Classical mechanics. Principles of classical mechanics Foundation of classical mechanics

(January 4, 1643, Woolsthorpe, near Grantham, Lincolnshire, England - March 31, 1727, London) - English mathematician, mechanic, astronomer and physicist, creator of classical mechanics, member (1672) and president (since 1703) of the Royal Society of London.

One of the founders of modern physics, formulated the basic laws of mechanics and was the actual creator of a unified physical program for describing all physical phenomena based on mechanics; discovered the law of universal gravitation, explained the motion of the planets around the Sun and the Moon around the Earth, as well as the tides in the oceans, laid the foundations of continuum mechanics, acoustics and physical optics.

Childhood

Isaac Newton was born in a small village in the family of a small farmer who died three months before the birth of his son. The baby was premature; there is a legend that he was so small that he was placed in a sheepskin mitten lying on a bench, from which he once fell out and hit his head hard on the floor.

When the child was three years old, his mother remarried and left, leaving him in the care of his grandmother. Newton grew up sickly and unsociable, prone to daydreaming. He was attracted by poetry and painting, he, far from his peers, made kites, invented a windmill, a water clock, a pedal cart.

The beginning of school life was difficult for Newton. He studied poorly, was a weak boy, and once classmates beat him until he lost consciousness. To endure such a humiliating situation was unbearable for the proud Newton, and there was only one thing left: to stand out with academic success. By hard work, he achieved the fact that he took first place in the class.

Interest in technology made Newton think about the phenomena of nature; he was also deeply involved in mathematics. Jean Baptiste Biot later wrote about this: “One of his uncles, finding him one day under a hedge with a book in his hands, immersed in deep reflection, took the book from him and found that he was busy solving a mathematical problem. Struck by such a serious and active direction of such a young man, he persuaded his mother not to resist further the desire of her son and send him to continue his studies. After serious preparation, Newton entered Cambridge in 1660 as a Subsizzfr`a (the so-called poor students who were obliged to serve the members of the college, which could not but burden Newton).

The beginning of creativity. Optics

In six years, Newton completed all the degrees of the college and prepared all his further great discoveries. In 1665 Newton became a master of arts.

In the same year, when the plague was raging in England, he decided to temporarily settle in Woolsthorpe. It was there that he began to actively engage in optics; The search for ways to eliminate chromatic aberration in lens telescopes led Newton to research what is now called dispersion, i.e., the dependence of the refractive index on frequency. Many of the experiments he conducted (and there are more than a thousand of them) have become classic and are repeated today in schools and institutes.

The leitmotif of all research was the desire to understand the physical nature of light. At first, Newton was inclined to think that light is waves in the all-penetrating ether, but later he abandoned this idea, deciding that the resistance from the ether should have noticeably slowed down the movement of celestial bodies. These arguments led Newton to the idea that light is a stream of special particles, corpuscles, emitted from a source and moving in a straight line until they encounter obstacles. The corpuscular model explained not only the straightness of light propagation, but also the law of reflection (elastic reflection), and - though not without an additional assumption - the law of refraction. This assumption consisted in the fact that light corpuscles, flying up to the surface of water, for example, should be attracted by it and therefore experience acceleration. According to this theory, the speed of light in water must be greater than in air (which conflicted with later experimental data).

Laws of mechanics

The formation of corpuscular ideas about light was clearly influenced by the fact that at that time the work that was destined to become the main great result of Newton's works was already completed - the creation of a single physical picture of the World based on the laws of mechanics formulated by him.

This picture was based on the idea of ​​material points - physically infinitely small particles of matter and the laws governing their movement. It was precisely the precise formulation of these laws that gave Newton's mechanics completeness and completeness. The first of these laws was, in fact, the definition of inertial frames of reference: it is in such systems that material points that do not experience any influences move uniformly and rectilinearly. The second law of mechanics plays a central role. It says that the change in quantity, movement (the product of mass and speed) per unit of time is equal to the force acting on a material point. The mass of each of these points is a fixed quantity; in general, all these points "do not wear out", according to Newton, each of them is eternal, that is, it can neither arise nor be destroyed. Material points interact, and force is the quantitative measure of influence on each of them. The task of finding out what these forces are is the root problem of mechanics.

Finally, the third law - the law of "equality of action and reaction" explained why the total momentum of any body that does not experience external influences remains unchanged, no matter how its constituent parts interact with each other.

Law of gravity

Having posed the problem of studying various forces, Newton himself gave the first brilliant example of its solution by formulating the law of universal gravitation: the force of gravitational attraction between bodies whose dimensions are much smaller than the distance between them is directly proportional to their masses, inversely proportional to the square of the distance between them and directed along the connecting their straight line. The law of universal gravitation allowed Newton to give a quantitative explanation of the motion of the planets around the Sun and the Moon around the Earth, to understand the nature of sea tides. This could not but make a huge impression on the minds of researchers. The program of a unified mechanical description of all natural phenomena - both "terrestrial" and "heavenly" for many years was established in physics. Moreover, for two centuries many physicists considered the very question of the limits of applicability of Newton's laws to be unjustified.

In 1668 Newton returned to Cambridge and he soon received the Lucas Chair in Mathematics. Before him, this department was occupied by his teacher I. Barrow, who ceded the department to his beloved student in order to financially provide for him. By that time, Newton was already the author of the binomial and the creator (simultaneously with Leibniz, but independently of him) of the method of fluxions - what is now called differential and integral calculus. In general, that was the most fruitful period in Newton's work: in seven years, from 1660 to 1667, his main ideas were formed, including the idea of ​​the law of universal gravitation. Not limited to theoretical studies alone, in the same years he designed and began to create a reflecting telescope (reflective). This work led to the discovery of what later became known as "lines of equal thickness" interference. (Newton, realizing that here the “quenching of light by light” is manifested, which did not fit into the corpuscular model, tried to overcome the difficulties that arose here by introducing the assumption that corpuscles in light move in waves - “tides”). The second of the manufactured telescopes (improved) was the reason for the presentation of Newton as a member of the Royal Society of London. When Newton refused membership, citing lack of funds to pay membership dues, it was considered possible, given his scientific merits, to make an exception for him, exempting him from paying them.

Being by nature a very cautious (not to say timid) person, Newton, against his will, sometimes found himself drawn into discussions and conflicts that were painful for him. Thus, his theory of light and colors, presented in 1675, caused such attacks that Newton decided not to publish anything on optics while he was alive. gook, his most bitter opponent. Newton had to take part in political events. From 1688 to 1694 he was a Member of Parliament. By that time, in 1687, his main work, The Mathematical Principles of Natural Philosophy, was published - the basis of the mechanics of all physical phenomena, from the movement of celestial bodies to the propagation of sound. For several centuries ahead, this program determined the development of physics, and its significance has not been exhausted to this day.

Newton's disease

Constant huge nervous and mental stress led to the fact that in 1692 Newton fell ill with a mental disorder. The immediate impetus for this was a fire in which all the manuscripts prepared by him perished. Only by 1694 he, according to the testimony Huygens, "... is already beginning to understand his book "Beginnings"".

The constant oppressive feeling of material insecurity was undoubtedly one of the causes of Newton's illness. Therefore, it was important for him to be the caretaker of the Mint with the preservation of a professorship at Cambridge. Zealously setting to work and quickly achieving notable success, he was appointed director in 1699. It was impossible to combine this with teaching, and Newton moved to London. At the end of 1703 he was elected President of the Royal Society. By that time, Newton had reached the pinnacle of fame. In 1705, he was elevated to the dignity of knighthood, but, having a large apartment, six servants and a rich departure, he remains still alone. The time for active creativity is over, and Newton is limited to preparing the publication of Optics, reprinting the Elements and interpreting the Holy Scriptures (he owns the interpretation of the Apocalypse, an essay on the prophet Daniel).

