Characteristics of thermal radiation. Radiation from a heated body Radiation from heated bodies

Laws of thermal radiation. Radiant warmth.

This may be news to some, but the transfer of temperature occurs not only by thermal conductivity through the touch of one body to another. Each body (Solid, liquid and gaseous) emits heat rays of a certain wave. These rays, leaving one body, are absorbed by another body and take on heat. And I will try to explain to you how this happens, and how much heat we lose with this radiation at home. (I think many will be interested to see these numbers). At the end of the article we will solve a problem from a real example.

The article will contain three-story formulas and integral expressions for mathematicians, but do not be afraid of them, you don’t even have to delve into these formulas. In the problem, I will give you formulas that can be solved in one go, and you don’t even need to know higher mathematics, it’s enough to know elementary arithmetic.

I have been convinced of this more than once that while sitting by a fire (usually a large one) my face was burned by these rays. And if I covered the fire with my palms and my arms were extended, it turned out that my face stopped burning. It is not difficult to guess that these rays are as straight as light. It is not the air circulating around the fire, or even the air, that burns me, but the direct, invisible heat rays coming from the fire.

In space, there is usually a vacuum between planets and therefore the transfer of temperatures is carried out exclusively by heat rays (All rays are electromagnetic waves).

Thermal radiation has the same nature as light and electromagnetic rays (waves). Simply, these waves (rays) have different wavelengths.

For example, wavelengths in the range of 0.76 - 50 microns are called infrared. All bodies at room temperature + 20 °C emit mainly infrared waves with wavelengths close to 10 microns.

Any body, unless its temperature is different from absolute zero (-273.15 ° C), is capable of sending radiation into the surrounding space. Therefore, any body emits rays onto the bodies surrounding it and, in turn, is influenced by the radiation of these bodies.

Any furniture in the house (chair, table, walls and even a sofa) emits heat rays.

Thermal radiation can be absorbed or passed through the body, and can also simply be reflected from the body. The reflection of heat rays is similar to that of a light ray reflected from a mirror. The absorption of thermal radiation is similar to how a black roof becomes very hot from the sun's rays. And the penetration or passage of rays is similar to how rays pass through glass or air. The most common type of electromagnetic radiation in nature is thermal radiation.

Very close in its properties to a black body is the so-called relict radiation, or cosmic microwave background - radiation filling the Universe with a temperature of about 3 K.

In general, in the science of thermal engineering, in order to explain the processes of thermal radiation, it is convenient to use the concept of a black body in order to qualitatively explain the processes of thermal radiation. Only a black body can make calculations easier in some way.

As described above, any body is capable of:

Black body- this is a body that completely absorbs thermal energy, that is, it does not reflect rays and thermal radiation does not pass through it. But do not forget that a black body emits thermal energy.

That is why it is so easy to apply calculations to this body.

What difficulties arise in calculations if the body is not a black body?

A body that is not a black body has the following factors:

These two factors complicate the calculation so much that “mother, don’t worry.” It's very difficult to think so. But scientists haven’t really explained how to calculate the gray body. By the way, a gray body is a body that is not a black body.

There is also a concept: White body and transparent body, but more on that below.

Thermal radiation has different frequencies (different waves), and each individual body can have a different wavelength of radiation. In addition, when the temperature changes, this wavelength can change, and its intensity (radiation strength) can also change.

All these factors will complicate the process so much that it is difficult to find a universal formula for calculating energy losses due to radiance. And therefore, in textbooks and in any literature, a black body is used for calculations, and other gray bodies are used as part of the black body. To calculate the gray body, the blackness coefficient is used. These coefficients are given in reference books for some materials.

Let's look at an image that confirms the complexity of calculating emissivity.

The figure shows two balls that contain particles of this ball. Red arrows are rays emitted by particles.

Consider a black body.

Inside the black body, deep inside there are some particles that are indicated in orange. They emit rays that absorb other nearby particles, which are indicated in yellow. The rays of orange particles of a black body are not able to pass through other particles. And therefore, only the outer particles of this ball emit rays over the entire area of the ball. Therefore, the black body calculation is easy to calculate. It is also generally accepted that a black body emits the entire spectrum of waves. That is, it emits all available waves of different lengths. A gray body can emit part of the wave spectrum, only of a certain wavelength.

Consider a gray body.

Inside the gray body, the particles inside emit some of the rays that pass through other particles. And this is the only reason why the calculation becomes more complicated.

Thermal radiation- this is electromagnetic radiation that arises as a result of the conversion of the energy of thermal motion of body particles into radiation energy. It is the thermal nature of the excitation of elementary emitters (atoms, molecules, etc.) that contrasts thermal radiation with all other types of luminescence and determines its specific property to depend only on the temperature and optical characteristics of the emitting body.

Experience shows that thermal radiation is observed in all bodies at any temperature other than 0 K. Of course, the intensity and nature of the radiation depend on the temperature of the emitting body. For example, all bodies with a room temperature of + 20 ° C emit mainly infrared waves with wavelengths close to 10 microns, and the Sun emits energy, the maximum of which is at 0.5 microns, which corresponds to the visible range. At T → 0 K, bodies practically do not emit.

Thermal radiation leads to a decrease in the internal energy of the body and, consequently, to a decrease in body temperature, to cooling. A heated body releases internal energy due to thermal radiation and cools to the temperature of the surrounding bodies. In turn, by absorbing radiation, cold bodies can heat up. Such processes, which can also occur in a vacuum, are called radiation.

Pure black body- a physical abstraction used in thermodynamics, a body that absorbs all electromagnetic radiation incident on it in all ranges and does not reflect anything. Despite the name, a completely black body can itself emit electromagnetic radiation of any frequency and visually have color. The radiation spectrum of a completely black body is determined only by its temperature.

Table:

(Temperature range in Kelvin and their Color)

up to 1000 Red

1000-1500 Orange

1500-2000 Yellow

2000-4000 Pale yellow

4000-5500 Yellowish white

5500-7000 Pure white

7000-9000 Bluish white

9000-15000 White-blue

15000-∞ Blue

By the way, based on the wavelength (color), we determined the temperature of the sun, it is about 6000 Kelvin. Coals typically glow red. Does this remind you of anything? You can determine the temperature by color. That is, there are devices that measure the wavelength, thereby determining the temperature of the material.

The blackest real substances, for example, soot, absorb up to 99% of incident radiation (i.e., have an albedo of 0.01) in the visible wavelength range, but they absorb infrared radiation much less well. The deep black color of some materials (charcoal, black velvet) and the pupil of the human eye is explained by the same mechanism. Among the bodies of the Solar System, the Sun has the properties of a completely black body to the greatest extent. By definition, the Sun reflects virtually no radiation. The term was coined by Gustav Kirchhoff in 1862.

According to the spectral classification, the Sun belongs to the G2V type (“yellow dwarf”). The surface temperature of the Sun reaches 6000 K, so the Sun shines with almost white light, but due to the absorption of part of the spectrum by the Earth's atmosphere near the surface of our planet, this light acquires a yellow tint.

Absolutely black bodies absorb 100% and at the same time heat up, and vice versa! a heated body - radiates 100%, this means that there is a strict pattern (formula of black body radiation) between the temperature of the Sun - and its spectrum - since both the spectrum and temperature have already been determined - yes, the Sun has no deviations from these parameters!

In astronomy there is such a diagram - “Spectrum-Luminosity”, and so our Sun belongs to the “main sequence” of stars, to which most other stars belong, that is, almost all stars are “absolutely black bodies”, strange as it may seem... Exceptions - white dwarfs, red giants and novae, supernovae...

This is someone who didn’t study physics at school.

A completely black body absorbs ALL radiation and emits more than all other bodies (the more a body absorbs, the more it heats up; the more it heats up, the more it emits).

Let us have two surfaces - gray (with a blackness coefficient of 0.5) and absolutely black (with a blackness coefficient of 1).

The emissivity coefficient is the absorption coefficient.

Now, by directing the same flux of photons, say 100, onto these surfaces.

A gray surface will absorb 50 of them, a black surface will absorb all 100.

Which surface emits more light - in which 50 photons or 100 “sits”?

Planck was the first to correctly calculate black body radiation.

Solar radiation roughly obeys Planck's formula.

And so let's start studying the theory...

Radiation refers to the emission and propagation of electromagnetic waves of any kind. Depending on the wavelength, there are: X-ray, ultraviolet, infrared, light (visible) radiation and radio waves.

X-ray radiation- electromagnetic waves, the energy of photons of which lies on the scale of electromagnetic waves between ultraviolet radiation and gamma radiation, which corresponds to wavelengths from 10−2 to 103 Angstroms. 10 Angstrom = 1 nm. (0.001-100 nm)

Ultraviolet radiation(ultraviolet, ultraviolet, UV) - electromagnetic radiation, occupying the range between the violet boundary of visible radiation and x-ray radiation (10 - 380 nm).

Infrared radiation- electromagnetic radiation, occupying the spectral region between the red end of visible light (with wavelength λ = 0.74 μm) and microwave radiation (λ ~ 1-2 mm).

Now the entire range of infrared radiation is divided into three components:

Short wavelength region: λ = 0.74-2.5 µm;

Mid-wave region: λ = 2.5-50 µm;

Long wavelength region: λ = 50-2000 µm;

Visible radiation- electromagnetic waves perceived by the human eye. The sensitivity of the human eye to electromagnetic radiation depends on the wavelength (frequency) of the radiation, with the maximum sensitivity occurring at 555 nm (540 terahertz), in the green part of the spectrum. Since sensitivity gradually decreases to zero as one moves away from the maximum point, it is impossible to indicate the exact boundaries of the spectral range of visible radiation. Typically, the region of 380-400 nm (750-790 THz) is taken as the short-wave boundary, and 760-780 nm (385-395 THz) as the long-wave boundary. Electromagnetic radiation with these wavelengths is also called visible light, or simply light (in the narrow sense of the word).

Radio emissions(radio waves, radio frequencies) - electromagnetic radiation with wavelengths of 5 10−5-1010 meters and frequencies, respectively, from 6 1012 Hz and up to several Hz. Radio waves are used to transmit data in radio networks.

Thermal radiation is the process of propagation in space of the internal energy of a radiating body by electromagnetic waves. The causative agents of these waves are the material particles that make up the substance. The propagation of electromagnetic waves does not require a material medium; in a vacuum they propagate at the speed of light and are characterized by wavelength λ or oscillation frequency ν. At temperatures up to 1500 °C, the main part of the energy corresponds to infrared and partly light radiation (λ=0.7÷50 µm).

It should be noted that radiation energy is not emitted continuously, but in the form of certain portions - quanta. The carriers of these portions of energy are elementary particles of radiation - photons, which have energy, quantity of motion and electromagnetic mass. When radiation energy hits other bodies, it is partially absorbed by them, partially reflected, and partially passes through the body. The process of converting radiation energy into internal energy of an absorbing body is called absorption. Most solids and liquids emit energy of all wavelengths in the range from 0 to ∞, that is, they have a continuous emission spectrum. Gases emit energy only in certain wavelength ranges (selective emission spectrum). Solids emit and absorb energy through their surface, and gases through their volume.

The energy emitted per unit time in a narrow range of wavelengths (from λ to λ+dλ) is called the flux of monochromatic radiation Qλ. The radiation flux corresponding to the entire spectrum in the range from 0 to ∞ is called the integral, or total, radiant flux Q(W). The integral radiant flux emitted from a unit surface of a body in all directions of hemispherical space is called the integral radiation density (W/m2).

To understand this formula, consider the image.

It was not by chance that I depicted two versions of the body. The formula is valid only for a square-shaped body. Since the radiating area must be flat. Provided that only the surface of the body emits. Internal particles do not emit.

Knowing the radiation density of the material, you can calculate how much energy is spent on radiation:

It is necessary to understand that the rays emanating from the plane have different radiation intensities in relation to the normal of the plane.

Lambert's law. Radiant energy emitted by a body spreads in space in different directions with different intensities. The law that establishes the dependence of radiation intensity on direction is called Lambert's law.

