Fundamental laws of physics. Basic concepts and laws of physics and properties of elementary particles of matter

Helen Czerski

Physicist, oceanographer, presenter of popular science programs on the BBC.

When it comes to physics, we present some formulas, something strange and incomprehensible, unnecessary to an ordinary person. We may have heard something about quantum mechanics and cosmology. But between these two poles is precisely everything that makes up our daily life: planets and sandwiches, clouds and volcanoes, bubbles and musical instruments. And they are all governed by a relatively small number of physical laws.

We can constantly observe these laws in action. Take, for example, two eggs - raw and boiled - and spin them, and then stop. The boiled egg will remain motionless, the raw one will begin to rotate again. This is because you only stopped the shell, and the liquid inside continues to rotate.

This is a clear demonstration of the law of conservation of angular momentum. Simplified, it can be formulated as follows: starting to rotate around a constant axis, the system will continue to rotate until something stops it. This is one of the fundamental laws of the universe.

It comes in handy not only when you need to distinguish a boiled egg from a raw one. It can also be used to explain how the Hubble Space Telescope, being without any support in space, aims the lens at a certain part of the sky. It just has spinning gyroscopes inside, which essentially behave the same as a raw egg. The telescope itself rotates around them and thus changes its position. It turns out that the law, which we can test in our kitchen, also explains the device of one of the most outstanding technologies of mankind.

Knowing the basic laws governing our daily life, we stop feeling helpless.

To understand how the world around us works, we must first understand its basics -. We have to understand that physics is not just weird scientists in laboratories or complicated formulas. It is right in front of us, available to everyone.

Where to start, you might think. Surely you noticed something strange or incomprehensible, but instead of thinking about it, you told yourself that you are an adult and you do not have time for this. Chersky advises not to dismiss such things, but to start with them.

If you don't want to wait for something interesting to happen, put raisins in your soda and see what happens. Watch spilled coffee dry up. Tap the spoon on the edge of the cup and listen for the sound. Finally, try dropping the sandwich so that it doesn't fall butter-side down.

The session is approaching, and it's time for us to move from theory to practice. Over the weekend, we sat down and thought that many students would do well to have a collection of basic physics formulas handy. Dry formulas with explanation: short, concise, nothing more. A very useful thing when solving problems, you know. Yes, and in the exam, when exactly what was cruelly memorized the day before can “jump out” of my head, such a selection will serve you well.

Most of the tasks are usually given in the three most popular sections of physics. This Mechanics, thermodynamics And Molecular physics, electricity. Let's take them!

Basic formulas in physics dynamics, kinematics, statics

Let's start with the simplest. Good old favorite rectilinear and uniform movement.

Kinematic formulas:

Of course, let's not forget about the movement in a circle, and then move on to the dynamics and Newton's laws.

After the dynamics, it's time to consider the conditions for the equilibrium of bodies and liquids, i.e. statics and hydrostatics

Now we give the basic formulas on the topic "Work and energy". Where would we be without them!

Basic formulas of molecular physics and thermodynamics

Let's finish the section of mechanics with formulas for vibrations and waves and move on to molecular physics and thermodynamics.

Efficiency, Gay-Lussac's law, the Clapeyron-Mendeleev equation - all these sweet formulas are collected below.

By the way! There is a discount for all our readers 10% on .

Basic formulas in physics: electricity

It's time to move on to electricity, although thermodynamics loves it less. Let's start with electrostatics.

And, to the drum roll, we finish with the formulas for Ohm's law, electromagnetic induction and electromagnetic oscillations.

That's all. Of course, a whole mountain of formulas could be given, but this is useless. When there are too many formulas, you can easily get confused, and then completely melt the brain. We hope that our cheat sheet of basic formulas in physics will help you solve your favorite problems faster and more efficiently. And if you want to clarify something or have not found the formula you need: ask the experts student service. Our authors keep hundreds of formulas in their heads and click tasks like nuts. Contact us, and soon any task will be "too tough" for you.

Let's look into this a bit. What Snow meant by saying you can't win is that since matter and energy are conserved, you can't gain one without losing the other (that is, E=mc²). It also means that you need to supply heat to run the engine, but in the absence of a perfectly closed system, some heat will inevitably escape into the open world, leading to the second law.

The second law - losses are inevitable - means that due to increasing entropy, you cannot return to the previous energy state. Energy concentrated in one place will always tend to places of lower concentration.

Finally, the third law - you can't get out of the game - refers to the lowest theoretically possible temperature - minus 273.15 degrees Celsius. When the system reaches absolute zero, the movement of molecules stops, which means that entropy will reach its lowest value and there will not even be kinetic energy. But in the real world it is impossible to reach absolute zero - only very close to it.

Strength of Archimedes

After the ancient Greek Archimedes discovered his principle of buoyancy, he allegedly shouted "Eureka!" (Found!) and ran naked through Syracuse. So says the legend. The discovery was so important. Legend also says that Archimedes discovered the principle when he noticed that the water in the bathtub rises when a body is immersed in it.

According to Archimedes' principle of buoyancy, the force acting on a submerged or partially submerged object is equal to the mass of fluid that the object displaces. This principle is of paramount importance in density calculations, as well as in the design of submarines and other ocean-going vessels.

Evolution and natural selection

Now that we have established some of the basic concepts of how the universe began and how physical laws affect our daily lives, let's turn our attention to the human form and find out how we got to this point. According to most scientists, all life on Earth has a common ancestor. But in order to form such a huge difference between all living organisms, some of them had to turn into a separate species.

In a general sense, this differentiation has occurred in the process of evolution. Populations of organisms and their traits have gone through mechanisms such as mutations. Those with more survival traits, like brown frogs that camouflage themselves in swamps, were naturally selected for survival. This is where the term natural selection comes from.