Newton was buried in Westminster Abbey. The inscription on his grave ends with the words: "Let mortals rejoice that such an adornment of the human race lived in their midst."

At the turn of the XIX-XX centuries. the limits of applicability of classical mechanics were identified (see the section "Limitations of applicability of classical mechanics" at the end of the article). It turned out that it gives exceptionally accurate results, but only in those cases when it is applied to bodies whose speed is much less than the speed of light, and whose dimensions are much larger than the dimensions of atoms and molecules, and at distances or conditions when the speed of propagation of gravity can be considered infinite ( a generalization of classical mechanics to bodies moving at an arbitrary speed is relativistic mechanics, and to bodies whose dimensions are comparable to atomic ones - quantum mechanics; quantum relativistic effects are considered by quantum field theory).

Nevertheless, classical mechanics retains its value because it:

1. Much easier to understand and use than other theories.
2. In an extensive range, it describes reality quite well.

Classical mechanics can be used to describe the motion of a very wide class of physical objects: both ordinary objects of the macrocosm (such as a spinning top and a baseball), and objects of astronomical dimensions (such as planets and stars), and many microscopic objects.

Encyclopedic YouTube

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✪ Lecture 1. | 8.01 Physics I: Classical mechanics, autumn 1999

✪ Quantum mechanics 1 - Failure of classical physics

✪ Physics - Newton's first and second laws

✪ Mechanics - Basic concepts of mechanics

✪ Mechanics. Newton's laws. Forces

Subtitles

Basic concepts

Classical mechanics operates with several basic concepts and models. Among them should be highlighted:

• Space . It is believed that the movement of bodies occurs in space, which is Euclidean, absolute (does not depend on the observer), homogeneous (any two points in space are indistinguishable) and isotropic (any two directions in space are indistinguishable).
• Time is a fundamental concept postulated in classical mechanics. It is believed that time is absolute, homogeneous and isotropic (the equations of classical mechanics do not depend on the direction of the flow of time).
• The reference system consists of a reference body (some body, real or imaginary, relative to which the movement of a mechanical system is considered), a device for measuring time and a coordinate system.
• Mass is a measure of the inertia of bodies.
• A material point is a model of an object that has a mass, the dimensions of which are neglected in the problem being solved. Bodies of non-zero size can experience complex motions because their internal configuration can change (for example, the body can rotate or deform). Nevertheless, in certain cases, the results obtained for material points are applicable to such bodies, if we consider such bodies as aggregates of a large number of interacting material points. Material points in kinematics and dynamics are usually described by the following quantities:
  • Radius vector r → (\displaystyle (\vec (r)))- a vector drawn from the origin of coordinates to that point in space, which serves as the current position of the material point
  • Velocity is a vector that characterizes the change in the position of a material point with time and is defined as the derivative of the radius vector with respect to time: v → = d r → d t (\displaystyle (\vec (v))=(\frac (d(\vec (r)))(dt)))
  • Acceleration is a vector that characterizes the change in the speed of a material point with time and is defined as the derivative of speed with respect to time: a → = d v → d t = d 2 r → d t 2 (\displaystyle (\vec (a))=(\frac (d(\vec (v)))(dt))=(\frac (d^(2 )(\vec (r)))(dt^(2))))
  • Mass - a measure of the inertia of a material point; is assumed to be constant in time and independent of any features of the motion of a material point and its interaction with other bodies.
  • Impulse (another name is the amount of motion) is a vector physical quantity equal to the product of the mass of a material point and its speed: p → = m v → . (\displaystyle (\vec (p))=m(\vec (v)).)
  • Kinetic energy - the energy of motion of a material point, defined as half the product of the mass of the body and the square of its speed: T = m v 2 2 . (\displaystyle T=(\frac (mv^(2))(2)).) or T = p 2 2 m . (\displaystyle T=(\frac (p^(2))(2m)).)
  • Force is a vector physical quantity, which is a measure of the intensity of the impact on a given body of other bodies, as well as physical fields. It is a function of the coordinates and velocity of a material point, which determines the time derivative of its momentum.
  • If the work of the force does not depend on the type of trajectory along which the body moved, but is determined only by its initial and final positions, then such a force is called potential. The interaction that occurs through potential forces can be described by potential energy. By definition, potential energy is a function of body coordinates U (r →) (\displaystyle U((\vec (r)))) such that the force acting on the body is equal to the gradient from this function, taken with the opposite sign: F → = − ∇ U (r →) . (\displaystyle (\vec (F))=-\nabla U((\vec (r))).)

Basic Laws

Galileo's principle of relativity

The basic principle on which classical mechanics is based is the principle of relativity, formulated by G. Galileo on the basis of empirical observations. According to this principle, there are infinitely many frames of reference in which a free body is at rest or moves with a constant speed in absolute value and direction. These frames of reference are called inertial and move relative to each other uniformly and rectilinearly. In all inertial frames of reference, the properties of space and time are the same, and all processes in mechanical systems obey the same laws. This principle can also be formulated as the absence of absolute reference systems, that is, reference systems that are somehow distinguished relative to others.

Newton's laws

The basis of classical mechanics is Newton's three laws (formulating these laws, Newton used the term "body", although in fact they are talking about material points).

Newton's second law is not enough to describe the motion of a particle. Additionally, a description of the force is required. F → (\displaystyle (\vec (F))), obtained from consideration of the essence of the physical interaction in which the body participates.

Law of energy conservation

The law of conservation of energy is a consequence of Newton's laws for closed conservative systems (that is, systems in which only conservative forces act). The fundamental basis of this law is the property uniformity of time, and the relationship between the law of conservation of energy and this property is again expressed by Noether's theorem.

Spread to extended bodies

Classical mechanics also includes a description of the complex motions of extended non-point objects. The extension of the laws of Newtonian mechanics to such objects was largely due to Euler. The modern formulation of Euler's laws also uses the apparatus of three-dimensional vectors.

The above expressions for momentum and kinetic energy are valid only in the absence of a significant electromagnetic contribution. In electromagnetism, Newton's second law for a current-carrying wire is violated if the contribution of the electromagnetic field to the momentum of the system is not taken into account; such a contribution is expressed in terms of the Poynting vector divided by c 2 , where c is the speed of light in free space.

Story

Antiquity

Classical mechanics originated in antiquity mainly in connection with the problems that arose during construction. The first of the sections of mechanics to be developed was statics, the foundations of which were laid in the works of Archimedes in the 3rd century BC. e. He formulated the lever rule, the theorem on the addition of parallel forces, introduced the concept of the center of gravity, laid the foundations of hydrostatics (the force of Archimedes).

Middle Ages

new time

17th century

The laying of the foundations of classical mechanics was completed by the works of Isaac Newton, who formulated the laws of mechanics in the most general form and discovered the law of universal gravitation. In 1684, he also established the law of viscous friction in liquids and gases.

Also in the 17th century, in 1660, the law of elastic deformations was formulated, bearing the name of its discoverer Robert Hooke.

18th century

19th century

Classical mechanics is a self-consistent theory, that is, within its framework there are no statements that contradict each other. In general, it is compatible with other "classical" theories (such as classical electrodynamics and classical thermodynamics), but at the end of the 19th century, some inconsistencies between these theories emerged; overcoming these discrepancies marked the formation of modern physics. In particular:

• The equations of classical electrodynamics are non-invariant with respect to Galilean transformations: since these equations include (as a physical constant, constant for all observers) the speed of light, then classical electrodynamics and classical mechanics are compatible only in one chosen frame of reference - associated with the ether. But experimental verification did not reveal the existence of the ether, and this led to the creation of a special  theory of relativity (under which the equations of mechanics were modified).
• Some statements of classical thermodynamics are also incompatible with classical mechanics: their application together with the laws of classical mechanics leads to the Gibbs paradox (according to which it is impossible to accurately determine the value of entropy) and to the ultraviolet catastrophe (the latter means that

“Think of the benefit that good examples bring us, and you will find that the memory of great people is no less useful than their presence”

Mechanics is one of the most ancient Sciences. It arose and developed under the influence public practice requests and also thanks to abstracting activity of human thinking. Even in prehistoric times, people created buildings and observed the movement of various bodies. Many laws of mechanical motion and balance of material bodies were known by mankind through repeated repetitions, purely experimentally. This socio-historical experience, passed down from generation to generation, and was the the source material on the analysis of which mechanics as a science developed. The emergence and development of mechanics was closely associated with production, With needs human society. “At a certain stage in the development of agriculture,” writes Engels, “and in certain countries (raising water for irrigation in Egypt), and especially along with the emergence of cities, large buildings and the development of handicrafts, developed and Mechanics. Soon it also becomes necessary for shipping and military affairs.

