The law of the relationship of mass and energy in the theory of relativity by Albert Einstein is expressed as a simple formula E = mc 2 . This expression has become the subject of much thought about the nature of energy in particle theory. Currently, the reliability of this physical expression is confirmed by a number of experiments.
Albert Einstein
In the XVII century, the discovery by Isaac Newton of physical laws that simultaneously apply to earthly and celestial bodies struck his contemporaries and created a harmonious theory of mechanics from a mathematical point of view, which was called classical physics. Nevertheless, at the end of the 19th century, a sufficient number of phenomena accumulated in physics that could not be explained in the framework of Newtonian mechanics. Albert Einstein was able to solve the emerging problems by creating his theory of relativity. This theory laid the foundation for all modern physics.
The postulates and conclusions of the theory of relativity did not obey common sense. Since the beginning of the 20th century, the achievements of physics have become increasingly specialized and cannot be understood by a simple person. However, already during the life of the scientist, many conclusions of his theory of relativity were confirmed experimentally. Thanks to his ideas, A. Einstein is considered one of the most striking and famous physicists. At the very least, mankind knows no equal to him. One of these ideas is the law of the relationship of mass and energy.
Physical concepts of energy and mass
There are various types of energy, for example, thermal, kinetic, electric and others. In physics, energy is measured in joules. This physical quantity cannot appear from nothing, just as it cannot simply disappear, it can only go into various forms.
Mass in physics is related to the amount of matter that constitutes a given body. Mass, like energy, cannot disappear without a trace, but can change its shape, for example, go from a solid to a liquid state. The mass is measured in kilograms.
Publications
Albert Einstein's famous publications on the relationship of mass and energy are articles with the following titles:
- "Does the inertia of the body depend on the amount of energy contained in it."
- "On the electrodynamics of bodies in motion."
These articles were published in the German journal Annalen der Physik. In them, the scientist sets out the basics of his special theory of relativity. The main thesis for the second article is the following hypothesis:
If the body releases energy L in the form of radioactive radiation, then its mass decreases by L / c 2 .
In this case, radiation is equivalent to the concept of kinetic energy in physics, and mass means a physical quantity with the same name at rest. Note that in this article, the published expression reflects only the change in mass, and not the entire mass of the object. When the scientist published the formula for the relationship of mass and energy Ξm = L / c 2 , where c is the speed of light in vacuum, then this was only a hypothesis that has not yet received its experimental substantiation.
Experimental confirmation of transformations between mass and energy
Every student knows who discovered the law of the relationship of mass and energy. Mass and energy are manifestations of the same thing. Therefore, according to A. Einstein himself, under certain conditions, these physical quantities can be converted reversibly into each other. In situations concerning ordinary human life, such transformations do not occur, or rather they are so insignificant that they are not felt. At the beginning of the 20th century, the law of the relationship between Einstein's mass and energy was experimentally proved.
Paris, 1933 Irene and Frederic Joliot-Curie photographed a process in which energy passes into mass: a high-energy photon generated a positron and an electron near the nucleus of an atom, which were detected from the tracks left in the bubble chamber. In this process, part of the pulse was transferred to the atomic nucleus.
A process opposite to that described was also observed. When the positron was launched into the bubble chamber, then, colliding with the atoms of the substance, it lost its energy until it practically stopped. At rest, the positron meets with some valence electron of the atom of matter, and both particles disappear, generating a pair of photons that scatter in opposite directions.
Another experimental manifestation of the law of the relationship between mass and energy are nuclear reactions in a reactor. In particular, the splitting of the nucleus into small components with the release of elementary particles and energy in the form of radiation. Measurements of the mass of all fragments of the nucleus after its fission show that this physical quantity is smaller than the mass of the initial nucleus. The difference in the masses of the reagent and the products is converted into electromagnetic radiation. Using the law of the relationship of mass and energy E = mc 2 , the energy of this electromagnetic radiation can be calculated accurately.
Is mass and energy the same thing?
The famous expression of the great scientist, connecting mass and energy, is a direct consequence of the special theory of relativity. Moreover, according to the formula E = mc 2 , it turns out that a huge amount of mass in physics corresponds to huge energy.
However, to understand this law, one should know that not every mass can be converted into energy, just as not every energy is transformed into a substance with a given mass. For example, a bar of chocolate contains about 1,000 kJ of energy that the human body can use, and not 3,600,000,000,000 kJ of energy that the formula predicts.
The energy of food products that the human body can use is reserved in certain intermolecular chemical bonds. Most of the energy is stored in the molecules and atoms themselves, and it turns out to be inaccessible for metabolic processes. This fact explains why in the processes that lead to a change in the structure and composition of atomic nuclei, a large amount of energy is released.
Conservation of mass and energy
One of the main principles of the theory of relativity requires energy conservation in any spatial coordinate system. According to this principle, the famous law of the relationship of mass and energy of Einstein is valid only for the state of rest. When the body begins to move, then a multiplier called the Lorentz factor must already be added to this law. As a result, the formula takes the form shown in the figure.
Thanks to the introduction of the Lorentz factor, the law of the relationship of mass and energy for the relativistic case was formulated.
Relativistic mass
Using the Einstein equations taking into account the Lorentz factor, we can say that if a body with a finite mass m begins to move with velocities v close to the speed of light c, then its energy E tends to infinity. This conclusion can be interpreted so that the mass of the body becomes infinite, and there is not a single force that could give any speed to this mass. It is for this reason that the speed of light cannot be achieved by any object that has a finite mass at rest.
Note that at speeds that are comparable to the speed of an electromagnetic wave, the rest mass of the body does not change, only the relativistic mass changes, which has a different interpretation than the mass of the body associated with its inertia. In order to avoid confusion with the concept of mass in physics, many scientists recommend using only the concept of an inert constant mass m 0 at any speed. In this case, only the energy of system E.
The concept of relativistic mass is not any real physical concept. The fact is that speed and force are vector quantities. If we accept the fact that a body that moves at near-light speeds infinitely increases its relativistic mass, then any finite force applied in the direction of its motion will give this body an infinitely small acceleration. However, the same force that acts perpendicular to the velocity vector of the body can give it some finite acceleration according to Newtonβs second law. In this case, it will be used exactly the inert body mass m 0 .
Momentum or body momentum
By analogy with the introduction of the Lorentz factor for the relativistic case for energy, it can also be introduced for the momentum of the body. As a result, it turns out that the energy of the system can be expressed as follows: E 2 = (pc) 2 + (m 0 c 2 ) 2 , where p is the momentum of the body.
This expression finds application to describe the energy of particles that do not have a rest mass. Such elementary particles are photons. For them, the second term of the presented expression becomes equal to 0, and the photon energy takes the form: E = pc.
Thermonuclear fusion and nuclear decay
Nuclear decay is one of the main sources of energy today. At nuclear power plants, they use radioactive uranium, which is part of the lanthanide group of the periodic table. When an uranium atom is irradiated with neutrons, it becomes unstable and breaks up into two unequal nuclei and some other particles. The mass of all decay products in total is less than the mass of the uranium atom, this difference goes into the radiation energy, which is used to convert into electrical energy.
Thermonuclear fusion is a promising way to use the law of the relationship of mass and energy for human needs. This process consists in the fusion of two atoms of heavy hydrogen with the formation of a helium atom. The mass of the product is less than the mass of the reagents. Plants for controlled thermonuclear fusion are currently being actively developed.