Gravitation theory of elementary particles. Part 2
Beginning: Gravitation theory of elementary particles.
Contents:
8. The field of a gravitational dipole
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We introduce concept of a gravitational dipole as systems, consisting of two equal dot masses. The concept of a dipole exists in an electrostatics, but there charges have an opposite sign. In case of gravitation, any weight always has a positive sign as it is created by energy of the electromagnetic field.
We will place the beginning of coordinates in the center of a dipole. We will direct axis Y along the line connecting the centers of mass of gravitational objects, and axis X then will be perpendicular this line. Both mass of identical size (m), but carried in space on rather long distance 2α (that need to consider structure of gravitational bodies has disappeared), and are in points (1) and (2). A point with coordinates (x, y) - any point on the plane in which we will define intensity of a gravitational field. As through a straight line and a point it is always possible to carry out the plane, the considered task will be two-dimensional (in this plane without axis Z as the components of the gravitational field intensity along axis Z it will be equal to zero).
According to the law of universal gravitation, the size of the gravitational field intensity in a point with coordinates (x, y), the gravitational field created by a source with a mass of m located in a point (1) of r_{1} removed on distance, it will be equal:
(138)
where G - is the gravitational constant.
Similarly, the size of the gravitational field intensity in a point with coordinates (x, y), the gravitational field created by a source with a mass of m located in a point (2) of r_{2} removed on distance, it will be equal:
(139)
Apparently from the presented drawing and trigonometry, the distance square from a source of a gravitational field to a point of supervision will be:
(140)
and for other source:
(141)
There is a temptation to substitute r_{1} and r_{2} in expressions for Г_{1} (138) and Г_{2} (139), and then to put both numbers (as it often becomes in mathematics), but then we will receive result, approximately true on big (in comparison with a) distances, and in a near zone we will receive frankly incorrect result.
We will arrive as the physics demands. For addition of two vectors, what is intensity of a gravitational field (Г_{1} and Г_{2}); we will spread out them to components along axes X and Y.
(142)
(143)
(144)
(145)
Then it is necessary to put the identical Г_{1} and Г_{2} components.
(146)
(147)
The size module of the vector of the gravitational field intensity created by a gravitational dipole is equal to a root square of the sum of squares his component, and will be:
148)
Not such beautiful expression, as has turned out at simple substitution of r_{1} and r_{2} in Г_{1} and Г_{2}, but the truth.
In a distant zone when a^{2} can be neglected, the received expression will become simpler:
(149)
where
(150)
It has turned out that the doubled weight, in a distant zone creates the gravitational field of the doubled intensity decreasing under the law 1/R^{2}. But it is only for a distant zone, and in a near zone, where the main energy of a gravitational field, result absolutely other is concentrated.
As appears from the equation of the gravitational field intensity of a dipole, intensity is equal to zero, both at infinitely long distance, and in the center of a dipole. Follows from the last that near a gravitational dipole there is an area with lowered (but other than zero) intensity of the field.
In case of distinction of size of mass of gravitational objects, we will arrive similarly. We will spread out Г_{1} and Г_{2} to components along axes X and Y.
(151)
(152)
(153)
(154)
Then it is necessary to put the identical Г_{1} and Г_{2} components again.
(155)
(156)
The size module of a vector of the gravitational field intensity created by pair of gravitational bodies, mass of m_{1} and m_{2} (which are in points (1) and (2)) is equal:
(157)
If as a source of a gravitational field to take symmetric to a component of a gravitational field of an elementary particle (see a formula 98):
(158)
that instead of (157) will turn out the interesting equation is whiter:
(159)
where: r_{0~} - is the radius of an elementary particle in the field theory.
The equations (146-148) are fair for the gravitational field created by the based molecule of substance consisting of two any atoms and work in space, outside a molecule. In a molecule it is necessary to consider structure of kernels and distribution of an electronic cloud of each atom. In turn the equations (155-157) with a good accuracy describe a gravitational field of couple of based elementary particles. The exact equation of a gravitational field won’t be such simple and evident. As we see, (m_{1} + m_{2}) out of limits of a square root can’t be taken out - it will lead to wrong result, especially in a near zone where the main energy of a gravitational field is concentrated.
The received equations of the field of a gravitational dipole differ from the equations of the field of an electric dipole in an electrostatics - but and had to happen: gravitation and electromagnetism belong to different fundamental interactions of the nature.
Conclusion: in the nature there is no gravitational field created by the molecule consisting of couple of atoms (1 and 2) and the weight equal to the mass sum of these atoms - in the nature there are gravitational fields created by elementary particles of atom 1 and atom 2 and this field has asymmetrical structure, develops by rules of addition of vectors in each point of space, but not as scalar sizes. Having replaced the vector sum of gravitational fields of elementary particles with some average abstract value (having ignored their exact coordinates, defect of weight, orientation a back), we will lose gravitational fields of nuclear kernels (in which the main energy of gravitational fields of substance is concentrated) and as a result we will pass from physics to mathematical fairy tales.