First the manuscripts and scientific reports in the field of mechanics that have survived to this day belong to ancient scholars of Egypt and Greece. The oldest papyri and books, in which studies of some of the simplest problems of mechanics have been preserved, relate mainly to various problems. statics, i.e. the doctrine of balance. First of all, here it is necessary to name the works of the outstanding philosopher of ancient Greece (384-322 BC), who introduced the name Mechanics for a wide field of human knowledge, in which the simplest movements of material bodies, observed in nature and created by man during his activities, are studied.

Aristotle was born in the Greek colony of Stagira in Thrace. His father was a physician to the Macedonian king. In 367, Aristotle settled in Athens, where he received a philosophical education at the Academy of the famous idealist philosopher in Greece. Plato. In 343 Aristotle took over teacher of Alexander the Great(Alexander the Great said: “I honor Aristotle on a par with my father, since if I owe my life to my father, then I owe Aristotle everything that gives her a price”), later the famous commander of the ancient world. His philosophical school, called the school peripatetics, Aristotle founded in 335 in Athens. Some philosophical provisions of Aristotle have not lost their significance to the present day. F. Engels wrote; "The ancient Greek philosophers were all born elemental dialecticians, and Aristotle, the most universal head among them, has already explored all the essential forms of dialectical thinking." But in the field of mechanics, these broad universal laws of human thinking did not receive a fruitful reflection in the works of Aristotle.

Archimedes owns a large number technical inventions, including the simplest water-lifting machine (archimedean screw), which has found application in Egypt for draining cultivated lands flooded with water. He showed himself as military engineer while defending his hometown of Syracuse (Sicily). Archimedes understood the power and great significance for mankind of accurate and systematic scientific research, and proud words are attributed to him: “ Give me a place to stand on and I will move the earth."

Archimedes was killed by the sword of a Roman soldier during the massacre arranged by the Romans during the capture of Syracuse. Tradition says that Archimedes, immersed in the consideration of geometric figures, said to a soldier who approached him: "Do not touch my drawings." The soldier, seeing in these words an insult to the power of the victors, cut off his head, and the blood of Archimedes stained his scientific work.

famous ancient astronomer Ptolemy(II century AD - there is evidence that Ptolemy (Claudius Ptolemaeus) lived and worked in Alexandria from 127 to 141 or 151. According to Arabic legend, he died at the age of 78.) in his work " The Great Mathematical Construction of Astronomy in 13 Books"developed a geocentric system of the world, in which the apparent movements of the firmament and planets were explained on the assumption that the Earth is motionless and is at the center of the universe. The entire firmament makes a complete revolution around the Earth in 24 hours, and the stars participate only in the daily movement, while maintaining their relative position unchanged; planets, moreover, move relative to the celestial sphere, changing their position relative to the stars. The laws of the apparent motions of the planets were established by Ptolemy to such an extent that it became possible to predict their positions relative to the sphere of the fixed stars.

However, the theory of the structure of the universe, created by Ptolemy, was erroneous; it led to extraordinarily complex and artificial schemes of the motion of the planets and in a number of cases could not fully explain their apparent movements relative to the stars. Particularly large inconsistencies between calculations and observations were obtained with predictions of solar and lunar eclipses made many years ahead.

Ptolemy did not adhere strictly to the methodology of Aristotle and conducted systematic experiments on the refraction of light. Physiological-optical observations Ptolemy have not lost their interest to date. The angles of light refraction found by him during the transition from air to water, from air to glass and from water to glass were very accurate for its time. Ptolemy remarkably combined strict mathematician and subtle experimenter.

In the era of the Middle Ages, the development of all sciences, as well as mechanics, was strongly slowed down. Moreover, during these years the most valuable monuments of science, technology and art of the ancients were destroyed and destroyed. Religious fanatics wiped out all the achievements of science and culture from the face of the earth. Most of the scientists of this period blindly adhered to the scholastic method of Aristotle in the field of mechanics, considering all the provisions contained in the writings of this scientist to be unconditionally correct. The geocentric system of the world of Ptolemy was canonized. Speech against this system of the world and the basic principles of the philosophy of Aristotle were considered a violation of the foundations of the Holy Scripture, and researchers who decided to do this were declared heretics. “The priesthood killed the living in Aristotle and immortalized the dead,” wrote Lenin. Dead, empty scholasticism filled the pages of many treatises. Ridiculous problems were posed, and exact knowledge was persecuted and withered. A large number of works on mechanics in the Middle Ages were devoted to finding " perpetuum mobile”, i.e. perpetual motion machine operating without receiving energy from outside. These works, for the most part, contributed little to the development of mechanics (Mohammed well expressed the ideology of the Middle Ages, saying: "If the sciences teach what is written in the Koran, they are superfluous; if they teach otherwise, they are godless and criminal"). “The Christian Middle Ages left nothing to science,” says F. Engels in Dialectics of Nature.

The intensive development of mechanics began in renaissance from the beginning of the 15th century in Italy, and then in other countries. In this era, especially great progress in the development of mechanics was achieved thanks to the work (1452-1519), (1473-1543) and Galilee (1564-1642).

Famous Italian painter, mathematician, mechanic and engineer, Leonardo da Vinci engaged in research on the theory of mechanisms (he built an elliptical lathe), studied friction in machines, investigated the movement of water in pipes and the movement of bodies along an inclined plane. He was the first to recognize the extreme importance of the new concept of mechanics - the moment of force relative to a point. Investigating the balance of forces acting on the block, he established that the role of the shoulder of force is played by the length of the perpendicular dropped from the fixed point of the block to the direction of the rope carrying the load. The equilibrium of the block is possible only if the products of forces and the lengths of the corresponding perpendiculars are equal; in other words, the equilibrium of the block is possible only under the condition that the sum of the static moments of forces relative to the weight gain point of the block will be equal to zero.

A revolutionary revolution in the views on the structure of the universe was carried out by a Polish scientist who, as figuratively written on his monument in Warsaw, "stopped the Sun and moved the Earth." new, heliocentric system of the world explained the movement of the planets, based on the fact that the Sun is a fixed center, around which all the planets move in circles. Here are the original words of Copernicus, taken from his immortal work: “What appears to us as the movement of the Sun does not come from its movement, but from the movement of the Earth and its sphere, with which we revolve around the Sun, like any other planet. So, the Earth has more than one movement. The apparent simple and retrograde motions of the planets are not due to their motion, but to the motion of the Earth. Thus, one movement of the Earth is sufficient to explain so many apparent inequalities in the sky.

In the work of Copernicus, the main feature of the motion of the planets was revealed and calculations were made related to the predictions of solar and lunar eclipses. The explanations of the apparent return motions of Mercury, Venus, Mars, Jupiter, and Saturn relative to the sphere of the fixed stars have acquired clarity, distinctness, and simplicity. Copernicus clearly understood the kinematics of the relative motion of bodies in space. He writes: “Every perceived change in position occurs due to the movement of either the observed object or the observer, or due to the movement of both, if, of course, they are different from each other; for when the observed object and the observer move in the same way and in the same direction, no movement is noticed between the observed object and the observer.

