4D ROTATION AND SPHERE PACKING
 

4D ROTATION AND SPHERE PACKING

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December 10, 2009. About a midnight from 8 to 9 of December at the Collider they risen up temporarily the energy of collisions to 1.18 TeV per proton. In the early morning December 9 in the sky of Norway people could see such picturesque image.

Then I saw this figure I remembered at once the idea about magnetic wasps. I wrote about them in some Russian-language forums earlier:
http://physics-animations.com/cgi-bin/forum.pl?forum=new&mes=64416&resp=15
There is a small hope that plasma bubbles will leave the Earth and will be rejected into cosmos. Such objects can be named by “magnetic wasps”. I give very small probability of such behavior of magnetic holes, less than one percent, inside catastrophic fraction, which is measured by dozens of percents. Thus, magnetic wasps could lead only to local catastrophe…

Magnetic wasps have not only magnetic poles, but also electric poles. In this case the capture of protons by wasps is asymmetric. This gives them jet engines. This explains huge velocities of remnants on cosmic catastrophes”

But later I learned that the figure did not connected with Collider, but it is the result of unsuccessful launch of Russian rocket Bulava.

My yesterdays (look bottom) sad assumption remains valid, but shifted almost a day. Collider operates intermittently: the problems with the injection, then with cryo systems.


December 9, 2009. Today, about midnight, CERN plans to implement a collision with the energy of 0.45 TeV per proton under high density. Two colliding beams will contain four bunch; each of which will contain 20 billion protons. If this experiment will be carried out within a few hours, then I give 10% probability that the microscopic magnetic holes will be created. The most likely, the time of growth of magnetic holes till the consumption of the whole Earth is about one day.This means that tomorrow night the magnetic field of growing magnetic hole will push us all to the equator of the Earth in a single high ocean wave. From there we will start into space, being mixed with mud and with all the water of the whole planet.

This frog levitates (hanging in the air) in a magnetic field with induction of 16 teslas, because of the diamagnetism of water, and, as you know, living beings are composed mainly of water.

The magnetic field will accelerate us so that we will overtake Voyagers. Around us the water will turn into frozen dirty foam of very low density. The solar wind will give these new formed comets a further acceleration. An hour later the comets will be hit by wreckage of the crust of exploded Earth and by a powerful gamma radiation. After a few years (thousands of years) we will be overtaken by the shock wave from exploded Sun. Well, after a millions of years, we could reach to the closest star systems to sow where our viruses, DNA and the seeds of poplars, daisies, etc.


December, 7. 07.30 GMT.
Now they have cryo problems.
Possible causes from my point of view:
1) Microscopic magnetic holes are already created and emit the radiation.
2) Usual breakage.

Now I go to Moscow State University to talk with physicists.

By the way, while I fighting in Moscow, two cars with seven policemen come to my home in Feodosia couple of days ago. They asked my neighbors: am I adequate; can I beat anyone; can I beat my wife?

This arrival possibly connected with my letters to some presidents of European countries, which I sent a week ago:

Collisions of protons with energies about 1 TeV can lead to MAGNETIC collapse and explosion of Earth with probability about 30%. Thus, you can kill me and my relatives.

Please, advice me, what can I do to stop you:

1) To kill some citizens from your countries?
2) To kill myself in front of your Embassy?
3) ???

Ivan Gorelik. darkenergy@yandex.ru
http://darkenergy.narod.ru/
+7 (8)965 372 00 36

Calm down, gentlemen. I am not able to kill anybody. I wrote this in order to make you think: what are you doing.


December, 6, 2009. 06.30 GMT.

CERN started collisions of protons with energy 0.45 TeV per proton. Both beams have four bunches of protons.

If magnetic moment of x-boson equal to magnetic moment of proton this energy is sufficient to create the microscopic magnetic hole.

It is needed from 1000 seconds to 1000 days to destroy the Earth. Let’s wait and see.

If we’ll survive now, CERN will add the quantity of bunches per beam and will raise the energy of collisions.

CERN started the experiment despite the courts and our appeals. CERN is terrorist organization.

Most of physicists are coward, or stupid, or smug, not able to understand where this experiment will lead us.


December, 5, 2009.
At last, the news about the most dangerous thing, which can be created at LHC, was published in well-known media edition. 'Doctor Dark Energy': The Ultimate LHC eccentric? http://www.theregister.co.uk/2009/12/04/dr_dark_energy/

At the end of the article the author try to calm the readers that LHC will collide protons with the energy only about 450 GeV.

But the calculation (two independent approaches) gives us the value about 250 GeV.