Lambert's law establishes that the amount of radiant energy emitted by a surface element in the direction of another element is proportional to the product of the amount of energy emitted along the normal by the magnitude of the spatial angle made by the direction of the radiation with the normal

See image.

The intensity of each ray can be found using the trigonometric function:

That is, it is a kind of angle coefficient and it strictly obeys the trigonometry of the angle. The coefficient only works for a black body. Since nearby particles will absorb the side rays. For a gray body, it is necessary to take into account the number of rays passing through the particles. Reflection of rays must also be taken into account.

Consequently, the greatest amount of radiant energy is emitted in a direction perpendicular to the radiation surface. Lambert's law is completely valid for an absolutely black body and for bodies with diffuse radiation at a temperature of 0 - 60°C. Lambert's law does not apply to polished surfaces. For them, radiation emission at an angle will be greater than in the direction normal to the surface.

Below we will definitely consider more voluminous formulas for calculating the amount of heat lost by the body. But for now it is necessary to learn something additional about the theory.

A little about definitions. Definitions will come in handy to express yourself correctly.

Note that most solids and liquids have a continuous (continuous) radiation spectrum. This means that they have the ability to emit rays of all wavelengths.

Even an ordinary table in a room, like a solid body, can emit X-ray or ultraviolet radiation, but its intensity is so low that we not only don’t notice it, its value in relation to other waves can approach zero.

Radiant flux (or radiation flux) is the ratio of radiant energy to radiation time, W:

where Q is radiation energy, J; t - time, s.

If a radiant flux emitted by an arbitrary surface in all directions (i.e. within a hemisphere of arbitrary radius) occurs in a narrow range of wavelengths from λ to λ+Δλ, then it is called a monochromatic radiation flux

The total radiation from the surface of the body over all wavelengths of the spectrum is called the integral or total radiation flux Ф

The integral flux emitted from a unit surface is called the surface flux density of the integral radiation or emissivity, W/m2,

The formula can also be used for monochromatic radiation. If thermal monochromatic radiation falls on the surface of a body, then in the general case a part equal to B λ of this radiation will be absorbed by the body, i.e. will be converted into another form of energy as a result of interaction with matter, part F λ will be reflected, and part D λ will pass through the body. If we assume that the radiation incident on the body is equal to unity, then

B λ +F λ +D λ =1

where B λ, F λ, D λ are absorption and reflection coefficients, respectively

and body transmission.

When within the spectrum the values of B, F, D remain constant, i.e. do not depend on wavelength, there is no need for indices. In this case

If B = 1 (F = D = 0), then a body that completely absorbs all radiation incident on it, regardless of the wavelength, direction of incidence and polarization state of the radiation, is called a black body or a complete emitter.

If F=1 (B=D=0), then the radiation incident on the body is completely reflected. In the case when the surface of the body is rough, the rays are reflected scatteredly (diffuse reflection), and the body is called white, and when the surface of the body is smooth and the reflection follows the laws of geometric optics, then the body (surface) is called mirror. In the case when D = 1 (B = F = 0), the body is permeable to heat rays (diathermic).

Solids and liquids are practically opaque to thermal rays (D = 0), i.e. athermic. For such bodies

There are no absolutely black bodies, as well as transparent or white bodies, in nature. Such bodies must be regarded as scientific abstractions. But still, some real bodies can be quite close in their properties to such idealized bodies.

It should be noted that some bodies have certain properties in relation to rays of a certain wavelength, and different properties in relation to rays of a different length. For example, a body may be transparent to infrared rays and opaque to visible (light) rays. The surface of a body can be smooth in relation to rays of one wavelength and rough for rays of another wavelength.

Gases, especially those under low pressure, in contrast to solids and liquids, emit a line spectrum. Thus, gases absorb and emit rays of only a certain wavelength, but they can neither emit nor absorb other rays. In this case, they talk about selective absorption and emission.

In the theory of thermal radiation, an important role is played by a quantity called the spectral flux density of radiation, or spectral emissivity, which is the ratio of the density of the radiant flux emitted in an infinitesimal wavelength interval from λ to λ+Δλ to the size of this wavelength interval Δλ, W/ m 2,

where E is the surface density of the radiant flux, W/m2.

Now I hope you understand that the calculation process is becoming extremely difficult. We still have to work and work in this direction. Each material must be tested at different temperatures. But for some reason there is practically no data on the materials. Or rather, I did not find an experimental reference book on materials.

Why is there no such materials guide? Because thermal radiation is very small, and I think it is unlikely to exceed 10% in our living conditions. Therefore, they are not included in the calculation. When we fly into space often, then all the calculations will appear. Or rather, our astronautics has accumulated data on materials, but it is not yet freely available.

Law of absorption of radiant energy

Each body is capable of absorbing some part of the radiating energy, more on this below.

If a radiant flux falls on any body of thickness l (see figure), then in the general case it decreases as it passes through the body. It is assumed that the relative change in radiant flux along the path Δl is directly proportional to the path of the flux:

The proportionality coefficient b is called the absorption index, which generally depends on the physical properties of the body and the wavelength.

Integrating over the range from l to 0 and taking b constant, we obtain

Let us establish a connection between the spectral absorption coefficient of the body B λ and the spectral absorption coefficient of the substance b λ.

From the definition of the spectral absorption coefficient B λ we have

After substituting values into this equation, we obtain the relationship between the spectral absorption coefficient B λ and the spectral absorption index B λ.

The absorption coefficient B λ is equal to zero at l 1 = 0 and b λ = 0. For a large value of bλ, a very small value of l is sufficient, but still not equal to zero, so that the value of B λ is as close to unity as desired. In this case, we can say that absorption occurs in a thin surface layer of the substance. Only in this understanding is it possible to talk about surface absorption. For most solids, due to the large value of the absorption coefficient b λ, “surface absorption” occurs in the indicated sense, and therefore the absorption coefficient is greatly influenced by the state of its surface.

Bodies, although with a low absorption coefficient, such as gases, can, if they are sufficiently thick, have a large absorption coefficient, i.e. are made opaque to rays of a given wavelength.

If b λ =0 for the interval Δλ, and for other wavelengths b λ is not equal to zero, then the body will absorb incident radiation of only certain wavelengths. In this case, as mentioned above, we speak of a selective absorption coefficient.

Let us emphasize the fundamental difference between the absorption coefficient of a substance b λ and the absorption coefficient B λ of a body. The first characterizes the physical properties of a substance in relation to rays of a certain wavelength. The value of B λ depends not only on the physical properties of the substance of which the body consists, but also on the shape, size and condition of the surface of the body.

Laws of radiation of radiant energy

Max Planck theoretically, based on electromagnetic theory, established a law (called Planck’s law) expressing the dependence of the spectral emissivity of a black body E 0λ on the wavelength λ and temperature T.

where E 0λ (λ,T) is the emissivity of the black body, W/m 2 ; T - thermodynamic temperature, K; C 1 and C 2 - constants; C 1 =2πhc 2 =(3.74150±0.0003) 10-16 W m2; C 2 =hc/k=(1.438790±0.00019) 10 -2; m K (here h=(6.626176±0.000036) 10 -34 J s is Planck’s constant; c=(299792458±1.2) m/s is the speed of propagation of electromagnetic waves in free space: k is Boltzmann’s constant. )

From Planck's law it follows that spectral emissivity can be zero at a thermodynamic temperature equal to zero (T=0), or at a wavelength λ = 0 and λ→∞ (at T≠0).

Consequently, a black body emits at any temperature above 0 K. (T > 0) rays of all wavelengths, i.e. has a continuous (continuous) emission spectrum.

From the above formula we can obtain a calculated expression for the emissivity of a black body:

Integrating within the range of changes in λ from 0 to ∞ we obtain

As a result of expanding the integrand into a series and integrating it, we obtain a calculated expression for the emissivity of a black body, called the Stefan-Boltzmann law:

where E 0 is the emissivity of the black body, W/m 2 ;

σ - Stefan Boltzmann constant, W/(m 2 K 4);

σ = (5.67032 ± 0.00071) 10 -8 ;

T - thermodynamic temperature, K.

The formula is often written in a form more convenient for calculation:

We will use this formula for calculations. But this is not the final formula. It only applies to black bodies. How to use it for gray bodies will be described below.

where E 0 is the black body emissivity; C 0 = 5.67 W/(m 2 K 4).

The Stefan-Boltzmann law is formulated as follows: the emissivity of a black body is directly proportional to its thermodynamic temperature to the fourth power.

Spectral distribution of black body radiation at different temperatures

λ - wavelength from 0 to 10 µm (0-10000 nm)

E 0λ - should be understood as follows: As if there is a certain amount of energy (W) in the volume (m 3) of a black body. This does not mean that it emits such energy only from its external particles. Simply, if we collect all the particles of a black body in a volume and measure the emissivity of each particle in all directions and add them all up, then we will get the total energy in the volume, which is indicated on the graph.

As can be seen from the location of the isotherms, each of them has a maximum, and the higher the thermodynamic temperature, the greater the value of E0λ corresponding to the maximum, and the maximum point itself moves to the region of shorter waves. The shift of the maximum spectral emissivity E0λmax to the region of shorter waves is known as

Wien's displacement law, according to which

T λ max = 2.88 10 -3 m K = const and λ max = 2.88 10 -3 / T,

where λ max is the wavelength corresponding to the maximum value of spectral emissivity E 0λmax.

So, for example, at T = 6000 K (the approximate temperature of the solar surface), the maximum E 0λ is located in the region of visible radiation, into which about 50% of the solar emissivity falls.

The elementary area under the isotherm, shaded on the graph, is equal to E 0λ Δλ. It is clear that the sum of these areas, i.e. the integral represents the blackbody emissivity E 0 . Therefore, the area between the isotherm and the x-axis depicts the black body emissivity on the conventional scale of the diagram. At low values of thermodynamic temperature, the isotherms pass in close proximity to the abscissa axis, and the indicated area becomes so small that it can practically be considered equal to zero.

The concepts of so-called gray bodies and gray radiation play a large role in technology. Gray is a non-selective thermal emitter capable of emitting a continuous spectrum, with spectral emissivity E λ for waves of all lengths and at all temperatures, constituting a constant fraction of the spectral emissivity of a black body E 0λ i.e.

The constant ε is called the emissivity coefficient of the thermal emitter. For gray bodies, the emissivity coefficient ε

The graph schematically shows the wavelength distribution curves of the spectral emissivity of a black body E λ (ε = 1) and the spectral emissivity of a gray body E λ of the same temperature as the black body (at ε = 0.5 and ε = 0.25). Gray body emissivity

Work

called gray body emissivity.

The emissivity values obtained from experience are given in the reference literature.

Most bodies used in technology can be mistaken for gray bodies, and their radiation is considered gray radiation. More accurate studies show that this is only possible as a first approximation, but it is sufficient for practical purposes. The deviation from the Stefan-Boltzmann law for gray bodies is usually taken into account by taking the emissivity C to depend on temperature. In this regard, the tables indicate the temperature range for which the value of emissivity C is experimentally determined.

In the following, to simplify conclusions, we will assume that the emissivity of a gray body does not depend on temperature.