Truly scientific Copernican theory made it possible to obtain a number of important practical results: to increase the accuracy of astronomical tables, to reform the calendar (introducing a new style), and to determine the length of the year more strictly.

Works of the brilliant Italian scientist Galilee were fundamental to the development speakers.
Dynamics as a science was founded by Galileo, who discovered many very important properties of uniformly accelerated and uniformly slow motions. The foundations of this new science were set forth by Galileo in a book entitled "Conversations and Mathematical Proofs Concerning Two New Branches of Science Relating to Mechanics and Local Motion." In chapter III, on dynamics, Galileo writes: “We are creating a new science, the subject of which is extremely old. In nature, there is nothing ancient movement, but it is precisely with regard to it that philosophers have written very little significant. Therefore, I have repeatedly studied its features by experience, which are quite deserving of this, but until now either unknown or unproven. So, for example, they say that the natural motion of a falling body is accelerated motion. However, the extent to which the acceleration increases has not yet been indicated; as far as I know, no one has yet proved that the spaces traversed by a falling body at the same time intervals are related to each other as successive odd numbers. It was also noticed that the thrown bodies or projectiles describe a certain curved line, but no one indicated that this line is a parabola.

Galileo Galilei (1564-1642)

Before Galileo, forces acting on bodies were usually considered in a state of equilibrium and the action of forces was measured only by static methods (lever, scales). Galileo pointed out that force is the cause of the change in speed, and thus established dynamic method comparison of forces. Galileo's research in the field of mechanics is important not only for the results that he managed to obtain, but also for his consistent introduction to mechanics. experimental movement research method.

So, for example, the law of isochronism of pendulum oscillations at small angles of deflection, the law of motion of a point along an inclined plane were investigated by Galileo through carefully staged experiments.

Thanks to the works of Galileo, the development of mechanics is firmly associated with the demands technology, And scientific experiment systematically introduced as fruitful research method phenomena of mechanical movement. Galileo in his conversations directly says that observing the work of the “first” masters in the Venetian arsenal and talking with them helped him understand “the causes of phenomena that were not only amazing, but also seemed at first completely unbelievable.” Many provisions of Aristotle's mechanics were specified by Galileo (as, for example, the law on the addition of motions) or very ingeniously refuted by purely logical reasoning (refutation by setting up experiments was considered insufficient at that time). We present here Galileo's proof to characterize the style. refuting Aristotle's position that heavy bodies on the surface of the Earth fall faster, and light bodies fall more slowly. The reasoning is given in the form of a conversation between a follower of Galileo (Salviati) and Aristotle (Simplicio):

« Salviati: ... Without further experience, by a brief but convincing reasoning, we can clearly show the incorrectness of the statement that heavier bodies move faster than lighter ones, implying bodies of the same substance, i.e. such as those of which Aristotle speaks . In fact, tell me, Señor Simplicio, do you admit that every falling body has a certain speed by nature, which can be increased or decreased only by introducing a new force or obstacle?
Simplicio: I have no doubt that the same body in the same medium has a constant speed, determined by nature, which cannot increase except from the application of a new force, or decrease except from an obstacle that slows down the movement.
Salviati: Thus, if we have two falling bodies, the natural speeds of which are different, and we combine the faster one with the slower one, then it is clear that the motion of the body falling faster will be somewhat delayed, and the motion of the other will be somewhat accelerated. Do you object to this position?
Simplicio: I think that this is quite correct.
Salviati: But if this is so, and if at the same time it is true that a large stone moves, say, with a speed of eight cubits, while another, smaller one, with a speed of four cubits, then by joining them together, we should get a speed less than eight elbows; but two stones joined together make a body greater than the original, which had a speed of eight cubits; therefore, it turns out that a heavier body moves at a lower speed than a lighter one, and this is contrary to your assumption. You see now how, from the position that heavier bodies move faster than lighter ones, I could conclude that heavier bodies move less quickly.

The phenomena of a uniformly accelerated fall of a body on Earth were observed by numerous scientists before Galileo, but none of them could discover the true causes and correct laws that explain these everyday phenomena. Lagrange notes on this occasion that "an extraordinary genius was needed to discover the laws of nature in such phenomena that were always before our eyes, but the explanation of which, nevertheless, always eluded the research of philosophers."

So, Galileo was the founder of modern dynamics. Galileo clearly understood the laws of inertia and independent action of forces in their modern form.

Galileo was an outstanding observing astronomer and an ardent supporter of the heliocentric worldview. Radically improving the telescope, Galileo discovered the phases of Venus, the satellites of Jupiter, spots on the Sun. He waged a persistent, consistently materialistic struggle against the scholasticism of Aristotle, the dilapidated system of Ptolemy, and the anti-scientific canons of the Catholic Church. Galileo is one of the great men of science, "who knew how to break the old and create the new, in spite of any obstacles, in spite of everything."
The works of Galileo were continued and developed (1629-1695), who developed the theory of oscillations of a physical pendulum and installed laws of action of centrifugal forces. Huygens extended the theory of accelerated and retarded motions of one point (translational motion of a body) to the case of a mechanical system of points. This was a significant step forward, as it made it possible to study the rotational motions of a rigid body. Huygens introduced the concept of moment of inertia of the body about the axis and defined the so-called swing center" physical pendulum. When determining the swing center of a physical pendulum, Huygens proceeded from the principle that "a system of weighty bodies moving under the influence of gravity cannot move in such a way that the common center of gravity of the bodies rises above its original position." Huygens also showed himself as an inventor. He created the design of pendulum clocks, invented the balancer-regulator of the pocket watch, built the best astronomical tubes of that time and was the first to clearly see the ring of the planet Saturn.

To describe speeds that are not small compared to the speed of light, special relativity is needed. In the event that objects become extremely massive, general relativity becomes applicable. However, a number of contemporary sources do incorporate relativistic mechanics into classical physics, which they claim represents classical mechanics in its most advanced and precise form.

Description of the theory

The basic concepts of classical mechanics are introduced below. For simplicity, often models of real objects as point particles (objects with negligible size). The motion of a point particle is characterized by a small number of parameters: its position, mass, and forces applied to it. Each of these parameters is discussed in turn.

In reality, the kind of objects that classical mechanics can describe always have a non-zero size. (Physics Very small particles, such as the electron, are more accurately described by quantum mechanics.) Objects with non-zero size have more complex behavior than hypothetical point particles, due to additional degrees of freedom, for example, a baseball can spin while it is moving. However, the results for point particles can be used to study such objects by treating them as composite objects made up of a large number of point particles acting together. The center of mass of a composite object behaves like a point particle.

Position and its derivatives

Position about a point particle are defined with respect to a coordinate system centered at an arbitrary fixed reference point in space called the origin conclusion. A simple coordinate system can describe the position of a particle R with a vector written by an arrow with an inscription G, which points from the origin O to the point P. In general, point particles do not have to be stationary with respect to O. In cases where R moves relative to O , R defined as a function of T, time . In pre-Einstein relativity (known as Galilean relativity), time is considered absolute, meaning the time interval that is observed to elapse between any pair of events is the same for all observers. In addition to relying on absolute time, classical mechanics assumes Euclidean geometry for the structure of space.

speed and speed

Mathematically, if the speed of the first object in the previous discussion is denoted by the vector U = Ud , and the speed of the second object along the vector about = aboute , Where at is the speed of the first object, v is the speed of the second object, and d And e are unit vectors in the directions of motion of each object respectively, then the speed of the first object, as shown by the second object

Similarly, the first object sees the speed of the second object as

When both objects are moving in the same direction, then this equation can be simplified

Or, ignoring direction, the difference can only be given in terms of speed:

acceleration

An inertial frame is a frame of reference, during which an object interacting without any forces (an idealized situation) appears either at rest or moves uniformly in a straight line. This is the fundamental definition of an inertial frame of reference. They are characterized by the requirement that all forces input to the observer of physical laws come from identifiable sources, induced fields such as the electrostatic field (caused by a static electric charge), the electro-magnetic field (caused by the motion of charges), the gravitational field (caused by mass), and etc.