You can multiply these two theories by many, many times, and actually Darwin did this in the 19th century. Evolution and natural selection explain the enormous diversity of life on Earth.

Albert Einstein's general theory of relativity was, and remains, a major discovery that forever changed our view of the universe. Einstein's main breakthrough was the statement that space and time are not absolute, and gravity is not just a force applied to an object or mass. Rather, gravity has to do with the fact that mass warps space and time itself (spacetime).

To make sense of this, imagine that you are driving across the Earth in a straight line in an easterly direction from, say, the northern hemisphere. After a while, if someone wants to accurately determine your location, you will be much south and east of your original position. This is because the earth is curved. To drive straight east, you need to take into account the shape of the Earth and drive at an angle slightly north. Compare a round ball and a sheet of paper.

Space is pretty much the same. For example, it will be obvious to the passengers of a rocket flying around the Earth that they are flying in a straight line in space. But in reality, the space-time around them is curving under the force of Earth's gravity, causing them to both move forward and stay in Earth's orbit.

Einstein's theory had a huge impact on the future of astrophysics and cosmology. She explained a small and unexpected anomaly in Mercury's orbit, showed how starlight bends, and laid the theoretical foundations for black holes.

Heisenberg uncertainty principle

Einstein's expansion of relativity taught us more about how the universe works and helped lay the groundwork for quantum physics, leading to a completely unexpected embarrassment of theoretical science. In 1927, the realization that all the laws of the universe are flexible in a certain context led to the startling discovery of the German scientist Werner Heisenberg.

Postulating his uncertainty principle, Heisenberg realized that it was impossible to know two properties of a particle simultaneously with a high level of accuracy. You can know the position of an electron with a high degree of accuracy, but not its momentum, and vice versa.

Later, Niels Bohr made a discovery that helped explain the Heisenberg principle. Bohr found that the electron has the qualities of both a particle and a wave. The concept became known as wave-particle duality and formed the basis of quantum physics. Therefore, when we measure the position of an electron, we define it as a particle at a certain point in space with an indefinite wavelength. When we measure the momentum, we consider the electron as a wave, which means we can know the amplitude of its length, but not the position.

Introduction

1. Newton's laws

1.1. Law of inertia (Newton's first law)

1.2 Law of motion

1.3. Law of conservation of momentum (Law of conservation of momentum)

1.4. Forces of inertia

1.5. Viscosity law

2.1. Laws of thermodynamics

1. 
   Law of gravity

3.2. Gravitational interaction

3.3. Celestial mechanics

1. 
   Strong gravitational fields

3.5. Modern classical theories of gravity

Conclusion

Literature

Introduction

The fundamental laws of physics describe the most important phenomena in nature and the universe. They allow us to explain and even predict many phenomena. So, relying only on the fundamental laws of classical physics (Newton's laws, the laws of thermodynamics, etc.), humanity successfully explores space, sends spacecraft to other planets.

I want to consider in this work the most important laws of physics and their relationship. The most important laws of classical mechanics are Newton's laws, which are sufficient to describe phenomena in the macrocosm (without taking into account high values ​​of speed or mass, which is studied in GR - General Relativity, or SRT - Special Relativity.)

1. 
   Newton's laws

Newton's laws of mechanics - three laws underlying the so-called. classical mechanics. Formulated by I. Newton (1687). First law: “Every body continues to be held in its state of rest or uniform and rectilinear motion until and insofar as it is forced by applied forces to change this state.” The second law: "The change in momentum is proportional to the applied driving force and occurs in the direction of the straight line along which this force acts." The third law: "There is always an equal and opposite reaction to an action, otherwise, the interactions of two bodies against each other are equal and directed in opposite directions."

1.1. Zako ́ n ine ́ rtions (First Law New ́ tone) : a free body, which is not affected by forces from other bodies, is in a state of rest or uniform rectilinear motion (the concept of speed here applies to the center of mass of the body in the case of non-translational motion). In other words, bodies are characterized by inertia (from Latin inertia - “inactivity”, “inertia”), that is, the phenomenon of maintaining speed if external influences on them are compensated.

Frames of reference in which the law of inertia is fulfilled are called inertial frames of reference (ISR).

The law of inertia was first formulated by Galileo Galilei, who, after many experiments, concluded that no external cause is needed for a free body to move at a constant speed. Prior to this, a different point of view (dating back to Aristotle) ​​was generally accepted: a free body is at rest, and in order to move at a constant speed, the application of a constant force is necessary.

Subsequently, Newton formulated the law of inertia as the first of his three famous laws.

Galileo's principle of relativity: in all inertial frames of reference, all physical processes proceed in the same way. In a frame of reference brought to a state of rest or of uniform rectilinear motion relative to an inertial frame of reference (conditionally “at rest”), all processes proceed in exactly the same way as in a frame at rest.

It should be noted that the concept of an inertial frame of reference is an abstract model (some ideal object considered instead of a real object. An absolutely rigid body or a weightless thread serve as examples of an abstract model), real frames of reference are always associated with some object and the correspondence of the actually observed movement of bodies in such systems with the results of the calculations will be incomplete.

1.2 Law of motion - a mathematical formulation of how a body moves or how a movement of a more general form occurs.

In the classical mechanics of a material point, the law of motion is three dependences of three spatial coordinates on time, or the dependence of one vector quantity (radius vector) on time, of the form

The law of motion can be found, depending on the task, either from the differential laws of mechanics or from integral ones.

Law of energy conservation - the basic law of nature, which consists in the fact that the energy of a closed system is conserved in time. In other words, energy cannot arise from nothing and cannot disappear into nowhere, it can only pass from one form to another.

