Arc Effect

Do you know, than the Sun reminds the empty ball?

This logical deduction led to the conclusion, which was a heresy. Such heretical conclusion must be tested by different methods. In a couple of years, in summer of 2002, I had found the second method of this problem solution. I began to discuss this problem in Internet. This discussion had convinced me in my correctness. I am very thankful to all participants of discussion. Especially to Tiber (nickname), who tried to refute the Arc Effect, and who made several interesting deductive steps in order to defend the standard approach. In my bottom proof I will use his steps, to prove the Arc Effect. This proving method can be named the analytical proof.

In autumn of 2003 I had received another proof, which can be named the mathematical proof, and which is applicable not only to gas, but to any medium of interacting particles.

In 2003 I had made the computer program, which solves the systems of differential equations, which could not be solved by usual way. This program had given me the series of interesting results, first of all, - the expanded theorem of virial. Analyses of these results can be regarded as program proof of Arc Effect. There is one more proof, - historical. I found out that one of the first persons, who had said about the hollow planets and stars was famous Leonard Euler. His name can be found in math and physics books such frequently as the name of Einstein, or even more. Consequently, the rating of wisdom of Euler is comparable to rating of Einstein. Great physicists did not accept the conclusion of Euler about the hollow planes and stars. This paradox is more paradoxical than Special Relativity of Einstein. That is why those great physicists are weaklings and got to the camp of misguided. But Euler was correct. And the new equation of Hydrostatic equilibrium is correct, because it meets the conclusions of Euler.

Hydrostatic law. Standard approach.

How to compute the pressure in the depth of a planet or a star? These objects have the spherically symmetrical fields. Let's at first investigate the field, with parallel force lines.

Let's divide the object on the series of parallel layers with the thickness dr. If in one layer there is already the pressure p, then in the bottom layer will be the pressure p+dp. In order to find dp, it is necessary to divide the weight dF of the upper layer by its surface S.

dp = - dF / S = - dM g / S = - rg dV / S = - rg dr.

dp/dr = - rg. (1)

The sign minus occurs because dr directed up, and the weight dF directed down. If we use the concentration n of particles of mass m then

dp/dr = - nmg, (1,a)

or through the potential energy dP in gravity field

dp/dr = - n dP/dr. (1,b)

Thus we had received several forms of the hydrostatic law, which is used not only to the field with parallel force lines, but to all objects, including planets and stars.

Analytical proof of the Arc Effect.

Potential and kinetic energies (P, K) of a particle of gas, moving in the gravity field of the object, constantly changes at the time from one collision to another collision with other particles, but the sum of these energies remains the same. The selection of zero-point of potential energy can be arbitrary. Then we can suppose that potential energy at the moment just after the collision is equal to its kinetic energy but with opposite sign. Then at every moment till the next collision the sum of these energies will also be equal to zero.

P + K = 0. (2)

Between the collisions the particles move by ellipse-like trajectories and we can divide the kinetic energy on two items

K = K_u + K_w, (3)

mv²/2 = mu²/2 + mw²/2, (4)

where: u - the radial velocity of a particle; w - tangential velocity of a particle; K_u, K_w - radial and tangential parts of the kinetic energy. It is clear that the radial part of kinetic energy is responsible for the radial increment of pressure. Combining (2) and (3) we'll have

P + K_u + K_w = 0. (5)

K_u = - P - K_w = - P - L²/(2mr²). (6)

The radial kinetic energy can be changed by the effective potential energy W with the opposite sign.

W = P + L²/(2mr²). (7)

The change of potential energy is responsible for the change of the radial kinetic energy. The change of the radial kinetic energy is responsible for the radial increment of pressure. Consequently, now we can change the equation (1,b) which is valid for the homogeneous field, substituting in it the value P by W, and denoting some values by indexes _L.

dp_L/dr = - n_L dW_L/dr. (8)

Index shows us that this increment is partial, which is made only by n_L particles, having the angular moment L.

