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For a long time, quantum mechanics confidently believed that when the speed of a body changes, its mass changes. This mass was called "relativistic" to emphasize its variability. At present, this optimism has faded a little.

Previously, many venerable scientists, with all the power of their genius, tried to show why and how body mass should increase with increasing speed. And this was partially successful and it turned out that the mass always increased according to the relation m = (1).

This phenomenon, for example, was confirmed in Kaufman's experiments with particles. But no one understood why the mass of a body suddenly increases with an increase in the speed of the body, and even increases to infinity. Few people were interested in where this mass comes from. No one could explain this phenomenon, so many scientists and ignoramuses did not believe it. They believed their eyes, their experience - the mass is a constant value. There is no "relativistic mass" period. But, both those who believe in the existence of such a mass, and those who do not believe, with the greatest persistence admit that the photon does not have mass. When you read about it, you see how not far we have moved away from the Neanderthal. If someone had told a Neanderthal sitting in a cave that there was a waterskin in his cave, he would never have believed it. I would point to the skull of a mammoth and say that there is not even a drop of water in the cave. No matter what you tell him about humidity, evaporation, about molecules, no matter what formulas you give him, he would probably remain unconvinced. So are we - a photon has momentum, energy, speed, but not mass. We know that the electron has mass, and everyone knows this. We know everything, except for the orthodox, that the electron emits photons. Well, one photon emitted an electron, changed its speed, accelerated it again, it again emitted some photon, etc. This can be done in the collider without difficulty. So what? Did the electron remain the same after all the radiations? Or did the energy fly away, but the mass remained? Did you manage to squeeze all the energy out of the electron in the Large Collider and get the Higgs boson?

See what kind of porridge? Understand whether this mass exists, or it does not exist, or it is somehow not like that. Someone has already proved or convincingly suggested that the mass of a particle does not depend on its speed and is an invariant. So expression (1) is meaningless.

Everything falls into place if you understand that the photon has mass. True, this is a very small value and we cannot measure it, just as the Neanderthal could not measure the evaporated amount of water. R. Feynman in his QED says that the force of gravitational interaction “...between two electrons 1 with 40 zeros is times weaker than the electric one (possibly with 41 zeros)”.

Sergei Semikov, a passionate admirer of the emission theory of Walter Ritz, writes in his article “On the nature of mass and time” (an article published in the magazine "Inzhener" No. 5, 2006):

“Since the electrical interaction F of two electrons is 1042 times stronger than the gravitational G, then approximately as many rheons should contain one electron. In this case, it is understandable why an electron, constantly emitting myriads of rheons, almost does not lose weight”.

For some reason he called Rheons "particles that carry electromagnetic influences", according to Ritz.

And I intuitively want to believe in it. Now hardly anyone believes that the electron is some kind of monolith. The assumption that an electron consists of 100, 1000 or even a million small particles does not warm the soul either. If there were 100 or 1000 components in an electron, this would manifest itself in something.

Common sense says that if a part is taken from something, then it has lost a part of the taken away. If it was a mass, then it is now less. Not to be confused with a pit: we choose one there, and another is added. Thus, it can be assumed that after the emission of a photon (it can be many quanta), the electron did not “become heavier”, but, on the contrary, “better”. And when a photon is absorbed, a real, and not conditional, “weighting” of the electron occurs. So the mass of an electron is quite an additive quantity. And how can you see this “weighting”? Where could it come from? Perhaps this was observed in the accelerator. If an electron is accelerated in an accelerator, then it can be seen that obtaining acceleration by the same value at a speed of 10 km / s and 1000 km / s requires different power for the accelerating unit. From this it is easy to conclude that the mass of the electron has increased. And indeed, it has increased only not absolutely (it has absolutely decreased), but relative to the force that gives it acceleration. How did it happen? Imagine a flat, or close to it, electric field, so it will always automatically happen if the accelerating field is larger in area than the electron field. It gives acceleration to the electron. After the photon was emitted, part of the mass (charge) was lost. And the charge is distributed in the electron in inverse proportion to the square of the radius. As a result, the mass will decrease more slowly than the cross section of the charge, i.e. electron. This means that per unit mass for the same acceleration, more and more density of the accelerating field will be required. Hence the appearance of "weighting". If the force were not distributed, but point, then such an effect would not be observed. In fairness, it should be said that all this can be calculated and confirmed or refuted this hypothesis. And it would be desirable to do this, since the situation is very bad, especially in the field of education.