Emissivity coefficients of some materials

(Material / Temperature in °C / Value E)

Oxidized aluminum / 200-600 / 0.11 -0.19

Polished aluminum / 225-575 / 0.039-0.057

Red brick / 20 / 0.93

Fireproof brick / - / 0.8-0.9

Oxidized copper / 200-600 / 0.57-0.87

Oxidized lead / 200 / 0.63

Polished steel / 940-1100 / 0.55-0.61

Turned cast iron / 830-910 / 0.6-0.7

Oxidized cast iron / 200-600 / 0.64-0.78

Polished aluminum / 50-500 / 0.04-0.06

Bronze / 50 / 0.1

Galvanized sheet iron, shiny / 30 / 0.23

White tin, old / 20 / 0.28

Polished gold / 200 - 600 / 0.02-0.03

Matt brass / 20-350 / 0.22

Polished copper / 50-100 / 0.02

Polished nickel / 200-400 / 0.07-0.09

Shiny tin / 20-50 / 0.04-0.06

Polished silver / 200-600 / 0.02-0.03

Rolled steel sheets / 50 / 0.56

Oxidized steel / 200-600 / 0.8

Highly oxidized steel / 500 / 0.98

Cast iron / 50 / 0.81

Asbestos cardboard / 20 / 0.96

Planed wood / 20 / 0.8-0.9

Fireproof brick / 500-1000 / 0.8-0.9

Fireclay brick / 1000 / 0.75

Red brick, rough / 20 / 0.88-0.93

Varnish black, matte / 40-100 / 0.96-0.98

White varnish / 40-100 / 0.8-0.95

Oil paints of various colors / 100 / 0.92-0.96

Lamp carbon / 20-400 / 0.95

Glass / 20-100 / 0.91-0.94

White enamel / 20 / 0.9

Kirchhoff's law

Kirchhoff's law establishes the relationship between emissivity and absorption coefficient of a gray body.

Let us consider two parallel gray bodies of infinite extent with flat surfaces of area A each.

An infinitely extended plane makes it possible to approximate calculations for finding real radiation in practical and theoretical experiments. In theoretical experiments, the real value is found using integral expressions, and in experiments, a larger plane brings the calculations closer to real values. Thus, we, as it were, extinguish the influence of unnecessary lateral and angular radiation, which flies away and is not absorbed by the experimental plates, with a large infinite plane.

That is, if the coefficient is multiplied by the emissivity, we get the resulting emission value (W).

We can assume that all the rays sent by one body completely fall on the other. Let us assume that the transmittance coefficients of these bodies are D 1 = D 2 = 0 and there is a heat-transparent (diathermic) medium between the surfaces of the two planes. Let us denote by E 1 , B 1 , F 1 , T 1 , and E 2 , B 2 , F 2 , T 2 the emissivity, absorption, reflection and surface temperatures of the first and second bodies, respectively.

The flux of radiant energy from surface 1 to surface 2 is equal to the product of the emissivity of surface 1 and its area A, i.e. E 1 A, from which part of E 1 B 2 A is absorbed by surface 2, and part of E 1 F 2 A is reflected back to surface 1. From this reflected flux E 1 F 2 A, surface 1 absorbs E 1 F 2 B 1 A and reflects E 1 F 1 F 2 A. FROM the reflected energy flow E 1 F 1 F 2 A, surface 2 will again absorb E 1 F 1 F 2 B 2 A and reflect E 1 F 1 F 2 A, etc.

Similarly, radiant energy is transferred by flow E 2 from surface 2 to surface 1. As a result, the flux of radiant energy absorbed by surface 2 (or given off by surface 1)

The flux of radiant energy absorbed by surface 1 (or given off by surface 2),

In the final result, the flux of radiant energy transferred from surface 1 to surface 2 will be equal to the difference between the radiant fluxes Ф 1→2 and Ф 2→1, i.e.

The resulting expression is valid for all temperatures T 1 and T 2 and, in particular, for T 1 = T 2. In the latter case, the system under consideration is in dynamic thermal equilibrium, and based on the second law of thermodynamics, it is necessary to put Ф 1→2 = Ф 2→1 which follows

E 1 B 2 = E 2 B 1 or

The resulting equality is called Kirchhoff's law: the ratio of the emissivity of a body to its absorption coefficient for all gray bodies at the same temperature is the same and equal to the emissivity of a black body at the same temperature.

If a body has a low absorption coefficient, such as a well-polished metal, then this body also has low emissivity. On this basis, to reduce heat loss by radiation into the external environment, heat-releasing surfaces are covered with sheets of polished metal for thermal insulation.

When deriving Kirchhoff's law, gray radiation was considered. The conclusion will remain valid even if the thermal radiation of both bodies is considered only in a certain part of the spectrum, but nevertheless has the same character, i.e. both bodies emit rays whose wavelengths lie in the same arbitrary spectral region. In the limiting case we come to the case of monochromatic radiation. Then

those. for monochromatic radiation, Kirchhoff's law should be formulated as follows: the ratio of the spectral emissivity of any body at a certain wavelength to its absorption coefficient at the same wavelength is the same for all bodies at the same temperatures, and is equal to the spectral emissivity of a black body at the same length waves and the same temperature.

We conclude that for a gray body B = ε, i.e. the concepts of “absorption coefficient” B and “blackness coefficient” ε for a gray body coincide. By definition, the emissivity coefficient does not depend on either temperature or wavelength, and therefore, the absorption coefficient of a gray body also does not depend on either wavelength or temperature.

Radiation of gases

Radiation from gases differs significantly from radiation from solids. Absorption and emission of gases - selective (selective). Gases absorb and emit radiant energy only in certain, rather narrow intervals Δλ wavelengths - the so-called bands. In the rest of the spectrum, gases do not emit or absorb radiant energy.

Diatomic gases have a negligibly small ability to absorb radiant energy, and therefore a low ability to emit it. Therefore, these gases are usually considered diathermic. Unlike diatomic gases, polyatomic gases, including triatomic gases, have a significant ability to emit and absorb radiant energy. Of the triatomic gases in the field of thermotechnical calculations, carbon dioxide (CO 2) and water vapor (H 2 O), which each have three emission bands, are of greatest practical interest.

Unlike solids, the absorption index for gases (of course, in the region of absorption bands) is small. Therefore, for gaseous bodies it is no longer possible to talk about “surface” absorption, since the absorption of radiant energy occurs in a finite volume of gas. In this sense, absorption and emission of gases are called volumetric. In addition, the absorption coefficient b λ for gases depends on temperature.

According to the absorption law, the spectral absorption coefficient of a body can be determined by:

For gaseous bodies, this dependence is somewhat complicated by the fact that the gas absorption coefficient is affected by its pressure. The latter is explained by the fact that absorption (radiation) is more intense, the greater the number of molecules that encounter the beam on its path, and the volume number of molecules (the ratio of the number of molecules to volume) is directly proportional to the pressure (at t = const).

In technical calculations of gas radiation, absorbing gases (CO 2 and H 2 O) are usually included as components in the gas mixture. If the pressure of the mixture is p, and the partial pressure of the absorbing (or emitting) gas is p i, then instead of l it is necessary to substitute the value p i 1. The value p i 1, which is the product of the gas pressure and its thickness, is called the effective thickness of the layer. Thus, for gases the spectral absorption coefficient

The spectral absorption coefficient of a gas (in space) depends on the physical properties of the gas, the shape of the space, its dimensions and the temperature of the gas. Then, in accordance with Kirchhoff’s law, the spectral emissivity

Emissivity within one spectral band

This formula is used to determine the emissivity of a gas into free space (emptiness). (Free space can be considered as black space at 0 K.) But gas space is always limited by the surface of a solid body, which in general has a temperature T st ≠ T g and emissivity coefficient ε st

The emissivity of a gas in a confined space is equal to the sum of the emissivities taken over all spectral bands:

Experimental studies have shown that the emissivity of gases does not follow the Stefan-Boltzmann law, i.e. depending on the fourth power of absolute temperature.

However, for practical calculations of gas radiation, the law of fourth powers is used, introducing an appropriate correction to the value of the gas emissivity coefficient ε g:

Here ε g = f(T,p l)

Average beam path length

where V is the gas volume; A is the surface area of the shell.

Emissivity of a gas whose components are CO 2 and H 2 O (combustion gases) to the shell of a gray body

in which the last term takes into account the intrinsic radiation of the shell.

The so-called effective emissivity factor of the shell ε" st, greater than ε st, due to the presence of radiating gas.

Gas emissivity coefficient at gas temperature t g

The emissivity values ε CO2 and ε H2O depending on temperature at different values of the parameter p i l are shown in the figure.

The correction factor β is determined from the graph.

The emission and absorption bands for C0 2 and H 2 0 somewhat overlap each other, and therefore part of the energy emitted by one gas is absorbed by the other. Therefore, the emissivity coefficient of a mixture of carbon dioxide and water vapor at a wall temperature t st

where Δε g is the correction taking into account the specified absorption. For gaseous combustion products of conventional composition, Δε g = 2 - 4% and can be neglected.

It can be assumed that at ε st = 0.8 + 1.0, the effective emissivity coefficient of the shell is ε" st = 0.5(ε st + 1).

These features of radiation and absorption of gases make it possible to establish the mechanism of the so-called “greenhouse effect,” which has a significant impact on the formation and change of the Earth’s climate.

Most solar radiation passes through the atmosphere and heats the Earth's surface. In turn, the Earth emits infrared radiation, causing it to cool. However, part of this radiation is absorbed by polyatomic (“greenhouse”) gases in the atmosphere, which consequently plays the role of a “blanket” that retains heat. At the same time, the greatest impact on global warming is exerted by such “greenhouse” gases as carbon dioxide (55%), freons and related gases (25%), methane (15%), etc.

Some laws will be touched upon further on the next page. There will also be a detailed explanation of how thermal radiation occurs through a window. Some factors affecting heat transfer by radiation will be described, as well as real-life radiation problems.

It was experimentally discovered that thermal radiation from a heated body attracts - and does not repel! - nearby atoms. Although the phenomenon is based on well-known effects of atomic physics, it went undetected for a long time and was theoretically predicted only four years ago.

Shift in energy levels due to thermal radiation

Recently, the archive of electronic preprints appeared, reporting experimental confirmation that thermal radiation from a hot body is capable of attracting nearby atoms to the body. The effect looks, at first glance, unnatural. Thermal radiation emitted by a heated body flies away from the source - so why is it capable of causing force? attraction?!

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In the discussion, as almost always happens now, one of the options for “explanation” is postulated. In fact, its applicability had to be justified.
Igor! You are a very good person. For many years now you have been rolling the stone of your mission.
What is gravity? Has its mechanical consideration become scientific again?
In the described experiment, a change in inertia was recorded.
The rest is from the evil one, right?
The train of thought about the wave board is very interesting. (I'm one of the former myself).
Still, there may be various simple effects. For example, movement towards a lower bottom. In this situation, each subsequent wave may be slightly lower and still have a vertical component.

I wonder if adding nanotubes to asphalt has anything to do with the topology premium?
No?
Are EM waves not drawn on the plane?
Well, yes,... yes.
And again these vortices are at the Descartes level

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The main value of this article is that it destroys some stereotypes and makes you think, which contributes to the development of creative thinking. I am very glad that such articles have begun to appear here.

You can dream up a little. If we further reduce the energy of the body (object), including the energy of internal interactions in elementary particles, then the energy of the object will become negative. Such an object will be pushed out by ordinary gravity and will have the property of antigravity. In my opinion, the modern vacuum of our World does not have absolute zero energy - because... it is a well-structured environment, as opposed to absolute chaos. It’s just that the vacuum energy level in the energy scale is assumed to be zero. Therefore, there may be an energy level lower than the vacuum energy level - there is nothing mystical about this.

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"Returning to the original theoretical paper from 2013, we mention the potential importance of this effect not only for atomic experiments, but also for cosmic phenomena. The authors considered the forces acting inside a dust cloud with a density of 1 g/cm3, heated to 300 K and consisting of particles of size 5 micron."
Is there a mistake here? The density of the dust cloud is too high, like that of the upper layer of regolith.
And by the phenomenon itself: and if we take a more non-trivial version of the problem - the effect of thermal radiation on a non-polarizable particle, for example, an electron. Where will the force be directed? The heater is 100% dielectric.

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Yes, this is a high density, on the verge of dust particles sticking together.
An isolated electron has no energy levels and has nothing to lower. Well, it does not have a dipole moment, within the error limits (there is a link in the text to the search for the electron EDM). Therefore, this force does not act on him. In addition, it is charged, photons are scattered well on it, so in general it will simply be repelled due to pressure.

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The far-IR spectrum is convenient because photon energies are still low, so all requirements are met. Lower temperatures are also suitable, but the effect there is already very weak. At temperatures of thousands of degrees, the scattering of photons is already much stronger, and it overcomes this effect.