The law of conservation of energy is found in various branches of physics and manifests itself in the conservation of various types of energy. For example, in classical mechanics, the law manifests itself in the conservation of mechanical energy (the sum of potential and kinetic energies). In thermodynamics, the law of conservation of energy is called the first law of thermodynamics and speaks of the conservation of energy in total with thermal energy.

Since the law of conservation of energy does not refer to specific quantities and phenomena, but reflects a general pattern that is applicable everywhere and always, it is more correct to call it not a law, but the principle of conservation of energy.

A special case - The law of conservation of mechanical energy - the mechanical energy of a conservative mechanical system is conserved in time. Simply put, in the absence of forces such as friction (dissipative forces), mechanical energy does not arise from nothing and cannot disappear anywhere.

Ek1+Ep1=Ek2+Ep2

The law of conservation of energy is an integral law. This means that it is made up of the action of differential laws and is a property of their combined action. For example, it is sometimes said that the impossibility of creating a perpetual motion machine is due to the law of conservation of energy. But it's not. In fact, in every project of a perpetual motion machine, one of the differential laws is triggered and it is he who makes the engine inoperable. The law of conservation of energy simply generalizes this fact.

According to Noether's theorem, the law of conservation of mechanical energy is a consequence of the homogeneity of time.

1.3. Zako ́ n save ́ and ́ pulse (Zako ́ n save ́ if ́ movement quality) asserts that the sum of the momenta of all bodies (or particles) of a closed system is a constant value.

From Newton's laws, it can be shown that when moving in empty space, momentum is conserved in time, and in the presence of interaction, the rate of its change is determined by the sum of the applied forces. In classical mechanics, the law of conservation of momentum is usually derived as a consequence of Newton's laws. However, this conservation law is also true in cases where Newtonian mechanics is inapplicable (relativistic physics, quantum mechanics).

Like any of the conservation laws, the momentum conservation law describes one of the fundamental symmetries, the homogeneity of space

Newton's third law explains what happens to two interacting bodies. Take for example a closed system consisting of two bodies. The first body can act on the second with some force F12, and the second - on the first with the force F21. How are the forces related? Newton's third law states that the action force is equal in magnitude and opposite in direction to the reaction force. We emphasize that these forces are applied to different bodies, and therefore are not compensated at all.

The law itself:

The bodies act on each other with forces directed along the same straight line, equal in magnitude and opposite in direction: .

1.4. Forces of inertia

Newton's laws, strictly speaking, are valid only in inertial frames of reference. If we honestly write down the equation of motion of a body in a non-inertial frame of reference, then it will differ in appearance from Newton's second law. However, often, to simplify the consideration, some fictitious "inertia force" is introduced, and then these equations of motion are rewritten in a form very similar to Newton's second law. Mathematically, everything here is correct (correct), but from the point of view of physics, a new fictitious force cannot be considered as something real, as a result of some real interaction. We emphasize once again: “inertial force” is just a convenient parametrization of how the laws of motion differ in inertial and non-inertial frames of reference.

1.5. Viscosity law

Newton's law of viscosity (internal friction) is a mathematical expression relating the stress of internal friction τ (viscosity) and the change in the velocity of the medium v ​​in space

(strain rate) for fluid bodies (liquids and gases):

where the value of η is called the coefficient of internal friction or the dynamic coefficient of viscosity (CGS unit - poise). The kinematic coefficient of viscosity is the value μ = η / ρ (the CGS unit is Stokes, ρ is the density of the medium).

Newton's law can be obtained analytically by methods of physical kinetics, where viscosity is usually considered simultaneously with thermal conductivity and the corresponding Fourier law for thermal conductivity. In the kinetic theory of gases, the coefficient of internal friction is calculated by the formula

where is the average speed of the thermal motion of molecules, λ is the mean free path.

2.1. Laws of thermodynamics

Thermodynamics is based on three laws, which are formulated on the basis of experimental data and therefore can be accepted as postulates.

* 1st law of thermodynamics. It is a formulation of the generalized law of conservation of energy for thermodynamic processes. In its simplest form, it can be written as δQ \u003d δA + d "U, where dU is the total differential of the internal energy of the system, and δQ and δA are the elementary amount of heat and the elementary work done on the system, respectively. It should be borne in mind that δA and δQ cannot considered as differentials in the usual sense of this concept.From the point of view of quantum concepts, this law can be interpreted as follows: dU is the change in the energy of a given quantum system, δA is the change in the energy of the system due to the change in the population of the energy levels of the system, and δQ is the change in the energy of the quantum system due to change in the structure of energy levels.

* 2nd law of thermodynamics: The second law of thermodynamics excludes the possibility of creating a perpetual motion machine of the second kind. There are several different, but at the same time equivalent formulations of this law. 1 - Postulate of Clausius. A process in which no other changes occur, except for the transfer of heat from a hot body to a cold one, is irreversible, that is, heat cannot move from a cold body to a hot one without any other changes in the system. This phenomenon is called energy dissipation or dispersion. 2 - Kelvin's postulate. The process in which work is converted into heat without any other changes in the system is irreversible, that is, it is impossible to convert all the heat taken from a source with a uniform temperature into work without making other changes in the system.

* 3rd law of thermodynamics: Nernst's theorem: The entropy of any system at absolute zero temperature can always be taken equal to zero

3.1. Law of gravity

Gravity (universal gravitation, gravitation) (from Latin gravitas - “gravity”) is a long-range fundamental interaction in nature, to which all material bodies are subject. According to modern data, it is a universal interaction in the sense that, unlike any other forces, it gives the same acceleration to all bodies without exception, regardless of their mass. Primarily gravity plays a decisive role on a cosmic scale. The term gravity is also used as the name of a branch of physics that studies the gravitational interaction. The most successful modern physical theory in classical physics describing gravity is the general theory of relativity; the quantum theory of gravitational interaction has not yet been built.

