Lefties are talented people. Among brilliant people every fifth is left-handed

In classical physics, a system is understood as a collection of some parts interconnected 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 regular relationship and interdependence of the phenomena of the material and spiritual world is called determinism. The central concept of determinism is the proposition of the existence causation; causality occurs when one phenomenon gives rise to another phenomenon (consequence).

Classical physics stands on the positions of rigid determinism, which is called Laplacian - 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 the 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 existing state of the universe as a consequence of the previous state and as the cause of the next. The mind, which at a given moment would know all the forces acting in nature, and the relative position of all its constituent entities, if it were still so vast as to take into account all these data, would cover with the same formula the movements of the largest bodies of the Universe. and the lightest atoms. Nothing would be unreliable for him, and the future, like the past, would stand before his eyes. Traditionally, this hypothetical being, which could (according to Laplace) predict the development of the universe, is called "Laplace's demon" in science.

In the classical period of the development of natural science, the idea is affirmed that only dynamic laws fully characterize causality in nature.

Laplace tried to explain the whole world, including physiological, psychological, social phenomena, from the point of view of mechanistic determinism, which he considered as a methodological principle for building any science. Laplace saw an example of the form of scientific knowledge in celestial mechanics. Thus, Laplacian determinism denies the objective nature of chance, the concept of the probability of an event.

The further development of natural science led to new ideas of causality and effect. For some natural processes, it is difficult to determine the cause - for example, radioactive decay occurs by chance. 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 today's natural science, modern determinism offers a variety of objectively existing forms of interconnection between processes and phenomena, many of which are expressed in the form of relationships that do not have pronounced causal relationships, that is, do not contain the moments of the generation of one by the other. 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 a universal effective causality, outside of which there is not a single phenomenon of reality, including the so-called random phenomena, in the aggregate of which static laws are manifested.

Science continues to develop, enriched with new concepts, laws, principles, which indicates the limitations of Laplacian determinism. However, classical physics, in particular classical mechanics, still has its own niche of application. Its laws are quite applicable for relatively slow motions, the speed of which is much less than the speed of light. The significance of classical physics in the modern period was well defined by one of the founders of quantum mechanics, Niels Bohr: “No matter how far phenomena go beyond the framework of classical physical explanation, all experimental data must be described using classical concepts. The justification for this is simply to state the exact meaning of the word "experiment". We use the word "experiment" to refer to a situation in which we can tell others what we have done and what we have learned. Therefore, the experimental setup and the results of observations must be described unambiguously in the language of classical physics.”

Newton's classical mechanics has played and still plays a huge role in the development of natural science. It explains many physical phenomena and processes in terrestrial and extraterrestrial conditions, and forms the basis of many technical achievements. On its foundation, natural-scientific methods of research in various branches of natural science were formed.

In 1667, Newton formulated three laws of dynamics - the fundamental laws of classical mechanics.

Newton's first law: any material point (body) retains a state of rest or uniform rectilinear motion until the impact from other bodies makes it change this state.

For a quantitative formulation of the second law of dynamics, the concepts of acceleration a, body mass t and force F. Acceleration characterizes the rate of change in the speed of the body. Weight- one of the main characteristics of material objects, which determines their inertial (inertial mass) and gravity (heavy, or gravitational, mass) properties. Strength- this is a vector quantity, a measure of the mechanical impact on the body from other bodies or fields, as a result of which the body acquires acceleration or changes its shape and size.

Newton's second law: the acceleration acquired by a material point (body) is proportional to the force causing it and inversely proportional to the mass of the material point (body): .

Newton's second law is valid only in inertial frames of reference. Newton's first law can be derived from the second. Indeed, if the resultant forces are equal to zero (in the absence of influence on the body from other bodies), the acceleration is also equal to zero. However, Newton's first law is considered as an independent law, and not as a consequence of the second law, since it is he who asserts the existence of inertial frames of reference.

The interaction between material points (bodies) is determined by Newton's third law: any action of material points (bodies) on each other has the character of interaction; the forces with which material points act on each other are always equal in absolute value, oppositely directed and act along the straight line connecting these points: .

