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It is necessary to recall that in the model of “Logical Physics” by Rod Johnson we see the following:

There are no “solid particles”, there are only groupings of energy.
each quantum dimension can be geometrically explained as a form of structured, intersecting energy fields.
atoms are counter-rotating energy forms in the form of Platonic Solids, namely counter-rotating octahedron and tetrahedron. Moreover, each vibration/pulsating form corresponds to a certain basic density of the ether.
throughout the Universe, all levels of density or dimensions are structured from two primary levels of ether, continuously interacting with each other.

According to Johnson's model, there is a , which continuously intersects with our reality in every atom, at the tiniest level. Each atom has one geometry in our reality and an opposite, inverse geometry in parallel reality. The two geometries rotate in opposite directions within each other. Each stage of this process takes you through.

However, since traditional scientists have not yet visualized Plato's Solids nested within each other, dividing common axis and capable of spinning in opposite directions, they have lost the picture of quantum reality.

Most people already know that thermal radiation and light are created by something very simple—the movement of bursts of electromagnetic energy known as “photons.”

However, until 1900, it was believed that light and heat did not move in the form of discrete units of “photons,” but rather smoothly, fluidly, and inextricably. Physicist Max Planck was the first to discover that at the tiniest level, light and heat move in “pulsations” or “packets” of energy measuring 10 -32 cm (compared to this size, the atomic nucleus would be the size of a planet!)

Interestingly, the faster the oscillation, the larger the packets, and, accordingly, the slower the oscillation, the smaller the packets.

Planck discovered that the relationship between the speed of oscillation and the size of the packet always remains constant, no matter how you measure them. The constant relationship between swing speed and packet size is known as Wein's Distribution Law.

Planck discovered a single number expressing this ratio. It is now known as “Planck's Constant”.

An article by Caroline Hartman (December 2001 issue of the journal Science and Technology of the 21st Century) is devoted exclusively to the discoveries of Max Planck. She reveals that the puzzle created by his discoveries remains unsolved:

“Today, in order to gain deeper insight into the structure of the atom, it is our duty to continue the research of scientists such as Curie, Lise Meitner and Otto Hahn.
But the fundamental questions: What causes the movement of electrons, whether it obeys certain geometric laws, and why some elements are more stable than others, do not yet have answers and await new advanced hypotheses and ideas.”

In this note we can already see the answer to Hartman’s question. As we said, Planck's discoveries were made as a result of the study of thermal radiation. The introductory paragraph in Caroline Hartman's article is a perfect description of his achievements:

“One hundred years ago, on December 14, 1900, physicist Max Planck (1858-1947) announced the discovery of a new radiation formula that could describe all the patterns observed when matter is heated, when it begins to emit heat of different colors.
Moreover, the new formula was based on one important assumption - the radiation energy is not constant, radiation occurs only in packets of a certain size.
The difficulty is how to make the assumption behind the “formula” physically understandable. What is meant by “energy packets” that are not even constant, but change in proportion to the frequency of oscillation (Wein’s Law of Distribution)?”

A little later Hartman continues:

“Planck knew that whenever you come across a seemingly insoluble problem in Nature, there must be more complex patterns underlying it; in other words, there must be a different “geometry of the Universe” than previously thought.
For example, Planck always insisted that the reliability of Maxwell's equations should be reconsidered because physics had reached a stage of development at which the so-called “laws of physics” were no longer universal.”

The grain of Planck's work can be expressed simple equation, which describes how radiant matter releases energy in “packets” or bursts.

This equation E = hv, Where E is the final measured energy, v– frequency of vibration of the radiation releasing energy, and h– known as “Planck’s Constant”, which regulates the “flow” between v And E.

Planck's constant is 6,626 . It is an abstract expression because it expresses a pure relationship between two quantities and does not need to be assigned to any specific measurement category other than that.

Planck did not discover this constant by miracle; rather, he meticulously deduced it through the study of many different types thermal radiation.

This is the first major mystery that Johnson clears up in his research. He recalls that the (rectangular) Cartesian coordinate system is used to measure Planck's constant.

This system is named after its creator Rene Descartes and means that cubes are used to measure three-dimensional space.

It has become so commonplace that most scientists don't even consider it anything unusual - just its length, width and height.

Experiments such as Planck's use a small cube to measure energy moving through a specific region of space. In the Planck measurement system, for the sake of simplicity, this cube was naturally assigned a volume of “unit”.

However, when Planck wrote his constant, he didn't want to deal with a decimal number, so he shifted the volume of the cube to 10. This made the constant equal 6,626 instead of 0,6626 .

What was really important was the relationship between something inside the cube (6.626) and the cube itself (10).

It doesn't matter whether you assign the cube a volume of one, ten, or any other number, since the ratio always remains constant. As we have said, Planck unraveled the constant nature of this relationship only through meticulous experiments over many years.

Remember that depending on the size of the bag you are releasing, you will need to measure it using a different sized cube.