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I wasn't talking about a heated body. And about other emitters and spectra.
All we are discussing here are ripple effects. This means they cannot be limited only to the IR range.
Do I understand correctly that depending on the size of the particle it is necessary to select the appropriate wavelength?
For heavy atoms or hydrogen atoms, do you need to select your frequency so that the attraction is maximum?
Now a cool idea is spinning in my head on how to test this, for example, on waves in a pool or sea.
Those. make a mechanical toy that will float against the waves.
What do you think about this possibility?

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- 1) The wavelength must be significantly larger than the particle size.
  2) The system itself should not interact with external influences as a whole; interaction is carried out only due to induced polarization.
  3) There must be a discrete spectrum of excitations, and the energies of the quanta must be significantly less than the distances between levels, otherwise the waves will be easily scattered and thereby exert pressure. When these conditions are met, the effect no longer depends on the wavelength.
  4) The force must be vector, not scalar, in order to lower the energy of the system.
  Now imagine if this can be implemented for waves on water.
  
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  - I see some of this effect well in the real world. I love racing yachts. And masters of sports in yachting win regattas precisely due to the ability to sail correctly against the wave. Those. if everything is done correctly, the oncoming waves give the yacht additional energy.
    In fact, this is a paradox. But it is clearly visible in racing. As soon as the waves rise, a “quantization” immediately occurs according to skill levels)) Amateurs slow down, and the pros, on the contrary, receive an additional advantage.
    So such a toy is quite real.
    I set up my yacht so that it sailed without steering or any intervention against the wind and against the waves without any problems.
    If you dig deeper, it is this setting that gives the maximum advantage.
    Let's put it this way, if you imagine a point source of strong wind in the middle of the lake, then my yacht will tend to it and go in circles ad infinitum...
    a very beautiful and real analogy, for example, the movement of the earth around the sun)))
    and it seems that there is some force that drags the yacht towards the source of the wind.
    By the way, you can take the problem to the elements and estimate, for example, the minimum distance at which the yacht can approach the source of the wind.
    Let me remind you that a yacht under sail tacks against the wind, describing something like a sinusoid. She turns only through the nose. If she turns around, the magic will disappear and she will go back with the wind.
    
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    I think you're a little confused. In tack there are no effects similar to those described. There is a complex sum of well-defined forces, which gives a resultant force, which has a non-zero negative projection along the wind direction axis.
    
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Here is a simple experiment on our topic. Can you explain?

Why is a curved path faster than a straight path?

Obviously, if we observe this on our scale, then in the quantum world it will be exactly the same. And in the macro world too.

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A trivial school physics problem. We simplify the model to one straight trajectory with a small angle to the horizontal - and a trajectory in the form of a line with a break, where the first section is inclined to the horizon much more strongly, and the second section has an even smaller slope than the first trajectory. The beginning and end of the trajectories are the same. Let's neglect friction. And we will calculate the time of arrival at the “finish” for cargo along one and the other route. The 2nd point N. (eighth-graders know what this is) will show that the time of arrival to the finish line along the second trajectory is less. If you now supplement the problem with the second part of the installation, representing a mirror image relative to the vertical at the end of the trajectory, slightly round the edges, you will get your case. Banality. Level "C" on the Unified State Examination in Physics. Not even an Olympiad problem in terms of complexity

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- I like your idea of simplification. Maybe this will help the kids. Give me time to think and try to talk to teenagers.
  And if without simplification and everything is so banal, then what form of trajectory is the fastest?
  
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“At temperatures of thousands of degrees, the scattering of photons is already much stronger, and it overcomes this effect.”...

That's it!!!
Presumably this effect works in a limited area and corresponding types of energy interactions. “Frequency dispersion” and its corresponding dynamics prevail in the boundary zones. Volodya Lisin tried to unearth some of the nuances of these processes in 1991, but
I probably didn’t have time. (I just couldn’t get through to him.). In my opinion, this effect fades as temperature gradients and (intensity of convection currents) in the analyzed zone decrease.
http://maxpark.com/community/5302/content/3334997#comment-44 797112
#10 MAG » 09/04/2015, 22:02
http://globalwave.tv/forum/viewtopic.php?f=20&t=65
Centuries flew by, but without miracles... - “neither here nor here”: (Movie 7. Heat and temperature)
https://www.youtube.com/watch?v=FR45i5WXGL8&index=7& list=PLgQC7tmTSjqTEDDVkR38piZvD14Kde
rYw

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Funny effect. It may shed light on the first gram problem in planet formation - how microscopic dust can clump together in a cloud of gas and dust. While an atom, say, hydrogen, is far from particles, it is in practically isotropic thermal radiation. But if two specks of dust inadvertently approach it, then, interacting with the atom with their radiation, they will receive an impulse towards each other! The force is many times greater than gravitational force.

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For dust particles to stick together, you don’t need to use such cool physics. What about “specks of dust”? We all understand that we are most likely talking about H2O, as the main solid component in many clouds? Compounds of carbon with hydrogen are excessively volatile (up to pentane), I won’t say anything at all about ammonia, substances other than H, He, C, N, O are in the minority, and there is also little hope for complex organics. So the solid will be mostly water. It is likely that in real gas clouds, ice-snowflakes move quite chaotically and relatively quickly, I believe that at a speed of at least centimeters per second. An effect like the one in the article simply will not create such a potential for snowflakes to collide - the characteristic relative speeds of snowflakes are too high and snowflakes pass each other’s potential hole in a fraction of a second. But no problem. Snowflakes already often collide and, purely mechanically, lose energy. At some point, they will stick together due to molecular forces at the moment of contact and remain together, so that snow flakes will form. Here, to roll small and very loose snowballs, neither thermal nor gravitational attraction is needed - only gradual mixing of the cloud is required.
I also believe that the calculation in the article has a gross error. The pairwise attraction of dust grains was taken into account. But dust in a dense cloud is opaque and gives uniform heat from all sides, i.e. we have a speck of dust inside a warm hollow chamber. And why would it fly to the area of the nearest pollen? Those. For gravity to work, you need cold space, but in a dense cloud it is not visible, which means there is no thermal gradient.

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- >I also believe that the calculation in the article has a gross error. The pairwise attraction of dust grains was taken into account. But dust in a dense cloud is opaque and gives uniform heat from all sides, i.e. we have a speck of dust inside a warm hollow chamber.
  This is where I disagree. Here we can draw an analogy with plasma. In the approximation of an ideal collisionless plasma, everything is approximately as you say: the average field is considered, which, in the absence of external charges and currents, is equal to zero - the contributions from charged particles completely compensate each other. However, when we begin to consider individual ions, it turns out that the influence from the nearest neighbors is still present, and it must be taken into account (which is done through the Landau collision integral). The characteristic distance beyond which one can forget about pairwise interaction is the Debye radius.
  For the interaction under consideration, I believe, a similar parameter will be infinite: the integral of 1/r^2 converges. For a rigorous proof, it would be necessary to construct a kinetic equation for a “fog” of droplets with such an interaction. Well, or use the Boltzmann equation: the scattering cross section is finite, which means you don’t have to be as sophisticated as in a plasma by introducing an average field.
  Well, I thought it was an interesting idea for an article, but everything is trivial. :(
  But in the article under discussion, they did it very simply: they estimated the total potential energy of a spherical cloud of microparticles with a Gaussian distribution. There is a ready-made formula for gravity; we calculated it for this interaction (on the asymptotics r>>R). And it turned out that there is a noticeable region where the contribution of gravity is much smaller.
  
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  - > For the interaction under consideration, I believe a similar parameter will be infinite
    Maybe zero? In general, I didn’t really understand your post, there is an overabundance of mathematics that I don’t know, when it’s simpler here - for there to be an unbalanced force, you need a radiation density gradient, when there is no gradient, there is no force, because it is the same in all directions.
    > And it turned out that there is a noticeable region where the contribution of gravity is much smaller.
    Could you be a little more specific? I don't really understand how this effect could help the formation of anything in space to be of any significance. To me, this is a useless calculation. It’s like proving that the effect is more than 100,500 times stronger than the gravitational interaction between neighboring atoms in the atmosphere of Jupiter - I agree, but this is only because the gravitational interaction of individual dust grains is, in general, not interesting at all. But at least gravity is not shielded.
    The effect, I believe, intensifies in the near field when the distance approaches 0, but this is already a description of how exactly the collision of dust particles occurs if they have already collided.
    PS: the potential of a dust grain in thermal radiation, as I understand it, does not depend on the order of magnitude on the size of the cloud - this potential depends only on the radiation density, i.e. on the temperature and degree of opacity of the cloud. The degree of opacity in order of magnitude can be taken as 1. It turns out that it doesn’t matter what kind of cloud we have, only the average temperature around us matters. How large is this potential if expressed in terms of kinetic energy m/s? (I can do the math, but maybe there is a ready-made solution?) Also, if the cloud is opaque, then the potential of the cloud as a whole will be a function of the surface area of the cloud. Curiously, we got the same surface tension, but in a slightly different way. And inside the cloud the dust will be free.
    
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You open the article from 2013, look, it’s not difficult, everything is described there in ordinary human language.

For illustration, they took a cloud of finite radius 300 meters and stupidly substituted numbers into formulas for the situation inside and outside the cloud. The main point is that even outside, at a distance of almost a kilometer from the center, thermal attraction is still stronger than gravitational attraction. This is just to get a feel for the scale of the effect. They recognize that the real situation is much more complex and must be modeled carefully.

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Dust is mainly represented (at 400 °K) by olivine, soot and silicon particles. Red supergiants smoke them.
Dust grains convert kinetic energy into heat. And they interact not with each other, but with nearby atoms or molecules that are transparent to radiation. Since r is in a cube, then the dust particles that are within a millimeter or centimeter from the ATOM each pull it towards themselves, and a resultant force appears that brings the dust particles together. At the same time, dust grains per meter are ignored due to a decrease in the interaction force by billions (or even trillions) of times.

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“This radiation diverges in all directions, so its energy density decreases with distance as 1/r2. An atom, being nearby, feels this radiation - because it lowers its energy. And since the atom strives to lower its interaction energy as much as possible, it is energetically advantageous for it to move closer to the ball - after all, the reduction in energy is most significant there!”
But, excuse me, if an atom rushes towards a heated ball, then it will not lower its energy in any way, but, on the contrary, will only increase it. I believe that this is not a correct explanation.

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Then I came up with a problem. Let there be a thermally stabilized chamber composed of two black hemispheres of different radii, oriented in different directions, and an additional flat ring. Let the left hemisphere have a smaller radius than the right, a flat partition makes the chamber area closed. Let the atom be at the center of curvature of each of the two hemispheres and motionless. Let the hemispheres be warm. The question is - will the atom experience thermal force in one direction?

Here I see 2 solutions: 1) thermal equilibrium will quickly arise in such a chamber, i.e. The radiation density will be the same on all sides, and the same at any point in the chamber. If the density of thermal radiation in the chamber does not depend on the selected point, then the potential for interaction with radiation does not change, which means there is no force.
2) Wrong decision. We divide the wall into surface elements of equal area and integrate the force of interaction of the atom with the surface element. It turns out that the flat ring makes a zero contribution, and the closer left surface has quadratically fewer points, each of which drags cubed times stronger - i.e. a speck of dust flies to the nearest surface, i.e. left.

As you can see, the answer is completely different.

Explanation of the contradiction. If we have a radiating element of a non-spherical shape, then it does not shine equally in all directions. As a result, we have a gradient of radiation density, the direction of which is not directed towards the emitter. Next, we get this: breaking a complex surface into points, and considering them as ROUND specks of dust becomes completely incorrect.