Here F 12 - force acting on the first material point from the second; F 21 - the force acting on the second material point from the first. These forces are applied to different material points (bodies), always act in pairs and are forces of the same nature. Newton's third law allows the transition from the dynamics of a single material point to the dynamics of a system of material points characterized by pair interaction.

Fourth Law, formulated by Newton is the law of universal gravitation.

The logical chain of this discovery can be built as follows. Reflecting on the motion of the Moon, Newton concluded that it is kept in orbit by the same force under which the stone falls to the ground, i.e. gravitational force: "The moon gravitates towards the Earth and by the gravitational force constantly deviates from rectilinear motion and is kept in its orbit." Using the formula of his contemporary Huygens for centripetal acceleration and astronomical data, he found that the centripetal acceleration of the Moon is 3600 times less than the acceleration of a stone falling to the Earth. Since the distance from the center of the Earth to the center of the Moon is 60 times the radius of the Earth, we can assume that The force of gravity decreases with the square of the distance. Then, on the basis of Kepler's laws describing the motion of the planets, Newton extends this conclusion to all planets. ( “The forces by which the principal planets deviate from rectilinear motion and are kept in their orbits are directed towards the Sun and are inversely proportional to the squares of the distances to its center»).

Finally, having stated the position about the universal nature of the forces of gravity and their identical nature on all planets, showing that “the weight of a body on any planet is proportional to the mass of this planet”, establishing experimentally the proportionality of the mass of a body and its weight (gravity), Newton concludes that the force of gravity between bodies is proportional to the mass of these bodies. So the famous law of universal gravitation was established, which is written as:

where γ is the gravitational constant, first experimentally determined in 1798 by G. Cavendish. According to modern data, γ \u003d 6.67 * 10 -11 N × m 2 / kg 2.

It is important to note that in the law of universal gravitation, mass acts as gravity measures, i.e. determines the force of gravity between material bodies.

Newton's laws allow us to solve many problems of mechanics - from simple to complex. The range of such problems expanded significantly after the development by Newton and his followers of a new mathematical apparatus for that time - differential and integral calculus, which is currently widely used to solve various problems of natural science.

Classical mechanics and Laplacian determinism. Causal explanation of many physical phenomena in the late 18th - early 19th century. led to the absolutization of classical mechanics. A philosophical doctrine arose mechanistic determinism,- founded by P. Laplace, a French mathematician, physicist and philosopher. Laplacian determinism expresses the idea absolute determinism- confidence that everything that happens has a reason in the human concept and is a necessity known and still unknown to the mind. Its essence can be understood from Laplace’s statement: “Contemporary events have a connection with previous events based on the obvious principle that no object can begin to be without the cause that produced it ... The will, however free, cannot give rise to actions, even those that are considered neutral ... We must consider the present state of the universe as the result of its previous state and the cause of its subsequent state. A mind that, at any given moment, would know all the forces acting in nature, and the relative disposition of its constituent parts, if, moreover, it were vast enough to subject these data to analysis, would embrace in a single formula the movements of the most enormous bodies in the Universe and the lightest atom; nothing would be unclear to him, and the future, like the past, would be before his eyes ... The curve described by the molecule of air or vapor is controlled just as strictly and definitely as the planetary orbits: between them there is only the difference which is imposed by our ignorance." These words echo the belief of A. Poincaré: “Science is deterministic, it is such a priori [initially], it postulates determinism, since it could not exist without it. She is so a posteriori [from experience]: if she postulated it from the very beginning as a necessary condition for her existence, then she then strictly proves it by her existence, and each of her victories is a victory for determinism.

Further development of physics showed that for some natural processes it is difficult to determine the cause. For example, radioactive decay occurs by chance. Such processes are objectively random, and not because we cannot indicate their cause due to a lack of our knowledge. At the same time, science did not stop developing, but was enriched with new laws, principles and concepts, which indicates the limitations of the classical principle - Laplacian determinism. An absolutely accurate description of the past and the prediction of the future for a colossal variety of material objects, phenomena and processes is a difficult task and devoid of objective necessity. Even for the simplest object - a material point - due to the finite accuracy of measuring instruments, an absolutely accurate prediction is also unrealistic.

The methods of empirical and theoretical knowledge are schematically presented in Fig.4.