In the methodical collection "To help the teacher and the student" ed.POIPKRO, 1998, No. 6, pp. 106-111. Co-author N.V. Ryabtseva published an article How the myth of "relativistic mass" arose. It says:

“The idea of ​​the dependence of the mass of an electron on the speed of its movement was put forward by Kaufman in 1896-98. He carried out experiments on the deflection of cathode rays in a magnetic field. Naturally, in his calculations, he used the classical expressions for the momentum and kinetic energy of the electron (it will take another 7-9 years before the creation of SRT). Kaufman's calculations led to a formula from which it followed that the specific charge of an electron, e/m, depends on its velocity. And since even Faraday formulated the law of conservation of electric charge, Kaufman suggested that the mass of an electron depends on the speed”.

And what is the conclusion from this quote? Those who have not read this article will never guess. There is only one conclusion - the concept of relativistic mass was introduced before the advent of SRT. The writers of this article were not interested in the fact that the specific charge of an electron e/m depends on its speed. What physical phenomena occurred that led to a change in the ratio of charge and mass? What has changed in the electron itself? What and how did the force act on the electron? Why did they decide that the mass, and not the charge, or both, changed in this ratio? These and other questions did not interest them. And even the fact that the photon, in their opinion, has no mass, is accepted as an indisputable fact, although there is no justification for this. The word "relativistic" is perceived as "green", "high" or whatever. "Relativistic" means relative. Relative - in relation to what? Regarding the force accelerating this mass. The mass does not have to increase absolutely, assuming the force to be constant. The mass can decrease absolutely, but the force can decrease even faster and it turns out that the mass increases relative to the force. This is what Kaufman saw, and this confirms the existence of the phenomenon of mass relativism. When in a collider or any other accelerator everyone increases and increases the total power in order to accelerate a particle, then less and less power gets to the share of this particle, and it seems that its mass is growing.

You are directly amazed by our scientists:

“And only in 1977 a university textbook on SRT by V. A. Ugarov was published, in which for the first time in our educational literature not only the concept of RM was not used, but also a special paragraph was included, in which the absence of any physical content in RM was logically shown. But school and university programs in physics, extensive popular science and any other literature related to SRT continued to discuss with enthusiasm the dependence of the mass of a moving body on the speed of its movement. It required the intervention of a prominent Soviet theoretical physicist L.B. Okun, who published a large article in the international journal "Advances in the Physical Sciences" under the title "The concept of mass" (1989). Then the journal "Physics at School" published an article by one of the authors of this report entitled "Does a relativistic mass exist?" (1994). Earlier, his textbook was published (G.A. Rozman Special Theory of Relativity (1992). These and other publications about RM forced the compilers of school and university programs and teaching aids to finally exclude the concept of RM. New school textbooks appeared ("Physics-11" under the editorship of A.A. Pinsky, "Physics-11" under the editorship of Shakhmaev N.M. "Physics-10" Gromov S.V.), outlining the basics of SRT at the modern scientific and methodological level. Let's hope that the new generation of teachers will not use the concept of RM and physics will forget one more myth related to the interpretation of SRT” .

I don’t know how the respected V. A. Ugarov logically showed “absence of any physical content in RM”, but I think it’s not “more logical” than Mr. Rozman proved that a ball in any ISO will look like a ball. We will not analyze this example, but note that Rozman's logic is that signals from all points of the cube, to the eye or other recording device, arrive simultaneously, which is possible only from a photograph of the cube.