Indeed, that is smaller than the collision energy of Tevatron. But is it possible to create a magnetic hole at Tevatron, colliding protons and antiprotons? Magnetic field in the central point between these flying by particles is equal to zero, B = 0. But at the LHC B = 2B1.

That is smaller than the energy of cosmic rays. But look at my model with two 10-kg bottles with neutrons. You will see that the bottle, corresponding to cosmic rays, will be safe. But the bottle, corresponding to LHC collisions, will transform the town into Hiroshima.

The 250 GeV energy per colliding proton was already achieved at RHIC. Experimentalists could see collapses – fireballs – about four years ago. It is possible that those fireballs are experimental proves of magnetic holes. Those holes evaporated immediately because the RHIC collided heavy nuclei, containing many protons and neutrons. Will such holes evaporate at LHC, or will created magnetic holes begin to capture the slowly moving protons of Earth?

One of the authors of documents about the safety of LHC, Igor Tkachev, is 100% confident that at the center of our Galaxy there is a huge black hole.
I am 95 % confident that at the center of our Galaxy there is a huge magnetic hole. I think that magnetic hole, besides the magnetic field, has axial-symmetric gravity field, stretching mostly in the plane of our Galaxy. This explains the huge velocities of peripheral stars of our Galaxy. In other words, - there is no any dark matter in our Universe. Its role is performed by magnetic holes. There is no any dark energy in our Ever Young Universe. Its role is performed by cosmic background radiation. Hubble constant is not the parameter of Universe expansion, but the angular frequency of 4-d rotation of Universe. 13.34 billion years is not the age of Universe, but the time of one full 4-d rotation of Ever Young Universe. Energy sources of stars in Ever Young Universe are different from the sources in Big Bang Universe. Our energy sources can be described by corrected formula of Hawking. This formula must contain the square root from Dirac’s big number. This formula describes the luminosity of stars, but not the black holes evaporation. In our model there are no black holes, but there can be extremely rapid gravity collapses, ending by disappearance of gravity funnel and huge gamma-burst. Gravity collapse is the final part of magnetic collapse if the mass of the magnetic hole is sufficient and if its configuration is correspondent.

Astronomers, show me, please, black holes.
No?
But, I can to show you the picturesque magnetic hole.
Here it is:

Magnetic holes explain us the cause of several astronomical pulses: gamma-bursts, huge radio jets, the annihilation lines of electron-positron pairs, huge velocities of remnants of cosmic catastrophes, the absence of civilizations which are older, than those, who can build powerful colliders.

People, please, stop powerful colliders immediately.
Collisions with energy, more than 100 GeV must be banned by international law, otherwise our Solar system will look like SN 1987A.

Somebody asks: Is it possible you are wrong with your theories. Is it possible?

If I was not confident, I would not fear LHC, I would sleep calmly, but, as can you see, I am in shock now.

Somebody asks: How have you determined, with such certainty, that your right?
You still have provided no proof at all that you are correct.


Two mathematical proves. Dozen of supplementary arguments.

Somebody asks: Is it possible that you are overly fearful and that scaring the public is a irresponsible, immoral and unethical thing to do if you have no proof at all of your theories?

I said the truth. Are bigbangers responsible and honest in their gaining the ruling position in science? Look at the open letter of anti bigbangers, signed by thousand of famous scientists, who are rejected the idea of Big Bang: http://www.cosmologystatement.org/
There is no pluralism in science now. Science was transformed into religious dogma by bigbangers. Because of this I have no job in science. Because of this the Earth can undergo the big bang, but this bang will not prove the Big Bang theory.

People, please, stop powerful colliders immediately.
Collisions with energy, more than 100 GeV must be banned by international law.


Send police to CERN and arrest Rolf Heuer and all his bigbangers. He is deadly dangerous for all humanity. He can kill you today with great probability.

December 2, 2009 I have delivered petition to the Prosecutor’s Office of Russia.


To Prosecutor’s Office of Russia.
From Ivan Gorelik (address, phone, passport data)
Statement


1. Please bring to criminal responsibility the authors of documents on the Large Hadron Collider Safety Assessment, because these documents contain crude errors and false statements. See Annex 1.
2. Please contact the law enforcement bodies of the European Union and demand the immediate termination of the experiment at the Collider, since the experiment could lead to the magnetic collapse and to the collaptical explosion of the Earth.
Grounds:
A. 20 November 2009 an international committee ConCERNed filed a complaint to the European Court of Human Rights in Geneva to stop the experiment at the Collider, but CERN continues experiment and increase the energy of collisions and their frequency. http://www.lhc-concern.info/
B. Physicists of CERN considered only four items of dangerous objects that can be created at the collider, and ignored the theory of magnetic holes. I have repeatedly appealed to higher authorities about the danger of magnetic holes. Calculation of magnetic holes is shown here: http://darkenergy.narod.ru/magtren.html
3. I beg to bring to the United Nations the issue of an international ban on the collision of particles with energies higher than 0.1 TeV.

