In 1905, Albert Einstein published his theory of relativity, which somewhat changed the understanding of science about the world around us. Based on his assumptions, the formula for the relativistic mass was obtained.
Special 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 an increase in mass with an increase in speed. If the speed of the system is much less than the speed of light (υ << c=3 108), then these changes will practically not be 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 such indicators as body mass, its length and the time of any process will change. Using the following formulas, it is possible to calculate these values in a moving reference frame, including the mass of a relativistic particle.
Here l0, m0 and t0 - body length, its mass and the process time in a stationary system, and υ is the speed of the object.
According to Einstein's theory, no body can accelerate faster 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 the speed. Accordingly, the rest mass is the mass of the body, which at the moment of measurement is at rest (in the absence of movement), that is, its speed is zero.
The relativistic mass of a body is one of the main parameters in describing motion.
Conformity 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 systems moving at a speed comparable to the speed of light. Therefore, it was necessary to change all the equations of dynamics using Lorentz transformations - a change in the coordinates of a body or point and time of the process during 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 equally and equally. Thus, the laws of nature are in no way dependent on the choice of frame of reference.
From the Lorentz transformations, the main coefficient of relativistic mechanics is expressed, which is described above and is called the letter α.
The correspondence principle itself is quite simple - it says that any new theory in some particular case will give the same results asprevious. 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 motion is described by the special theory of relativity. There is even a group of particles whose existence is possible only when moving at the speed of light - these are called particles without mass or simply massless, since at rest their mass is zero, therefore these are unique particles that have no analogous option in non-relativistic, classical mechanics.
That is, the rest mass of a relativistic particle can be zero.
A particle can be called relativistic if its kinetic energy can be compared with the energy expressed by the following formula.
This formula determines the required speed condition.
The energy of a particle can also be greater than its rest energy - these are called ultrarelativistic.
Quantum mechanics in the general case and quantum field theory for a more extensive description are used to describe the motion of such particles.
Appearance
Similar particles (both relativistic and ultrarelativistic) in their natural form exist only in cosmic radiation, that is, radiation whose source is outside the Earth, of an electromagnetic nature. They are artificially created by man.in special accelerators - with the help of them, several dozen types of particles were found, and this list is constantly updated. Such a facility is, for example, the Large Hadron Collider located in Switzerland.
Electrons that appear during β-decay can also sometimes reach sufficient speed to classify them as relativistic. The relativistic mass of an electron can also be found using the indicated formulas.
The concept of mass
Mass in Newtonian mechanics has several mandatory properties:
- The gravitational attraction of bodies arises from their mass, that is, it directly depends on it.
- The mass of the body does not depend on the choice of 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 occur and which is closed, then its mass will practically not change (except for diffusion transfer, which is very slow for solids).
- The mass of a compound body is made up of the masses of its individual parts.
Principles of Relativity
Galilean principle of relativity
This principle was formulated for non-relativistic 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.
Einstein's principle of relativity
This principle is based on two postulates:
- Galileo's principle of relativityis also used in this case. That is, in any CO, absolutely all the laws of nature work in the same way.
- The speed of light is absolutely always and in all reference systems the same, regardless of the speed of the light source and the screen (light receiver). To prove this fact, a number of experiments were carried out, which fully confirmed the initial guess.
Mass in relativistic and Newtonian mechanics
Unlike Newtonian mechanics, in relativistic theory, mass cannot be a measure of the amount of material. Yes, and the relativistic mass itself is defined 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 to energy rather than mass - that is, the main factor that determines any body or elementary particle is its energy or momentum. The momentum can be found using the following formula
However, the rest mass of a particle is a very important characteristic - its value is a very small and unstable number, so measurements are approached with maximum speed and accuracy. The rest energy of a particle can be found using the following formula
- Similar to Newton's theories, in an isolated system, the mass of a body 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 inertiamoving body.
- The relativistic mass of a moving body is not determined by the influence of gravitational forces on it.
- If the mass of a body is zero, then it must move at the speed of light. The converse is not true - not only massless particles can reach the speed of light.
- The total energy of a relativistic particle is possible using the following expression:
Nature of mass
Until some time in science it was believed that the 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 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 increase
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 practically not be noticeable, but this effect will still be present.
One can give a simple example - another running out of time in a train moving at a speed of 60 km/h. Then, according to the following formula, the parameter change coefficient is calculated.
This formula was also described above. Substituting all the data into it (for c ≈ 1 109 km/h), we get the following result:
Obviously the change is extremely small and does not change the clock in a way that is noticeable.
