Mechanics

MECHANICS (from the Greek mechane - machine), the science of motion. Until the 17th century, knowledge in this area was almost limited to empirical observations, often erroneous. In the 17th century, the properties of motion began to be derived mathematically from a few basic principles. In the 18th century, the principles of mechanics were generalized to the point where they could be reduced to a single system of equations, and M. became a purely mathematical science. In the 20th century, delicate physical experiments forced these principles to be refined, and classical M. underwent significant changes (relativistic M. of the theory of relativity and quantum M.). However, only classical M. still finds direct practical applications. Its principles, established in 1687 by Newton, are as follows: 1) every material body, left to itself, remains at rest or continues to move uniformly and rectilinearly until some external cause (i.e., force) changes this state of the body; 2) the change in the amount of motion of a body (i.e., velocity multiplied by mass) in a unit of time is equal to the acting force and is directed along this latter; 3) the action of a force is always accompanied by a reaction equal to it; 4) any two material bodies act on each other with forces proportional to their masses and inversely proportional to the square of their mutual distance; the coefficient of this proportionality is the same for all bodies. All laws of classical M. remain unchanged, whether we consider the space in which the studied motions occur to be stationary or that it itself moves uniformly and rectilinearly. In relativistic M., proposed in 1916 by Einstein, the principles of M. are generalized so that the laws of M. remain unchanged, whether we consider the space in which the studied motions occur to be stationary or that it itself moves in any way. Quantum M., being created at present by the work of a number of scientists, considers that in reality not all movements that are consistent with the principles of classical or relativistic mechanics are possible. It allows only movements associated with certain quantities of mechanical action (i.e., momentum multiplied by the distance traveled). Classical mechanics is usually divided into the following three disciplines: kinematics - the doctrine of the forms of motion regardless of the causes causing motion (i.e., forces), statics - the doctrine of the equilibrium of forces, and dynamics - the doctrine of motion under the action of forces. Statistical mechanics occupies a somewhat special position. It studies phenomena related to the motion of a large number of bodies moving independently of each other (molecules, stars). Statistical mechanics is based on the theory of probabilities. Created only in the second half of the 19th century, statistical mechanics does not yet possess such perfect methods as the science of the motion of individual bodies.

V. Glivenko. Wave mechanics, according to modern physical concepts, governs intra-atomic and intra-molecular movements, in short, movements occurring on a very small scale. The impetus for the emergence of wave M. was the difficulties associated with the dual nature of light: one group of optical phenomena (interference, diffraction) can be explained exclusively as a consequence of the wave nature of light, while another (photoelectric effect, Compton effect) with equal necessity forces us to attribute a corpuscular nature to light (see Quantum theory). Moreover, the development of the theory of the structure of atoms and molecules led physicists (after many failures) to a firm conviction that the laws of classical M., even with the corrections introduced by the theory of relativity, are not strictly applicable to microscopic (intra-atomic) processes. In search of a way out of all these difficulties, de Broglie (de Broglie) in 1925 put forward a bold hypothesis, consisting in the fact that the duality of corpuscular and wave properties is universal and equally inherent in both light and matter. Just as a light ray possesses not only wave properties manifested in interference and diffraction, but also corpuscular properties manifested in phenomena related to energy exchange, so every electron possesses not only particle properties but also wave properties. What is the nature of the wave process associated with particles of matter - this question de Broglie left open, and it continues to be so to this day; however, by allowing the existence of 'matter waves', it could easily be shown that their wavelength must be expressed by the following formula: λ = h/mv, where m is the mass of the particle, v is its velocity and h = 6.57 × 10^-27, the so-called 'Planck constant'. - de Broglie's hypothesis, despite all its paradoxicality, proved to be very fruitful and very soon received brilliant experimental confirmation. It turned out that just like light, particles of matter can experience interference, and the wavelength determined from the interference pattern of matter waves exactly coincides with that calculated by de Broglie's formula. If de Broglie laid the foundation for the 'wave theory of matter', then the complete system of wave M. was created by Schrödinger (Schrödinger). Relying on the ideas of de Broglie, Schrödinger developed the analogy between optical and mechanical phenomena, indicated as early as the 1850s by Hamilton (W. Hamilton). The elementary phenomena of geometric optics (reflection and refraction) can be equally well explained in terms of both wave and corpuscular theories. Generalizing this analogy, it can be shown that the equations describing the motion of particles from the point of view of classical M. formally coincide with the equations of geometric optics, and vice versa. But the laws of geometric optics are strictly applicable only when the dimensions of objects significantly exceed the wavelength. When we move into the microscopic region of objects, the observed phenomena are complicated by the diffraction of light beams, which can only be explained from the point of view of wave concepts. Schrödinger put forward a brilliant idea that a completely similar situation exists in the field of M. As long as we operate with macroscopic objects, the laws of classical M. must have strict application; but as soon as we move into the region of microscopic phenomena (intra-atomic processes), classical M. proves to be insufficient and, just as in the case of optics, it is necessary to use wave concepts. All optical phenomena in the most general case can be calculated by means of the so-called 'wave equation'. By analogy with this, Schrödinger gave the 'wave equation of matter', from which all results previously obtained by the old quantum theory by means of very artificial and arbitrary premises were immediately obtained automatically. In addition to this, Schrödinger's equation allowed solving a large number of new questions that were previously inaccessible to solution, and at present this equation is one of the most firmly established and comprehensive equations of mathematical physics. Despite all its fruitfulness, wave M. still remains, although an extremely powerful, but formally mathematical method, the physical content of which is far from clear. It would be erroneous to identify 'matter waves' with ordinary electromagnetic optical waves. It is sufficient to point out that only in the case of a single electron can one imagine the propagation of de Broglie waves in ordinary three-dimensional space; for several electrons, the waves should be referred to a fictitious multidimensional 'configuration space'. - In addition to solving purely physical questions, wave M. has raised a number of important philosophical problems. Among them, the so-called 'Heisenberg uncertainty principle' plays the greatest role, according to which we are fundamentally unable to simultaneously determine the position and velocity of a particle with absolute accuracy. An increase in the accuracy of determining the position of a particle is associated with a decrease in the accuracy of determining the velocity, and vice versa, and the product of the inaccuracies of these quantities cannot be less than Planck's constant h. If we take into account that the order of magnitude of h is 10^-27, then it is clear that this inaccuracy has no practical significance. Nevertheless, the importance of Heisenberg's principle is very significant, since the inaccuracy prescribed by it is not associated with any temporary imperfection of our instruments, but is deeply rooted in the very nature of the world around us, E. Shpolsky.