And yet, whatever is inside the cube will always have 6.626 cube volume units if the cube itself has a volume of 10 units, regardless of the dimensions involved.

Right now it should be noted - the magnitude 6,626 very close to 6,666 , which is exactly 2/3 of 10. Therefore, one should ask: “Why are they so important? 2/3 ?”

Based on simple measurable geometric principles explained by Fuller and others, we know that if a tetrahedron were placed perfectly inside a sphere, it would fill exactly 1/3 of the total volume of the sphere. That is 3.333 from 10.

In fact a photon consists of two tetrahedra joined together, which is what we see in the figure.

The total volume (energy) moving through the cube will be exactly 2/3 (6.666) of the total volume of the cube, which Planck assigned the number 10 to.

Buckminster Fuller was the first to discover that a photon is composed of two tetrahedra. He announced this to the world in 1969 at Planet Planning, after which it was completely forgotten.

A small difference of 0.040 between the “net” 6.666 or 2/3 ratio and Planck's constant of 6.626 is created specific vacuum capacity, which absorbs some energy.

The specific capacitance of a vacuum can be calculated accurately using what is known as the Coulomb equation.

In simpler terms, the aetheric energy of the “physical vacuum” will absorb a small amount of any energy passing through it.

Therefore, as soon as we take into account the Coulomb equation, the numbers work perfectly. Moreover, if we measure space using tetrahedral coordinates instead of cubic ones, there is no need for Planck's equation E = hv. In this case, energy will be measured equally on both sides of the equation, that is, E (energy) will equal v (frequency), and there is no need for a “constant” between them.

The “ripples” of energy demonstrated by Planck's constant are known to quantum physicists as “photons.” We usually think of “photons” as carriers of light, but this is only one of their functions.

What's more important is that When atoms absorb or release energy, it is transferred in the form of “photons.”

Researchers such as Milo Wolf remind us that the only thing we know for sure about the term “photon” is that it is impulse passing through the ether/energy field of the zero point.

Now we can see that this information contains a geometric component, which suggests that atoms must also have the same geometry.

Another discovered anomaly that demonstrates the presence of geometry at the quantum level is Bell's Unevenness Theorem.

In this case, two photons are released in opposite directions. Each photon is emitted from a separate excited atomic structure. Both atomic structures are made up of identical atoms, and both decay at the same rate.

This allows two “paired” photons with the same energetic qualities to be released simultaneously in opposite directions. Both photons then pass through polarizing filters such as mirrors, which should theoretically change the direction of travel.

If one mirror is positioned at an angle of 45 o and the other at an angle of 30 o, it would be natural to expect that the angular rotations of the photons would be different.

However, when this experiment was performed, despite the difference in the angles of the mirrors, the photons simultaneously made the same angular rotation!

The degree of accuracy of the experiment is staggering, as described in the book by Milo Wolf:

“In the most recent experiment by Elaine Aspect, to completely eliminate any possibility of local influences from one detector to another, Dalibard and Roger used acoustic-optical switches at a frequency of 50 MHz, shifting sets of polarizers during the flight of photons ...

Bell's theorem and the results of the experiment indicate that parts of the Universe are connected to each other at some internal level (that is, not obvious to us), and these connections are fundamental (quantum theory is fundamental).

How can we understand them? And although the problem has been analyzed very deeply (Wheeler and Zurek, 1983; d'Espagnat, 1983; Herbert, 1985; Stap, 1982; Bohm and Healy, 1984; Pagels, 1982; and others), a solution has not been found.

The authors tend to agree with the following description of nonlocal connections:
1. They connect events in separate places without known fields or matter.
2. They do not weaken with distance; be it a million kilometers or a centimeter.
3. They appear to travel faster than the speed of light.”

Undoubtedly, within the framework of science, this is a very puzzling phenomenon.

Bell's theorem states that energetically paired “photons” are actually held together by a single geometric force, namely the tetrahedron, which continues to expand (get larger) as the photons separate.

As the geometry between them expands, the photons will continue to maintain the same angular phase position relative to each other.

The next point of study is the electromagnetic wave itself.

As most people know, an electromagnetic wave has two components—an electrostatic wave and a magnetic wave—that move together. Interestingly, the two waves are always perpendicular to each other.

To visualize what is happening, Johnson asks to take two pencils of the same length and set them perpendicular to each other; and the distance between them should be equal to the length of the pencil:

Now we can connect each end of the top pencil to each end of the bottom pencil. By doing this, we get a four-sided object made up of equilateral triangles between two pencils, that is, a tetrahedron.

The same process can be done with an electromagnetic wave by taking the total height of the electrostatic or magnetic wave (which have the same height or amplitude) as the fundamental length, like the pencils in the picture.

In the figure below you can see that if we connect the lines using the same process, the electromagnetic wave actually copies the “hidden” (potential) tetrahedron:

It is important to mention here that this secret has been repeatedly discovered by various thinkers only to be forgotten by science again.