3.2. Gravitational interaction

Gravitational interaction is one of the four fundamental interactions in our world. In the framework of classical mechanics, the gravitational interaction is described by Newton's law of universal gravitation, which states that the force of gravitational attraction between two material points of mass m1 and m2, separated by a distance R, is

Here G is the gravitational constant, equal to m³ / (kg s²). The minus sign means that the force acting on the body is always equal in direction to the radius vector directed to the body, i.e., gravitational interaction always leads to the attraction of any bodies.

The gravity field is potential. This means that it is possible to introduce the potential energy of the gravitational attraction of a pair of bodies, and this energy will not change after moving the bodies along a closed contour. The potentiality of the gravitational field entails the law of conservation of the sum of kinetic and potential energy, and when studying the motion of bodies in a gravitational field, it often greatly simplifies the solution. In the framework of Newtonian mechanics, the gravitational interaction is long-range. This means that no matter how a massive body moves, at any point in space the gravitational potential depends only on the position of the body at a given moment in time.

Large space objects - planets, stars and galaxies have a huge mass and, therefore, create significant gravitational fields. Gravity is the weakest force. However, since it operates at all distances and all masses are positive, it is nevertheless a very important force in the universe. For comparison: the total electric charge of these bodies is zero, since the substance as a whole is electrically neutral. Also, gravity, unlike other interactions, is universal in its effect on all matter and energy. No objects have been found that have no gravitational interaction at all.

Due to its global nature, gravity is responsible for such large-scale effects as the structure of galaxies, black holes and the expansion of the Universe, and for elementary astronomical phenomena - the orbits of planets, and for simple attraction to the Earth's surface and falling bodies.

Gravity was the first interaction described by a mathematical theory. In ancient times, Aristotle believed that objects with different masses fall at different speeds. Only much later, Galileo Galilei experimentally determined that this was not the case - if air resistance is eliminated, all bodies accelerate equally. Isaac Newton's law of gravity (1687) was a good description of the general behavior of gravity. In 1915, Albert Einstein created the General Theory of Relativity, which more accurately describes gravity in terms of the geometry of spacetime.

3.3. Celestial mechanics and some of its tasks

The section of mechanics that studies the motion of bodies in empty space only under the influence of gravity is called celestial mechanics.

The simplest task of celestial mechanics is the gravitational interaction of two bodies in empty space. This problem is solved analytically to the end; the result of its solution is often formulated in the form of Kepler's three laws.

As the number of interacting bodies increases, the problem becomes much more complicated. So, the already famous three-body problem (that is, the motion of three bodies with non-zero masses) cannot be solved analytically in a general form. With a numerical solution, the instability of solutions with respect to the initial conditions sets in rather quickly. When applied to the solar system, this instability makes it impossible to predict the motion of the planets on scales exceeding a hundred million years.

In some special cases, it is possible to find an approximate solution. The most important is the case when the mass of one body is significantly greater than the mass of other bodies (examples: the solar system and the dynamics of Saturn's rings). In this case, in the first approximation, we can assume that light bodies do not interact with each other and move along Keplerian trajectories around a massive body. Interactions between them can be taken into account within the framework of perturbation theory and averaged over time. In this case, non-trivial phenomena can arise, such as resonances, attractors, randomness, etc. A good example of such phenomena is the non-trivial structure of Saturn's rings.

Despite attempts to describe the behavior of a system of a large number of attracting bodies of approximately the same mass, this is not possible due to the phenomenon of dynamic chaos.

3.4. Strong gravitational fields

In strong gravitational fields, when moving at relativistic speeds, the effects of the general theory of relativity begin to appear:

Deviation of the law of gravity from Newtonian;

Delay of potentials associated with the finite speed of propagation of gravitational perturbations; the appearance of gravitational waves;

Nonlinear effects: gravitational waves tend to interact with each other, so the principle of superposition of waves in strong fields is no longer valid;

Changing the geometry of space-time;

The emergence of black holes;

3.5. Modern classical theories of gravity

Due to the fact that the quantum effects of gravity are extremely small even under the most extreme experimental and observational conditions, there are still no reliable observations of them. Theoretical estimates show that in the overwhelming majority of cases one can confine oneself to the classical description of the gravitational interaction.

There is a modern canonical classical theory of gravity - the general theory of relativity, and many hypotheses that refine it and theories of varying degrees of development that compete with each other (see the article Alternative theories of gravity). All of these theories give very similar predictions within the approximation in which experimental tests are currently being carried out. The following are some of the major, most well developed or known theories of gravity.

Newton's theory of gravity is based on the concept of gravity, which is a long-range force: it acts instantly at any distance. This instantaneous nature of the action is incompatible with the field paradigm of modern physics and, in particular, with the special theory of relativity created in 1905 by Einstein, inspired by the work of Poincaré and Lorentz. In Einstein's theory, no information can travel faster than the speed of light in a vacuum.

Mathematically, Newton's gravitational force is derived from the potential energy of a body in a gravitational field. The gravitational potential corresponding to this potential energy obeys the Poisson equation, which is not invariant under Lorentz transformations. The reason for the non-invariance is that the energy in the special theory of relativity is not a scalar quantity, but goes into the time component of the 4-vector. The vector theory of gravity turns out to be similar to Maxwell's theory of the electromagnetic field and leads to negative energy of gravitational waves, which is associated with the nature of the interaction: like charges (masses) in gravity attract, and not repel, as in electromagnetism. Thus, Newton's theory of gravity is incompatible with the fundamental principle of the special theory of relativity - the invariance of the laws of nature in any inertial frame of reference, and the direct vector generalization of Newton's theory, first proposed by Poincaré in 1905 in his work "On the Dynamics of the Electron", leads to physically unsatisfactory results .