December 2, 2009. Signature.
Annex on three sheets from my page Russian language page Crude Errors and Lie in the Safety Assessment of Collider. http://darkenergy.narod.ru/tezru.html English language analog of this page you can find here: http://darkenergy.narod.ru/tezeng.html


November, 30. CERN had risen up the energies of beams to 1.18 TeV.
I wrote a following letter to some leaders of CERN:

Collisions of protons with energies about 1 TeV can lead to MAGNETIC collapse and explosion of Earth with probability about 30%. Thus, you can kill me and my relatives.

Please, advice me, what can I do to stop you:

1) To kill some citizens from your countries?
2) To kill myself in front of your Embassy?
3) ???

Ivan Gorelik. darkenergy@yandex.ru
http://darkenergy.narod.ru/
+7 (8)965 372 00 36


November 28, we  widespread a Leaflet of protest.


November 27 at 12.00 I and my son tried to held the meeting of protest near the Moscow State University. At 12.30 we were taken into police office, where we continued to protest for about 4 hours. At last militia had made our photos from different positions, took our finger-prints, returned our megaphone-siren and wished us a success in our straggle.


First collisions were performed, November 23.
Now CERN is ready to rise up the energy of collisions.
------------------------------------
Today, November 24, I'll try to organize a meeting of protest against CERN.
Moscow, Zubovskij bulvar, 4. Near the Russian Informational Agency "Novosti".


STOP CERN! A call to reasonable people all over the world.

In a several days the first high energy collisions of protons will be implemented by CERN at Large Hadron Collider. This can lead to the explosion of our planet and to extermination of our humankind.
We, citizens of Russia, Byelorussia and Ukraine, are planning to fulfill several actions. We call you to make the same in your countries.
1. The 20-th of November 2009 we’ll start to distribute the Leaflet in order to say people about the real deadly danger of the LHC experiment.
2. The 23-rd of November we’ll try to block the entrances to the Russian Academy of Sciences, Moscow State University and so on. No one person can enter these buildings until authorities of these organizations would say at media about their rejection and ban of the experiment.
3. The 29-th of November, that is a day before the first planned collisions, we’ll perform another action. The essence of this action we’ll be expounded additionally.
This plan will be canceled any day, if CERN leaders we’ll refuse the LHC experiment.
We were forced to go to these extreme measures. Previously, we have repeatedly made more loyal measures: appealed to the superior authorities, but CERN continues to go ahead and can kill us very soon. We can not sit silently for our execution.
November 16, 2009.
1. Ivan Gorelik, http://darkenergy.narod.ru/biz.html
2. Vasiliy Golota, http://n-t.ru/tp/ng/ps.htm
3. Vladimir Acjucovskij, http://www.atsuk.dart.ru 
4. Evgeniy Dovgel, http://dovgel.com/kvv.htm
5. Valentina Golovina.
6. Julia Polognjuk.
7. Sergey Vertinskij.
8. Tatiana Pravdina.
9. Vyacheslav Satane.
10. Nikolay Ermolajev.


Dogs of CERN’s Boss threatened to put me into jail.

Yesterday (several days ago) some man, possibly from Rolf Heuer environment, had phoned me and asked – did I threaten to Heuer. The conversation was ended by the threat to put me into jail and by saying that our phone conversation was recorded.

Dear CERN leaders, I feel myself as a prisoner, sentenced to be killed. Those are you, who already deadly scared many citizens of the whole Earth. They, probably, feel themselves as doomed to death. We do not know exactly the day when you will shoot us, and we do not know will we survive.

Our feelings of fear are different. These feelings depend from the probability, which some person gives to catastrophic scenario. Year ago, September 2008, I thought that the probability of the global catastrophe, caused by LHC, is hidden somewhere in the region 10^-6-10^-5. That was not so scary; - this risk probability is analogues to die in an air plane catastrophe. This probability did give me the possibility to sleep quite calmly. But in the period of the last year I had developed the theory of magnetic hole. My probability value of global catastrophe had grown almost each week, because I received dozens of proving arguments and two independent mathematical proves. I studied CERN’s documents about safety of LHC and found there three crude errors and lie assertions. Now I know that probability of Earth explosion, caused by LHC, is not 10^-31, as it follows from CERN documents, but it is hidden somewhere in the region 5-90%. Do you understand this value? Can I sleep calmly now? Who are you now in my eyes, potential killer?