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Here an even more interesting problem came to mind. Let us have a heat emitter in the form of a flat black ring, the outer and inner radii of which are equal to R and r. And exactly on the axis of the ring, at a distance h, there is an atom. Count h<

Solution 1 (wrong!). Break the ring into “specks of dust”, then take the integral of the force of attraction of the atom and the elements of the ring over the surface. The calculation is not interesting, because one way or another, we get that the atom is drawn into the ring.
Solution 2. The ring cannot shine from the end or shines vanishingly little, i.e. the energy potential of the atom at points of the plane of the ring turns to 0 (maximum potential). The radiation of the ring will be non-zero at points whose height h above the plane of the ring is different from 0; at these points there will be a non-zero potential (less than 0). Those. we have a radiation density gradient, which locally (at h~=0, h<

It seems to me that solution 1 contains an error, I seem to understand where, but I cannot explain it in simple words.

This problem shows this. An atom is not attracted to an object emitting heat, i.e. the force vector is not directed towards the radiating surface. We don’t care at all WHERE the radiation comes FROM, we care HOW MUCH radiation is at a given point and what the radiation density gradient is. The atom moves towards the radiation density gradient, and this gradient can be directed even towards that half-plane in which there is not a single point of the emitter.

Problem 3. The same ring as in step 2, but the atom is initially at the point h=0. This state is equilibrium and symmetrical, but unstable. The solution would be spontaneous symmetry breaking. The atom will be pushed out from the position of the center of symmetry, because it is unstable.

I also draw attention to the fact that there is no need to replace the cloud with attracted dust particles. It will turn out bad. If 3 grains of dust stand on the same straight line and slightly shade one another, then the symmetry will be spontaneously broken, this is not the case in gravitational forces, because gravity is not shielded.

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I have a question (not only for Igor, but for everyone). How does potential energy enter into the gravitational mass of a system? I would like to sort this issue out. For example, the universe consists of dust grains evenly distributed in space, which gravitationally interact with each other. Obviously, such a system has high potential energy, since there is a state of the system in which these dust grains are concentrated into galaxies, each of which has less potential energy, in comparison with the dust grains scattered throughout space of which they consist. The specific question is: is the potential energy of this system included in the gravitational mass of the universe?
It seems to me that this question is related to the topic raised by PavelS. In an infinite universe, it is impossible to identify a sphere that covers it. And inside any other sphere, for example, enveloping a galaxy, the gravitational potential created by matter located behind the sphere (located on large scales almost uniformly in space) does not affect the behavior of bodies inside this sphere. Therefore, we can talk about the entry of potential energy into the gravitational mass only in relation to local inhomogeneities in the distribution of matter.

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I didn't raise this question. :) It also seemed to me that the expansion of the universe, taking into account dark energy and the reddening of photons, violates the law of conservation of energy, but if you really want to, you can turn around and say that the total energy of the universe is still 0, because the substance is in a potential well, and the more substance, the deeper the well. What I bought it for is why I sell it - I’m not good at details myself.
About potential energy, it is usually considered less than zero. Those. free particles are zero, bound particles are already less than 0. So negative potential energy works like negative mass (mass defect) - the mass of the system is less than the mass of the individual components. For example, during the collapse of a supernova, the potential energy goes into a big minus, and the difference in the masses of what was and what became can be emitted outward in the form of photons (rather, not photons but actually neutrinos).

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- The article discusses the manifestations of potential energy in a system. If there is a potential gradient of this energy in the system, then a force arises. You quite rightly noted that in some conditions there is no gradient, due to complete symmetry (the atom is inside a sphere). I continued the analogy in relation to the universe, where as a whole there is no gradient of potential gravitational energy. There are only local manifestations of it.
  There is a statement that the mass of matter mainly consists of the kinetic energy of quarks and gluons, plus a small particle due to the Higgs field. If we assume that this mass also contains negative potential energy, then this statement is not true.
  Proton mass is 938 MeV. The total mass of quarks, as determined by physicists, is approximately 9.4 MeV. There is no mass defect here. I want to understand, in general, whether potential energy is in any way taken into account by the general theory of relativity, as a mass generator, or not. Or there is simply energy there - which is the sum of kinetic energy and potential energy.
  “For example, during the collapse of a supernova, the potential energy goes into a big minus, and the difference in the masses of what was and what became can be emitted outward in the form of photons (rather, not photons but actually neutrinos).”
  So what - a hole because the substance that fell into it and is in a deep potential hole does not become lighter, perhaps by the amount of the mass of energy - the substance that it returned back.
  
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  - "except for the amount of mass of energy - matter that it returned back"
    This “unless” can be as large as you like. So, having lost a kilogram in the black hole, she will be less massive by less than 1 kg. In practice, up to 30% of the falling mass is emitted as X-rays by the accretion disk, but the number of falling protons does not decrease. It is not matter that is emitted, but X-rays. It is not customary to call X-ray by the term substance.
    Read the news about the collision of two black holes, and the result there is also noticeably worse than the total of the original holes.
    And finally, the question is WHERE you are with your scales. In what frame of reference and at what point? The measurement method is everything. Depending on this, you intend to measure different masses, but IMHO this is more of a terminological issue. If an atom is inside a neutron star, then you cannot measure its mass except by comparing it with a neighboring test body that is nearby. In this regard, the mass of an atom does not decrease when falling into a hole, but the mass of the total system is not equal to the sum of the masses of the components. I believe this is the most accurate terminology. In this case, the mass of the system is always measured relative to an observer outside this system.
    
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    - The term “magnitude of mass of energy - matter” here means “magnitude of mass of energy and mass of matter.” X-rays have rest mass if locked in a box of mirrors or in a black hole. Gravitational waves also carry energy and must be taken into account in the mass generator in general relativity. I apologize for the inaccuracy of the wording.
      Although, as I know, the practically stationary gravitational field itself is not taken into account in the composition of mass in general relativity. Therefore, the potential field energy should also not be taken into account. Moreover, potential energy is always relative. Or am I wrong? In this connection, the statement that the mass of the universe is 0 due to the negative energy (and mass) of the gravitational field is nonsense.
      In the example with a black hole, if we assume that in the process of falling into the hole, for example, a kilogram of potatoes, nothing came back out, I think that the black hole increases its mass by this kilogram. If you do not take into account the potential energy of potatoes in the composition of the mass, then the arithmetic looks like this. When a potato falls into a hole, it acquires greater kinetic energy. Due to this, it increases its mass, if viewed from outside the hole. But at the same time, when viewed from the outside, all processes in potatoes slow down. If we correct for time dilation, then the mass of the potato when looking at it from an external frame of reference will not change. And the black hole will increase its mass by exactly 1 kilogram.
      
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“For example, the universe consists of dust particles evenly distributed in space, which gravitationally interact with each other.”

Your model is already contradictory and unrelated to reality. You can come up with a bunch of such examples and come to any conclusion each time.
And entropy will be a factor in the orderliness of your system. And potential energy will not give you any interesting results, since it is relative to the chosen reference point and the Observer.

In the real world, a similar model is a crystal. In it, atoms are evenly distributed in space and interact with each other.
Correct me if I'm wrong.

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“Your model is already contradictory and unrelated to reality.”
Regarding inconsistency, this must be proven. In terms of compliance with reality - maybe. This is a hypothetical model. It has been simplified a bit for better understanding.
“And entropy will be a factor in the orderliness of your system...”
Agree.

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- If you enjoy wave theories of physics and like to model them, then try to explain this effect in our amazing universe.
  It manifests itself on all scales.
  https://cs8.pikabu.ru/post_img/2017/01/30/0/1485724248159285 31.webm
  I posted this for the AI above too. It will be interesting to see the rationale behind it too.
  
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  Sorry for being blunt, but this is a banal mechanic of the first year of university. However, the phenomenon itself should be understandable to even a strong student. Please understand that I cannot waste time on random requests. In general, it is better to stick to the topic of the news when commenting on news.
  
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  - - Do you seriously believe that physics comes down to listing all possible problems and a list of solutions to them? And that a physicist, seeing a problem, opens this magic list, looks for problem number one million in it, and reads the answer? No, understanding physics means seeing a phenomenon, understanding it, writing formulas that describe it.
      When I say that this is banal 1st year physics, it means that a physics student after a normal mechanics course is able to solve it on his own. A normal student does not look for a solution, he solves the problem himself.
      Sorry for the rebuke, but this widespread attitude is very depressing. This is the basis for most people's misunderstanding of what science does and how it does it.
      
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      - I absolutely agree with you. There is no greater pleasure than solving a problem yourself. It's like a drug))
        I was just asking a question in a friendly manner.
        I have an average level overall in solving problems in physics. At the All-Union Physics Olympiads, I was in the middle. But in programming and modeling I managed to climb higher. but here a different way of thinking is at work.
        
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        I cannot clearly formulate the essence of this phenomenon in simple words. (some kind of stupor in my head). Exactly the point. To transfer it to another model and also explain it to schoolchildren.
        
        This experiment can be thought of as a signal passing through. And it travels along a curved trajectory faster.
        Where does this gain in time come from?
        Obviously, the shape of the trajectory also affects this delay. If you make very deep holes, the ball simply will not overcome the hole, losing energy due to air resistance at high speeds.
        If you pose the problem as determining the optimal shape of the trajectory, then the problem seems to cease to be a school problem. We are already getting into many different functions and shapes of the trajectory.
        Can we take this problem to the elements? It seems to me that it would be useful for many people judging by the reaction of people. And this task reflects reality well.
        
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        Honestly, I don’t understand how, when participating in all-Union Olympiads, you don’t see this phenomenon. Especially coupled with the fact that, according to you, you cannot clearly formulate the essence of this phenomenon.
        Do you understand that the time it takes to travel a trajectory depends not only on its length, but also on its speed? Do you understand that the speed at the bottom is greater than at the top? Can you combine these two facts into the general understanding that a longer trajectory does not necessarily mean more time? It all depends on the increase in speed with increasing length.
        It is enough to understand this phenomenon to stop being surprised by the effect. And a specific calculation for an arbitrary trajectory will require careful recording of the integral (and this is where 1st year of university is needed). There, of course, it will be different for different trajectories, but it can be shown that for a fairly flat trajectory of any shape, going strictly below the straight line, the travel time will always be less.
        >I'm having fun with the Time theory now.
        This is a very dangerous formulation. So dangerous that I proactively ask you not to write anything on such topics in the comments on elements. Thanks for understanding.
        
        Answer
        
        I see this phenomenon, I understand it, and I can take the integral over any shape of the trajectory and easily write a program for the calculation.
        But when I go with teenagers to the experimentarium and explain to them in simple language how everything works, it is precisely on this phenomenon that I fail. Maybe it's age that's taking its toll))
        And the skill of quickly and easily seeing the final answer goes away if you don’t constantly practice. Probably like in sports. At 40 years old it’s hard to spin on the horizontal bar like in your youth... and do somersaults)))
        I never thought that discussing Time is taboo))). Moreover, this is the foundation. Reading Hawking and seeing how they popularized these ideas, I was sure that they were capturing the minds of the world's researchers.
        Maybe you misunderstood me?
        But this is just a conversation... and of course I’m not going to break the rules and promote any heresy and unfounded personal theories)) This is at least not decent...
        But the brain requires food and something new)))
        
        Answer
        
        As for the Olympics. My experience has shown that the really cool guys are not those who solve new problems, but those who come up with them. There are only a few of them. This is a different dimension and view of the world. A chance 5-minute conversation with such a person at one of the Olympiads completely changed my life and brought me out of deep illusions and actually saved my life.
        He joked that “Doctor of Science” gets his title for treating injured colleagues who were unable to climb one of the slides.
        This person argued that the top winners of the Olympiads then dissolve in the scientific community and do not bring new discoveries and results. Therefore, without constant broad development of your knowledge and real skills, the path to something new will not be visible.
        And in general, the Olympics are a pure sport with luck, courage, cunning, with a lot of injuries and crippling of the psyche of children, including me. But this is life)))
        
        Answer

Myth and Legend Busters have already refuted your assumption.
https://www.youtube.com/watch?v=XsKhzk4gn3A

The effect is independent of materials and friction.
Also, according to your version, if we replace the balls with sliding weights, the effect will disappear.

Also, faster balls experience more air resistance. Drag is proportional to the square of the speed. And yet this does not stop them from coming first.