The key concept of inertials is the method for identifying them. For practical purposes, reference frames that are not accelerating relative to distant stars (extremely distant points) are regarded as good approximations to inertial ones. Non-inertial frames of reference accelerate with respect to the existing inertial frame of reference. They form the basis for Einstein's theory of relativity. Due to relative motion, particles in non-inertial appear to be moving in ways that have not been elucidated by forces from existing fields in the reference frame. Thus, it turns out that there are other forces that enter the equation of motion only as a result of relative acceleration. These forces are called fictitious forces, inertial forces, or pseudo-forces.

The transformations have the following consequences:

• v "= v - U(speed v"particles in terms of S"is slower U than its speed V from point of view S)
• "= (particle acceleration is the same in any inertial reference frame)
• F "= F(the force acting on the particle is the same in any inertial frame of reference)
• the speed of light is not a constant in classical mechanics, and the non-special position of the given speed of light in relativistic mechanics has an analogue in classical mechanics.

For some tasks, it is convenient to use rotating coordinates (reference frames). Thus, one can either keep the mapping in a convenient inertial frame of reference, or introduce additional fictitious centrifugal force and Coriolis force.

strength; Newton's second law

If work is done while moving a particle from G 1 to G 2 is the same no matter which path is taken, the strength is called conservative. The force of gravity is a conservative force, as is the force due to an idealized spring as given by Hooke's law. The force due to friction is not conservative.

constant in time. This is often useful, as many commonly encountered forces are conservative.

Beyond Newton's laws

Classical mechanics also describes more complex movements of extended objects, not pointwise. Euler's laws provide an extension of Newton's laws in this area. The concepts of angular momentum rely on the same calculus used to describe one-dimensional motion. The rocket equation expands the concept of the rate of change of an object's momentum to include the effects of an object "losing mass".

There are two important alternative formulations of classical mechanics: Lagrange mechanics and Hamilton mechanics. These and other modern preparations tend to bypass the concept of "force", rather than referring to other physical quantities such as energy, velocity, and momentum, to describe mechanical systems in generalized coordinates.

The above expression for momentum and kinetic energy is valid only when there is no significant electromagnetic contribution. In electromagnetism, Newton's second law for conductive wires fails if it does not include the field contribution to the system's electromagnetic momentum, expressed by the Poynting vector divided by With 2 , where With is the speed of light in free space.

Limits of applicability

Many branches of classical mechanics are simplifications or approximations of more precise forms; two of the most accurate being general relativity and relativistic statistical mechanics. Geometric optics is an approximation to the quantum theory of light, and does not have a superior "classical" form.

When both quantum mechanics and classical mechanics cannot be applied, such as at the quantum level with many degrees of freedom, quantum field theory (QFT) is of use. QFT deals with small distances and high speeds with a large number of degrees of freedom, as well as the possibility of any change in the number of particles throughout the interaction. When handling large degrees of freedom at the macroscopic level, statistical mechanics becomes useful. Statistical mechanics describes the behavior of a large (but countable) number of particles and their interactions in general at the macroscopic level. Statistical mechanics is mainly used in thermodynamics for systems that lie outside the boundaries of the assumptions of classical thermodynamics. In the case of high speed objects approaching the speed of light, classical mechanics is enhanced. In the case where objects become extremely heavy (i.e. their Schwarzschild radius is not negligible for a given application), the deviation from Newtonian mechanics will become apparent and can be quantified using the parametrized post-Newtonian formalism. In this case, General Relativity (GR) becomes applicable. However, there is still no theory of quantum gravity that combines GR and QFT in the sense that it can be used when objects become extremely small and heavy.

Newtonian approximation to special relativity

In special relativity, the momentum of a particle is given by

Where T is the rest mass of the particle, V his speed, v is a module V, A With is the speed of light.

If V very small compared to With , v 2 / With 2 is approximately equal to zero, and so

So the Newtonian equation R = Tv is an approximation of the relativistic equation for bodies moving at a low speed compared to the speed of light.

For example, the relativistic cyclotron frequency of a cyclotron, gyrotron, or high voltage magnetron is given by

Where e c is the classical frequency of an electron (or other charged particle) with kinetic energy T and (rest of) mass m 0 circling in a magnetic field. The (rest) electron mass is 511 keV. Thus, the frequency correction is 1% for a DC magnetic vacuum tube at an accelerating voltage of 5.11 kV.

Classical approximation to quantum mechanics

The beam approximation of classical mechanics breaks down when the de Broglie wavelength is not much smaller than other dimensions of the system. For non-relativistic particles, this wavelength

Classical mechanics is the same extreme high frequency approximation as geometric optics. It is more often exact as it describes particles and a body with rest mass. They have more momentum and therefore shorter de Broglie wavelengths than massless particles like light with the same kinetic energy.

story

The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science, engineering and technology.

After Newton, classical mechanics became the main field of study in mathematics as well as physics. Several repeated preparations gradually made it possible to find solutions to a much larger number of problems. The first notable reformulation was in 1788 by Joseph Louis Lagrange. Lagrangian mechanics was in turn re-formulated in 1833 by William Rowan Hamilton.

Some difficulties were discovered at the end of the 19th century, which could only be solved with the help of more modern physics. Some of these difficulties are related to compatibility with electromagnetic theory, and the famous Michelson-Morley experiment. The solution to these problems led to the special theory of relativity, often still considered part of classical mechanics.

The second set of difficulties were related to thermodynamics. Combined with thermodynamics, classical mechanics leads to the Gibbs paradox of classical statistical mechanics, in which entropy is not a well-defined quantity. Black body radiation has not been explained without an introduction

From Wikipedia, the free encyclopedia

classical mechanics- a kind of mechanics (a section of physics that studies the laws of change in the positions of bodies in space over time and the causes that cause it), based on Newton's laws and Galileo's principle of relativity. Therefore, it is often called Newtonian mechanics».

Classical mechanics is subdivided into:

statics (which considers the equilibrium of bodies)

kinematics (which studies the geometric property of motion without considering its causes)

dynamics (which considers the movement of bodies).

Classical mechanics gives very accurate results if its application is limited to bodies whose speeds are much less than the speed of light, and whose dimensions are much larger than the dimensions of atoms and molecules. Relativistic mechanics is a generalization of classical mechanics for bodies moving at an arbitrary speed, and quantum mechanics for bodies whose dimensions are comparable to atomic ones. Quantum field theory considers quantum relativistic effects.

Nevertheless, classical mechanics retains its value because:

it is much easier to understand and use than other theories

in a wide range, it describes reality quite well.

Classical mechanics can be used to describe the motion of objects such as tops and baseballs, many astronomical objects (such as planets and galaxies), and sometimes even many microscopic objects such as molecules.

Classical mechanics is a self-consistent theory, that is, within its framework there are no statements that contradict each other. However, its combination with other classical theories, such as classical electrodynamics and thermodynamics, leads to insoluble contradictions. In particular, classical electrodynamics predicts that the speed of light is constant for all observers, which is inconsistent with classical mechanics. At the beginning of the 20th century, this led to the need to create a special theory of relativity. When considered together with thermodynamics, classical mechanics leads to the Gibbs paradox, in which it is impossible to accurately determine the amount of entropy, and the ultraviolet catastrophe, in which a completely black body must radiate an infinite amount of energy. Attempts to solve these problems led to the emergence and development of quantum mechanics.

10 ticket MECHANICAL PICTURE OF THE WORLD. THERMODYNAMICS

Thermodynamics(Greek θέρμη - “heat”, δύναμις - “force”) - a branch of physics that studies the relationships and transformations of heat and other forms of energy. Chemical thermodynamics, which studies physical and chemical transformations associated with the release or absorption of heat, as well as heat engineering, have separated into separate disciplines.