So, Rolf Heuer, go on, send your dogs here, into my town.
My anger grows every day with the nearing of the day of proton collisions at LHC.
I do not know what I’ll do in the end of November.
I hate you, your CERN, your countries authorities.
(...)

Application.

November the 30-th, according to the preliminary plan for the Large Hadron Collider, the collisions of protons with energies of 0.45 TeV will be implemented, the 14-th of December - collisions with energies of 3.5 TeV. If the magnetic collapse starts, it will be impossible to stop it. It will end with ejection of the Earth’s shell into outer space.

I give the following probabilities:
A. 10% - magnetic collapse will start at 0.45 TeV;
B. 50% - magnetic collapse will start at 3.5 TeV, if A did not happen;
C. 70% - magnetic collapse will start at 7 TeV, if B did not happen.
30% I leave to my mistake.

Why is such confidence?

Compare Newtonian black hole and magnetic hole:
GMm / r = mc^2 / 2;
pB = mc^2.

It was obtained two independent proofs that the equality pB = mc^2 is reachable at the energies of modern colliders, http://darkenergy.narod.ru/magtren.html
There are many arguments in favor the fact that magnetic holes exist, and astronomers see them, but call them on the error as black holes, http://darkenergy.narod.ru/argen.html 
It was found several crude errors and criminal lies in the assessment documents about the safety of LHC, http://darkenergy.narod.ru/tezeng.html 

The rate of MH’s growth is not known exactly. Magnetic Hole can destroy the Earth in the period from 1000 seconds to 1000 days. If the second is correct, then you will wish to bomb the LHC yourself. But then it would not save you already, because magnetic holes would already grow inside the Earth.

Here is explanation of the most visible crude error, made in 2003 safety article.

1. Let the length of free path of a particle is equal to 1 meter, r = 1 m.
Let the radius of the object is equal to 1000 meters, R = 1000 m.
How many collisions will undergo the particle in order to exit the object?

Solution. R/r = 1000. N = (R/r)^2 = 1 000 000.

2. How many Earth’s protons will be ruined by dangerous particle, if R/r = 10^9?

A. CERN’s solution: N = (R/r)^2 = 10^18.
B. My solution: The Earth has its own gravity field. Consequently, the trajectory of a particle between collisions will not be straight line, but curved to the center of attraction. As a result the dangerous particle will constantly drift to the center of the Earth. As a result the dangerous particle will ruin about N/n Earth’s protons, where: N – the total number of Earth’s protons; n – the number of created dangerous particles.

Another crude error, made in the CERN’s safety documentation, is in equating of the consequences of protons collisions at LHC with collisions of cosmic particles with atmospheric ones.

To see the drastic difference between such consequences, let’s make two thought experiments.
There are two 10 kg bottles with neutrons.
Additional requirements, used in the model: 1. free neutrons do not decay; 2. proton do not capture neutron; 3. any nuclei, heavier than proton, can capture free neutron; 4. neutrons do not interact with the matter of bottle; 5. the density of neutrons in the bottle is the same as of water.

A. Let somebody put one slowly moving nucleus into the bottle. Neutrons will begin to be captured by the growing and dividing nuclei. In a couple of moments this laboratory will be exploded a town will look like Hiroshima after the nuclear attack.
B. If somebody will bombard the same bottle by nuclei, having the kinetic energy about several TeV, he will see that nuclei are ruined in collisions and formed a cloud of protons and neutrons.

A. Approximate way of reactions can look like this dividing chain:
He3+n -> He4;
He4+n -> He5;
He5+n -> He6 -> Li6+e;
Li6+n -> Li7;
Li7+n -> Li8 -> Be8+e;
Be8+n -> Be9;
Be9+n -> Be10;
...
U235+n -> X+Y+2n
X+n ->...; Y+n ->...
two branches;
...
four branches;
...
eight branches;
...
Collaptical explosion!

B. Nuclei with TeV kinetic energy will be ruined by high energy collisions with neutrons in the backward order in crude approximation.

Nuclear collapse is impossible because the repulsive electrostatic forces of protons. That is way, I named nuclei by “nuclear quasi-holes”.
Magnetic collapse has no limit. Magnetic hole will grow till there is the food, - the matter of planet or star.

The biggest error of CERN physicists is in the equating the consequences of A and B.
A. Collisions of protons at LHC;
B. Collisions of cosmic protons with atmospheric protons.

Similarity: Energies in A and B are sufficient in order to make microscopic magnetic holes.

