The relativistic mass of a particle

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

Special theory of relativity

The whole point is that in systems moving relative to each other, any processes proceed somewhat differently. Specifically, this is expressed, for example, in increasing the mass with increasing speed. If the velocity of the system is much less than the speed of light (υ << c = 3 · 10 ⁸ ), then these changes will not be practically noticeable, since they will tend to zero. However, if the speed of movement is close to the speed of light (for example, it is one-tenth of the speed of light), then such indicators as body weight, its length and time of any process will change. Using the following formulas it is possible to calculate these values in a moving reference system, including the mass of a relativistic particle.

Here l ₀ , m ₀ and t ₀ are the length of the body, its mass and the time of the process in the stationary system, and υ is the speed of the object's motion.

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

Rest Mass

The question of the rest mass of a relativistic particle 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.

The relativistic mass of the body is one of the main parameters in describing the motion.

Principle of conformity

After the appearance of Einstein's theory of relativity, some revision of the Newtonian mechanics used for several centuries was required, 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 do not depend in any way 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 simple enough: it says that any new theory in some particular particular case will yield 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 that moves at 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 zero.

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

This formula determines the necessary speed condition.

The energy of the 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 and ultrarelativistic) exist naturally 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 appearing in β-decay can also sometimes reach a sufficient speed in order to classify them as relativistic. The relativistic mass of an 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 when it changes.
• The inertia of the body is measured by its mass.
• If the body is in a system in which no processes occur and which is closed, then its mass will practically not change (except diffusion transmission, which takes place very slowly in 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 for nonrelativistic mechanics and is expressed as follows: regardless of whether the systems are at rest or whether they make any movement, all 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 the same in all frames of reference, 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 relativistic theory the 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.

• However, the rest mass of the particle is a very 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.

• 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 at 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:

The nature of mass

Until some time in science it was believed that the mass of any particle is caused by electromagnetic nature, but by now it became 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 arising 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 the theorems and laws described above can 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 outflow in a train moving at a speed of 60 km / h. Then, according to the following formula, the coefficient of parameters change is calculated.

This formula was also described above. Substituting all the data into it (for c ≈ 1 · 10 ⁹ km / h), we get the following result:

Obviously, the change is extremely small and does not change the performance of the clock so that it is noticeable.