Our Skolkovo will not soon turn into Silicon Valley if we study from such textbooks.

I don't know where I came from, where I'm going, or even who I am.

E. Schrödinger

In a number of works, an interesting effect was noted, which consisted in a change in the weight of objects in the presence of rotating masses. The change in weight occurred along the axis of rotation of the mass. In the works of N. Kozyrev, a change in the weight of a rotating gyroscope was observed. Moreover, depending on the direction of rotation of the gyroscope rotor, either a decrease or an increase in the weight of the gyroscope itself occurred. In the work of E. Podkletnov, a decrease in the weight of an object located above a superconducting rotating disk, which was in a magnetic field, was observed. In the work of V. Roshchin and S. Godin, the weight of a massive rotating disk made of magnetic material, which itself was a source of a magnetic field, was reduced.

In these experiments, one common factor can be identified - the presence of a rotating mass.

Rotation is inherent in all objects of our Universe, from the microcosm to the macrocosm. Elementary particles have their own mechanical moment - spin, all planets, stars, galaxies also rotate around their axis. In other words, the rotation of any material object around its axis is its inherent property. A natural question arises: what is the reason for such a rotation?

If the hypothesis about the chronofield and its impact on space is correct, then we can assume that the expansion of space occurs due to its rotation under the influence of the chronofield. That is, the chronofield in our three-dimensional world expands space, from the area of ​​subspace to the area of ​​superspace, spinning it according to a strictly defined dependence.

As already noted, in the presence of a gravitational mass, the energy of the chronofield decreases, space expands more slowly, which leads to the appearance of gravity. As you move away from the gravitational mass, the energy of the chronofield increases, the rate of expansion of space increases, and the gravitational effect decreases. If in any area near the gravitational mass in any way to increase or decrease the rate of expansion of space, then this will lead to a change in the weight of objects located in this area.

It is likely that experiments with rotating masses have caused such a change in the rate of expansion of space. Space somehow interacts with the rotating mass. With a sufficiently high speed of rotation of a massive object, it is possible to increase or decrease the speed of expansion of space and, accordingly, change the weight of objects located along the axis of rotation.

The author made an attempt to test the experimentally stated assumption. An aircraft gyroscope was taken as a rotating mass. The scheme of the experiment corresponded to the experiment of E. Podkletnov. Loads of materials of different densities were balanced on an analytical balance with a measurement accuracy of up to 0.05 mg. The weight of the cargo was 10 gr. A gyroscope was placed under the weighing pan with a load, which rotated at a fairly high speed. The frequency of the gyroscope power supply was 400 Hz. Gyroscopes of different masses with different moments of inertia were used. The maximum weight of the gyroscope rotor reached 1200 g. The gyroscopes were rotated both clockwise and counterclockwise.

Long-term experiments from the second half of March to August 2002 did not give positive results. Minor deviations of the weight within one division were sometimes observed. They could be attributed to errors arising due to vibrations or other, any external influences. However, the nature of these deviations was unambiguous. When rotating the gyroscope counterclockwise, a decrease in weight was observed, and clockwise - an increase.

During the experiment, the position of the gyroscope, the direction of its axis, changed at different angles to the horizon. But this did not give any results either.

In his work, N. Kozyrev noted that a change in the weight of the gyroscope could be detected in late autumn and winter, and even in this case, the readings changed during the day. Obviously, this is due to the position of the Earth relative to the Sun. N. Kozyrev conducted his experiments at the Pulkovo observatory, which is located near 60° north latitude. In winter, the position of the Earth relative to the Sun is such that the direction of gravity at this latitude is almost perpendicular to the plane of the ecliptic (7 °) in the daytime. Those. the axis of rotation of the gyroscope was practically parallel to the axis of the ecliptic plane. In the summer, in order to obtain a result, the experiment had to be tried at night. Perhaps the same reason did not allow to repeat the experiment of E. Podkletnov in other laboratories.