Difference: Velocities of created holes relatively surrounding matter are drastically great.
A. Magnetic holes, made on LHC, can have very small velocities, such as slow nucleus entered into the neutron-bottle, and exploded the town.
B. According to conservation law of 4-momentum, cosmic holes have relativistic velocities, such as TeV nuclei, destructed in the neutron-bottle.

Result:
A. LHC’s holes will capture slowly moving particles and grow. The bigger hole becomes – the bigger its rate of growth.
B. Atmosphere particles move relatively holes with relativistic velocities and, correspondingly, they have TeV kinetic energy, relatively holes. As a result, magnetic holes will be ruined almost immediately. Such collisions lead to creation of showers of secondary particles. Physicists observe such showers.

In our upper model with two neutron-bottles we could see that bombardment of bottle by eV-nuclei can lead to Hiroshima-like explosion, but TeV-nuclei bombardment are safe. Correspondingly LHC-collisions can destroy the Earth; cosmic-atmospheric particle collisions occur constantly and safe.

Most of physicists are confident that heavy particles, created at LHC will decay.
That is a deadly error.

LHC can create a particle with the mass by 10 000 times greater than the mass of proton.

To imagine this, compare the masses of a human and of a railway train.

Imagine what will happen, if biologists would make a creature with the mass of railway train, but having the human size. What will happen to you if this creature would seat at the roof of your house, exactly over you? Any roof will be broken and you would be smashed into a thin film and pushed deep into the ground.

Now imagine a proton, as soap bubble, and a liquid drop of the same size.
What will happen to protons, if the bubble has a field, attracting protons?
Protons would be ruined and their remnants would condense onto the drop.

Particle physicists think that proton consists from three point-like quarks (u, u, d). In fact, proton can be composed from some continuous substance, rotating with relativistic velocity. This rotating substance creates three mixed electro-magneto-weak poles (u, u, d). In a strong magnetic field this three-pole construction can be ruined, and the two-pole construction can be created. This process is accompanied by ejection of positron.

There are two independent math proves that this reconstruction can be performed at energies about 0,25 TeV per colliding particle, if the magnetic moment of resulting two-pole particle is the same as the magnetic moment of proton. If its value is different, then the needed energy would also be different.

We know two types of explosions: chemical and nuclear. Astronomers see the third type of explosions – collaptical. At nuclear explosion only a few thousand’s parts of explosive rest energy is realized in the form of radiation and kinetic energy of fragments. At some stellar collaptical explosions about a half of rest energy of the star is released in the form of radiation and kinetic energy of the rejected stellar shell. What type of collaptical explosions do astronomers observe: gravitational into black hole or magnetic into magnetic hole?
Is it possible to switch the magnetic collapse at collider?
My answers: The observed collapses are magnetic ones. Magnetic collapse can be switched on by powerful colliders.

LHC will be switched on in the mead-November; the first collisions are waited in a few weeks later. Do we survive or do we start into outer space?

The Earth after the magnetic collapse will transform into a small region of exited superconducting vacuum. This region’s diameter is about 10 meters. The thickness is about 2.5 meters. The strength of magnetic field in this region is about 1016 teslas. Because of the strong magnetic interaction, this small magnetic hole will move on spiral trajectory to the Sun. As a result, the Sun will explode and astronomy amateurs from neighbor stellar systems (alien free thinkers) will observe novae or supernovae phenomenon. Alien stephen hawkings will say: “The world will not come to an end when the LHC turns on. The LHC is absolutely safe. ... Collisions releasing greater energy occur millions of times a day in the earth's atmosphere and nothing terrible happens”

The next crude error of CERN physicists is hidden in the formula of magnetic* catalyses of proton decay

M + p = M + e+.

More correct formula must contain the number n:

M{n} + p = M{n+1} + e+.

This number shows the number of x-bosons in magnetic hole. These bosons have the equal quantum numbers. Magnetic hole works as laser. The word “laser” originated as an acronym for Light Amplification by Stimulated Emission of Radiation. Laser creates the same photons, which are bosons with zero mass energy. Because of zero mass, photons fly away from laser with the speed of light. Magnetic trap creates x-bosons, which have non-zero rest mass. These bosons do not fly away but becomes the constituent part of magnetic hole. The bigger is the number n – the bigger is the rate of magnetic collapse of ordinary matter into magnetic hole.

* Physicist usually say: “monopole catalyses of proton decay”, I say that magnetic hole is magnetic dipole and M in my upper formulas denotes magnetic dipole.

According to Russian online “opinion poll” at November 17, 2009, 51% of respondents had said that LHC is the dearth threat. But as we can see, CERN continues their preparations to this crime experiment. Conclusion - the science is criminal now!