Tom Bearden's work has shown conclusively that James Clerk Maxwell knew this when he wrote his complex “quaternion” equations.

The hidden tetrahedron is also observed by Walter Russell, and later by Buckminster Fuller. While making his discoveries, Johnson was unaware of previous breakthroughs.

The next point to consider is spin*. For many years, physicists have known that energetic particles “spin” when they move.
* spin (spin, - rotation), the actual moment of momentum of a microparticle, which has a quantum nature and is not associated with the movement of the particle as a whole; measured in units of Planck's constant and can be an integer (0, 1, 2,...) or a half-integer (1/2, 3/2,...)

For example, it seems that, while moving in an atom, “electrons” continuously make sharp turns of 180 o or “half spins”.

It is often observed that “quarks” undergo “1/3” or “2/3” spin as they move, which allowed Gell-Mann to organize their motions into tetrahedrons or other geometries.

None of the representatives of traditional science has given an adequate explanation of why this happens.

Johnson's model shows that the 180 o "spin" of the electron clouds is created by the motion of the octahedron.

It is important to realize that the 180 o motion actually results from two 90 o rotations of each octahedron.

To remain in the same position in the matrix of the geometry surrounding it, the octahedron must “tip back”, that is, 180 o.

The tetrahedron, in order to remain in the same position, must perform either 120 o (1/3 spin) or 240 o (2/3 spin) of rotation. The same process explains the mystery of the spiral movement of torsion waves. Wherever you are in the Universe, even “in a vacuum,” the ether will always pulsate in these geometric shapes, forming a matrix.

Therefore, any momentary impulse moving in the ether will pass along the edges of geometric “liquid crystals” in the ether.

Therefore, the spiral motion of a torsion wave is created by the simple geometry that the wave must pass through as it travels.

FINE STRUCTURE CONSTANT

The fine structure constant is more difficult to visualize than the previous constants.

We have included this section for those who would like to see how far the “matrix” model goes. The fine structure constant is another aspect of quantum physics that some mainstream scientists have not even heard of, perhaps because it is completely inexplicable to those who tend to believe in particle-based models.

Think of the electron cloud as being like a flexible rubber ball, and every time a “photon” of energy is absorbed or released (known as pairing), the cloud stretches and flexes as if it is shaking.

The electron cloud will always "hit" in a fixed, precise proportion to the size of the photon.

This means that photons bigger size will have larger “impacts” on the electron cloud, smaller photons will have smaller “impacts” on the electron cloud. This ratio remains constant regardless of the units of measurement.

Like Planck's constant, the fine-structure constant is another “abstract” number. This means that we will get the same proportion, no matter in what units we measure it.

This constant has been continuously studied through spectroscopic analysis, and in his book Strange theory of light and matter physicist Richard P. Feynman explained this mystery. (It should be remembered that the word “pairing” means the joining or separation of a photon and an electron.)

"There is a very deep and beautiful question related to the observed pairing constant e, - the amplitude of a real electron to emit or absorb a real photon. This simple experimentally determined number is close to 0,08542455 .
Physicists prefer to remember this number as the inverse of its square - about 137,03597 with the last two decimal places uncertain.
It remains a mystery today, although it was discovered more than 50 years ago.
You would immediately want to know where the mating number came from: is it related to π or perhaps with the base of natural logarithms?
No one knows this, this is one of the greatest mysteries of physics - a magic number that has come to us and is not understandable to humans.
We know what type of dance should be practiced for very precise measurement this number, but we do not know what type of dance should be performed on the computer in order to get this number, without making a secret of it."

In Johnson's model, the fine structure constant problem has a very simple academic solution.

As we said, the photon moves along two tetrahedrons connected together, and the electrostatic force inside the atom is supported by the octahedron.

We obtain the fine structure constant simple comparison volumes of a tetrahedron and octahedron upon their collision. Everything we do is divide the volume of the tetrahedron inscribed in the sphere by the volume of the octahedron inscribed in the sphere. We obtain the fine structure constant as the difference between them. To show how this is done requires some further explanation.

Since a tetrahedron is completely triangular, no matter how it is rotated, the three vertices of any of its faces will divide the circle into three equal parts of 120 o each.

Therefore, to bring the tetrahedron into balance with the geometry of the matrix surrounding it, you only need to rotate it 120 o so that it ends up in the same position as before.

This is easy to see if you visualize a car with triangular wheels and want it to move so that the wheels look like they did before. To do this, each triangular wheel must turn exactly 120 o.

In the case of an octahedron, to restore equilibrium it always has to be turned “upside down” or 180 o.

If you liked the car analogy, then the wheels should be shaped like a classic diamond.

To make the diamond look the same as it did at the beginning, you will have to turn it upside down, that is, 180 o.

The following quote from Johnson explains the fine structure constant based on this information:

“(If you) consider the static electric field as an octahedron and the dynamic magnetic field as a tetrahedron, then the geometric ratio (between them) is 180:120.