Fig.4. Methods of empirical and theoretical knowledge

Observation is a purposeful, organized perception of objects and phenomena. Scientific observations are carried out to collect facts that strengthen or refute a particular hypothesis and are the basis for certain theoretical generalizations.

An experiment is a method of research that differs from observation by an active character. This observation is under special controlled conditions.

Measurement is the material process of comparing a quantity with a standard, a unit of measurement. The number expressing the ratio of the measured quantity to the standard is called the numerical value of this quantity.

4. Newtonian mechanics. Laplace determinism

In 1667, Newton formulated three laws of dynamics - the fundamental laws of classical mechanics.

Newton's first law: any material point (body) retains a state of rest or uniform rectilinear motion until the impact from other bodies makes it change this state.

For a quantitative formulation of the second law of dynamics, the concepts of acceleration a, body mass t and strength F. Acceleration characterizes the rate of change in the speed of the body. Weight- one of the main characteristics of material objects, which determines their inertial (inertial mass) and gravity (heavy, or gravitational, mass) properties. Strength- this is a vector quantity, a measure of the mechanical impact on the body from other bodies or fields, as a result of which the body acquires acceleration or changes its shape and size.

Newton's second law: the acceleration acquired by a material point (body) is proportional to the force causing it and inversely proportional to the mass of the material point (body):
.

Fourth Law, formulated by Newton is the law of universal gravitation.

where γ is the gravitational constant, first experimentally determined in 1798 by G. Cavendish. According to modern data, γ \u003d 6.67 * 10 -11 N × m 2 / kg 2.

It is important to note that in the law of universal gravitation, mass acts as gravity measures, i.e. determines the force of gravity between material bodies.

Classical mechanics and Laplacian determinism. Causal explanation of many physical phenomena in the late 18th - early 19th centuries. led to the absolutization of classical mechanics. A philosophical doctrine arose mechanistic determinism,- founded by P. Laplace, a French mathematician, physicist and philosopher. Laplacian determinism expresses the idea absolute determinism- confidence that everything that happens has a reason in the human concept and is a necessity known and still unknown to the mind. Its essence can be understood from Laplace’s statement: “Contemporary events have a connection with previous events based on the obvious principle that no object can begin to be without the cause that produced it ... The will, however free, cannot give rise to actions, even those that are considered neutral ... We must consider the present state of the universe as the result of its previous state and the cause of its subsequent state. A mind that, at any given moment, would know all the forces acting in nature, and the relative disposition of its constituent parts, if, moreover, it were vast enough to subject these data to analysis, would embrace in a single formula the movements of the most enormous bodies in the Universe and the lightest atom; nothing would be unclear to him, and the future, like the past, would be before his eyes ... The curve described by the molecule of air or vapor is controlled just as strictly and definitely as the planetary orbits: between them there is only the difference which is imposed by our ignorance." These words echo A. Poincare's conviction: “Science is deterministic, it is such a priori [originally], it postulates determinism, since it could not exist without it. She is such and a posteriori [from experience]: if she postulated it from the very beginning as a necessary condition of her existence, then she then strictly proves it by her existence, and each of her victories is a victory of determinism.

Thanks to the purposeful work of natural scientists, science was brought to such a stage of development that, it would seem, nothing could resist the strict certainty of its laws. Thus, Pierre Laplace, who lived in the 19th century, expressed his view of the Universe as a completely deterministic object: “nothing will be uncertain, and the future, like the past, will be presented before our eyes.” For example, if we know the exact position of the planets and the Sun at a given moment, then, according to the laws of attraction, we can accurately calculate what state the solar system will be in at any other moment in time. But Laplace wanted to see even more in the determinism of the laws of the universe: he argued that there are similar laws for everything, including for humans. This doctrine of determinism has been fundamentally destroyed by quantum theory.

Let's compare how classical mechanics differs from quantum mechanics. Let there be a system of particles. In classical mechanics, the state of the system at each moment of time is determined by the value of the coordinates and momenta of all particles. All other physical parameters, such as: energy, temperature, mass, etc., can be determined from the coordinates and momenta of the particles of the system. The determinism of classical mechanics is that "the future state of a system is completely and uniquely determined if its initial state is given."