Einstein began searching for a theory of gravity that would be compatible with the principle of the invariance of the laws of nature with respect to any frame of reference. The result of this search was the general theory of relativity, based on the principle of identity of gravitational and inertial mass.

The principle of equality of gravitational and inertial masses

In classical Newtonian mechanics, there are two concepts of mass: the first refers to Newton's second law, and the second to the law of universal gravitation. The first mass - inertial (or inertial) - is the ratio of the non-gravitational force acting on the body to its acceleration. The second mass - gravitational (or, as it is sometimes called, heavy) - determines the force of attraction of the body by other bodies and its own force of attraction. Generally speaking, these two masses are measured, as can be seen from the description, in different experiments, so they do not have to be proportional to each other at all. Their strict proportionality allows us to speak of a single body mass in both non-gravitational and gravitational interactions. By a suitable choice of units, these masses can be made equal to each other.

The principle itself was put forward by Isaac Newton, and the equality of masses was verified by him experimentally with a relative accuracy of 10−3. At the end of the 19th century, Eötvös carried out more subtle experiments, bringing the accuracy of the verification of the principle to 10−9. During the 20th century, experimental techniques made it possible to confirm the equality of masses with a relative accuracy of 10−12-10−13 (Braginsky, Dicke, etc.).

Sometimes the principle of equality of gravitational and inertial masses is called the weak principle of equivalence. Albert Einstein put it at the basis of the general theory of relativity.

The principle of movement along geodesic lines

If the gravitational mass is exactly equal to the inertial mass, then in the expression for the acceleration of a body, on which only gravitational forces act, both masses are reduced. Therefore, the acceleration of the body, and hence its trajectory, does not depend on the mass and internal structure of the body. If all bodies at the same point in space receive the same acceleration, then this acceleration can be associated not with the properties of the bodies, but with the properties of the space itself at this point.

Thus, the description of the gravitational interaction between bodies can be reduced to a description of the space-time in which the bodies move. It is natural to assume, as Einstein did, that bodies move by inertia, that is, in such a way that their acceleration in their own reference frame is zero. The trajectories of the bodies will then be geodesic lines, the theory of which was developed by mathematicians back in the 19th century.

The geodesic lines themselves can be found by specifying in space-time an analogue of the distance between two events, traditionally called an interval or a world function. The interval in three-dimensional space and one-dimensional time (in other words, in four-dimensional space-time) is given by 10 independent components of the metric tensor. These 10 numbers form the space metric. It defines the “distance” between two infinitely close points of space-time in different directions. The geodesic lines corresponding to the world lines of physical bodies whose speed is less than the speed of light turn out to be the lines of the greatest proper time, that is, the time measured by a clock rigidly fastened to the body following this trajectory.

Modern experiments confirm the motion of bodies along geodesic lines with the same accuracy as the equality of gravitational and inertial masses.

Conclusion

Some interesting conclusions immediately follow from Newton's laws. So, Newton's third law says that, no matter how the bodies interact, they cannot change their total momentum: the law of conservation of momentum arises. Further, it is necessary to require that the interaction potential of two bodies depends only on the modulus of the difference in the coordinates of these bodies U(|r1-r2|). Then the law of conservation of the total mechanical energy of interacting bodies arises:

Newton's laws are the basic laws of mechanics. All other laws of mechanics can be derived from them.

At the same time, Newton's Laws are not the deepest level of formulation of classical mechanics. Within the framework of Lagrangian mechanics, there is only one formula (recording mechanical action) and one single postulate (bodies move in such a way that the action is minimal), and from this all Newton's laws can be derived. Moreover, within the framework of the Lagrangian formalism, one can easily consider hypothetical situations in which the action has some other form. In this case, the equations of motion will no longer resemble Newton's laws, but classical mechanics itself will still be applicable ...

Solution of the equations of motion

The equation F = ma (that is, Newton's second law) is a differential equation: acceleration is the second derivative of the coordinate with respect to time. This means that the evolution of a mechanical system in time can be unambiguously determined if its initial coordinates and initial velocities are specified. Note that if the equations describing our world were first-order equations, then such phenomena as inertia, oscillations, and waves would disappear from our world.

The study of the Fundamental laws of physics confirms that science is progressively developing: each stage, each discovered law is a stage in development, but does not give definitive answers to all questions.

Literature:

1. 
   Great Soviet Encyclopedia (Newton's Laws of Mechanics and other articles), 1977, “Soviet Encyclopedia”
2. 
   Online encyclopedia www.wikipedia.com

Federal Agency for Education

GOU VPO Rybinsk State Aviation Academy. P.A. Solovyova

Department of General and Technical Physics

ABSTRACT

Topic: “Fundamental laws of physics”

Group ZKS-07

Lecturer: Vasilyuk O.V.

10.2. FUNDAMENTAL PHYSICAL LAWS

Fundamental physical laws are the most complete to date, but an approximate reflection of objective processes in nature. Various forms of motion of matter are described by various fundamental theories. Each of these theories describes well-defined phenomena: mechanical or thermal motion, electromagnetic phenomena.
There are more general laws in the structure of fundamental physical theories, covering all forms of motion of matter and all processes. These are the laws of symmetry, or invariance, and the laws of conservation of physical quantities associated with them.