At the latitude of the city of Zhitomir (about 50°N), where the experiments were carried out by the author, the angle between the direction of gravity and the perpendicular to the plane of the ecliptic is almost 63° in summer. Perhaps for this reason, only minor deviations were observed. But it is also possible that the effect was also on balancing weights. In this case, the difference in weight manifested itself due to the different distance from the weighed and balancing weights to the gyroscope.

One can imagine the following mechanism of weight change. The rotation of gravitational masses and other objects and systems in the Universe occurs under the influence of the chronofield. But the rotation occurs around a single axis, the position of which in space depends on some factors that are still unknown to us. Accordingly, in the presence of such rotating objects, the expansion of space under the influence of the chronofield acquires a directed character. That is, in the direction of the axis of rotation of the system, the expansion of space will occur faster than in any other direction.

Space can be represented as a quantum gas that fills everything even inside the atomic nucleus. There is an interaction between space and the material objects within which it is located, which can be enhanced under the influence of external factors, for example, in the presence of a magnetic field. If the rotating mass is located in the plane of rotation of the gravitational system and rotates in the same direction at a sufficiently high speed, then along the axis of rotation the space will expand faster due to the interaction of space and the rotating mass. When the direction of gravity and the expansion of space coincide, then the weight of objects will decrease. With the opposite rotation, the expansion of space will slow down, which will lead to an increase in weight.

In those cases where the directions of action of the force of gravity and the expansion of space do not coincide, the resulting force changes insignificantly and is difficult to register.

The rotating mass will change the intensity of the gravitational field in a particular place. In the formula for the strength of the gravitational field g = (G· M) / R 2 gravitational constant G and the mass of the earth M cannot change. Therefore, the value changes R is the distance from the center of the earth to the object being weighed. Due to the additional expansion of space, this value increases by Δ R. That is, the load, as it were, rises above the Earth's surface by this amount, which leads to a change in the intensity of the gravitational field g" = (G· M) / (R + Δ R) 2 .

In the case of slowing down the expansion of space, the value of Δ R will be deducted from R which will lead to weight gain.

Experiments with weight changes in the presence of a rotating mass do not allow high measurement accuracy to be achieved. Perhaps the speed of rotation of the gyroscope is not enough to noticeably change the weight, since the additional expansion of space is not very significant. If such experiments are carried out with quantum clocks, then a higher measurement accuracy can be achieved by comparing the readings of two clocks. In an area where space expands faster, the chronofield strength increases, and the clock will run faster and vice versa.

Information sources:

1. Kozyrev N.A. On the possibility of experimental investigation of the properties of time. // Time in Science and Philosophy. Praga, 1971. P. 111...132.
2. Roshchin V.V., Godin S.M. Experimental study of nonlinear effects in a dynamic magnetic system. , 2001.
3. Yumashev V.E.

SPECIAL RELATIVITY 3 - MASS AND ENERGY

In the above work on Einstein's theory of relativity (see p. 163), it is proved that the mass of a body depends on its speed, and if energy is imparted to the body, its mass increases, and with the loss of energy, its mass decreases.

Mass is a measure of inertia, that is, the property of a body to maintain a state of motion or rest. Einstein proved that the mass m of a body depends on its speed υ in accordance with the equation m = γ m 0, where m 0 is the rest mass of the body, γ is the Lorentz factor equal to (1 - υ 2 /c 2) - 1/2 .

Energy is the ability of a body to do work. The scientist proved that if the body is given the amount of energy ΔE, then its mass changes by Δm in accordance with the equation ΔE = Δts 2, where c is the speed of light in vacuum. Any body of mass m has a total energy E = mc 2

Changes in mass due to changes in the amount of energy are insignificant for chemical reactions and the movement of objects relative to the Earth.