4D ROTATION AND SPHERE PACKING


In 2d space, i.e., in plane, around one sphere we can arrange six spheres of exactly the same radius.
In 3d space, around one sphere we can arrange 12 spheres of the same radius.
In 4d space, around one four-dimensional sphere we can arrange 24 spheres of the same radius.

On the bottom gif-animated picture you can see the example of the densest packing in the 4d space. For our convenience the spheres are shown with diminished radii, in order, we could see the behind spheres. The fourth dimension is associated with color. We are situated at the point "green" on the color coordinate.

The left group of spheres is rotating in the horizontal plane xy.
The middle group of spheres is rotating in the vertical-color plane zs.
The right group of spheres is rotating in both planes: xy and zs.

Four-dimensional rotation has an interesting property; - the right thing is constantly transforms into the left thing, and visa verse. Figure to speech, in order to make the right shoe from the left one, we must turn it in the plane zs on p radians. It looks as fantasy, and in reality we can not make such transformations. But the physicists can make such procedures with elementary particles.

In the bottom text you can see an example of coordinates of the centers of spheres under the densest packing. The first six points give the densest packing in 2d space; the first 12 points give the densest packing in 3d space; and at last, the first 24 points give the densest packing in 4d space.
Designation: the stroke means square root, for example: 3'=sqtr(3).
Let's designate the central sphere by the digit "0". Then its coordinates are (0, 0, 0, 0). The spheres, contacting with the central sphere we'll designate by digits: 1, 2, 3,.. 24. Let's name these 24 spheres by "shell spheres". Coordinates of the spheres are written in the round brackets. The numbers of shell spheres contacting with the given shell sphere is written in the rectangular brackets.


1 (1, 0, 0, 0) [2,6,7,10,13,16,19,22]
2 (1/2, -3'/2, 0, 0) [1,3,7,12,15,16,21,22]
3 (-1/2, -3'/2, 0, 0) [2,4,8,12,15,17,21,23]
4 (-1, 0, 0, 0) [3,5,8,11,14,17,20,23]
5 (-1/2, 3'/2, 0, 0) [4,6,9,11,14,18,20,24]
6 (1/2, 3'/2, 0, 0) [1,5,9,10,13,18,19,24]
7 (1/2, -1/(3'2), 2'/3', 0) [1,2,8,9,13,15,19,21]
8 (-1/2, -1/(3'2), 2'/3', 0) [3,4,7,9,14,15,20,21]
9 (0, 1/3', 2'/3', 0) [5,6,7,8,13,14,19,20]
10 (1/2, 1/(3'2), -2'/3', 0) [1,6,11,12,16,18,22,24]
11 (-1/2, 1/(3'2), -2'/3', 0) [4,5,10,12,17,18,23,24]
12 (0, -1/3', -2'/3', 0) [2,3,10,11,16,17,22,23]
13 (1/2, 1/(3'2), 1/6', 1/2') [1,6,7,9,14,15,16,18]
14 (-1/2, 1/(3'2), 1/6', 1/2') [4,5,8,9,13,15,17,18]
15 (0, -1/3', 1/6', 1/2') [2,3,7,8,13,14,16,17]
16 (1/2, -1/(3'2), -1/6', 1/2') [1,2,10,12,13,15,18]
17 (-1/2, -1/(3'2), -1/6', 1/2') [3,4,11,12,14,15,16,18]
18 (0, 1/3', -1/6', 1/2') [5,6,10,11,13,14,16,17]
19 (1/2, 1/(3'2), 1/6', -1/2') [1,6,7,9,20,21,22,24]
20 (-1/2, 1/(3'2), 1/6', -1/2') [4,5,8,9,19,21,23,24]
21 (0, -1/3', 1/6', -1/2') [2,3,7,8,19,20,22,23]
22 (1/2, -1/(3'2), -1/6', -1/2') [1,2,10,12,19,21,23,24]
23 (-1/2, -1/(3'2), -1/6', -1/2') [3,4,11,12,20,21,22,24]
24 (0, 1/3', -1/6', -1/2') [5,6,10,11,19,20,22,23]

In order to transit from the turn to rotation, we must express the coordinates with the help of functions sin and cos. Here is the piece of program, which helps us to express the coordinates after every equal interval of time, corresponding to the turn at p/30 radians at both planes of rotation.