10.2.1. Laws of conservation of physical quantities
10.2.1.1. Law of conservation of mass
10.2.1.2. Law of conservation of momentum
10.2.1.3. Law of conservation of charge
10.2.1.4. The law of conservation of energy in mechanical processes

10.2.1. Laws of conservation of physical quantities

The laws of conservation of physical quantities are statements according to which the numerical values ​​of these quantities do not change with time in any processes or classes of processes. In fact, in many cases, conservation laws simply follow from symmetry principles.
The idea of ​​conservation first appeared as a purely philosophical conjecture about the presence of the unchanging (stable) in an ever-changing world. Even ancient philosophers-materialists came to the concept of matter as the indestructible and uncreatable basis of everything that exists. On the other hand, the observation of constant changes in nature led to the idea of ​​the perpetual motion of matter as its important property. With the advent of the mathematical formulation of mechanics, conservation laws appeared on this basis.
Conservation laws are closely related to the symmetry properties of physical systems. In this case, symmetry is understood as the invariance of physical laws with respect to a certain group of transformations of the quantities included in them. The presence of symmetry leads to the fact that for a given system there is a conserved physical quantity. If the symmetry properties of a system are known, it is usually possible to find a conservation law for it, and vice versa.
So the conservation laws are:
1. Represent the most general form of determinism.
2. Confirm the structural unity of the material world.
3. They make it possible to draw a conclusion about the nature of the system's behavior.
4. They discover the existence of a deep connection between the various forms of motion of matter.
The most important conservation laws valid for any isolated systems are:
- the law of conservation and transformation of energy;
- the law of conservation of momentum;
- the law of conservation of electric charge;
- the law of conservation of mass.
In addition to universal ones, there are conservation laws that are valid only for a limited class of systems and phenomena. So, for example, there are conservation laws that operate only in the microcosm. This:
- the law of conservation of baryon or nuclear charge;
- law of conservation of lepton charge;
- isotopic spin conservation law;
- the law of conservation of strangeness.
In modern physics, a certain hierarchy of conservation laws and symmetry principles has been discovered. Some of these principles are fulfilled in any interactions, while others - only in strong ones. This hierarchy is clearly manifested in the internal principles of symmetry that operate in the microcosm.
Consider the most important conservation laws.

10.2.1.1. Law of conservation of mass

The transformations and changes of matter in nature are infinitely varied. Researchers were worried about the question: is the substance preserved during these changes? Each of us had to watch how any thing, even steel, wears out over time, decreases in size. But does this mean that the smallest particles of metal disappear without a trace? No, they just get lost, scatter in different directions, thrown out with rubbish, fly away, creating dust.
Other transformations take place in nature. For example, you smoke a cigarette. A few minutes pass and nothing remains of the tobacco, except for a small pile of ash and a light bluish smoke that has dissipated in the air. Or, for example, a candle is burning. Gradually it becomes smaller and smaller. Not even ashes remain here. Burning without residue, the candle and what it consists of undergo a chemical transformation of the substance. Particles of tobacco and a candle do not scatter to the sides, do not gradually get lost in different places. They burn and outwardly disappear without a trace.
Observing nature, people have long paid attention to other phenomena, when the substance seems to arise from “nothing”. So, for example, from a small seed a large plant grows in a flower pot, and the weight of the earth contained in the pot remains almost the same. Can something that exists in the world really disappear or, on the contrary, appear out of nothing? In other words, is the matter from which all the diversity of our world is built is destructible or indestructible?
For 2400 years BC. e. the famous philosopher of Ancient Greece Democritus wrote that: “Nothing can come from nothing, nothing that exists can be destroyed.”
Much later, in the XVI-XVII centuries. this idea was revived and expressed already by many scientists. However, such statements were only a guess, and not a scientific theory, confirmed by experiments. For the first time, this position was proved and confirmed by experience by the great Russian scientist M.V. Lomonosov.
Lomonosov was firmly convinced of the indestructibility of matter, that nothing in the world could disappear without a trace. With any changes in substances, chemical interactions - whether simple bodies combine to form complex ones, or, conversely, complex bodies decompose into separate chemical elements - the total amount of matter remains unchanged. In other words, for all changes, the total weight of the substance must remain unchanged. Suppose that as a result of any reaction two interacting substances disappear and an unknown third is obtained - the weight of the newly formed compound must be equal to the weight of the first two.
Understanding perfectly well the significance of the laws of conservation, the indestructibility of matter for science, Lomonosov sought confirmation of his thoughts. He decided to repeat the experiments of the English scientist of the 17th century. R. Boyle.
Boyle was interested in the changes in the weight of a metal when heated. He set up the following experiment: he placed a piece of metal in a glass retort and weighed it.
Then, having soldered the narrow neck of the vessel, he heated it on fire. Two hours later, Boyle removed the vessel from the flame, broke off the neck of the retort and, having cooled it, weighed it. The metal has increased in weight.
Boyle saw the reason in the fact that the smallest particles of the “matter of fire” penetrate through the glass into the vessel and combine with the metal. At the time of Boyle and Lomonosov, scientists explained incomprehensible phenomena of nature with the help of various elusive “matters”, but they could not say what they were. Lomonosov did not recognize the existence of mysterious "matter". He was sure that the reason for the increase in weight lies elsewhere, and decided to prove that there is no “fine all-penetrating matter of fire”, and also that during chemical transformations, the total weight of the substance of the elements participating in the reaction remains unchanged.
Lomonosov repeated Boyle's experiment and got the same result: the weight of the metal increased. Then he modified the experiment: after heating the retort on fire and cooling it down, the vessel is weighed without breaking off the neck. So he proved that "without the admission of external air, the weight of the burned metal will remain in one measure, no matter of fire penetrates into the retort."
The increase in weight in the case when the retort was opened before weighing, Lomonosov explained by the dependence on the absorption of air by the metal. Now we know that when heated, metals oxidize, combine with oxygen. In Boyle's experiment, the metal takes oxygen from the air in a closed retort. At the same time, its weight increases exactly as much as the weight of air in the retort decreases. Due to this, the total weight of the closed retort and the body placed in it does not change. Although oxidation occurs here, the total amount of the substance does not decrease or increase - the weight of the substances participating in the reaction does not change. But when the retort is opened, in place of the oxygen of the air that was absorbed by the metal, outside air will burst into the flask, as a result of which the weight of the retort will increase.
So M.V. Lomonosov discovered the law of conservation of matter, or, as it is called, the law of conservation of mass. Seventeen years after Lomonosov, this law was confirmed by numerous experiments by the French chemist A. Lavoisier. Subsequently, the law of conservation of mass was repeatedly confirmed by numerous and varied experiments. At present, it is one of the basic laws underlying the sciences of nature.