Let's have more realistic ideas. These things directly reflect the way our world works.

Answer

- In general, rolling friction has nothing to do with it...))
  The effect works in models without friction and air.
  You can make magnets and pump out the air.
  But calculating the shape of the trajectory that is the fastest is kind of a cool problem.
  Professionals in classical mechanics can probably intuitively predict the answer.
  
  Answer
  - It dawned on me that the experiment in your video resembles a Foucault pendulum. Obviously, the fastest trajectory for the ball will be a circular arc with the smallest possible radius (up to a semicircular path = 1 half-wave with the ridge down). For a pendulum, the paradox of a longer trajectory and at the same time greater speed is solved due to the smaller radius of the described arc, i.e. the length of the pendulum arm, on which the period of its oscillation depends.
    In this case, any deviation of the ball’s movement from strictly circular is undesirable, since it should have a negative effect on its average speed. The rectilinear motion of the ball in the video is akin to the oscillations of a pendulum with a very long arm, which, as everyone understands, has the longest period of oscillation. Therefore, the lowest ball speed is observed there.
    Looks like I did without integrals ;)
    Interesting problem!
    
    Answer
    - We need to prove it mathematically and test the hypothesis. But it sounds interesting... one of the latest versions was that this is an inverted cycloid.
      I have a lot of stuff like that in stock.
      For example:
      The most seemingly banal problem on energy conservation for school, but it shows exactly the understanding of potential energy and kinetic energy that nicolaus was talking about. The problem for him broke the brains of many, even guys who were serious in physics.
      We take a machine with a winding spring. We put it on the floor and let go. Due to the spring, it accelerates to speed V. We write down the law of conservation of energy and calculate the energy of the spring.
      0 + E(springs) = mV^2/2
      Now attention! We move to an equal inertial system that moves towards the car. Roughly speaking, we are moving towards the car at speed V.
      Relative to us, at the beginning the speed of the car was V, after acceleration it will be 2V.
      We calculate the energy of the spring.
      E(springs) + mV^2/2 = m(2v)^2/2
      E(springs) = 3mV^2/2
      The energy of the spring suddenly increased relative to another inertial reference frame.
      Moreover, the faster you move towards the car, the greater the energy of the spring.
      How is this possible?
      Nicolaus is for you. The law of conservation has been violated. Hooray! it's done!))))
      This is also a fundamental understanding of processes and energy transfer.
      Kids love to cause problems)))
      
      Answer
      
      Your expression after “We calculate the energy of the spring” is incorrect.
      “And kids who ask questions are very rare.”
      Kids who ask questions are not uncommon. All children have a period of "why".
      In general, I will refrain from discussing with you so as not to inadvertently offend you. I like to make jokes that may not be understood.
      
      Answer

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No not like this. Vacuum energy level, i.e. empty space, determines the dynamics of the recession of galaxies. Do they accelerate or, on the contrary, slow down? This prevents you from moving the scale too freely. The vacuum potential cannot be chosen arbitrarily; it is completely measurable.

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Dear Igor! I, of course, understand that you are fed up with commentators after every news article is published. We should thank you for providing information about foreign developments, and not bullshit, but we are who we are. It is your right to generally send to the original source, because... This is a rewrite or Copy Paste with a technically correct translation, for which once again a separate ATP.
And now on the topic, if an atom, particle, any body without kinetics is moved closer to the source of electromagnetic radiation, then its total energy increases. And how it is redistributed inside the body (which increases (decreases) more, kinetic or potential), this does not affect the final result. Therefore, I said that the explanation of the authors of the article is not correct. In fact, there is no thermal force - it is the force of gravity. How does this happen? The answer is in the article: “Gravity of the Earth Photonic-quantum gravity”, published in the Hungarian journal (p. 79-94):
http://tsh-journal.com/wp-content/uploads/2016/11/VOL-1-No-5 -5-2016.pdf

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Igor, I don’t know if this is bad manners. But, in the light of numerous comments on this topic, it seems to me that there is a need to write a good popular science text, including about the concept of potential energy. Because, in my opinion, people are a little confused. Maybe, if you have time, you will try and write about the Lagrangians in a scientifically popular manner? It seems to me that with your talent and experience there will be a very necessary article. Such fundamental concepts are the most difficult to write about, I understand. But what do you think?

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Let me answer your question.

Here's what it says on Wikipedia:
The publication of Eagleworks' work has led to EmDrive being sometimes described as "NASA-tested", although the agency's official position is different: "This is a small project that has not yet led to practical results."

But from the text it is obvious that there is interest in this device and the creators were able to attract attention. Otherwise, no one would have allocated money. There's something there.
I suggest you wait a little and see the final results. This will save you time and effort. But you shouldn’t hope for miracles and dream about how established knowledge and experience will collapse)))
It is better to build something new than to try to break what our ancestors did.
In simple terms, if their device works, then there will be a person who will calmly describe everything within the framework of existing theories.

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- I understand your feelings well. Among my programmer friends who have developed thinking but no experience in working with the theory of physics, there are a lot of such sentiments. Dig up a video on YouTube, find some grandfather in the garage who built a perpetual motion machine, etc., their favorite pastime.
  It's always fun and a good reason to get together in nature and barbecue.
  And for me this is an opportunity to once again test my own knowledge and gaps. (Everyone has them. Some people are really shy and disguise them.)
  The crux of your question lies in basic physics. If you clearly get to the basics of the theory of physics, then you will understand a simple thing.
  As soon as the unique effect of emDrive is proven, and it is clear that this is not a disguised set of already known effects, then any competent physicist will come up with an explanation.
  But the proof of the experiment must be rigorous and all procedures have been fine-tuned over centuries. There are no obstacles here. You just need to follow clear procedures accepted in the scientific world.
  The world of real physics is a lot of money. And they are given only for a specific result. Nobody likes to waste time and fall into dummies. The penalties for mistakes are very strict. Before my eyes, people simply died within a few months when their hopes were crushed. And I’m silent about how many people simply go crazy, fixated on their ideas in attempts to “help all of humanity.”
  This is not normal.
  All physics is built on the simplest few ideas. Until you understand it thoroughly, it is better not to fight with windmills.
  One of the postulates of the fundamental theory of physics is the following: we can divide space and time indefinitely.
  And then the math comes in. You will also need a coin and a pencil.
  On one sheet of paper with this idea, you can derive the Maxwell distribution. And predict the random distribution of balls in a standard experiment and go for a walk up the dimensions.
  If you calmly do this exercise, then you understand what you are doing.
  In other words, before doing a somersault on the horizontal bar, you need to calmly and without thinking, pull yourself up by any means.
  In the theory of physics there is a point from which everything is built. You must be able to build all the basic formulas and theories from this point.
  Once you run along the main paths and trails several times, you will become an honest and real inhabitant of this world.
  And it is then that you will understand that the language of physics can describe any phenomena.
  A linguist friend of mine sees physics as a language for describing the real world. He doesn’t even believe in the electron))) And that’s his right...
  And my mathematician friends say that physics is mathematics with a drop of time (dt) added to it.
  Start with the very basics. Everything is clear and beautiful here)))
  
  Answer

“Thirdly, there is another force of attraction - gravitational force. It does not depend on temperature, but increases with body mass.”

I wouldn't be so sure that gravity is independent of temperature. The dynamics of particles increases with temperature, which means mass (at least relativistic) increases, which means gravity increases.
Generally speaking, taking into account the [actually] dynamic nature of gravitational forces, this very fact links the gravitational force with temperature as a dynamic characteristic of mechanical systems. But this is a topic for another conversation, or rather theory. ;)

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As far as I understand, in a “sound” field this effect is even easier to implement if the dipole is replaced with a membrane (for example, a soap bubble) with a resonance at a frequency higher than the one to which the sound generator is tuned. Still, it’s somehow easier to invest a kilowatt of energy into sound than into EM radiation))

It would be funny: soap bubbles are attracted to the speaker...

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Sound and music are generally convenient things for studying waves. This is my hobby.
If anyone is interested, here are my attempts to apply quantum physics and Schumann resonance in creativity.
https://soundcloud.com/dmvkmusic
This is 3D music, so you only need to listen to it with headphones or good speakers.
I have speakers and a whole studio and even soap bubbles.
I'll check your idea)))
Thank you!
Let's do more!)))

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“And since the atom strives to lower its interaction energy as much as possible, it is energetically advantageous for it to move closer to the ball - after all, there the reduction in energy is most significant!”
Some kind of crap, not an explanation, what the atom wants, something that benefits it. And of his own free will, he moves wherever he wants.
What a pity that there are no physicists now capable of explaining.
Not to mention that exposure to energy is explained to lower the energy level of the object. The second law of thermodynamics seems to be convulsing hysterically. Sorry.

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Unfortunately, during the discussion it was not possible to obtain a comprehensive answer to the question of potential energy. Therefore, I tried to figure it out myself (which took time). That's what came out of it.

Many answers were found in the presentation of the lecture by the remarkable Russian physicist Dmitry Dyakonov, “Quarks and where mass comes from.” http://polit.ru/article/2010/09/16/quarks/. Dmitry Dyakonov had one of the highest citation ratings; I think he is among the great physicists.

What’s surprising, compared to the lecture, is that I didn’t lie about anything in my assumptions when I wrote about the nature of potential energy.

This is what Dmitry Dyakonov said.

“Now I want to take you into a deep thought. Look at slide 5. Everyone knows that a bird sits on a wire, there are 500 kilovolts in the wire, but it doesn’t give a damn. Now, if the bird stretches out and grabs one wire with one paw, and the other with the other paw, it won’t be good. Why? Because they say that the electric potential itself has no physical meaning; it, as we like to say, is not observed. There is a more precise statement that the observed electric field strength is observed. Tension - who knows - is a gradient of potential."

The principle - that it is not the value of the electric potential itself that is observed, but only its change in space and time - was discovered back in the 19th century. This principle applies to all fundamental interactions and is called “gradient invariance” or (another name) “gauge invariance”.

“I started my list with gravitational interaction. It turns out that it is also built on the principle of gauge invariance, only it is independent not of “color”, not of potential, but of something else. I'll try to explain why.
Let's imagine that somewhere there is a large mass. For example, the Sun. The sun is a large mass. What does it do? It seems to bend flat space, and the space becomes curved. Very clear. Now we place the Earth nearby, it begins to revolve around the Sun. In fact, the image is quite geometric: space is squeezed and our planet Earth is spinning in this hole. Look at the slide - all the coordinate lines are distorted there. And this is what Einstein's most important achievement was when he put forward the general theory of relativity. He said that all observable physical phenomena should not depend on what kind of coordinate grid we deign to apply and what kind of clock we use.
Why I brought this here, because this is also a kind of “gauge invariance”.

Curvature is an observable thing, and in a mathematical sense, electric field strength is also a kind of curvature. But we don’t see the potential; the bird sitting on one wire is alive.”

Based on this, we can conclude that potential energy should not be considered as a source of mass, because otherwise the mass and physical processes will depend on the reporting system from which the observation is made.

This idea is reinforced by Dmitry Dyakonov’s answer to the question about the mass of the electromagnetic field.

“Dmitry: Please tell me, do force fields, for example, electric and gravitational fields, have mass?
Dmitry Dyakonov: If they have, then it is very small, and the conventional wisdom is that they are massless.
Dmitry: I meant something a little different. Let's say we have a capacitor, between the plates of which there is an electric field. Does this field have mass?
Dmitry Dyakonov: No.
Dmitry: Does it have energy?
Dmitry Dyakonov: Yes.
Dmitry: And mc??
Dmitry Dyakonov: Okay, concoct for me a closed system, that is, including a capacitor, a battery, a hydroelectric power station, a solar source, and so on. When you concoct a closed system, we will measure its mass, and I will say that E, which is mc? from this mass - this is the rest energy of this closed system. I make no other statements.
Dmitry: So the field energy, in essence, is the energy of the battery, wires and plates?
Dmitry Dyakonov: Of course. You need to take a closed system, you can make a judgment about it.”

