In 1905, Albert Einstein published his theory of relativity, which somewhat changed the concept of science about the world. Based on his assumptions, the formula of relativistic mass was obtained.
Special theory of relativity
The whole point is that in systems moving relative to each other, any processes occur somewhat differently. Specifically, this is expressed, for example, in an increase in mass with increasing speed. If the speed of the system is much less than the speed of light (Ο
<< c = 3 Β· 10 8 ), then these changes will be practically not noticeable, since they will tend to zero. However, if the speed of movement is close to the speed of light (for example, equal to one tenth of it), then indicators such as body weight, its length and time of any process will change. Using the following formulas it is possible to calculate these values ββin a moving reference frame, including the mass of a relativistic particle.
Here l 0 , m 0 and t 0 are the length of the body, its mass and time of the process in a fixed system, and Ο
is the speed of the object.
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 depending on speed. Accordingly, the rest mass is called the mass of the body, which at the time of measurement is kept at rest (in the absence of movement), that is, its speed is zero.
Relativistic body mass is one of the main parameters in describing movement.
Compliance principle
After the advent of Einstein's theory of relativity, some revision of the Newtonian mechanics used for several centuries was required, which could no longer be used when considering reference frames moving at a speed comparable to the speed of light. Therefore, it was necessary to change all the equations of dynamics using the Lorentz transformations β changing the coordinates of a body or a point and time of a process during the transition between inertial reference systems. The description of these transformations is based on the fact that in every inertial reference frame all physical laws work the same and equally. Thus, the laws of nature in no way depend on the choice of a frame of reference.
From the Lorentz transformations, the main coefficient of relativistic mechanics is expressed, which is described above and is called the letter Ξ±.
The correspondence principle itself is quite simple - it says that any new theory in a particular particular case will give the same results as the previous one. Specifically, in relativistic mechanics this is reflected in 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 - such are called particles without mass or simply massless, because at 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 a 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.
This formula determines the necessary speed condition.
Particle energy can also be greater than its rest energy - these are called ultrarelativistic.
To describe the motion of such particles, quantum mechanics is used in the general case and quantum field theory for a more extensive description.
Appearance
Such particles (both relativistic and ultrarelativistic) in their natural form exist only in cosmic radiation, that is, radiation whose source is outside the Earth, of electromagnetic nature. But they are artificially created by humans in special accelerators - with the help of them several dozen types of particles were found, and this list is constantly updated. A similar installation is, for example, the Large Hadron Collider, located in Switzerland.
Electrons appearing during Ξ² decay can also sometimes reach a sufficient velocity in order to classify them as relativistic. The relativistic mass of an electron can also be found by the indicated formulas.
Mass concept
Mass in Newtonian mechanics has several mandatory properties:
- The gravitational attraction of bodies arises because of their mass, that is, it directly depends on it.
- Body mass does not depend on the choice of a reference system and does not change when it changes.
- The inertia of a body is measured by its mass.
- If the body is in a system in which no processes take place and which is closed, then its mass will practically not change (except for diffusion transmission, which occurs very slowly in solids).
- The mass of a composite body is composed of the masses of its individual parts.
Principles of relativity
- The principle of relativity Galileo.
This principle was formulated for nonrelativistic mechanics and is expressed as follows: regardless of whether the systems are at rest or whether they are making any movement, all processes in them proceed the same way.
- The principle of relativity of Einstein.
This principle is based on two postulates:
- Galileo's principle of relativity is also used in this case. That is, in any SO absolutely all the laws of nature work the same.
- The speed of light is absolutely always the same in all reference systems, regardless of the speed of movement of the light source and the screen (light receiver). To prove this fact, a series of experiments were carried out that fully confirmed the initial conjecture.
Mass in Relativistic and Newtonian Mechanics
- Unlike Newtonian mechanics, in relativistic theory, mass cannot be a measure of the amount of material. And the relativistic mass itself is determined in some more extensive way, leaving it possible to explain, for example, the existence of particles without mass. In relativistic mechanics, special attention is paid more to energy than to mass - that is, the main factor determining any body or elementary particle is its energy or impulse. Momentum 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, therefore, they are suitable for measurements with maximum speed and accuracy. The rest energy of a particle can be found by the following formula.
- Similar to Newton's theories, in an isolated system, body mass is constant, that is, does not change with time. It also does not change during the transition from one CO to another.
- There is absolutely no measure of inertia of a moving body.
- The relativistic mass of a moving body is not determined by the influence 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 - not only massless particles can reach the speed of light.
- The full energy of a relativistic particle is possible using the following expression:
Nature of the mass
Until some time in science, it was believed that the mass of any particle is due to the electromagnetic nature, but by now it has become known that only a small part of it can be explained in this way - the main contribution is made by the nature of strong interactions arising from gluons. However, this method cannot explain the mass of a dozen particles, the nature of which has not yet been elucidated.
Relativistic Mass Gain
The result of all the theorems and laws described above can be expressed in a fairly understandable, albeit surprising, process. If one body moves relative to another at any speed, then its parameters and the parameters of the bodies 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.
You can give a simple example - another time expiration in a train moving at a speed of 60 km / h. Then, according to the following formula, the coefficient of change of parameters is calculated.
This formula has also been described above. Substituting all the data into it (at c β 1 Β· 10 9 km / h), we obtain the following result:
Obviously, the change is extremely small and does not change the performance of the watch so that it is noticeable.