If you consider them as spheres with volumes expressed in radians, simply divide the volumes by each other and you will get a fine-grained constant.”

The term “volume in radians” means that you calculate the volume of an object in terms of its radius, which is half the width of the object.

Interesting: after Johnson showed that the fine structure constant can be thought of as the relationship between an octahedron and a tetrahedron, as energy moving from one to the other, Jerry Iuliano discovered that it can be thought of as the “residual” energy that arises when we squeeze sphere into a cube or expand the cube into a sphere!

Such changes of expansion and contraction between two objects are known as “tessellation,” and Iuliano's calculations are not difficult to perform, it's just that no one had thought of doing it before.

In Iuliano's calculations, the volume of the two objects does not change; Both the cube and the sphere have volume 8π·π 2 .

If we compare them to each other, the only difference is the amount of surface area. The additional surface area between the cube and the sphere is equal to the fine-structure constant.

You ask: “How can a fine-structure constant be both the relation between an octahedron and a tetrahedron and the relation between a cube and a sphere?”

This is another aspect of the magic of “symmetry” at work, where we see that different geometric shapes can have the same properties because they all nest within each other with perfect harmonious relationships.

The views of both Johnson and Iuliano demonstrate that we are dealing with the work of geometrically structured energy in the atom.

It is also important to remember that Iuliano's discoveries demonstrate the classical geometry of “squaring the circle.”

This position has long been a central element in the esoteric traditions of “sacred geometry,” as it was believed to show the balance between the physical world, represented by the square or cube, and the spiritual world, represented by the circle or sphere.

And now we can see that this is another example of “hidden knowledge” encrypted in a metaphor so that over time people will regain a true understanding of the secret science behind the metaphor.

They knew that until we discovered the fine structure constant, we would not understand what we were observing. That is why this ancient knowledge was preserved - to show us the key.

And the key is that sacred geometry has always been present in quantum reality; it has simply remained unexplained until now, as conventional science continues to be shackled to old-fashioned “particle” models.

In this model, it is no longer necessary to limit atoms to a certain size; they are able to expand and retain the same properties.

Once we understand what is happening in the quantum realm, we will be able to create materials that are ultra-strong and ultra-light, because we now know the precise geometric arrangements that force atoms to bond together more efficiently.

It was said that the pieces of the wreckage at Roswell were incredibly light and yet so strong that they could not be cut, burned or destroyed. These are the kinds of materials we will be able to create once we fully understand the new quantum physics.

We remember that quasicrystals They store heat very well and often do not conduct electricity, even if the metals in their composition are naturally good conductors.

Likewise, microclusters do not allow magnetic fields to penetrate into the clusters themselves.

Johnson's physics states that such a geometrically perfect structure is perfectly connected, so no thermal or electromagnetic energy can pass through it. The internal geometry is so compact and precise that there is literally no “room” for the current to move between the molecules.

Planck's constant defines the boundary between the macroworld, where Newton's laws of mechanics apply, and the microworld, where the laws of quantum mechanics apply.

Max Planck, one of the founders of quantum mechanics, came to the ideas of energy quantization while trying to theoretically explain the process of interaction between recently discovered electromagnetic waves ( cm. Maxwell's equations) and atoms and thereby solve the problem of black body radiation. He realized that to explain the observed emission spectrum of atoms, it is necessary to take for granted that atoms emit and absorb energy in portions (which the scientist called quanta) and only at certain wave frequencies. The energy transferred by one quantum is equal to:

Where v is the radiation frequency, and h — elementary quantum of action, representing a new universal constant, which soon received the name Planck's constant. Planck was the first to calculate its value based on experimental data h = 6.548 × 10 -34 J s (in the SI system); according to modern data h = 6.626 × 10 -34 J s. Accordingly, any atom can emit a wide spectrum of interconnected discrete frequencies, which depends on the orbits of the electrons in the atom. Niels Bohr would soon create a coherent, albeit simplified, model of the Bohr atom, consistent with the Planck distribution.

Having published his results at the end of 1900, Planck himself - and this is clear from his publications - at first did not believe that quanta were a physical reality and not a convenient one. mathematical model. However, when five years later Albert Einstein published a paper explaining the photoelectric effect based on energy quantization radiation, in scientific circles Planck's formula was no longer perceived as a theoretical game, but as a description of a real physical phenomenon at the subatomic level, proving the quantum nature of energy.

Planck's constant appears in all equations and formulas of quantum mechanics. In particular, it determines the scale from which the Heisenberg uncertainty principle comes into force. Roughly speaking, Planck's constant shows us the lower limit of spatial quantities beyond which quantum effects cannot be ignored. For grains of sand, say, the uncertainty in the product of their linear size and speed is so insignificant that it can be neglected. In other words, Planck’s constant draws the boundary between the macrocosm, where Newton’s laws of mechanics apply, and the microcosm, where the laws of quantum mechanics come into force. Having been obtained only for a theoretical description of a single physical phenomenon, Planck’s constant soon became one of the fundamental constants of theoretical physics, determined by the very nature of the universe.