Let's substitute (7) into (8)

dp_L/dr = - n_L (dP/dr - L²/(mr³)). (9)

Knowing that

dP/dr = mg, (10)

and

L²/(mr³) = m²w²r²/(mr³)= mw²/r, (11)

we'll have the equation

dp_L/dr = - n_L(mg - mw²/r). (12)

The pressure is additive, consequently

dp/dr = dp₁/dr + dp₂/dr + .. + dp_i/dr

dp/dr = - mg(n₁ + n₂ + … + n_i) + (m/r)*(n₁w₁ + n₂w₂ + … + n_iw_i)

dp/dr = -mng + (m/r) ₀Integral^w.max w²dn. (13)

The value (1/n) ₀Integral^w.max w²dn is the average value of a square of tangent velocity [w²]. Consequently

dp/dr = -mng + mn[w²]/r. (14)

If the distribution of velocities is isotropic, then

[w²] = (2/3)[v²]. (15)

And

dp/dr = - mng + (2/3)mn[v²]/r, (16)

or

dp/dr = - r(g - (2/3)v²/r). (17)

Using the generally known relations p=nkT, r=nm, (3/2)kT=mv²/2, we can write

dp/dr = - rg + 2p/r.

Thus we have proved that the hydrostatic law for real gas in the spherically symmetrical field must have the Arc Effect item 2p/r. The classical hydrostatic law must be changed by the new one, if we work with spherically symmetrical field.

Mathematical proof of the Arc Effect.

Equilibrium in the spherically symmetrical problem without field.

Did you see the flat fan? It can be gathered into a rod. You also can imagine the volume fan, which also can be gathered into a rod.

Let's suppose that we gathered the Sun in a rod. Thus we can sum the forces of weight of all particles, and their vector sum now will not be equal to zero, because all forces are parallel now. We transformed the three-dimensional Sun into one-dimensional. In the further text we will use the word FORCE and we'll understand that it is the sum of radial forces, gathered together by turn. In order to underline this unusual method of force summing, I'll write the word FORCE in capital letters.

Under gathering the center of the object will coincide with the zero-point of the axis r. The surface of the object of radius R will coincide with the point R on axis r. Let's suppose that the axis r goes in positive direction and also in negative direction.

It is obvious, that the object will accelerate into negative direction of axis r, if the sum of FORCES directed inward, will be greater then the sum of FORCES directed out of the object. The object will accelerate into positive direction of axis r, if the sum of FORCES directed inward, will be smaller then the sum of FORCES directed out of the object. The object will not accelerate along axis r, if the sum of FORCES directed inward and out of the object will be equal to zero.

These reasoning can be repeated the same, relatively to the any internal spherical shell of the object.

Let some homogeneous medium, for example, water, gas, dust is placed into a spherical vessel and squeezed by the vessel to the certain pressure p. There is no any outside field. According to this section the medium does not create own gravity field. Consequently, the pressure everywhere will be the same.

Let's investigate the thin layer between two spheres with radii r and r+dr. The centers of these spheres coincide with the center of the vessel.

Internal and external layers apply two FORCES to our investigated layer. The surface of external sphere is bigger then the surface of internal sphere by the value dS. The sum of these two FORCES is not equal to zero. It is directed inward and we will write it with the minus sign. The origin of this FORCE is clear it begins from the stretched shell of a vessel. That is why this FORCE can be named as POTENTIAL FORCE.

df_pot = - pdS.

There are no any additional FORCES. Consequently, the layer must accelerate into negative direction of axis r. But acceleration is impossible in the equilibrium state. Recalling that according to quantum mechanics, particles continue to move even under the zero temperature, and taking into account that external sphere is bigger than the internal sphere by the value dS, we come to conclusion, that KINETIC FORCE compensates the POTENTIAL FORCE. KINETIC FORCES directed upward and we will take them with the plus sign.

df_kin = pdS.

The equilibrium equation for thin layer will have the form:

df_pot + df_kin = 0.
- pdS + pdS = 0.

Equilibrium in the spherically symmetrical problem with gravity field.

If the object keeps itself by the gravity forces and if it does not squeezed by the outer shell, then the equilibrium equation will not have the item dfpot, but will receive instead the GRAVITY FORCE item df_grav. Besides the pressures in this case inside and outside the layer are not equal now, and the equation will receive now one more item, PRESSURE GRADIENT FORCE, df_grad.

df_grav + df_grad + df_kin = 0.
- gSr dr - Sdp + pdS = 0.

Dividing by S and dr, we'll have the new hydrostatic law

dp/dr = - rg + 2p/r.

Spherically symmetrical object with gravity field, enclosed by shell with pressure p₀.

Let's imagine the elastic spherical shell situated concentrically inside the gaseous object with gas inside and outside the shell. Let's blow out the gas, situated outside the shell. Let temperature of the shell remain the same. Then the equation for pressure gradient will be the same as in the above section. It will be valid at the interval lasting from r=0 to r=R_shell.