In thermodynamics, one does not deal with individual molecules, but with macroscopic bodies consisting of a huge number of particles. These bodies are called thermodynamic systems. In thermodynamics, thermal phenomena are described by macroscopic quantities - pressure, temperature, volume, ..., which are not applicable to individual molecules and atoms.

In theoretical physics, along with phenomenological thermodynamics, which studies the phenomenology of thermal processes, statistical thermodynamics is singled out, which was created for the mechanical justification of thermodynamics and was one of the first sections of statistical physics.

Thermodynamics can be applied to a wide range of topics in science and technology, such as engines, phase transitions, chemical reactions, transport phenomena, and even black holes. Thermodynamics is important to other areas of physics and chemistry, chemical engineering, aerospace engineering, mechanical engineering, cell biology, biomedical engineering, materials science, and is useful in other areas such as economics [

11 ticket ELECTRODYNAMICS

Electrodynamics- a branch of physics that studies the electromagnetic field in the most general case (that is, time-dependent variable fields are considered) and its interaction with bodies that have an electric charge (electromagnetic interaction). The subject of electrodynamics includes the relationship between electrical and magnetic phenomena, electromagnetic radiation (under different conditions, both free and in various cases of interaction with matter), electric current (generally speaking, alternating) and its interaction with an electromagnetic field (electric current can be considered under this as a set of moving charged particles). Any electrical and magnetic interaction between charged bodies is considered in modern physics as carried out through the electromagnetic field, and, therefore, is also the subject of electrodynamics.

Most often under the term electrodynamics the default is classical electrodynamics, which describes only the continuous properties of an electromagnetic field through a system of Maxwell's equations; to designate the modern quantum theory of the electromagnetic field and its interaction with charged particles, the stable term is usually used quantum electrodynamics.

12 ticket CONCEPT OF SYMMETRY IN NATURAL SCIENCE

Emmy Noether's theorem asserts that each continuous symmetry of a physical system corresponds to a certain conservation law. Thus, the law of conservation of energy corresponds to the homogeneity of time, the law of conservation of momentum to the homogeneity of space, the law of conservation of momentum to the isotropy of space, the law of conservation of electric charge to gauge symmetry, etc.

The theorem is usually formulated for systems with an action functional and expresses the invariance of the Lagrangian with respect to some continuous group of transformations.

The theorem was established in the works of the scientists of the Göttingen school D. Gilbert, F. KleinaiE. Noether. The most common formulation was proved by Emmy Noether in 1918.

Symmetry types found in mathematics and natural sciences:

bilateral symmetry - symmetry with respect to mirror reflection. (Bilateral symmetry)

symmetry of the nth order - symmetry with respect to rotations through an angle of 360 ° / n around any axis. Described by the group Z n .

axial symmetry (radial symmetry, ray symmetry) - symmetry with respect to rotations through an arbitrary angle around an axis. Described by the SO(2) group.

spherical symmetry - symmetry with respect to rotations in three-dimensional space through arbitrary angles. Described by the SO(3) group. Local spherical symmetry of space or medium is also called isotropy.

rotational symmetry is a generalization of the previous two symmetries.

translational symmetry - symmetry with respect to shifts of space in any direction by a certain distance.

Lorentz invariance - symmetry with respect to arbitrary rotations in Minkowski's space-time.

gauge invariance is the independence of the type of equations of gauge theories in quantum field theory (in particular, Yang-Mills theories) under gauge transformations.

supersymmetry - the symmetry of the theory with respect to the replacement of bosons by fermions.

higher symmetry - symmetry in group analysis.

Kainosymmetry is a phenomenon of electronic configuration (the term was introduced by S. A. Shchukarev, who discovered it), which determines the secondary periodicity (discovered by E. V. Biron).

13 ticket service station

Special theory of relativity(ONE HUNDRED; Also private theory of relativity) is a theory that describes movement, laws of mechanics, space-time relations at arbitrary speeds of movement that are less than the speed of light in vacuum, including those close to the speed of light. Within the framework of special relativity, Newton's classical mechanics is an approximation of low velocities. The generalization of SRT for gravitational fields is called the general theory of relativity.

The deviations in the course of physical processes from the predictions of classical mechanics described by the special theory of relativity are called relativistic effects, and the rates at which such effects become significant are relativistic speeds.

14 OTO ticket

General theory of relativity(general relativity; it. allgemeine Relativitätstheorie) is a geometric theory of gravity that develops the special theory of relativity (SRT), published by Albert Einstein in 1915-1916. Within the framework of the general theory of relativity, as in other metric theories, it is postulated that gravitational effects are due to non-force interaction of bodies and fields located in space-time, but to the deformation of space-time itself, which is associated, in particular, with the presence of mass-energy. General relativity differs from other metric theories of gravity by using Einstein's equations to relate the curvature of space-time to the matter present in it.

General relativity is currently the most successful theory of gravity, well supported by observations. The first success of general relativity was to explain the anomalous precession of Mercury's perihelion. Then, in 1919, Arthur Eddington reported observing the deflection of light near the Sun at the time of a total eclipse, which qualitatively and quantitatively confirmed the predictions of general relativity. Since then, many other observations and experiments have confirmed a significant number of the theory's predictions, including gravitational time dilation, gravitational redshift, signal delay in a gravitational field, and, so far only indirectly, gravitational radiation. In addition, numerous observations are interpreted as confirmation of one of the most mysterious and exotic predictions of the general theory of relativity - the existence of black holes.

Despite the stunning success of the general theory of relativity, there is discomfort in the scientific community, connected, firstly, with the fact that it cannot be reformulated as the classical limit of quantum theory, and secondly, with the fact that the theory itself indicates the limits of its applicability, since it predicts the appearance of irremovable physical divergences when considering black holes and, in general, space-time singularities. To solve these problems, a number of alternative theories have been proposed, some of which are also quantum. Current experimental evidence, however, indicates that any type of deviation from general relativity should be very small, if it exists at all.

15 ticket EXPANSION OF THE UNIVERSE.HUBBLE LAW

Universe expansion- a phenomenon consisting in an almost uniform and isotropic expansion of outer space on the scale of the entire Universe. Experimentally, the expansion of the Universe is observed in the form of the implementation of the Hubble law. Science considers the so-called Big Bang to be the beginning of the expansion of the Universe. Theoretically, the phenomenon was predicted and substantiated by A. Friedman at an early stage of development of the general theory of relativity from general philosophical considerations about the homogeneity and isotropy of the Universe.

Hubble law(the law of the general recession of galaxies) is an empirical law that relates the redshift of the galaxy to the distance to them in a linear way:

Where z- redshift of the galaxy D- distance to it H 0 is a proportionality factor, called the Hubble constant. With a small value z the approximate equality holds cz=V r, Where V r is the speed of the galaxy along the observer's line of sight, c- the speed of light. In this case, the law takes the classical form:

This age is the characteristic time of the expansion of the Universe at the moment and, up to a factor of 2, corresponds to the age of the Universe calculated using the standard Friedman cosmological model.

16 ticket FRIEDMAN MODEL. SINGULARITY

Friedman's universe(Friedman-Lemaitre-Robertson-Walker metric) is one of the cosmological models that satisfy the field equations of the general theory of relativity, the first of the non-stationary models of the Universe. Received by Alexander Fridman in 1922. The Friedman model describes a homogeneous isotropic non-stationary A universe with matter that has a positive, zero, or negative constant curvature. This work of the scientist became the main theoretical development of general relativity after the work of Einstein in 1915-1917.

gravitational singularity- the region of space-time through which it is impossible to continue the geodetic line. Often in it the curvature of the space-time continuum turns to infinity, or the metric has other pathological properties that do not allow physical interpretation (for example, cosmological singularity- the state of the Universe at the initial moment of the Big Bang, characterized by an infinite density and temperature of matter);

17 ticket BIG BANG THEORY. RELICT RADIATION

Relic radiation(or cosmic microwave background radiation from English cosmic microwave background radiation) - cosmic electromagnetic radiation with a high degree of isotropy and with a spectrum characteristic of an absolutely black body with a temperature of 2.725 K.