So where does mass come from in our world?

Dmitry Dyakonov: “As you can see, the whole history of science has consisted of us studying a wide variety of connected positions, and the sum of the masses of the components has always been greater than the whole. And now we reach the last bound state - these are protons and neutrons, which are made of three quarks, and here, it turns out, the opposite is true! The proton mass is 940 MeV - see slide 9. And the mass of the constituent quarks, that is, two u and one d, we add 4 + 4 + 7 and get only 15 MeV. This means that the sum of the component masses is not more than the whole, as usual, but less, and not just less, but 60 times less! That is, for the first time in the history of science we encounter a bound state in which everything is the opposite in comparison with the usual.

It turns out that empty space, vacuum, lives a very complex and very rich life, which is depicted here. In this case, this is not a cartoon, but a real computer simulation of real quantum chromodynamics, and the author is my colleague Derick Leinweber, who kindly provided me with this picture for demonstration. Moreover, what is remarkable is that the presence of matter has almost no effect on vacuum field fluctuations. This is a gluon field that fluctuates in such a strange way all the time.
And now we let quarks in there, see slide 13. What will happen to them? A rather interesting thing is happening. Here, too, the thought is not superficial, try to delve into it. Imagine two quarks, or a quark and an antiquark, that simultaneously find themselves in the vicinity of such a large fluctuation. Fluctuation creates a certain correlation between them. And correlation means that they interact.
Here I can just give an everyday image. You drain the water from the bath, a funnel is formed, where two matches fall, they are drawn into this funnel, and both of them spin the same way. That is, the behavior of two matches is correlated. And you can say that the funnel caused the interaction between the matches. That is, external influence induces interaction between objects that fall under this influence. Or, say, you are walking along Myasnitskaya, and it starts to rain. And for some reason, suddenly everyone raises some object above their head. This is correlated behavior, it turns out that people interact, but they do not directly interact, and the interaction was caused by an external influence, in this case, rain.
Everyone has probably heard about superconductivity, and if there are physicists in the room, they will explain that the mechanism of superconductivity is the condensation of so-called Cooper pairs of electrons in a superconductor. A similar phenomenon occurs here, only the quantum condensate is formed not by electrons, but by pairs of quarks and antiquarks.

What happens if a quark enters such a medium? A quark flies, it can knock out one quark that has already organized itself into such a pair, this one flies further, randomly falls into the next one, and so on, see slide 14. That is, the quark travels in a complex way through this medium. And this is what gives him mass. I can explain this in different languages, but, unfortunately, it won’t get any better.

The mathematical model of this phenomenon, which bears the beautiful name “spontaneous chiral symmetry breaking,” was first proposed back in 1961 simultaneously by our domestic scientists Vaks and Larkin and the wonderful Japanese scientist Nambu, who lived his entire life in America and in 2008, in a very old age, received the Nobel Prize for this work.”

The lecture had slide 14 showing how quarks travel. Based on this slide, it follows that the mass is formed due to the energy of quarks, and not the gluon field. And this mass is dynamic - arising as a result of energy flows (movement of quarks), under conditions of “spontaneous violation of chiral symmetry.”

All that I have written here are very brief excerpts from Dmitry Dyakonov’s lecture. It is better to read this lecture http://polit.ru/article/2010/09/16/quarks/ in full. There are beautiful slides explaining the meaning.

I’ll explain why during the discussion in this thread I asked questions about potential energy. In the answers, I wanted to read approximately the same as what was written in the presentation of Dmitry Dyakonov’s lecture, in order to further rely on these statements and continue the discussion. However, unfortunately, the discussion did not take place.

This is necessary to strengthen the position of the hypothesis of the evolution of matter. According to the hypothesis, mass in our universe arises as a result of the structuring of matter. Structuration is the formation of order against a background of chaos. Everything that is written in the presentation of Dmitry Dyakonov’s lecture, in my opinion, supports this hypothesis.

The structuring of matter can occur in several stages. Transitions between stages are accompanied by revolutionary changes in the properties of matter. These changes in physics are called phase transitions. It is now generally accepted that there were several phase transitions (Dmitry Dyakonov also wrote about this). The last of the phase transitions could have observable phenomena that cosmologists present as evidence of standard cosmological theory. Therefore, the observations do not contradict this hypothesis.

There is another interesting aspect here. To make calculations related to the effect, there is no need to measure the potential at all. In order to calculate the force that acts on the hair and its additional energy, it is necessary to measure the electrical charge (the number of electrons) that has gone into the boy's body, and also to know the geometric characteristics of the boy's body, including the characteristics of his hair, the size and location of surrounding electrically conductive bodies.

Answer

If the boy is inside a Faraday cage, then as far as I understand, even with electric power. contact with it, he will never receive email on his surface. charge.
When a cell is connected to a charged ball, the entire charge will be distributed over the surface of the cell. There will be no electricity inside it. stat. field, no charge. The potential on the boy's surface will also be zero and his hair will remain in place. I think even if he picks up a grounded wire in his hands, nothing will come of it to him. No charge, no potential difference, no current.
Those. in short, by placing the boy in a cage, you will thereby reset his email. potential. The potential will be invisible, because it's simply not there. :-)
The effect with potential difference can also be observed. To do this, it is enough to place another ball next to the boy, connected to another source or simply grounded. Now if the boy touches both balls at once, he will feel for himself what a potential difference is (children, don’t do this!).
Email We see potential not only through hair. There is another beautiful effect - St. Elmo's lights or simply - corona discharge: http://molniezashitadoma.ru/ogon%20elma.jpg

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> the beautiful effect with the boy’s hair is associated not with the potential of the electric field, but with the potential difference between the boy’s body and the environment (in other words, with the electric field strength)

Electrical tension Art. fields are not potential differences at all. ;-)
This is the main characteristic of el. Art. field, which characterizes each of its points: https://ru.wikipedia.org/wiki/Electric_field_tension
_______________

As for Dmitry Dyakonov, his statements seem strange to me, to put it mildly... Perhaps he was too carried away by his “quarks” and noticeably disconnected from the real world. :-)

How old was Bohr when he saved physics from the fall of an electron onto a nucleus with his statement that the fall occurs in jumps? Because orbits can be divided into clean and unclean!
So it worked out and share!
How old was Maxwell when he invented the electromagnetic field?
And many people understand that there is polarization!
Sometimes I feel like we've had a lot of respect drilled into us at too early an age.
I would be very grateful to Igor Ivanov if he made some excursion into the age of the great discoverers.
Sometimes it still seems to me that physics is afraid of clear formulations.
Or is he shying away?
....................
Not criticism, but balance.
Ege?

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I believe that Avogadro's law is true for all atoms (all chemical elements) without exception.
And I DO NOT KNOW what the weight of one atom is.
In the experiment that is described, there is NO parallel with the conditions of the “Avogadro test”. But there were different atoms there?
There is a possibility that we are trying to understand something completely different from what the experimenters wanted to find out.
........................
And how old are they, by the way?

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The problem of the movement of planet Earth relative to the Sun is the problem of three magnets. Two magnets of the same polarity directed towards each other are the Earth in its plane relative to the axis of the Sun. The Sun is the third magnet, spinning the Earth and other planets relative to their axes in proportion to their masses. The elliptical orbit of the Earth indicates that there is still some force acting from the “winter” chord of the ellipse. Cold small bodies of space also do not move freely in space, they have acquired acceleration. This study can only confirm that the gravitational force of the planets arises due to the sufficiently heated bases of the planets. That is, any planet in the solar system is hot inside.
Why aren't the Earth and other planets pulled close to the Sun? The system is dynamic, not static, the axes of the planets are parallel, so there are many tops. And the planets cannot change their poles, since this is equivalent to leaving their orbit.

- Do you think that it is possible for a body with a magnetic field and a satellite to move by inertia for an infinitely long time? In this case, the Earth should have two moons, located symmetrically. The behavior of the gyroscope explains the moment of inertia, and the equilibrium distribution of mass relative to the axis of rotation. If there is an imbalance on the top's disk relative to the axis, then its axis begins to describe a spiral. This also applies to the Earth; it has one satellite, which should have brought it out of orbit and carried it into space if its motion relative to the Sun were explained only by the mechanical moment of inertia. Here, magnetism from the Sun takes place so strong that it can compensate for the influence of the Moon on the Earth.
  The ordered movement of the planets and their satellites in the Solar System cannot be explained by anything other than magnetism. We, in the form of the Sun, have a kind of stator, being a rotor, but at the same time we are a stator for the Moon.
  
  Answer
  - Magnetic and electric fields are shielded, Ambrose. More precisely, they are shunted. But right now it doesn't matter.):
    How do you imagine a spring scale with a kilogram weight after covering it with a magnetic shield? Will the arrow run from right to left?
    It seemed to me that the gyroscope was a wonderful subject for developing thinking. Even the Chinese think so.
    Just think about it. The gyroscope can be freely moved along any of the three Cartesian axes! If you don’t notice the tilt of the gyroscope’s own axis in its reference to some imaginary base.
    For example, you can remove your mind's eye from the top until it becomes so small for the observer that thoughts will not arise to draw the axis of rotation through this “point”.
    By the way, Ambrose, have you ever had any thoughts about the axes of rotation of infinitesimal points?
    ............
    And so, this exceptional property of the gyroscope prompted scientists to look for the nature of ITS inertia, specific only to the gyroscope!
    Perhaps this was the first step of “science” back into the future of metaphysics. The first step that did not cause immune rejection by society. (the men have never seen such sadness in their lives)
    ....................
    Several years have passed.
    One genius suggested that the nature of the inertia of a material body is not inside the body, but in the space surrounding this body.
    This conclusion was as simple as it was stunning.
    Moreover, as a model for studying the nature of inertia, the gyroscope turned out to be the most convenient tool. After all, in laboratory settings it is easily accessible for observation! Unlike, for example, a stream of projectiles. Even if this flow is limited by a steel pipe.
    Can you imagine what a giant step science has taken?
    .................
    Well, yes.
    And I have no idea.
    Think Ambrose.
    Think.
    
    Answer
    - “One genius suggested that the nature of the inertia of a material body is not inside the body, but in the space surrounding this body.”
      I wonder if you are writing about the swing principle?
      But I'm talking about mine. What I wrote here (post dated 09/20/2017 08:05) refers to “spatial symmetry”. (Don't look for this term on the Internet as I use it). There in the post there was talk about the 4D case of spatial symmetry. (The fourth spatial coordinate is directed outward from the point.) In general, the directions of spatial symmetry are not equal. And this can be shown using a top (gyroscope) for one coordinate. Let's take a number axis. There is a direction of the number axis in the positive direction. And there is a negative one. So, these directions are not equal. If we move in the negative direction, then on this axis we will not find real numbers that are equal to the square root of the coordinate of this axis. The negative axis turns out to be sparse. In space it is impossible to clearly distinguish where the positive direction is and where the negative direction is. However, you can separate them using a top. The top, when moving in the direction along the axis of the top, forms a screw. Right and left. We will take the direction of the right screw as a positive direction, and the left one as a negative one. In this case, the positive and negative directions can be separated. So, in nature there are processes that sense the difference between movement in the positive and negative directions - or, in other words, they feel the rarefaction of the negative axis.
      Here http://old.site/nauchno-populyarnaya_biblioteka/43375 0/Mnogo_vselennykh_iz_nichego in a commentary to the article “Many universes from nothing” by the wonderful science fiction writer Pavel Amnuel, I wrote a point of view on the movement of the mother in our universe using “spatial symmetry”. This comment is a continuation of the post from 09/20/2017 08:05. This is exactly on the topic of the article under discussion. I would like to know your opinion.
      