But if we situate the whole object inside the shell and then begin to squeeze the object, or begin to heat the gas, then we'll receive another equation.

df_grav + df_grad + df_kin + df_pot = 0.
- gSr dr - Sdp + pdS - p₀dS= 0.

dp/dr = - rg + 2(p-p₀)/r.

Thus, the mathematical proof give us the new hydrostatic law in more general form, which is applicable not only for gaseous object, but for the object composed by any isotropic medium, consisting of mutually interacting particles. The object can be squeezed by the shell with pressure p₀. In the real stars the pressure of emitted light can play the role of the shell.

Program proof of the Arc Effect.
Expanded virial Theorem.

If we sum potential energies P_i of all stars in the stellar congestion and compare it with the total kinetic energy of all stars K, we'll have the interesting relation

P+2K = 0.

This equation is known as the virial theorem. Clausius proved it in 1870 for the system of classical material point particles interacting gravitationally.

Then this law was transferred to gas. The total kinetic energy of all particles K was symply changed by the internal energy of gas U.

P+2U = 0.

I found in the physical encyclopedia that if the system is in the state of turbulent movement of energy T and if it has the magnetic energy L_m, then the virial theorem has two additional terms.

P+L_m+2(U+T) = 0.

Now we shall see, how the magnetic energy L_m will transform into electromagnetic energy L=L_m+L_e, and how the internal energy of non existing ideal gas will transform into it's sister, the enthalpy H=U+pV, playing the role of internal energy in isobaric processes.

My computer program had showed me, that the virial theorem in the form P+2U = 0 is only valid for objects filled with the ideal gas. The ideal gas here is a system of material points, interacting gravitationally but not colliding with each other. Clausius investigated such system of particles. The hydrostatic law here has the classic form dp/dr = - rg. We cannot divide the object by the system of concentric shells, as it was made in the mathematical proof. The concentric shells can be thought as shells made of atoms of gas. But if there are no collisions then there are no shells.

When we consider the gas with mutually colliding particles, the shells, made of atoms, appear. The hydrostatic law receives the Arc Effect item 2p/r, and dp/dr = - rg+2p/r. The program computes the system of differential equations and gives the virial theorem in the following form:

P+2H = 0.
P+2(U+pV)=0.

When we consider the real gas, filled also by radiation, the hydrostatic law receives the radiative (') items, d(p+p')/dr = -(r+r')g+2p/r. The program computes the system of differential equations and gives the virial theorem in the following form

P+L+2H = 0,

where: L is the whole energy of radiation inside the object.

Pay attention that the radiative (') part does not enter onto the Arc Effect item. The cause is now clear, - photon gas is the ideal gas with non-interacting particles. Radiation presses the material shell, but radiation ray does not press onto the radiation ray. If you try to start the program with the equation, containing symmetric Arc Effect item, the program will not solve the system of equation correctly.

When we consider the ideal gas (with non-interacting particles), filled also by radiation, the classic hydrostatic law receives the radiative (') items, d(p+p')/dr = -(r+r')g. The program computes the system of differential equations and gives the virial theorem in the following form

P+L+2U = 0.

When we consider the gaseous object, filled also by radiation, and enclosed by the shell with pressure p₀, the hydrostatic law receives the shell's pressure item.

d(p+p')/dr = -(r+r')g+2(p-p₀)/r.

The program computes the system of differential equations and gives the virial theorem in the following form:

P+L+2(H-H₀) = 0.

The value 2H₀, taken with opposite sign, can be considered as the potential energy P_shell of the stretched shell. Consequently, the last equation can also be written in the form

P+P_shell+L+2H = 0.

Conclusion. The program gives us the expanded virial theorem and explained the difference between the behavior of gases, consisting of photons and of material particles. It also explained the difference between the behavior of gases consisting of colliding and non-colliding particles.

Classical hydrostatic law, dp/dr = -rg, is valid for non-existing objects, with parallel force lines.
Logical proof gives the Arc Effect item but with unknown coefficient, dp/dr = -rg+?p/r.
Analytical proof gives gives the Arc Effect item, dp/dr = -rg+2p/r.
Mathematical proof explains the role of the enclosing shell, dp/dr = -rg+2(p-p₀)/r.
Program proof shows the role of radiation, d(p+p')/dr = -(r+r')g+2p/r.

