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The relativistic mass of a particle

In 1905, Albert Einstein published hisThe theory of relativity, which somewhat changed the idea of ​​the science of the surrounding world. Based on his assumptions, the formula of the relativistic mass was obtained.

Special theory of relativity

The whole point is that in systems,moving with respect to each other, any processes proceed somewhat differently. Specifically, this is expressed, for example, in increasing the mass with increasing speed. If the speed of motion of the system is much less than the speed of light (υ << c = 3 · 108 ), то эти изменения практически не будут заметны, since they will tend to zero. However, if the speed of movement is close to the speed of light (for example, it is equal to one tenth of it), then such indicators as body mass, its length and time of any process will change. With the help of the following formulas it is possible to calculate these values ​​in a moving reference frame, including the mass of a relativistic particle.

The mass of a relativistic particle

Here l0, m0 and t0 - the length of the body, its mass and the time of the process in the stationary system, and υ - the speed of the movement of the object.

According to Einstein's theory, no body is capable of developing a speed greater than the speed of light.

Rest Mass

Вопрос массы покоя релятивистской частицы arises precisely in the theory of relativity, when the mass of a body or particle begins to change as a function of velocity. Accordingly, the rest mass is the mass of the body, which at the moment of measurement is contained at rest (in the absence of motion), that is, its velocity is zero.

Relativistic body mass is one of the main parameters in the description of motion.

Principle of conformity

After the appearance of the theory of relativity of EinsteinIt required some revision of the Newtonian mechanics used for several centuries, which could no longer be used in considering reference frames moving at a speed comparable to the speed of light. Therefore, it was required to change all the equations of dynamics using the Lorentz transformations-the change in the coordinates of the body or the point and time of the process in the transition between inertial frames of reference. The description of these transformations is based on the fact that in each inertial frame of reference all physical laws work identically and equally. Thus, the laws of nature in no way depend on the choice of the frame of reference.

From the Lorentz transformations, the principal coefficient of relativistic mechanics, which is described above and is called the letter α, is expressed.

The correspondence principle itself is quite simple: it issays that any new theory in some particular particular case will give the same results as the previous one. Specifically in relativistic mechanics, this is reflected by the fact that at speeds that are much less than the speed of light, the laws of classical mechanics are used.

Relativistic particle

A relativistic particle is a particle,which moves with a speed comparable to the speed of light. Their movement is described by a special theory of relativity. There is even a group of particles whose existence is possible only when moving at the speed of light - they are called particles without mass or simply massless, since in a state of rest their mass is zero, therefore they are unique particles that have no analogous variant in nonrelativistic, classical mechanics .

That is, the rest mass of the relativistic particle can be equal to zero.

A particle can be called relativistic if its kinetic energy can be comparable to the energy expressed by the following formula.

Relativistic mass

This formula determines the necessary speed condition.

The energy of a particle can also be greater than its rest energy - these are called ultrarelativistic.

To describe the motion of such particles, quantum mechanics in the general case and quantum field theory for a more extensive description are used.

Appearance

Similar particles (both relativistic, andultrarelativistic) in a natural form exist only in cosmic radiation, that is, radiation, whose source is outside the Earth, of an electromagnetic nature. Man they are artificially created in special accelerators - with the help of them were found several dozen species of particles, and this list is constantly updated. A similar installation is, for example, the Large Hadron Collider, located in Switzerland.

The electrons that appear when β decay also cansometimes reach a sufficient speed in order to classify them as relativistic. The relativistic mass of the electron can also be found from the above formulas.

The concept of mass

The mass in Newton's mechanics has several obligatory properties:

  • Gravitational attraction of bodies arises because of their mass, that is directly depends on it.
  • The mass of the body does not depend on the choice of the frame of reference and does not change with its change.
  • The inertia of the body is measured by its mass.
  • Если тело находится в системе, в которой не there are no processes and that is closed, then its mass will practically not change (except diffusion transmission, which takes place very slowly for solids).
  • The mass of a composite body consists of the masses of its individual parts.

Principles of relativity

  • Principle of relativity of Galileo.

This principle was formulated fornonrelativistic mechanics and is expressed as follows: regardless of whether the systems are in a state of rest or whether they make any movement, all the processes in them proceed in the same way.

  • The principle of Einstein's relativity.

This principle is based on two postulates:

  1. The Galilean principle of relativity is also used in this case. That is, in any SO absolutely all laws of nature work in the same way.
  2. The speed of light is absolutely always and in allframes of reference is the same, regardless of the speed of movement of the light source and the screen (the receiver of light). To prove this fact, a number of experiments were carried out, which completely confirmed the initial guess.

Mass in the relativistic and Newtonian mechanics

  • Unlike Newtonian mechanics, in the relativistictheory, mass can not be a measure of the amount of material. And the relativistic mass itself is determined by some more extensive method, leaving it possible to explain, for example, the existence of particles without mass. In relativistic mechanics, special attention is paid to energy rather than to mass - that is, the main factor that determines any body or elementary particle is its energy or momentum. The impulse can be found by the following formula.

Relativistic electron mass

  • However, the rest mass of the particle isvery important characteristic - its value is a very small and unstable number, so the measurements are suitable with the maximum speed and accuracy. The rest energy of the particle can be found by the following formula.

Relativistic body weight

  • Similarly to Newton's theories, in an isolated system the body mass is constant, that is, does not change with time. It also does not change when moving from one CO to another.
  • There is absolutely no measure of inertia of the moving body.
  • The relativistic mass of a moving body is not determined by the action of gravitational forces on it.
  • If the mass of the body is zero, then it must necessarily move with the speed of light. The converse is not true - the velocities of light can be achieved not only by massless particles.
  • The total energy of a relativistic particle is possible with the help of the following expression:

rest mass of a relativistic particle

The nature of mass

Until some time in science it was believed thatthe mass of any particle is due to electromagnetic nature, but by now it has become known that in this way it is possible to explain only a small part of it - the main contribution is made by the nature of the strong interactions that arise due to gluons. However, in this way it is impossible to explain the mass of a dozen particles, the nature of which has not yet been clarified.

The relativistic increase in mass

The result of all theorems and laws described abovecan be expressed in a fairly understandable, albeit amazing, process. If one body moves relative to another with any speed, then its parameters and the parameters of the bodies that are inside, if the original body is a system, change. Of course, at low speeds this will not be noticeable, but this effect will still be present.

One can give a simple example - another time out in a train moving at a speed of 60 km / h. Then, according to the following formula, the coefficient of parameters change is calculated.

formula of the relativistic mass

This formula has also been described above. Substituting all the data into it (for c ≈ 1 · 109 km / h), we get the following result:

relativistic mass increase

Obviously, the change is extremely small and does not change the hours so that it is noticeable.

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