      Answer
      - Unfortunately, I have not yet found your second comment on the article based on Amnuel. And only from 02.09.17. Perhaps I'm just not that deterministic?):
        There was a mention of Planck (as a spacecraft... a man and a steamship...)
        Actually interesting. When I realized that he calculated the constant of his name by simply dividing the known result by the Rayleigh formula, I almost burst with anger. Back in bursa, I also chipped off something similar. It turns out that not many people can see the relationships between formulas without bothering themselves with their exact modeling. ... How else would you spread this on bread?
        ):
        There was actually an interesting story there. People have invented the abstraction of an absolutely black body, which does not exist in nature.
        So take it, and find it!
        And what?
        Did scientists call space the firmament of heaven?
        - Figurines! Yes?
        They simply added matter to it, mixing it with energy.
        Well, at least that way.
        Even in that article, the possibility of a “collision of universes” is suggested.
        It is easier.
        -----------
        Now I will start with the second “if”, and I will mention the first later.
        Can?
        If we can distinguish two (several, as many as necessary) universes, then each of them must have a feature that phenomenologically allows such a selection.
        Scientists once tried to list such features in the so-called “set theory”.
        We will do it a little simpler. - Obviously, it is phenomenologically (from the point of view of convenience of describing the “collision”) that we can describe each of the universes simply as a “shell before the collision.”
        IF this is so, then our mind can operate
        COLLISION OF SHELLS.
        And if this is not so, then the mind that allowed the collision of universes is still mature, but not enough.
        IF two (several) shells collide, then...
        and now the first one will go if:
        IF the space of the initial and resulting shells is THREE DIMENSIONAL, then, in particular, a plane is formed.
        For example, the ecliptic plane.
        Which we were privileged to observe.
        Everything else is of less importance to me for now.
        It’s already getting long, and I haven’t answered the direct question yet. So I apologize in advance.
        No, I meant the main position of GTR.
        I first learned about Mach and his world center from my father. Still at school. By the way, I agree with you. - The idea formulated by Einstein “hovered in the atmosphere” created, in many respects, by the work of Mach. It's a pity that this is not included in the school curriculum.
        
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Thermal radiation of bodies

Main questions of the topic:

1. Characteristics of thermal radiation.

2. Laws of thermal radiation (Kirchhoff’s law, Stefan-Boltzmann law, Wien’s law); Planck's formula.

3. Physical foundations of thermography (thermal imaging).

4. Heat transfer from the body.

Any body at temperatures above absolute zero (0 K) is a source of electromagnetic radiation, which is called thermal radiation. It arises due to the internal energy of the body.

The range of electromagnetic wavelengths (spectral range) emitted by a heated body is very wide. In the theory of thermal radiation, it is often considered that the wavelength here varies from 0 to ¥.

The distribution of the energy of thermal radiation of a body over wavelengths depends on its temperature. At room temperature, almost all the energy is concentrated in the infrared region of the electromagnetic wave scale. At high temperatures (1000°C), a significant part of the energy is emitted in the visible range.

Characteristics of thermal radiation

1. Flux (power) of radiation F(sometimes indicated by the letter R) – energy emitted in 1 second from the entire surface of a heated body in all directions in space and in the entire spectral range:

, in SI . (1)

2. Energy luminosity R– energy emitted in 1 second from 1 m2 of body surface in all directions of space and in the entire spectral range. If S is the surface area of the body, then

, , in SI , (2)

It's obvious that .

3. Spectral luminosity density r λ- energy emitted in 1 second from 1 m 2 of body surface in all directions at wavelength λ in a single spectral range , →

Rice. 1

The dependence of r l on l is called spectrum thermal radiation of a body at a given temperature (at T= const). The spectrum gives the distribution of energy emitted by a body across wavelengths. It is shown in Fig. 1.

It can be shown that the energetic luminosity R equal to the area of the figure limited by the spectrum and axis (Fig. 1).

4. The ability of a heated body to absorb the energy of external radiation is determined monochromatic absorption coefficient a l,

those. a l equal to the ratio of the flux of radiation with wavelength l absorbed by the body to the flux of radiation of the same wavelength incident on the body. From (3.) it follows that and l – dimensionless quantity and .

By type of addiction A from l all bodies are divided into 3 groups:

1). Absolutely black bodies:

A= 1 at all wavelengths at any temperatures (Fig. 3, 1 ), i.e. A completely black body completely absorbs all radiation incident on it. There are no “absolutely black” bodies in nature; a model of such a body can be a closed opaque cavity with a small hole (Fig. 2). The beam entering this hole, after repeated reflections from the walls, will be almost completely absorbed.

The sun is close to a completely black body, its T = 6000 K.

2). Gray bodies: their absorption coefficient A < 1 и одинаков на всех длинах волн при любых температурах (рис. 3, 2 ). For example, the human body can be considered a gray body in problems of heat exchange with the environment.

3). All other bodies:

for them the absorption coefficient A< 1 и зависит от длины волны, т.е. A l = f(l), this dependence represents the absorption spectrum of the body (Fig. 3 , 3 ).

Thermal radiation - Electromagnetic radiation , the source of which is the energy of thermal motion of atoms and molecules

1. Characteristics of thermal radiation

Thermal radiation - This is the electromagnetic radiation of atoms and molecules that arises during their thermal movement.

If the radiating body does not receive heat from the outside, then it cools and its internal energy decreases to the average energy of thermal motion of particles of the environment. Thermal radiation is characteristic of all bodies at temperatures above absolute zero.

The characteristics of thermal radiation are radiation flux, energy luminosity, spectral density of energy luminosity, absorption coefficient.

Radiation flux F (radiant flux) is the average radiation power over a time significantly longer than the period of light oscillations:

In SI, radiation flux is measured in Watts (W).

The radiation flux per unit surface is called energetic luminosity yuR (radiant flux density):

. (2)

The SI unit of luminosity is 1 W/m2.

A heated body emits electromagnetic waves of various lengths. Let us select a small integral of wavelengths from  to  + d.

The energetic luminosity corresponding to this interval is proportional to the width of the interval:

. (3)

Where r  -spectral density of energy luminosity of a body , equal to the ratio of the energy luminosity of a narrow section of the spectrum to the width of this section. Unit of measurement r  in SI is 1 W/m3.

The dependence of the spectral density of energetic luminosity on wavelength is called body radiation spectrum .

Having integrated (3), we obtain an expression for the energetic luminosity of the body:

. (4)

The integration limits are taken in excess to take into account all possible thermal radiation.

The body's ability to absorb radiant energy is characterized by absorption coefficient.

Absorption coefficient equal to the ratio of the flux of radiation absorbed by a given body to the flux of radiation incident on it.

. (5)

The absorption coefficient depends on the wavelength, therefore for monochromatic flows the concept is introduced monochromatic absorption coefficient:

. (6)

The concepts of a completely black body and a gray body.

From formulas (5 and 6) it follows that absorption coefficients can take values from 0 to 1. Black bodies absorb radiation well: black paper, fabrics, velvet, soot, platinum black, etc. Body radiation with white and mirror surfaces absorbs radiation poorly. A body whose absorption coefficient is equal to unity for all frequencies is called absolutely black . It absorbs all radiation falling on it. A completely black body is a physical abstraction. There are no such bodies in nature. The model of an absolutely black body is a small hole in a closed opaque cavity (Fig.). A beam entering this hole, reflected many times from the walls, will be almost completely absorbed. Therefore, with a small hole in a large cavity, the beam will not be able to exit, that is, it will be completely absorbed. A deep hole, an open window not illuminated from inside the room, a well are examples of bodies approaching the characteristics of absolutely black.

Rice. 1. Model of a completely black body.

A body whose absorption coefficient is less than unity and does not depend on the wavelength of light incident on it is calledgray . There are no gray bodies in nature, but some bodies in a certain wavelength range emit and absorb as gray bodies. For example, the human body is sometimes considered gray, having an absorption coefficient of 0.9.

At the end of the 19th - beginning of the 20th centuries. discovered by V. Roentgen - X-rays (X-rays), A. Becquerel - the phenomenon of radioactivity, J. Thomson - electron. However, classical physics was unable to explain these phenomena.

A. Einstein's theory of relativity required a radical revision of the concept of space and time. Special experiments confirmed the validity of J. Maxwell's hypothesis about the electromagnetic nature of light. It could be assumed that the emission of electromagnetic waves by heated bodies is due to the oscillatory motion of electrons. But this assumption had to be confirmed by comparing theoretical and experimental data.

For theoretical consideration of the laws of radiation we used black body model , i.e. a body that completely absorbs electromagnetic waves of any length and, accordingly, emits all lengths of electromagnetic waves.

Austrian physicists I. Stefan and L. Boltzmann experimentally established that the total energy E, emitted per 1 black body per unit surface, proportional to the fourth power of absolute temperature T:

Where s = 5.67. 10 -8 J/(m 2. K-s) is the Stefan-Boltzmann constant.

This law was called Stefan-Boltzmann law. It made it possible to calculate the radiation energy of a completely black body from a known temperature.

Planck's hypothesis

In an effort to overcome the difficulties of the classical theory in explaining black body radiation, M. Planck in 1900 put forward the hypothesis: atoms emit electromagnetic energy in separate portions - quanta . Energy E

Where h=6.63 . 10 -34 J . c-Planck's constant.

Sometimes it is convenient to measure energy and Planck's constant in electron volts.

Then h=4.136 . 10 -15 eV . With. In atomic physics the quantity is also used

(1 eV is the energy that an elementary charge acquires when passing through an accelerating potential difference of 1 V. 1 eV = 1.6...10 -19 J).

Thus, M. Planck indicated a way out of the difficulties encountered by the theory of thermal radiation, after which a modern physical theory began to develop, called quantum physics.

Photo effect

Photoeffect called the emission of electrons from the surface of a metal under the influence of light. In 1888 G. Hertz discovered that when electrodes under high voltage are irradiated with ultraviolet rays, a discharge occurs at a greater distance between the electrodes than without irradiation.

The photoelectric effect can be observed in the following cases:

1. A zinc plate connected to an electroscope is charged negatively and irradiated with ultraviolet light. It discharges quickly. If you charge it positively, then the charge of the plate will not change.

2. Ultraviolet rays passing through the positive grid electrode hit the negatively charged zinc plate and knock out electrons from it, which rush towards the grid, creating a photocurrent recorded by a sensitive galvanometer.

Laws of the photoelectric effect

The quantitative laws of the photoelectric effect (1888-1889) were established by A. G. Stoletov.

He used a vacuum glass balloon with two electrodes. Light (including ultraviolet radiation) enters the cathode through quartz glass. Using a potentiometer, you can adjust the voltage between the electrodes. The current in the circuit was measured with a milliammeter.

As a result of irradiation, electrons knocked out of the electrode can reach the opposite electrode and create some initial current. As the voltage increases, the field accelerates the electrons and the current increases, reaching saturation, at which all the ejected electrons reach the anode.

If a reverse voltage is applied, the electrons are inhibited and the current decreases. With the so-called blocking voltage the photocurrent stops. According to the law of conservation of energy, where m is the mass of the electron, and υ max is the maximum speed of the photoelectron.

First Law

Investigating the dependence of the current in the cylinder on the voltage between the electrodes at a constant light flux to one of them, he established first law of the photoelectric effect.

The saturation photocurrent is proportional to the luminous flux incident on the metal .

Because The current strength is determined by the magnitude of the charge, and the luminous flux is determined by the energy of the light beam, then we can say:

h The number of electrons knocked out of a substance in 1 s is proportional to the intensity of light incident on this substance.

Second Law

By changing the lighting conditions on the same installation, A.G. Stoletov discovered the second law of the photoelectric effect: The kinetic energy of photoelectrons does not depend on the intensity of the incident light, but depends on its frequency.

From experience it follows that if the frequency of light is increased, then at a constant luminous flux the blocking voltage increases, and, consequently, the kinetic energy of photoelectrons also increases. Thus, the kinetic energy of photoelectrons increases linearly with the frequency of light.

Third Law

By replacing the photocathode material in the device, Stoletov established the third law of the photoelectric effect: for each substance there is a red limit of the photoelectric effect, i.e. there is a minimum frequency nmin, at which the photoelectric effect is still possible.

When n< n min ни при какой интенсивности волны падающего на фотокатод света фотоэффект не произойдет. Т.к. , тоminimum frequency light matches maximum wavelength.