The most general form of hydrostatic law:

d(p+p')/dr = -(r+r')g+2(p-p₀)/r.

The most general form of virial theorem:

P+P_shell+L+2H+2T = 0.

Look the page The Earth's Core Is Overheated Emptiness in order to see, what new hydrostatic law gives us.

To the index of Space Genetics

My Curriculum Vitae.

Ivan Gorelik.

Extremely urgent note, 2009.

Attention! Magnetic trap of Devil!

There is a very big probability that magnetic trap will kill us all, if we will not stop powerful colliders.

Magnetic trap is an object, unifying hypothetical objects, connected primarily by magnetic forces: neutron drop/liquid; neutron hole; magnetic hole ...

It is probable that the microscopic magnetic trap can be created at the collider. Magnetic trap will grow capturing the normal substance. As a result, magnetic trap can destroy the Earth.

Magnetic hole is a magnetic analog of the black hole. The black hole is bounded by gravitational forces, and the magnetic hole is bounded by magnetic forces, which are many-many times stronger than gravity forces.

Magnetic hole is a magnetic dipole, in the form of a circle, where there is the critical magnetic field. The lines of magnetic induction are directed perpendicular to the plane of the circle. Nucleons are microscopic magnets, and they can be easily captured by the critical field of the hole. As a result the hole is growing.

The approximate computation shows that the minimal possible magnetic hole, which can capture a nucleon, has a mass slightly more than one thousand masses of nucleons. The Tevatron collider is now working near this region. The Large Hadron Collider (LHC) will be able to create the particles with the rest mass, which are seven times more that the minimal possible mass of magnetic hole.

According to publications, LHC will create microscopic black holes. Most theorists suggest that these black holes will disappear, because of the Hawking evaporation. However, we know that there are several theories of gravity. Some theories did not even admit the existence of black holes. In addition, there are several theories of black holes. Therefore, confidence in the classical theory of black holes and in a process of evaporation of black holes is very poor.

For several years, some scientists argue and demand to ban the construction of powerful colliders. Among the known dangerous objects that may lead to global catastrophe are the following: microscopic black holes, strangelets, magnetic monopoles, vacuum bubbles. I learned about these disputes and concerns only in early September 2008. And then I immediately noticed that the objects, bounded by magnetic forces, were almost not analyzed.

In early September, I assumed that the probability of a global catastrophe is less than 0.000001. However, after three months of analysis of the objects, bounded by magnetic forces, and after the analysis of space observations, my assessment of the global disaster has surpassed dozens of percents.

Some theorists suggest that the Higgs bosons will be registered at the LHC. Higgs boson had received a new name, "the God particle". We know that the most of particles have their corresponding antiparticles. So, if there is a particle of God, then there is a particle of Devil. Two colliding particles can give two more massive particles, - the particle and its antiparticle, for example, an electron and positron. By adding the colliding energy, we can get the God particle and its anti-particle, the magnetic trap of Devil. Particles and antiparticles have diametrically opposed properties. Indeed, the Higgs boson causes the ordinary matter to have a mass. But the magnetic hole captures the substance and transforms its rest mass-energy into another form of matter, - the magnetic field of the Devil's trap. Say me now, are we have the right to touch the particle of God?

Microscopic magnetic holes created at the collider, will move to the center of the Earth, absorbing the matter in their path. Eventually they will merge together into a single and much stronger magnetic hole. The thin shell of the Earth, together with us, will be ejected into cosmic space, but the rest of the Earth will turn into an electric current loop of several meters radius. For comparison, the radius of a black hole of the same mass is 9 millimeters. Part of Earth’s mass will be transformed into magnetic field of neutron hole, and another part will be transformed into radiation and kinetic energy of the released shell.

Magnetic hole will not decay if it was born in such cold place, as the collider, where the temperature is close to 0 K. If the magnetic hole is born in a collision of space particle with atmospheric particle, it has a speed, which is close to the speed of light. As a result, such magnetic hole will evaporate almost immediately as a result of energetic collisions with atmospheric particles. Such evaporating magnetic hole will form a cosmic-ray particle shower. Such showers are observable.

Huge magnetic holes are also observable is cosmos.

In the remnants of supernova SN 1987A we can see a system of rings, which remind us the magnetic hole. It is possible that this magnetic hole is decaying now.

