Magic of numbers
We need to do mathematical digression before discussing structure of more complex atoms.
Mathematic is the queen of sciences. All other sciences use it to suit their own ends. But every science must be able to convert its tasks into mathematical language to solve these tasks correctly. So let’s draw attention at mathematical language.
Elementary mathematical ideas are based on such abstract conception as prime natural number. For example 1, 2, 3, 4, 5 etc. After giving some thought to this subject we can make a conclusion that number is a pure abstraction, that is abstract notion.
One apple isn’t equal to one orange; one kilogram of nails isn’t equal to the one kilogram of wool. Even the most identical things are not equal to each other. Rouble in my pocket isn’t equal to the rouble in your one. Even two your roubles are not equal to each other. There are more atoms in one than in other.
Taking a good look at the particles from microcosm we come to the same conclusion. For example one electron isn’t equal to any other, because they are located in different places and feel influence of different forces. So they will have different energies. Let’s discuss requirement of permutation symmetry, which says that nothing will change if we change places of two different particles. It looks irreproachable in abstract. But if we rest upon the principle of continuity and consider the process of transposition, we will understand that ways of transposition of the particles will be different. So work will be different too.
So positions of particles around will change. Now we can make an important conclusion.
Every transposition of particle (and emission too) is IRREVERSIBLE. It is impossible to restore initial state of everything. Returning force will make still more changes. Now we have logic proving of TIME IRREVERSIBILITY. We can get the same conclusion if remember that every transposition of particles will result in changing of bions location even if small area of space.
Let’s return to mathematics. It operates with such important conceptions as infinity (unboundedness of spatial remoteness on the one hand and limitlessness as lack of clear bound). In both cases we understand that these conceptions are certain sides of continuity.
Mathematical conception of the limit is very important too, because it gives us possibility to stop our calculations in certain moment if necessary approximation degree is already reached.
Such limit is the value of Planck's constant in case of so called “energy quantization”.
I want you to understand clear that NO ONE PHYSICAL, CHEMICAL and even MENTAL and SOCIAL PROCESS CAN START AND FINISH INSTANTLY. All occurs gradually, but degree of this gradualness can differ. This conception isn’t new. Aristotle affirmed: “Nature doesn’t make leaps”. Scientists based their theories on common discreteness, because they couldn’t rightly understand causes of some physical phenomena. It results in perfect nonsense, because they explained everything by instrumentality of virtual (imaginary) particles. But they don’t notice this absurd, because they are its authors. May be they only feign that they don’t notice, because it is impossible to understand their theories to the end, and there were no possibility to explain everything in other logic and obvious way.
Here are examples of such absurds. Chemists consider that common pair of electrons in atom ensures connection in atom. But I don’t agree. In the judgment of physicists electrons must repulse each other with great forces. How can they keep together such heavy nuclei? Chemists affirm that probability of being of electron in angular plane is equal to the zero. How does electron jump from one part of orbital to another? Why does carbon atom keep its excited state in diamond for so called hybridization of orbitals instead of coming to base condition as graphite?
Physicists explain everything by the instrumentality of virtual particles and refuse the annihilation to particle and antiparticle. They refuse even three-dimensionality of space to us, using Lorentz transforms (one-dimensional) in relativistic mechanics.
Taking the importance of mathematics into consideration we shouldn’t forget that it can’t reveal the essence of physical phenomena. For example we can calculate a force of interaction of two masses using the law of universal gravitation, but we have to understand that we can’t calculate lower limit of distance between interacting masses by the instrumentality of this formula. In that case we need to base our reasonings on other premises and make other conclusions.
It is clear that no one abstract value can be an argument in formula using for calculation of real physical value. But this occurs in case of using quantum numbers in Schrodinger equation (and imaginary unit is used in exponent).
It is worth mentioned that not every real process and dependence can be described by the instrumentality of formula. For example what formula is able to describe the fact that there are only five regular polyhedrons? Which dependence can describe number of vertexes of such polyhedrons?
I’m convinced that it is impossible to explain something by the instrumentality of obscure. We only can confuse and complicate it. So scientists are mistaken when they say: “People reach such tops when they can understand things, which are impossible to imagine”. Because we can understand only things we can imagine. And we can imagine everything, which exists in Universe. Thereupon let’s finish lyrical digression and continue our discussion.
Taking into account that location of electrons in atom is spatial task and electric forces carry central type, we make conclusion that electrons are located symmetrically around the nucleus on the surface of the sphere.
There are 6 “right” ways to divide sphere into several parts. The first divides sphere into parts by the instrumentality of circle passing through the center of the sphere. Some points chosen on the surface of the sphere and being the vertexes of regular polyhedrons will divide sphere’s surface into several identical parts.
There are forms of regular polyhedrons on the picture.
1 – dividing the sphere into two parts, other 5 ways are intended for plotting of regular polyhedrons.
2 – regular tetrahedron (4 vertexes)
3 – regular octahedron (8 vertexes)
4 – regular hexahedron – cube (8 vertexes)
5 – regular icosahedron (12 vertexes)
6 – regular dodecahedron (20 vertexes)
Cube is connected with other four types of regular polyhedrons. Centers of cube’s faces are the vertexes of octahedron and centers of octahedron’s faces are the vertexes of cube. We can inscribe regular tetrahedron into the cube. Ends of crossing diagonals of two parallel cube’s faces are the vertexes of the tetrahedron. Other four vertexes of cube are vertexes of second inscribed tetrahedron.
In case of inscribing cube into dodecahedron edges of the cube are diagonals of the dodecahedron’s faces. Every of five diagonals of the one face of dodecahedron can be the edge of the cube inscribed in dodecahedron. So we can inscribe 5 similar cubes into one dodecahedron.
We can choose one pair of points on every face of the cube and these 12 points will be the vertexes of icosahedron.
Cube is the single regular polyhedron which can fill the space without gaps by the instrumentality of adding one cube to another. So principle of continuity singles the cube out of other space figures.
Numbers of vertexes in regular polyhedrons (2, 4, 6, 8, 12, 20) are equal to the magic numbers of the nucleons in the nucleus. It is not usual coincidence.
We can ask luminaries in science about it. Why are these numbers magic in nuclear physics?
Pointed quality of cube is the reason of such fact that exactly 8 electrons compose full electron shell. There will be one more corroboration of this conclusion below.
Alternative site in Russian contains more information. It added new pages, pictures, and 8 clips of computer animation. Go to Russion version page.
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