Physical meaning

In quantum mechanics, impulse has the physical meaning of a wave vector, energy - frequency, and action - wave phase, but traditionally (historically) mechanical quantities are measured in other units (kg m/s, J, J s) than the corresponding wave ones (m −1, s−1, dimensionless phase units). Planck's constant plays the role of a conversion factor (always the same) connecting these two systems of units - quantum and traditional:

(impulse) (energy) (action)

If the system physical units was formed after the emergence of quantum mechanics and was adapted to simplify the basic theoretical formulas, Planck’s constant would probably simply be made equal to one, or, in any case, a more round number. In theoretical physics, the system of units c is very often used to simplify formulas, in it

Planck's constant also has a simple evaluative role in delimiting the areas of applicability of classical and quantum physics: it is compared with the magnitude of the action or angular momentum characteristic of the system under consideration, or the product of the characteristic impulse by characteristic size, or characteristic energy for a characteristic time, shows how applicable classical mechanics is to a given physical system. Namely, if is the action of the system, and is its angular momentum, then at or the behavior of the system is described with good accuracy by classical mechanics. These estimates are quite directly related to the Heisenberg uncertainty relations.

History of discovery

Planck's formula for thermal radiation

Main article: Planck's formula

Planck's formula is an expression for the spectral power density of black body radiation, which was obtained by Max Planck for the equilibrium radiation density. Planck's formula was obtained after it became clear that the Rayleigh-Jeans formula satisfactorily describes radiation only in the long-wave region. In 1900, Planck proposed a formula with a constant (later called Planck's constant), which was in good agreement with experimental data. At the same time, Planck believed that this formula was just a successful mathematical trick, but had no physical meaning. That is, Planck did not assume that electromagnetic radiation is emitted in the form of individual portions of energy (quanta), the magnitude of which is related to the frequency of the radiation by the expression:

The proportionality coefficient was later called Planck's constant, = 1.054·10−34 J·s.

Photo effect

Main article: Photo effect

The photoelectric effect is the emission of electrons by a substance under the influence of light (and, generally speaking, any electromagnetic radiation). condensed substances (solid and liquid) produce external and internal photoelectric effects.

The photoelectric effect was explained in 1905 by Albert Einstein (for which he received the Nobel Prize in 1921, thanks to the nomination of the Swedish physicist Oseen) on the basis of Planck's hypothesis about the quantum nature of light. Einstein's work contained an important new hypothesis - if Planck suggested that light is emitted only in quantized portions, then Einstein already believed that light exists only in the form of quantized portions. From the law of conservation of energy, when representing light in the form of particles (photons), Einstein’s formula for the photoelectric effect follows:

where - so-called work function (the minimum energy required to remove an electron from a substance), - the kinetic energy of the emitted electron, - the frequency of the incident photon with energy, - Planck's constant. This formula implies the existence of the red limit of the photoelectric effect, that is, the existence of the lowest frequency below which the photon energy is no longer sufficient to “knock out” an electron from the body. The essence of the formula is that the energy of a photon is spent on ionizing an atom of a substance, that is, on the work necessary to “tear out” an electron, and the remainder is converted into the kinetic energy of the electron.

Compton effect

Main article: Compton effect

Measurement methods

Using the laws of the photoelectric effect

At this method Measurements of Planck's constant use Einstein's law for the photoelectric effect:

where is the maximum kinetic energy of photoelectrons emitted from the cathode,

The frequency of the incident light, - the so-called. electron work function.

The measurement is carried out like this. First, the cathode of the photocell is irradiated with monochromatic light at a frequency, while a blocking voltage is applied to the photocell so that the current through the photocell stops. In this case, the following relationship takes place, which directly follows from Einstein’s law:

where is the electron charge.

Then the same photocell is irradiated with monochromatic light with a frequency and is similarly locked using voltage

Subtracting the second expression term by term from the first, we get

whence follows

Analysis of the X-ray bremsstrahlung spectrum

This method is considered the most accurate of the existing ones. It takes advantage of the fact that the frequency spectrum of bremsstrahlung X-rays has a precise upper limit, called the violet limit. Its existence follows from the quantum properties of electromagnetic radiation and the law of conservation of energy. Really,

where is the speed of light,

The wavelength of the X-ray radiation, - the charge of the electron, - the accelerating voltage between the electrodes of the X-ray tube.

Then Planck's constant is

Notes

1 2 3 4 Fundamental Physical Constants - Complete Listing
On the possible future revision of the International System of Units, the SI. Resolution 1 of the 24th meeting of the CGPM (2011).
Agreement to tie kilogram and friends to fundamentals - physics-math - 25 October 2011 - New Scientist

Literature

John D. Barrow. The Constants of Nature; From Alpha to Omega - The Numbers that Encode the Deepest Secrets of the Universe. - Pantheon Books, 2002. - ISBN 0-37-542221-8.
Steiner R. History and progress on accurate measurements of the Planck constant // Reports on Progress in Physics. - 2013. - Vol. 76. - P. 016101.