10.2.1.2. Law of conservation of momentum

Rest and movement of the body are relative, the speed of movement depends on the choice of the frame of reference. According to Newton's second law, regardless of whether the body was at rest or moved uniformly and rectilinearly, a change in its speed of movement can occur only under the action of a force, i.e. as a result of interaction with other bodies.
There is a physical quantity that changes equally for all bodies under the action of the same forces, if the time of action of the force is the same, equal to the product of the mass of the body and its speed and is called the momentum of the body. The change in momentum is equal to the momentum of the applied force. The momentum of a body is a quantitative characteristic of the translational motion of bodies.
Experimental studies of the interactions of various bodies - from planets and stars to atoms and electrons, elementary particles - have shown that in any system of bodies interacting with each other, in the absence of forces from other bodies that are not included in the system, or if the sum of acting forces is equal to zero, the geometric sum the momentum of the bodies remains constant.
A system of bodies that do not interact with other bodies that are not included in this system is called closed. Thus, in a closed system, the geometric sum of the momenta of the bodies remains constant for any interactions of the bodies of this system with each other. This fundamental law of nature is called the law of conservation of momentum.
A necessary condition for the applicability of the momentum conservation law to a system of interacting bodies is the use of an inertial frame of reference. Jet propulsion is based on the law of conservation of momentum, it is used in the calculation of directed explosions, for example, when laying tunnels in the mountains. Flight into space became possible thanks to the use of multi-stage rockets.

10.2.1.3. Law of conservation of charge

Not all natural phenomena can be understood and explained on the basis of the concepts and laws of mechanics, the molecular-kinetic theory of the structure of matter, and thermodynamics. These sciences do not say anything about the nature of the forces that bind individual atoms and molecules, hold the atoms and molecules of matter in a solid state at a certain distance from each other. The laws of interaction of atoms and molecules can be understood and explained on the basis of the idea that electric charges exist in nature.
The simplest and most everyday phenomenon in which the fact of the existence of electric charges in nature is revealed is the electrification of bodies upon contact. The interaction of bodies revealed during electrification is called electromagnetic interaction, and the physical quantity that determines electromagnetic interaction is called electric charge. The ability of electric charges to attract and repel indicates the presence of two different types of charges: positive and negative.
Electric charges can appear not only as a result of electrification when bodies come into contact, but also during other interactions, for example, under the influence of force (piezoelectric effect). But always in a closed system, which does not include charges, for any interactions of bodies, the algebraic (ie, taking into account the sign) sum of electric charges of all bodies remains constant. This experimentally established fact is called the law of conservation of electric charge.
Nowhere and never in nature do electric charges of the same sign arise and disappear. The appearance of a positive charge is always accompanied by the appearance of a negative charge equal in absolute value, but opposite in sign. Neither positive nor negative charges can disappear separately from each other if they are equal in absolute value.
The appearance and disappearance of electric charges on bodies in most cases is explained by the transitions of elementary charged particles - electrons - from one body to another. As you know, the composition of any atom includes a positively charged nucleus and negatively charged electrons. In a neutral atom, the total charge of the electrons is exactly equal to the charge of the atomic nucleus. A body consisting of neutral atoms and molecules has a total electric charge equal to zero.
If, as a result of any interaction, part of the electrons passes from one body to another, then one body receives a negative electric charge, and the second - a positive charge equal in absolute value. When two oppositely charged bodies come into contact, usually electric charges do not disappear without a trace, and an excess number of electrons passes from a negatively charged body to a body in which some of the atoms had an incomplete set of electrons on their shells.
A special case is the meeting of elementary charged antiparticles, for example, an electron and a positron. In this case, positive and negative electric charges really disappear, annihilate, but in full accordance with the law of conservation of electric charge, since the algebraic sum of the charges of an electron and a positron is equal to zero.

