 1. Note that there is no need to call this
function for timers whose timeout interval has expired, as they are automatically deactivated.
When timers are deleted, a race condition could potentially occur. When the del_time r() function returns, it only guarantees that the timer will be inactive (that is, its handler will not be executed in the future). However, on a multiprocessor machine, the timer handler may be running on another processor at this time. To deactivate a timer and wait for its handler to complete, which could potentially be running, you need to use the del_timer_syn c() function:
del_timer_sync(&my_timer);
Unlike the del_timer() function, del_timer_sync() cannot be called from an interrupt context.
Race Conditions Associated with Timers
Because timers execute asynchronously with respect to the currently executing code, several types of resource contention conditions can potentially arise. First of all, you should never use the following code as a replacement for the inod_timer() function.
del_timer (my_timer) ;
my_timer->expires = jiffies + new_delay;
add_timer(my_timer);
Second, in almost all cases you should use the del_timer_sync() function rather than the del_timer() function. Otherwise, you cannot guarantee that the timer handler is not currently running. Imagine that once the timer is removed, the code will free up memory or otherwise interfere with the resources that the timer handler is using. Therefore, the synchronous version is preferable.
Finally, you must ensure that all shared data accessed by the timer handler function is protected. The kernel performs this function asynchronously with respect to other code. Shared data must be protected as discussed in Chapters 8 and 9.
Implementation of timers
The kernel executes timer handlers in the context of a deferred interrupt handler after the timer interrupt has completed processing. The timer interrupt handler calls the update_process_time s() function, which in turn calls the run_local_timer s() function, which looks like this.
void run_local_timers(void)
raise_softirq(TIMER_SOFTIRQ);
A pending interrupt with number TIMER_SOFTIRQ is handled by the run_tirner_softir q() function. This function executes handlers on the local processor for all timers that have timed out. ( if there are any).
Timers are stored in a linked list. However, it would be unwise for the kernel to go through the entire list looking for timers that have timed out, or to keep the list sorted based on when the timers expired. In the latter case, inserting and deleting timers would take a long time. Instead, timers are divided into 5 groups based on their response time. Timers move from one group to another as the trigger time approaches. This grouping ensures that, in most cases, when executing the deferred interrupt handler responsible for executing timer handlers, the kernel will do little work to find timers that have expired. Therefore, the timer management code is very efficient.
Verb tense, denoting the relationship of action to the moment of speech, regardless of other tense forms in speech... Dictionary of linguistic terms T.V. Foal
absolute time- Verbal form of time, independent of other tense forms in a sentence, determined by its relationship with the moment of speech. I am reading a book; I was reading a book; I will be reading a book. compare: relative time... Dictionary of linguistic terms
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time (coordinate)- time sequence of existence (# flowering). what time. hours (# classes). year. era. times (former #). absolute time is a time determined by its relationship to the moment of speech. absolute time scale. relative time time,… … Ideographic Dictionary of the Russian Language
TIME- a grammatical category of a verb, the forms of which establish a temporal relationship between the named action and either the moment of speech (absolute tense) or another named action (relative tense) ... Big Encyclopedic Dictionary
TIME (grammatical category of verb)- TIME, a grammatical category of a verb, the forms of which establish a temporal relationship between the called action and either the moment of speech (absolute time) or another named action (relative time) ... encyclopedic Dictionary
Time (linguistics)- This term has other meanings, see Time (meanings). Time is a grammatical category of a verb, expressing the relationship of time of the situation described in speech to the moment of utterance of the utterance (that is, to the moment of speech or segment ... ... Wikipedia
Time (verb)
Time (grammar)- Time is a grammatical category of a verb, expressing the relationship of the time of the situation described in speech to the moment of utterance of the utterance (i.e., to the moment of speech or a period of time, which in the language is denoted by the word “now”), which is taken as ... ... Wikipedia
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