In order for a body with a mass of 1 kg to break away from the Earth and leave it, it needs to be supplied with an energy of 64 MJ, which will increase the mass of the body and the Earth by an insignificant amount.

In typical chemical reactions, energy changes of the order of an electron volt (1.6 x 10 19 J) are observed. In this case, the mass changes by a value much smaller than the mass of the electron.

Changes in mass caused by changes in energy are significant in nuclear reactions, where extremely powerful forces hold protons and neutrons together, overcoming the electrostatic repulsive forces of protons, except when the unstable nucleus decays. In nuclear reactions, energy changes occur on the order of MeV per nucleon, which is about a million times greater than in chemical reactions. Consequently, the change in mass with a change in energy by 1 MeV is quite significant in relation to the rest mass of the nucleon. The mechanism due to which the mass of a body changes with a change in energy is not yet completely clear, although there is a lot of experimental evidence for the equation E \u003d mc 2.

Yustai Igo

Does the mass of an electron change with its "energy state"?

When an electron absorbs a photon, it goes into a higher energy state and enters the upper orbit/shell.

Does (and should) this absorption of energy affect its mass (although incredibly little)?

Can we measure the mass of an electron while it is still bound to the nucleus?

Aron

Depends what mass you are referring to... Are you talking about gravitational mass or inertial mass or rest mass?

Jeffrey

@Aron That's a very misleading statement. I even want to say that this is completely wrong, since, as far as we know, inertial mass and gravitational mass are the same. What's more, if you're not trying to distinguish them with some big undertone (like mass-energy density), rest mass is also equivalent to the other two terms. I'm not sure what you are trying to achieve, but I think this is really confusing the issue at hand.

Aron

@geoffery. You are very wrong. Rest mass and inertial mass are NOT equivalent except at rest. Simple SR. Yes, inertial mass and gravitational mass in massive particles are equivalent to a few parts per million, but I'm not sure about things like holes.

Ruslan

@Aron No, you very wrong. According to the GR equivalence principle, inertial and gravitational masses are absolutely the same. And they are equal to rest mass. If you show otherwise, it will be a major discovery.

Peltio

Let's just add that for electrons interacting with a lattice of atoms (especially in semiconductors), there is also the concept of "effective mass". It's just a device for summing up the effect of an interaction (more or less like "relativistic mass"), but it will come in handy when working with crystals.

Answers

John Rennie

This is really an extended comment on Jeffrey's answer, so please describe Jeffrey's answer, not this one.

Mass of a hydrogen atom 1.67353270 × 10 − 27 " role="presentation" style="position: relative;"> 1.67353270× 10 1.67353270 × 10 − 27 " role="presentation" style="position: relative;"> 1.67353270 × 10 − 27 " role="presentation" style="position: relative;"> - 27 1.67353270 × 10 − 27 " role="presentation" style="position: relative;"> 1.67353270 × 10 − 27 " role="presentation" style="position: relative;">1.67353270 1.67353270 × 10 − 27 " role="presentation" style="position: relative;">× 1.67353270 × 10 − 27 " role="presentation" style="position: relative;">10 1.67353270 × 10 − 27 " role="presentation" style="position: relative;">- 1.67353270 × 10 − 27 " role="presentation" style="position: relative;">27 kg. If you add together the masses of a proton and an electron, they 1.67353272 × 10 − 27 " role="presentation" style="position: relative;"> 1.67353272× 10 1.67353272 × 10 − 27 " role="presentation" style="position: relative;"> 1.67353272 × 10 − 27 " role="presentation" style="position: relative;"> - 27 1.67353272 × 10 − 27 " role="presentation" style="position: relative;"> 1.67353272 × 10 − 27 " role="presentation" style="position: relative;">1.67353272 1.67353272 × 10 − 27 " role="presentation" style="position: relative;">× 1.67353272 × 10 − 27 " role="presentation" style="position: relative;">10 1.67353272 × 10 − 27 " role="presentation" style="position: relative;">- 1.67353272 × 10 − 27 " role="presentation" style="position: relative;">27 kg. The difference is about 13.6 eV, which is the ionization energy of hydrogen (although it should be noted that the experimental error in masses is not much less than the difference, so this is only an approximation).