Undoubtedly, in any experiment, measurements may have some inaccuracy, uncertainty, and, depending on the physical system under consideration, its future may turn out to be either sensitive or insensitive to this uncertainty. “But in principle (highlighted by us - V.R.) there is no limit to the accuracy that we could not achieve,” says Sam Treiman. “Therefore, in principle, ... there are no obstacles to predicting future developments.”

In quantum mechanics, there is also the concept of "state of the system". As in classical mechanics, the system, according to the laws, "... develops into such states that are completely determined if the initial state is given at some initial moment." Therefore, here the present determines the future. But “quantum states do not accurately specify the coordinates and momenta of particles; they determine only the probability (highlighted by us - V.R.)”. Randomness in quantum mechanics, - says V. P. Demutsky, - is one of its postulates.

The inevitability of a probabilistic description of a physical system in quantum mechanics is explained by Johann von Neumann: “... no repetition of successive measurements can introduce a causal order ... because atomic phenomena lie on the edge of the physical world, where any measurement introduces a change of the same order as the measured object itself, so that the latter changes in a significant way, mainly due to uncertainty relations.

At the quantum level, the “blurring” of conjugate characteristics, expressed by the Heisenberg uncertainty principle, is of decisive importance: the accuracy of measuring the coordinates and momentum of the system cannot be higher than Planck's constant, the minimum quantum of action.

According to this position, no experiment can lead to simultaneously accurate measurements of the coordinates and momentum of a particle. This uncertainty is connected not with the imperfection of the measuring system, but with the objective properties of the microworld. If we determine exactly the coordinate of a particle, then the value of its momentum is “blurred” and becomes more uncertain, the more precisely the coordinate is determined. Therefore, the classical understanding of the particle trajectory disappears in quantum mechanics. “In quantum physics, particles move along mysterious trajectories that extend along wave-like paths. A single electron can be everywhere within a wave pattern." For example, an electron may leave a photograph of its trajectory, but it may not have a strict trajectory. In connection with the consideration of the trajectories of atomic objects, the understanding of the trajectory proposed by Feynman seems surprising. According to his model, "the probability of a particle moving from point A to point B is equal to the sum of the probabilities of its movement along all possible trajectories connecting these points." Therefore, quantum theory allows a particle to be on any trajectory connecting two points, and therefore it is impossible to say exactly where the particle will be at a certain moment.

So, if classical physics considered inaccuracy to be a consequence of the imperfection of technology and the incompleteness of human knowledge, then quantum theory speaks of the fundamental impossibility of accurate measurements at the atomic level. Niels Bohr believed that "uncertainty is not the result of temporary ignorance, resolvable with further research, but the fundamental and inevitable limit of human knowledge."

Complementarity principle

Niels Bohr proposed the principle of complementarity, according to which, “we cannot say anything about the quantum world that would be similar to reality; in return, we acknowledge the validity of alternative and mutually exclusive methods.” The idea of the atomic world, in comparison with the idea of Aristotle (the world as an organism) and classical physics (the world is a machine), is indescribable. Classical physics assumed that there is an objective world that we can explore and measure without significantly changing it. But at the quantum level, it turns out to be impossible to explore reality without changing it. This applies, for example, to coordinate and momentum. “Knowing the position of a particle,” W. Heisenberg wrote, “in addition to knowing its speed or momentum.” We cannot define an additional quantity (eg speed) with the accuracy of the first (coordinate).

Generalizing this principle to living organisms, Bohr believed that "our knowledge that a cell lives is perhaps something additional to a complete knowledge of its molecular structure." If a complete knowledge of the structure of the cell, which can only be achieved through intervention, destroys the life of the cell, then, concludes Bohr, "it is logically possible that life precludes the full establishment of the underlying physico-chemical structures." On this basis, the chemical bonds of molecules are complementary to physical laws, biological ones to chemical ones, social ones to biological ones, social ones to mental ones, etc.

Thus, the principle of complementarity proposed by Bohr destroys the positions of determinism, which will be discussed in more detail below.

Portal for the student. Self-training

4. Newtonian mechanics. Laplace determinism

RELATED ARTICLES