fi = pi / 3
M = Sqr(2 / 3)
For t = 0 To 20
psi = 0 + t * pi / 30 'rotation in the plane zc
hi = 0 + t * pi / 30 'rotation in the plane xy
a(0) = 0 'coordinates of the central sphere
b(0) = 0
c(0) = 0
d(0) = 0
For i = 1 To 6 'coordinates of spheres 1, 2,.. 6.
a(i) = Cos(-fi * (i - 1) + hi)
b(i) = Sin(-fi * (i - 1) + hi)
c(i) = 0
d(i) = 0
Next
For i = 7 To 9
a(i) = Cos(-fi / 2 - 2 * fi * (i - 7) + hi) / Sqr(3)
b(i) = Sin(-fi / 2 - 2 * fi * (i - 7) + hi) / Sqr(3)
c(i) = M * Cos(psi)
d(i) = M * Sin(psi)
Next
For i = 10 To 12
a(i) = Cos(fi / 2 + 2 * fi * (i - 10) + hi) / Sqr(3)
b(i) = Sin(fi / 2 + 2 * fi * (i - 10) + hi) / Sqr(3)
c(i) = M * Cos(psi + pi)
d(i) = M * Sin(psi + pi)
Next
For i = 13 To 15
a(i) = -Cos(-fi / 2 - 2 * fi * (i - 13) + hi) / Sqr(3)
b(i) = -Sin(-fi / 2 - 2 * fi * (i - 13) + hi) / Sqr(3)
c(i) = M * Cos(psi + pi / 3)
d(i) = M * Sin(psi + pi / 3)
Next
For i = 16 To 18
a(i) = Cos(-fi / 2 - 2 * fi * (i - 16) + hi) / Sqr(3)
b(i) = Sin(-fi / 2 - 2 * fi * (i - 16) + hi) / Sqr(3)
c(i) = M * Cos(psi + pi + pi / 3)
d(i) = M * Sin(psi + pi + pi / 3)
Next
For i = 19 To 21
a(i) = a(i - 6)
b(i) = b(i - 6)
c(i) = M * Cos(psi + pi + 2 * pi / 3)
d(i) = M * Sin(psi + pi + 2 * pi / 3)
Next
For i = 22 To 24
a(i) = a(i - 6)
b(i) = b(i - 6)
c(i) = M * Cos(psi + 2 * pi / 3)
d(i) = M * Sin(psi + 2 * pi / 3)
Next

At every moment the distance between the central sphere and any of the shell spheres is equal to 1. At every moment the distance between any shell sphere and any of another shell spheres is equal or bigger than 1.
(I don't exclude that this piece of program can be written shorter.)

Earlier I have thought, that in n-dimensional space it is possible to pack m = 3*2n-1 spheres around the central sphere. But it turned out to be, that this formula is correct only for dimensions 2, 3, and 4.

To see the rotation in pseudo-Euclidean space-time open my Electron-model program http://darkenergy.narod.ru/SR2007.exe


Look also the page 4D - World.

To index of Space Genetics

My Curriculum Vitae.

Ivan Gorelik.


TopList


 


 

Extremely urgent note, 2009.

Attention! Magnetic trap of Devil!


Scientists, who cry about the safety of LHC, had already made a crime. 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.

People! Do not hope silently, that we will be saved again the next time. Make something!

News, links, the appeal about donations in order to make the Living Wall in front of LHC.

What will LHC give us, the particle of God, or magnetic trap of Devil?

Reproduction of biospheres and civilizations.

Magnetic trap of Devil..

Arguments,

News, links, the appeal about donations in order to make the Living Wall in front of LHC.

Magnetic trap. Figures.

 

 

The end of Extremely urgent note, 2009.
 


Four-dimensional Rotation of the Universe.

If our Universe is closed, then it can rotate. The last observations give several proves of this idea.

Non-Euclidean closed Universe can be imagined as three-sphere x2+y2+z2+q2=r2, arranged into Euclidean 4-d space, where q is aditional coordinate, associated with color. That is slightly remind us the left figure, without the central ball. That will be the rotation in 4-d space. We live in pseudo-Euclidean space-time. That is why, we must change the q-coordinate into ict-coordinate.

In order to see the rotation in the pseudo-Euclidean plane (x,ict) you can open my program http://darkenergy.narod.ru/SR2007.exe

It is very interesting that the length of two hyperboles after dividing of every element of hyperboles by corresponding γ is iqual to 2pri. And more, - the quantable velocity was found. As a result the time-axis can by finite and closed.

Now unite the two pictures and imagine the rotation of pseudo-Euclidean hyper-sphere: x2+y2+z2+(ict)2=r2

All points of the Universe can move with the same linear velocity c, and with the same angular velocity H.

The usual ball can not rotate such, that all it's point moved with the same linear velocity. In this sense the Universe is more homogeneous.