Planck's Constant Information About

Sokolnikov Mikhail Leonidovich,

Akhmetov Alexey Lirunovich

Sverdlovsk regional non-state fund

promoting the development of science, culture and art Patron of arts

Russia, Ekateriburg

Email: [email protected]

Abstract: The connection between Planck's constant and Wien's law and Kepler's third law is shown. Received exact value Planck constant for a liquid or solid state of aggregation of a substance, equal to

h = 4*10 -34 J*sec.

A formula has been derived that combines four physical constants - the speed of light - c, the Wien constant - b, the Planck constant - h and the Boltzmann constant - k

Keywords: Planck's constant, Wien's constant, Boltzmann's constant, Kepler's third law, quantum mechanics

The Foundation "Maecenas"
Sokolnikov M.L., Akhmetov A.L.

Yekaterinburg, Russian Federation

Email: [email protected]
Abstract: The connection to the Planck constant with Wien's displacement law and Kepler's third law. The exact value of Planck"s constant for the liquid or solid state of aggregation of matter equal to

h = 4*10 -34 J*s.
The formula that combines four physical constants - the speed of light - c,

Wien's displacement constant - in, Planck constant - h and the Boltzmann constant - k

Keywords: Planck constant, Wien's displacement constant, the Boltzmann constant, Kepler's third law, quantum mechanics

This physical constant was first stated by the German physicist Max Planck in 1899. In this article we will try to answer three questions:

1. What is the physical meaning of Planck’s constant?

2. How can it be calculated from real experimental data?

3. Is the statement that energy can be transferred only in certain portions – quanta – connected with Planck’s constant?

Introduction

Reading modern scientific literature, you involuntarily pay attention to how complex and sometimes vague the authors portray this topic. Therefore, in my article I will try to explain the situation in simple Russian language, without going beyond the level of school formulas. This story began in the second half of the 19th century, when scientists began to study in detail the processes of thermal radiation of bodies. To increase the accuracy of measurements in these experiments, special cameras were used, which made it possible to bring the energy absorption coefficient closer to unity. The design of these cameras is described in detail in various sources and I will not dwell on this, I will only note that they can be made from almost any material. It turned out that heat radiation is the radiation of electromagnetic waves in the infrared range, i.e. at frequencies slightly below the visible spectrum. During the experiments, it was found that at any specific body temperature, a peak of the maximum intensity of this radiation is observed in the spectrum of IR radiation of this body. With increasing temperature, this peak shifted towards shorter waves, i.e. to the region of higher frequencies of IR radiation. Graphs of this pattern are also available in various sources and I will not draw them. The second pattern was already truly surprising. It turned out that different substances at the same temperature have a radiation peak at the same frequency. The situation required a theoretical explanation. And then Planck proposes a formula connecting energy and frequency of radiation:

where E is energy, f is the radiation frequency, and h is a constant, which was later named after him. Planck also calculated the value of this quantity, which, according to his calculations, turned out to be equal to

h = 6.626*10 -34 J*sec.

Quantitatively, this formula does not describe real experimental data entirely accurately, and further you will see why, but from the point of view of a theoretical explanation of the situation, it completely corresponds to reality, which you will also see later.

Preparatory part

Next, we will recall several physical laws that will form the basis of our further reasoning. The first will be the formula for the kinetic energy of a body performing rotational motion along a circular or elliptical path. It looks like this:

those. the product of the body's mass and the square of the speed at which the body moves in orbit. The speed V is calculated using a simple formula:

where T is the period of revolution, and the radius of rotation is taken as R for circular motion, and for an elliptical trajectory, the semimajor axis of the trajectory ellipse. For one atom of a substance there is one formula that is very useful for us, connecting temperature with the energy of the atom:

Here t is the temperature in degrees Kelvin, and k is Boltzmann’s constant, which is equal to 1.3807*10 -23 J/K. If we take the temperature to be one degree, then, in accordance with this formula, the energy of one atom will be equal to:

(2) E = 4140*10 -26 J

Moreover, this energy will be the same for both the lead atom and the aluminum atom or any other atom chemical element. This is precisely the meaning of the concept “temperature”. From formula (1), valid for the solid and liquid state of matter, it is clear that the equality of energies for different atoms With different weight at a temperature of 1 degree is achieved only by changing the value of the square of the speed, i.e. the speed at which an atom moves in its circular or elliptical orbit. Therefore, knowing the energy of an atom at one degree and the mass of an atom expressed in kilograms, we can easily calculate the linear speed of a given atom at any temperature. Let us explain how this is done. specific example. Let's take any chemical element from the periodic table, for example, molybdenum. Next, take any temperature, for example, 1000 degrees Kelvin. Knowing from formula (2) the value of the energy of an atom at 1 degree, we can find out the energy of an atom at the temperature we take, i.e. multiply this value by 1000. It turns out:

(3) Energy of a molybdenum atom at 1000K = 4.14*10 -20 J

Now let's calculate the mass of a molybdenum atom, expressed in kilograms. This is done using the periodic table. In the cell of each chemical element, next to its serial number, its molar mass is indicated. For molybdenum it is 95.94. It remains to divide this number by Avogadro’s number equal to 6.022 * 10 23 and multiply the resulting result by 10 -3, since in the periodic table the molar mass is indicated in grams. It turns out 15.93 * 10 -26 kg. Further from the formula

mV 2 = 4.14*10 -20 J

calculate the speed and get

V = 510m/sec.