This shouldn't surprise you, because you have to add energy (in the form of a 13.6 eV photon) to split the hydrogen atom into a free proton and electron, and this adds mass according to Einstein's famous equation E = m c 2 " role="presentation" style="position: relative;"> E E = m c 2 " role="presentation" style="position: relative;"> E = m c 2 " role="presentation" style="position: relative;"> = m with E = m c 2 " role="presentation" style="position: relative;"> E = m c 2 " role="presentation" style="position: relative;"> 2 E = m c 2 " role="presentation" style="position: relative;"> E = m c 2 " role="presentation" style="position: relative;">E E = m c 2 " role="presentation" style="position: relative;">== E = m c 2 " role="presentation" style="position: relative;">m E = m c 2 " role="presentation" style="position: relative;">c E = m c 2 " role="presentation" style="position: relative;">2 So this is a direct example of the mass gain you describe.

However, it cannot be said that this is an increase in the mass of an electron or a proton. This is an increase in the mass of the combined system. The constant masses of the electron and proton are constant and do not depend on whether they are in atoms or move freely. The change in mass comes from a change in the binding energy of the system.

Jeffrey

The rest mass of a particle never changes. Its mass is a natural constant, and one of the numbers that uniquely identifies it (eg its rotation). On the other hand, the invariant mass of an atomic system does increase when an electron becomes excited, bringing the atom into a state of higher energy. In this sense, the atom (rather than the electron) becomes "heavier" due to the increased energy of the particles' internal configuration.

Yustai Igo

So the atom as a whole becomes heavier while the material of its composition remains with the same mass? By material, I mean particles. So the increase in the total mass of an atom that absorbs photons is increased due to its energy component, and not due to an increase in the mass of the particles?

Jeffrey

Basically yes. Conceptual explanation relies on the whole E = m c 2 " role="presentation" style="position: relative;"> E E = m c 2 " role="presentation" style="position: relative;"> E = m c 2 " role="presentation" style="position: relative;"> = m with E = m c 2 " role="presentation" style="position: relative;"> E = m c 2 " role="presentation" style="position: relative;"> 2 E = m c 2 " role="presentation" style="position: relative;"> E = m c 2 " role="presentation" style="position: relative;">E E = m c 2 " role="presentation" style="position: relative;">== E = m c 2 " role="presentation" style="position: relative;">m E = m c 2 " role="presentation" style="position: relative;">c E = m c 2 " role="presentation" style="position: relative;">2 idea. Roughly speaking, the increased energy of an atom is translated into an increased mass of the atom through relativistic effects. I think John's answer is an excellent explanation.

dmckee ♦

Correct only if you use text from the Eisenhower administration (to quote Physics SE regular edition) Invariant mass remains invariant. This answer is also not useful for a bound electron, which does not have a well-defined momentum.

Yustai Igo

I thought there was no such thing as "invariant mass" because all the matter in our universe is in constant motion. So all "rest masses" are a bit misleading if you keep the big picture of the cosmos in view. Not?

HolgerFiedler

@YoustayIgo: Great.

Jeffrey

@YoustayIgo That idea, which you explain in your comment here, is a common misconception caused by people hearing that moving particles get more massive. Under special relativity, a fast-moving particle is generally harder to accelerate than Newton's laws would predict, which are often—and misleadingly—like increasing the mass of a particle, when in fact it's just a fact of relativistic mechanics, which is non-newtonian mechanics. Relativity is a brave new world. Take it on your own terms.

dmckee ♦

@YoustayIgo The invariant mass of a particle or system is defined as the energy-momentum vector length four. As such it is a Lorentz scalar, and it is measured the same in any reference system. All Lorentz scalars (including proper time) have this property, which is why people who are serious about relativity rely heavily on them because they're just all kinds of calculations. Most relativists say only about the invariant mass, abandoning the unnecessary, outdated and misleading concept of "relativistic mass"; which does not mean that this concept cannot be defined and used.