It seems as if these rings embrace a hyperboloid. And now look at the electron, moving along two hyperboles in coordinates x, ict, in my electron model program. Each electron crosses the entire Universe in a period of time, which is equal to the classical period of the electron. This paradoxical conclusion is the consequence of the Special Relativity Theory. The ring structure of SN 1987A and our electron model have common visible properties. The Earth and the Sun can be turned into the same ring structure.

Magnetic collapse is much more rapid than the gravity collapse. At the process of magnetic collapse the nucleon turns such, that its magnetic dipole moment becomes parallel to the magnetic dipole moment of a trap. Gravity collapse needs displacing of a matter inside the Schwarzschild radius. The time interval of neutrino registration at neutrino observatories had proved the reality of magnetic collapse of dying stars.

Particle's collision energies and bombs:

Several eV - chemical bomb;
Several MeV - nuclear bomb;
Several TeV - hyper bomb.

Chemical bomb is accompanied by the change of chemical structure of matter.
Nuclear bomb is accompanied by the change of nuclear structure of matter.
Hyper bomb is accompanied by the transformation of solid matter into a field.

Scientific crime.

Only crazy people can try to create the particles with the rest mass, more than 1000 nucleon masses. It is very possible that in the region from 1000 to 7000 aum, hundreds types of particles and resonances can be created. It is clear, that the most of them will decay. But some of them will grow, capturing the ordinary matter.

Academician Migdal wrote 30 years ago about pion condensation in the strong fields. As a result he had come to conclusion that neutron stars can have any masses. My approximate computation also shows that the minimal possible neutron star can have a mass, about one thousand of nucleon masses. Such embryos of neutron star can by made in collider.

Not long ago the new strange unexpected particle was discovered at the Tevatron collider. It decays at several muons, up to eight units. Somebody had already named it the Halloween particle. I named it the muon hole. What will be made the next? The magnetic trap of Devil?

Majority of contemporary physicists imagine quark-gluon plasma as a suck with peas. That is a very dangerous imagination. Particles are not points with labels, where their quantum properties were written. Particles are not the material essences, independent of space-time; they are just space-time elements, strings. 

Dear reader, the situation is extremely serious. The physics now is in the deep crisis. Theorists, in order to save their religious Big Bang theory, invented “the dark energy" as a new either. They want now to test their wretched theories at the powerful Large Hadron Collider.

Those persons, with high ranks and high scientific degrees, who cry about the safety of LHC, had already made a crime now. The LHC was launched despite the fact that there were court trials. The Earth could be exploded the 21 of September 2008, but the accident, which had happened two days earlier, had saved us. Scientists-criminals continue to lie about the safety of the LHC, and are preparing the global terrorist crime now.

Dear reader! Big Bang adherents can lead the Earth to the utter destruction. Particle collisions with the energy more then 1 TeV must be prohibited by the international law. The science must be cleared from the Big Bang delusion. Big-bangers want to touch the particle of God, but thus, they lead us into the magnetic trap of Devil. People, will you silently endure the massacre?

Some documents and links.

In November 2008, I arrived to Moscow in order to file a lawsuit against the Russian Academy of Sciences and against the most active propagandists/promoters of the LHC launch. Unfortunately, for the lack of funds, I could not did it then.

In late November at the "meeting of four" there was decided to hear my report "What will LHC give us, the particle of God, or magnetic trap of Devil?" at a workshop in one of the leading institutions of Moscow. But later, I received a "retreat" from this institution.

In December, I sent the Letter to the President of Russia. In January, I received an answer in which it was stated that my letter was forwarded to the Russian Academy of Sciences.

In December, I sent the Letters to the Prosecutors Office of the Russian Federation. Soon after, I received the answer stating that my letter "was sent for review in the prescribed manner".

In the end of January I returned to Feodosia (Ukraine) and continued to inform about the risks of the global catastrophe. You can read some letters, which were send to the Google groups, - just click my Google-profile.

Reproduction of biospheres and civilizations. Who are you, dear reader: "a cell of good reason", "a curiosity cell", or "thoughtless muscular cell"?

Magnetic trap of Devil. Recent calculations show that it is not excluded that microscopic magnetic traps were already created, and they are growing now somewhere inside the Earth.

Arguments, proving that "The LHC will lead to global catastrophe"; "Magnetic holes exist"; "We will not be able to prevent the LHC launch and the following global catastrophe". Religious and mystic arguments.

Magnetic Hole. Pictures.

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