But we can find one dipole (axis-plane of rotation B) for every point A of such Universe. Moreover any point A has its proper axis-plane B and the point A is situated at B. The point A divides B on to rays. Let say, that this axis-plane is composed by axes z and ict. In every point of the Universe the square of 4-velocity (vg, icg), is equal to -c2. At the point A v=0. Consequently its g=1 and 4-velocyty of this point has only time component (0, ic). Point A moves here with the velocity of light only relatively the time-coordinate. All other points of this axis-plane has a spatial component of 4-velocity. Consequently all galaxies visible from A along the axis-plane (z,ict) will be transverse red-shifted along z-coordinate. But all galaxies laying on this axis-plane does not move relatively each other, - they rotate together along circumference in the plane (z,ict). The plane-axis (x,y), perpendicular to axis (z,ict) is circular and embraces the axis-plane at the distance R. It is also rotating. And the galaxies, visible in that direction will also be transverse red-shifted.

Such rotation explains many-many things, I can not write all here. And only make a note.
Rotation gives and explains:
the spin of every particle of Universe;
particle's quantum ψ-function;
the right-left asymmetry in galaxies spirality;
why the conventional age of the Universe is constant and is 13,34 billion years, always!
abnormal rotational velocities of peripheral stars in galaxies;
the critical density in such Universe is less...

If the velocity along the axes are slightly different we will see the multipole structure in the cosmic microwave background radiation; the difference in red-shifts of galaxies.  


 Some additions from different sources.


Kissing Number

[3] Problems of arranging balls densely arise in many situations, particularly in coding theory (the balls are formed by the sets of inputs that the error-correction would map into a single codeword).
The most important question in this area is Kepler's problem: what is the most dense packing of spheres in space? The answer is obvious to anyone who has seen grapefruit stacked in a grocery store, but a proof remains elusive. (It is known, however, that the usual grapefruit packing is the densest packing in which the sphere centers form a lattice.)

The colorfully named "kissing number problem" refers to the local density of packings: how many balls can touch another ball? This can itself be viewed as a version of Kepler's problem for spherical rather than Euclidean geometry.

[1] In mathematics, sphere packing problems concern arrangements of non-overlapping identical spheres which fill a space. Usually the space involved is three-dimensional Euclidean space. However, sphere packing problems can be generalised to two dimensional space (where the "spheres" are circles), to n-dimensional space (where the "spheres" are hyperspheres) and to non-Euclidean spaces such as hyperbolic space.
A regular arrangement (also called a periodic or lattice arrangement) is one in which the centres of the spheres form a very symmetric pattern called a lattice. Arrangements in which the spheres are not arranged in a lattice are called irregular or aperiodic arrangements. Regular arrangements are easier to handle than irregular ones—their high degree of symmetry makes it easier to classify them and to measure their densities.

[2] The number of equivalent hyperspheres in dimensions n which can touch an equivalent hypersphere without any intersections, also sometimes called the Newton number, contact number, coordination number, or ligancy.

Exact values for lattice packings are known for n=1 to 9 and n=24 (Conway and Sloane 1993, Sloane and Nebe). Odlyzko and Sloane (1979) found the exact value for 24-D.

Exact values for general packings are known for n=1, 2, 3, 4, 8, and 24. Musin developed a bounding method in 2003 to prove the 24-dimensional case, and his method also provides proofs for three and four dimensions (Pfender and Ziegler 2004).
 

SO(4)

[4] In mathematics, SO(4) is the four-dimensional rotation group; that is, the group of rotations about a fixed point in four-dimensional Euclidean space. The name comes from the fact that it is (isomorphic to) the special orthogonal group of order 4.

   Simple rotations
A simple rotation R about a rotation centre O leaves an entire plane A through O (axis-plane) pointwise invariant...

Half-lines from O in the axis-plane A are not displaced; half-lines from O orthogonal to A are displaced through α; all other half-lines are displaced through an angle < α.

      Double rotations
A double rotation R about a rotation centre O leaves only O invariant. Any double rotation has at least one pair of completely orthogonal planes A and B through O that are invariant as a whole, i.e. rotated in themselves. In general the rotation angles α in plane A and β in plane B are different. In that case A and B are the only pair of invariant planes, and half-lines from O in A, B are displaced through α, β, and half-lines from O not in A or B are displaced through angles strictly between α and β.

     Isoclinic rotations
If the rotation angles of a double rotation are equal then there are infinitely many invariant planes instead of just two, and all half-lines from O are displaced through the same angle. Such rotations are called isoclinic or equiangular rotations, or Clifford displacements. Beware: not all planes through O are invariant under isoclinic rotations; only planes that are spanned by a half-line and the corresponding displaced half-line are invariant.


Links:

1. Sphere packing. Wikipedia
2. Kissing Number
3. Sphere Packing and Kissing Numbers
4. SO(4)