10.2.1.4. The law of conservation of energy in mechanical processes

Mechanical energy is divided into two types: potential and kinetic. Potential energy characterizes interacting bodies, and kinetic energy characterizes moving ones. Both potential and kinetic energies change only as a result of such an interaction of bodies, in which the forces acting on the bodies do work that is different from zero.
Let us now consider the question of the change in energy during the interaction of bodies forming a closed system. If several bodies interact with each other only by gravitational and elastic forces and no external forces act, then for any interactions of bodies, the sum of the kinetic and potential energies of the bodies remains constant. This statement is called the law of conservation of energy in mechanical processes.
The sum of the kinetic and potential energies of bodies is called the total mechanical energy. Therefore, the law of conservation of energy can be formulated as follows: the total mechanical energy of a closed system of bodies interacting with the forces of gravity and elasticity remains constant.
The main content of the law of conservation of energy is not only to establish the fact of conservation of total mechanical energy, but also to establish the possibility of mutual transformations of kinetic and potential energies in an equal quantitative measure during the interaction of bodies.
The law of conservation of total mechanical energy in processes involving elastic and gravitational forces is one of the fundamental laws of mechanics. Knowledge of this law simplifies the solution of many problems that are of great importance in practical life.
For example, river energy is widely used to generate electricity. For this purpose, dams are built, rivers are blocked. Under the action of gravity, water from the reservoir behind the dam moves down the well at an accelerated rate and acquires some kinetic energy. When a fast-moving water stream collides with the blades of a hydraulic turbine, the kinetic energy of the translational movement of water is converted into the kinetic energy of the rotational movement of the turbine rotors, and then, using an electric generator, into electrical energy.
Mechanical energy is not conserved if friction forces act between bodies. A car moving along a horizontal section of the road after turning off the engine passes a certain distance and stops under the action of friction forces. During the braking of the car, the brake pads, car tires and asphalt heated up. As a result of the action of friction forces, the kinetic energy of the car did not disappear, but turned into the internal energy of the thermal motion of molecules.
Thus, in any physical interactions, energy does not arise, but only transforms from one form to another. This experimentally established fact is called the law of conservation and transformation of energy.
The sources of energy on earth are great and varied. Once upon a time, people knew only one source of energy - muscle strength and the strength of domestic animals. Energy was renewed through food. Machines now do most of the work, powered by various types of fossil fuels: coal, peat, oil, as well as water and wind energy.
If you trace the "pedigree" of all these various types of energy, it turns out that they are all the energy of the sun's rays. The energy of the outer space surrounding us is accumulated by the Sun in the form of the energy of atomic nuclei, chemical elements, electromagnetic and gravitational fields. The Sun, in turn, provides the Earth with energy, manifested in the form of wind and wave energy, tides, in the form of geomagnetism, various types of radiation (including radioactivity of the bowels, etc.), muscular energy of the animal world.
Geophysical energy is released in the form of natural disasters (volcanism, earthquakes, thunderstorms, tsunamis, etc.), metabolism in living organisms (which form the basis of life), useful work to move bodies, change their structure, quality, information transfer, storage energy in various types of batteries, capacitors, in the elastic deformation of springs, membranes.
Any forms of energy, turning into each other through mechanical movement, chemical reactions and electromagnetic radiation, eventually turn into heat and dissipate into the surrounding space. This phenomenon manifests itself in the form of explosive processes, combustion, decay, melting, evaporation, deformation, and radioactive decay. There is a circulation of energy in nature, characterized by the fact that in outer space not only chaos is realized, but also the reverse process to it - the ordering of structures, which are clearly seen primarily in star formation, transformation and the emergence of new electromagnetic and gravitational fields, and they again carry their energy new "solar systems". And everything goes back to normal.
The law of conservation of mechanical energy was formulated by the German scientist A. Leibniz. Then the German scientist Yu.R. Mayer, the English physicist J. Joule and the German scientist G. Helmholtz experimentally discovered the laws of conservation of energy in non-mechanical phenomena.
Thus, by the middle of the XIX century. the laws of conservation of mass and energy took shape, which were interpreted as the laws of conservation of matter and motion. At the beginning of the XX century. both of these conservation laws underwent a radical revision in connection with the advent of the special theory of relativity: when describing motions with velocities close to the speed of light, classical Newtonian mechanics was replaced by relativistic mechanics. It turned out that the mass, determined by the inertial properties of the body, depends on its speed and, therefore, characterizes not only the amount of matter, but also its movement. The concept of energy also underwent a change: the total energy turned out to be proportional to the mass (E = mс2). Thus, the law of conservation of energy in the special theory of relativity naturally combined the laws of conservation of mass and energy that existed in classical mechanics. Separately, these laws are not implemented, i.e. it is impossible to characterize the amount of matter without taking into account its movement and interaction.
The evolution of the law of conservation of energy shows that the laws of conservation, being drawn from experience, need from time to time experimental verification and refinement. It is impossible to be sure that with the expansion of the limits of human knowledge, a given law or its specific formulation will remain valid. The law of conservation of energy, becoming more and more precise, gradually turns from an indefinite and abstract statement into an exact quantitative form.

10.2.1.5. Laws of conservation in the microworld

Conservation laws play an important role in quantum theory, in particular, in elementary particle physics. Conservation laws define selection rules, violation of which would lead to violation of conservation laws. In addition to the listed conservation laws that take place in the physics of macroscopic bodies, many specific conservation laws have arisen in the theory of elementary particles, which make it possible to interpret the selection rules observed in experience. Such, for example, is the law of conservation of baryon or nuclear charge, which is valid for all types of interactions. According to him, nuclear matter is conserved: the difference between the number of heavy particles (baryons) and the number of their antiparticles does not change in any process. Light elementary particles - leptons (electrons, neutrinos, etc.) are also conserved.
There are also approximate conservation laws that are valid in some processes and violated in others. Such conservation laws make sense if one can specify the class of processes in which they are performed. For example, the laws of conservation of strangeness, isotopic spin, and parity are strictly observed in processes occurring due to the strong interaction, but are violated in processes of the weak interaction. The electromagnetic interaction violates the law of conservation of isotopic spin. Thus, studies of elementary particles again reminded us of the need to test the existing conservation laws in each field of phenomena. Complicated experiments are being carried out with the aim of detecting possible weak violations of the conservation laws in the microcosm.
The verification of the mechanical conservation laws is the verification of the corresponding fundamental properties of space-time. For a long time, it was believed that in addition to the listed symmetry elements (energy conservation is associated with the homogeneity of time, conservation of momentum - with the homogeneity of space), space-time has mirror symmetry, i.e. invariance under spatial inversion. Then parity should be preserved. However, in 1857, parity nonconservation in the weak interaction was experimentally discovered, which raised the question of revising the views on the symmetry of space-time and fundamental conservation laws (in particular, on the laws of conservation of energy and momentum).