Now it’s time for us to move on to the next question of the preparatory material. Let us recall such a concept as angular momentum. This concept was introduced for bodies moving in a circle. You can use a simple example: take a short tube, pass a cord through it, tie a weight of mass m to the cord and, holding the cord with one hand, spin the load above your head with the other hand. By multiplying the value of the speed of movement of the load by its mass and radius of rotation, we obtain the value of the angular momentum, which is usually denoted by the letter L. That is.

By pulling the cord down through the tube, we will reduce the radius of rotation. At the same time, the speed of rotation of the load will increase and its kinetic energy will increase by the amount of work that you do by pulling the cord to reduce the radius. However, by multiplying the mass of the load by the new values of speed and radius, we get the same value that we got before we reduced the radius of rotation. This is the law of conservation of momentum. Back in the 17th century, Kepler proved in his second law that this law is also observed for satellites moving around planets in elliptical orbits. When approaching the planet, the speed of the satellite increases, and when moving away from it it decreases. In this case, the mVR product remains unchanged. The same applies to planets moving around the Sun. Along the way, let us remember Kepler's third law. You may ask - why? Then, in this article you will see something that is not written about in any scientific source - the formula of Kepler’s third law of planetary motion in the microcosm. And now about the essence of this very third law. In the official interpretation, it sounds rather ornate: “the squares of the periods of revolution of the planets around the Sun are proportional to the cubes of the semi-major axes of their elliptical orbits.” Each planet has two personal parameters - the distance to the Sun and the time during which it makes one full revolution around the Sun, i.e. circulation period. So, if the distance is cubed, and then the resulting result is divided by the period squared, you will get some kind of value, let’s denote it with the letter C. And if you perform the above mathematical operations with the parameters of any other planet, you will get the same magnitude - C. Somewhat later, on the basis of Kepler's third law, Newton deduced the Law of Universal Gravitation, and another 100 years later Cavendish calculated the true value of the gravitational constant - G. And only after that the true meaning of this very constant - C became clear. It turned out that this is an encrypted value of the mass of the Sun, expressed in units of length cubed divided by time squared. Simply put, knowing the distance of the planet to the Sun and its period of revolution, you can calculate the mass of the Sun. Skipping simple mathematical transformations, I will inform you that the conversion factor is equal to

Therefore, the formula is valid, the analogue of which we will meet later:

(4) 4π 2 R 3 /T 2 G = M sun (kg)

Main part

Now you can move on to the main thing. Let's look at the dimension of Planck's constant. From reference books we see that the value of Planck's constant

h = 6.626*10 -34 J*sec.

For those who have forgotten physics, let me remind you that this dimension is equivalent to the dimension

kg*meter 2 /sec.

This is the dimension of angular momentum

Now let's take the formula for atomic energy

and Planck's formula

For one atom of any substance at a given temperature, the values of these energies must coincide. Considering that the frequency is the inverse of the radiation period, i.e.

and the speed

where R is the radius of rotation of the atom, we can write:

m4π 2 R 2 /T 2 = h/T.

From here we see that Planck’s constant is not angular momentum in its pure form, but differs from it by a factor of 2π. So we have determined its true essence. All that remains is to calculate it. Before we start calculating it ourselves, let's see how others do it. Looking at the laboratory work on this topic, we will see that in most cases Planck's constant is calculated from the photoelectric effect formulas. But the laws of the photoelectric effect were discovered much later than Planck derived his constant. Therefore, let's look for another law. He is. This is Wien's law, discovered in 1893. The essence of this law is simple. As we have already said, at a certain temperature, a heated body has a peak in the intensity of IR radiation at a certain frequency. So, if you multiply the temperature value by the value of the IR radiation wave corresponding to this peak, you will get a certain value. If we take a different body temperature, then the radiation peak will correspond to a different wavelength. But here, when multiplying these quantities, the same result will be obtained. Wien calculated this constant and expressed his law as a formula:

(5) λt = 2.898*10 -3 m*degree K

Here λ is the wavelength of IR radiation in meters, and t is the temperature value in degrees Kelvin. This law can be equated in its significance to Kepler's laws. Now, by looking at a heated body through a spectroscope and determining the wavelength at which the radiation peak is observed, you can use the formula of Wien’s law to remotely determine the temperature of the body. All pyrometers and thermal imagers operate on this principle. Although it's not that simple. The emission peak shows that most atoms in a heated body emit exactly this wavelength, i.e. have exactly this temperature. And the radiation to the right and left of the peak shows that the body contains both “underheated” and “overheated” atoms. In real conditions, there are even several “humps” of radiation. Therefore, modern pyrometers measure the intensity of radiation at several points in the spectrum, and then the results obtained are integrated, which makes it possible to obtain the most accurate results. But let's return to our questions. Knowing, on the one hand, that from formula (1) the temperature corresponds to the kinetic energy of the atom through constant coefficient 3k, and on the other hand, the product of temperature and wavelength in Wien’s law is also a constant, expanding the square of the speed in the formula for the kinetic energy of an atom into factors, we can write:

m4π 2 R 2 λ/T 2 = constant.

In the left half of the equation m is a constant, which means everything else is on the left side

4π 2 R 2 λ/T 2 – constant.

Now compare this expression with the formula of Kepler’s third law (4). Here, of course, we are not talking about the gravitational charge of the Sun, however, this expression encodes the value of a certain charge, the essence and properties of which are very interesting. But this topic is worthy of a separate article, so we will continue ours. Let's calculate the value of Planck's constant using the example of the molybdenum atom, which we have already taken as an example. As we have already established, the formula for Planck’s constant

Previously, we have already calculated the mass of a molybdenum atom and the speed of its movement along its trajectory. All we have to do is calculate the radius of rotation. How to do it? Wien's law will help us here. Knowing the temperature value of molybdenum = 1000 degrees, we can easily calculate the wavelength λ that will be obtained using formula (5)

λ = 2.898*10 -6 m.

Knowing that infrared waves propagate in space at the speed of light - c, we use a simple formula

Let's calculate the emission frequency of a molybdenum atom at a temperature of 1000 degrees. And this period will turn out

T = 0.00966 *10 -12 sec.

But this is exactly the frequency that the molybdenum atom generates while moving along its orbit of rotation. Previously, we already calculated the speed of this movement V = 510 m/sec, and now we also know the rotation frequency T. All that remains is from a simple formula

calculate the radius of rotation R. It turns out

R = 0.7845*10 -12 m.

And now all we have to do is calculate the value of Planck’s constant, i.e. Multiply values

atomic mass (15.93*10 -26 kg),

speed (510m/sec),

radius of rotation (0.7845*10 -12 m)

and twice the value of pi. We get

4*10 -34 j*sec.

Stop! In any reference book you will find the meaning

6.626*10 -34 j*sec!

Who is right? Using the indicated method, you yourself can calculate the value of Planck’s constant for atoms of any chemical elements at any temperature not exceeding the evaporation temperature. In all cases the value obtained is exactly

4*10 -34 j*sec,

6.626*10 -34 j*sec.

But. It is best for Planck himself to answer this question. Let's get into his formula

Let's substitute our value for its constant, and we calculated the radiation frequency at 1000 degrees on the basis of Wien's law, which has been retested hundreds of times and has withstood all experimental tests. Considering that frequency is the reciprocal of the period, i.e.

Let's calculate the energy of a molybdenum atom at 1000 degrees. We get

4*10 -34 /0.00966*10 -12 = 4.14*10 -20 J.

Now let’s compare the obtained result with another obtained using an independent formula, the reliability of which is beyond doubt (3). These results are consistent, which is the best evidence. And we will answer the last question - does Planck’s formula contain irrefutable evidence that energy is transferred only by quanta? Sometimes you read such an explanation in serious sources - you see, at a frequency of 1 Hz we have a certain energy value, and at a frequency of 2 Hz it will be a multiple of Planck’s constant. This is quantum. Gentlemen! The frequency value can be 0.15 Hz, 2.25 Hz or any other. Frequency is an inverse function of wavelength and for electromagnetic radiation is related through the speed of light function like

The graph of this function does not allow any quantization. And now about quanta in general. In physics, there are laws expressed in formulas that contain indivisible whole numbers. For example, the electrochemical equivalent is calculated using the formula atom mass/k, where k is an integer equal to the valency of the chemical element. Integers are also present when connecting capacitors in parallel when calculating the total capacity of the system. It's the same with energy. The simplest example is the transition of a substance into a gaseous state, where a quantum is clearly present in the form of the number 2. The Balmer series and some other relationships are also interesting. But this has nothing to do with Planck's formula. By the way, Planck himself was of the same opinion.

Conclusion

If the discovery of Wien's law can be compared in significance with Kepler's laws, then Planck's discovery can be compared with the discovery of the Law of Universal Gravitation. He turned the faceless Wien constant into a constant that has both dimension and physical meaning. Having proven that in a liquid or solid state of matter, angular momentum is conserved for atoms of any element at any temperature, Planck made a great discovery that allowed us to take a new look at the physical world around us. In conclusion, I will give an interesting formula derived from the above and combining four physical constants - the speed of light - c, the Wien constant - b, the Planck constant - h and the Boltzmann constant - k.

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