Jiza Mawuli Yao Emmanuel

I did an experiment to get data on the frequency of the circular motion (f) and how it relates to the length (L) of the pendulum. In the experiment, the pendulum is shifted through a large angle to perform a horizontal circle. Ten revolutions are timed.

It can be seen from the observation that the frequency f is inversely proportional to the length L of the pendulum, but directly proportional to the speed v of the circular motion.

f - kV / l. Introducing f--_w / 2pi and V-- rw f-- V/2pirL. From this equation, the frequency is inversely proportional to the radius r.

This math from my experiment had consequences for the atom and its electrons, which are: 1. Electrons close to the nucleus have high kinetic energy and they move at high speed, while those far away have high potential energy, and they move at low speed. Thus, the kinetic energy decreases as the radius increases. 2. This confirms the uncertainty principle, which focuses on the position and momentum of the electrons and their location at a given time. Electrons close to the nucleus have large momentum, so their position uncertainty is high, but those far from the nucleus have less momentum, so their momentum uncertainty is high. This is due to the frequency of their circular motion. 3. The observation explains why the size and mass of atoms increase by group in the periodic table, because the radius of the atoms increases and the frequency of the circular motion of electrons decreases. 4. The observation points to the fact that the mass and size of electrons depend on their distance from the nucleus, so electrons in the same atom have different masses, although the difference is insignificant and has different sizes. So electrons have size, although they may be point particles. I'm still working on the experiment. This experiment explains some of the absurdities in solar systems and their arrangement.

My name is Jidza Mawuli Yao Emmanuel from Ghana in West Africa. Lives in Volta. Teaching at Agbozume Senior High School - Ketu South District. Email: [email protected]

Recall from the course of general physics what Galileo's transformations are. These transformations are some way to determine whether a given case is relativistic or not. The relativistic case means movement at sufficiently high speeds. The magnitude of such velocities leads to the fact that the transformations of Galileo become impracticable. As you know, these coordinate transformation rules are just a transition from one coordinate system, which is at rest, to another (moving).

Remember that the speed corresponding to the case of relativistic mechanics is close to the speed of light. In this situation, Lorentz coordinate transformations come into play.

Relativistic momentum

Write out an expression for a relativistic momentum from a physics textbook. The classical formula of momentum, as you know, is the product of the body's mass and its speed. In the case of high speeds, a typical relativistic addition is added to the classical expression of the momentum in the form of the square root of the difference between unity and the square of the ratio of the speed of the body and the speed of light. This multiplier must be in , whose numerator is the classical representation of the momentum.

Pay attention to the form of the relation of the relativistic momentum. It can be divided into two parts: the first part of the product is the ratio of the classical mass of the body to the relativistic addition, the second part is the speed of the body. If we draw an analogy with the formula for the classical momentum, then the first part of the relativistic momentum can be taken as the total mass characteristic of the case of motion with high velocities.

Relativistic mass

Note that the mass of a body becomes dependent on the magnitude of its velocity if the relativistic expression is taken as the general form of the mass. The classical mass in the numerator of a fraction is called the rest mass. From its name it becomes clear that the body has it when its speed is zero.

If the speed of the body becomes close to the speed of light, then the denominator of the fraction of the expression for the mass tends to zero, and it tends to infinity. Thus, as the speed of a body increases, its mass also increases. Moreover, by the form of the expression for the mass of the body, it becomes clear that changes become noticeable only when the speed of the body is large enough and the ratio of the speed of movement to the speed of light is comparable to unity.