The existence of the CMB was predicted theoretically within the framework of the Big Bang theory. Although many aspects of the original Big Bang theory have now been revised, the fundamentals that made it possible to predict the temperature of the CMB have not changed. It is believed that the relict radiation has been preserved from the initial stages of the existence of the Universe and evenly fills it. Its existence was experimentally confirmed in 1965. Along with the cosmological redshift, the cosmic microwave background radiation is considered as one of the main confirmations of the Big Bang theory.

Big Bang(English) big bang) is a cosmological model describing the early development of the Universe, namely, the beginning of the expansion of the Universe, before which the Universe was in a singular state.

Usually now automatically combine the theory of the Big Bang and the model of the hot Universe, but these concepts are independent and historically there was also the idea of ​​a cold initial Universe near the Big Bang. It is the combination of the Big Bang theory with the theory of the hot Universe, supported by the existence of cosmic microwave background radiation, that is considered further.

18 ticket SPACE VACUUM

Vacuum(rel. vacuum- void) - space free from matter. In engineering and applied physics, vacuum is understood as a medium containing gas at pressures well below atmospheric pressure. Vacuum is characterized by the ratio between the mean free path of gas molecules λ and the characteristic size of the medium d. Under d the distance between the walls of the vacuum chamber, the diameter of the vacuum pipeline, etc. can be taken. Depending on the value of the ratio λ / d distinguish between low (), medium () and high () vacuum.

It is necessary to distinguish between concepts physical vacuum And technical vacuum.

19 ticket QUANTUM MECHANICS

Quantum mechanics- a section of theoretical physics that describes physical phenomena in which the action is comparable in magnitude to Planck's constant. The predictions of quantum mechanics can differ significantly from the predictions of classical mechanics. Because Planck's constant is extremely small compared to the action of everyday objects, quantum effects mostly only show up on microscopic scales. If the physical action of the system is much greater than Planck's constant, quantum mechanics goes organically into classical mechanics. In turn, quantum mechanics is a non-relativistic approximation (that is, an approximation of small energies compared to the rest energy of the massive particles of the system) of quantum field theory.

Classical mechanics, which well describes systems of macroscopic scales, is not capable of describing phenomena at the level of atoms, molecules, electrons and photons. Quantum mechanics adequately describes the basic properties and behavior of atoms, ions, molecules, condensed matter, and other systems with an electron-nuclear structure. Quantum mechanics is also capable of describing the behavior of electrons, photons, and other elementary particles, but a more accurate relativistically invariant description of the transformations of elementary particles is built within the framework of quantum field theory. Experiments confirm the results obtained with the help of quantum mechanics.

The basic concepts of quantum kinematics are the concepts of an observable and a state.

The basic equations of quantum dynamics are the Schrödinger equation, the von Neumann equation, the Lindblad equation, the Heisenberg equation, and the Pauli equation.

The equations of quantum mechanics are closely related to many branches of mathematics, including: operator theory, probability theory, functional analysis, operator algebras, group theory.

Completely black body- physical idealization used in thermodynamics, a body that absorbs all electromagnetic radiation incident on it in all ranges and reflects nothing. Despite the name, a black body itself can emit electromagnetic radiation of any frequency and visually have a color. The radiation spectrum of a black body is determined only by its temperature.

The importance of a blackbody in the question of the thermal radiation spectrum of any (gray and colored) bodies in general, in addition to being the simplest non-trivial case, is also in the fact that the question of the equilibrium thermal radiation spectrum of bodies of any color and reflection coefficient is reduced by the methods of classical thermodynamics to the question of radiation from an absolutely black body (and historically this was already done by the end of the 19th century, when the problem of radiation from an absolutely black body came to the fore).

The blackest real substances, for example, soot, absorb up to 99% of the incident radiation (that is, they have an albedo equal to 0.01) in the visible wavelength range, but they absorb infrared radiation much worse. Among the bodies of the Solar System, the Sun has the properties of an absolutely black body to the greatest extent.

The term was introduced by Gustav Kirchhoff in 1862.

20 ticket PRINCIPLES OF QUANTUM MECHANICS

All the problems of modern physics can be divided into two groups: the problems of classical physics and the problems of quantum physics. When studying the properties of ordinary macroscopic bodies, one almost never encounters quantum problems, because quantum properties become tangible only in the microcosm. Therefore, the physics of the 19th century, which studied only macroscopic bodies, was completely unaware of quantum processes. This is classical physics. It is typical for classical physics that it does not take into account the atomistic structure of matter. Now, however, the development of experimental technology has pushed the boundaries of our acquaintance with nature so widely that we now know, and, moreover, in great detail, the strictness of individual atoms and molecules. Modern physics studies the atomic structure of matter and, therefore, the principles of the old classical physics of the 19th century. had to change in accordance with the new facts, and change radically. This change in principles is the transition to quantum physics.

21 tickets CORPUSCULAR-WAVE DUALISM

Corpuscular-wave dualism- the principle that any object can exhibit both wave and particle properties. It was introduced during the development of quantum mechanics to interpret the phenomena observed in the microcosm from the point of view of classical concepts. A further development of the principle of wave-particle duality was the concept of quantized fields in quantum field theory.

As a classic example, light can be interpreted as a stream of corpuscles (photons), which in many physical effects exhibit the properties of electromagnetic waves. Light exhibits the properties of a wave in the phenomena of diffraction and interference at scales comparable to the wavelength of light. For example, even single photons passing through the double slit create an interference pattern on the screen, determined by Maxwell's equations.

Nevertheless, the experiment shows that a photon is not a short pulse of electromagnetic radiation, for example, it cannot be divided into several beams by optical beam splitters, which was clearly shown by an experiment conducted by French physicists Grangier, Roger and Aspe in 1986. The corpuscular properties of light are manifested in the photoelectric effect and in the Compton effect. A photon also behaves like a particle that is emitted or absorbed entirely by objects whose dimensions are much smaller than its wavelength (for example, atomic nuclei), or can generally be considered pointlike (for example, an electron).

At present, the concept of wave-particle duality is only of historical interest, since it served only as an interpretation, a way to describe the behavior of quantum objects, choosing analogies from classical physics for it. In fact, quantum objects are neither classical waves nor classical particles, acquiring the properties of the former or the latter only in some approximation. Methodologically more correct is the formulation of quantum theory in terms of path integrals (propagator), free from the use of classical concepts.

22 ticket THE CONCEPT OF THE STRUCTURE OF THE ATOM. MODELS OF THE ATOM

Thomson model of the atom(model "Pudding with raisins", eng. plum pudding model).J. J. Thomson proposed to consider the atom as some positively charged body with electrons enclosed inside it. It was finally refuted by Rutherford after his famous experiment on the scattering of alpha particles.

Nagaoka's early planetary model of the atom. In 1904, the Japanese physicist Hantaro Nagaoka proposed a model of the atom, built by analogy with the planet Saturn. In this model, electrons, united in rings, revolved around a small positive nucleus in orbits. The model turned out to be wrong.

Bohr-Rutherford planetary model of the atom. In 1911, Ernest Rutherford, having done a series of experiments, came to the conclusion that the atom is a kind of planetary system in which electrons move in orbits around a heavy positively charged nucleus located in the center of the atom ("Rutherford's model of the atom"). However, such a description of the atom came into conflict with classical electrodynamics. The fact is that, according to classical electrodynamics, an electron, when moving with centripetal acceleration, must emit electromagnetic waves, and, consequently, lose energy. Calculations showed that the time it takes for an electron in such an atom to fall onto the nucleus is absolutely negligible. To explain the stability of atoms, Niels Bohr had to introduce postulates that boiled down to the fact that an electron in an atom, being in some special energy states, does not radiate energy (“the Bohr-Rutherford model of the atom”). Bohr's postulates showed that classical mechanics is not applicable to describe the atom. Further study of the radiation of the atom led to the creation of quantum mechanics, which made it possible to explain the overwhelming majority of the observed facts.

Atom(other Greek ἄτομος- indivisible) - the smallest chemically indivisible part of a chemical element, which is the carrier of its properties. An atom consists of an atomic nucleus and electrons. The nucleus of an atom is made up of positively charged protons and uncharged neutrons. If the number of protons in the nucleus coincides with the number of electrons, then the atom as a whole is electrically neutral. Otherwise, it has some positive or negative charge and is called an ion. Atoms are classified according to the number of protons and neutrons in the nucleus: the number of protons determines whether an atom belongs to a certain chemical element, and the number of neutrons determines the isotope of this element.

Atoms of different types in different quantities, connected by interatomic bonds, form molecules.

23 ticket FUNDAMENTAL INTERACTIONS

Fundamental interactions- qualitatively different types of interaction of elementary particles of bodies composed of them.

Today, the existence of four fundamental interactions is reliably known:

gravitational

electromagnetic

strong

weak

At the same time, electromagnetic and weak interactions are manifestations of a single electroweak interaction.

Searches are underway for other types of fundamental interactions, both in the phenomena of the microworld and on a cosmic scale, but so far no other type of fundamental interaction has been discovered.

In physics, mechanical energy is divided into two types - potential and kinetic energy. The reason for the change in the movement of bodies (changes in kinetic energy) is the force (potential energy) (see Newton's second law). Exploring the world around us, we can notice a wide variety of forces: gravity, thread tension, spring compression force, collision force of bodies , friction force, air resistance force, explosion force, etc. However, when the atomic structure of matter was clarified, it became clear that all the variety of these forces is the result of the interaction of atoms with each other. Since the main type of interatomic interaction is electromagnetic, it turned out that most of these forces are just various manifestations of electromagnetic interaction. One of the exceptions is, for example, the force of gravity, which is caused by the gravitational interaction between bodies that have mass.

24 ticket ELEMENTARY PARTICLES AND THEIR PROPERTIES

Elementary particle- a collective term referring to micro-objects on a sub-nuclear scale that cannot be broken down into their component parts.

It should be borne in mind that some elementary particles (electron, photon, quarks, etc.) are currently considered structureless and are considered as primary fundamental particles. Other elementary particles (so-called constituent particles-proton, neutron, etc.) have a complex internal structure, but, nevertheless, according to modern concepts, it is impossible to separate them into parts (see Confinement).

The structure and behavior of elementary particles is studied by elementary particle physics.

Main article:Quarks

Quarks and antiquarks have never been found in a free state - this is explained by the phenomenon of confinement. Based on the symmetry between leptons and quarks, which is manifested in electromagnetic interaction, hypotheses are put forward that these particles consist of more fundamental particles - preons.

25 ticket CONCEPT OF BIFURCATION. BIFURCATION POINT

Bifurcation is the acquisition of a new quality in the movements of a dynamic system with a small change in its parameters.

The central concept of the bifurcation theory is the concept of a (non)rough system (see below). Any dynamical system is taken and such a (multi)parametric family of dynamical systems is considered that the original system is obtained as a special case - for any one value of the parameter (parameters). If the qualitative picture of the partition of the phase space into trajectories is preserved for the value of the parameters sufficiently close to the given one, then such a system is called rough. Otherwise, if such a neighborhood does not exist, then the system is called rough.

Thus, regions of rough systems appear in the parameter space, which are separated by surfaces consisting of non-rough systems. The theory of bifurcations studies the dependence of a qualitative picture when a parameter changes continuously along a certain curve. The scheme by which the qualitative picture changes is called bifurcation diagram.

The main methods of bifurcation theory are the methods of perturbation theory. In particular, it applies small parameter method(Pontryagin).

bifurcation point- change of the established operating mode of the system. A term from non-equilibrium thermodynamics and synergetics.

bifurcation point- the critical state of the system, in which the system becomes unstable relative to fluctuations and uncertainty arises: will the state of the system become chaotic or will it move to a new, more differentiated and high level of order. A term from the theory of self-organization.

26 ticket SYNERGETICS - THE SCIENCE OF OPEN SELF-ORGANIZING SYSTEMS

Synergetics(other Greek συν-- prefix with the meaning of compatibility and ἔργον- "activity") - an interdisciplinary direction of scientific research, the task of which is to study natural phenomena and processes based on the principles of self-organization of systems (consisting of subsystems). "... A science that studies the processes of self-organization and the emergence, maintenance, stability and decay of structures of the most diverse nature ...".

Synergetics was originally declared as an interdisciplinary approach, since the principles governing the processes of self-organization seem to be the same (regardless of the nature of the systems), and a common mathematical apparatus should be suitable for their description.

From an ideological point of view, synergetics is sometimes positioned as “global evolutionism” or “universal theory of evolution”, which provides a single basis for describing the mechanisms for the emergence of any innovations, just as cybernetics was once defined as “universal control theory”, equally suitable for describing any regulation and optimization operations. : in nature, in technology, in society, etc., etc. However, time has shown that the general cybernetic approach has far from justified all the hopes placed on it. Similarly, the broad interpretation of the applicability of synergetic methods is also criticized.

The basic concept of synergetics is the definition of structure as states, arising as a result of the multivariant and ambiguous behavior of such multi-element structures or multi-factor media that do not degrade to the thermodynamic averaging standard for closed systems, but develop due to openness, energy inflow from the outside, nonlinearity of internal processes, the appearance of special regimes with sharpening and the presence of more than one stable state. In the indicated systems, neither the second law of thermodynamics nor Prigogine's theorem on the minimum rate of entropy production is applicable, which can lead to the formation of new structures and systems, including those more complex than the original ones.

This phenomenon is interpreted by synergetics as a general mechanism of the direction of evolution observed everywhere in nature: from elementary and primitive to complex and more perfect.

In some cases, the formation of new structures has a regular, wave character, and then they are called autowave processes (by analogy with self-oscillations).

27 ticket THE CONCEPT OF LIFE. THE PROBLEM OF THE ORIGIN OF LIFE

Life- the active form of the existence of a substance, in a sense, the highest in comparison with its physical and chemical forms of existence; a set of physical and chemical processes occurring in the cell, allowing the exchange of matter and its division. The main attribute of living matter is the genetic information used for replication. More or less accurately define the concept of "life" can only enumerate the qualities that distinguish it from non-life. Life does not exist outside the cell, viruses exhibit the properties of living matter only after the transfer of genetic material into the cell [ source not specified 268 days] . Adapting to the environment, a living cell forms the whole variety of living organisms.

Also, the word "life" is understood as the period of existence of a single organism from the moment of occurrence to its death (ontogeny).

In 1860, the French chemist Louis Pasteur took up the problem of the origin of life. Through his experiments, he proved that bacteria are ubiquitous, and that non-living materials can easily be contaminated by living things if they are not properly sterilized. The scientist boiled various media in water in which microorganisms could form. Additional boiling killed the microorganisms and their spores. Pasteur attached a sealed flask with a free end to the S-shaped tube. Spores of microorganisms settled on a curved tube and could not penetrate into the nutrient medium. A well-boiled nutrient medium remained sterile; no life was found in it, despite the fact that air access was provided.

As a result of a series of experiments, Pasteur proved the validity of the theory of biogenesis and finally refuted the theory of spontaneous generation.

28 ticket THE CONCEPT OF THE ORIGIN OF OPARIN'S LIFE