8.1. The field of the rotating gravitational dipole, its gravity waves
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Let in the plane (the gravitational dipole rotating with f frequency is X, Y) the center of rotation coincides with the center of a dipole. We will combine the beginning of coordinates with the center of rotation.
We look for a gravitational field in this plane in a point, with coordinates (x, y), out of a dipole. Let in some time point the corner between the axis X and a straight line connecting masses is equal θ.
According to the law of universal gravitation, the size of the gravitational field intensity in a point with coordinates (x, y), the gravitational field created by a source with a mass of m located in a point (1) of r_{1} removed on distance, it will be equal:
(160)
Where G - is the gravitational constant.
Similarly, the size of the gravitational field intensity in a point with coordinates (x, y), the gravitational field created by a source with a mass of m located in a point (2) of r_{2} removed on distance, it will be equal:
(161)
Now we will define r_{1} and r_{2}. Apparently from the presented drawing and trigonometry:
(162)
(163)
(164)
and for other source:
(165)
(166)
(167)
From where we will receive components of vectors of the gravitational field intensity:
(168)
(169)
(170)
(171)
Then it is necessary to put the identical Г_{1} and Г_{2} components.
(172)
(173)
The size module of a vector The module of size of a vector created by a gravitational dipole is equal to a root square of the sum of squares his component, and will be:
(174)
In a distant zone when α^{2} it is possible to neglect, the received expression will become simpler:
(175)
where R - that is an average distance to a gravitational dipole.
We will substitute in (174) value θ=0 (cosθ=1, sinθ=0), we will receive value of the maximum intensity of a gravitational field:
(176)
Similarly, having substituted in (174) value θ=π/2 (cosθ=0, sinθ=1), we will receive value of the minimum intensity of a gravitational field:
(177)
Having used properties of symmetry of the field, the rotating gravitational dipole, the equation (176) and (177) it is possible to simplify, having entered:
(178)
Then, having put x=R and y=0, we will receive:
(179)
(180)
The difference (179) and (180) will give the doubled amplitude of the gravitational wave created by the rotating gravitational dipole:
(181)
where
(182)
Thus, the gravitational dipole weighing M, with distance between weight halves equal 2α, f rotating with a frequency across the axis, creates in space continuous gravitational waves, frequency 2f and wavelength
(183)
and amplitude (in the plane of rotation of a dipole):
(184)
But the multiplier 1/R^{2} - it lies on a surface, and now we will look that the square bracket at long distances gives (when δ < <1). For this purpose we will replace a multiplier of the second fraction of a bracket in degree 3/2 with the same expression in degree 1 increased by the two first the member of decomposition of a square root in a row Taylor (instead of a square root).
(185)
Then the square bracket will correspond:
(186)
Having substituted it in (184) we will receive:
(187)
As we see, the amplitude of the gravitational waves created by the rotating gravitational dipole at long distances from a source of waves (when α < < R) decreases under the law 1/R^{4}.
As appears from (187) statement that amplitude of gravitational waves decreases under the law 1/R - to the gravitational waves created by elementary particles of which material objects of the Universe consist, has no relation. Persons interested can independently find the field of the rotating gravitational dipole out of the plane of his rotation.
8.2. The field of an oscillating gravitational dipole, its gravity waves
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Let in the plane (the gravitational dipole oscillating with f frequency is X, Y), passing through a supervision point. We will combine the beginning of coordinates with the center of a dipole, and we will direct axis Y along the line connecting the centers of masses.
We look for a gravitational field in this plane in a point, with coordinates (x, y). Let in some time point the distance between masses has reached a maximum equal 2α_{1}.
Then the size of the gravitational field intensity in a point with coordinates (x, y), the gravitational field created by both sources with a mass of m, it will be equal:
(188)
(189)
(190)
where R - is the distance from the center of a dipole to a supervision point.
When (through certain time) masses as much as possible come nearer, to distance 2α_{2}, we will receive the new size of the gravitational field intensity in a point with coordinates (x, y), the gravitational field created by sources with a mass of m:
(191)
(192)
The difference of strength of a gravitational field will be:
(193)
(194)
We introduce designation:
(195)
Then (6) and (7) will correspond:
(196)
(197)
At long distances (when δ < < 1) the bracket fraction multiplier in degree 3/2 can be replaced with too expression in degree 1 increased by the three first the member of decomposition of a square root in a row Taylor.
(198)
And with a minus sign:
(199)
Then, having rejected δ^{6}, we will receive:
(200)
(201)
But
(202)
Then:
(203)
As it has turned out, the X-component aspires in zero under the law 1/R^{6}. We will look what will give a Y-component.
(204)
It has turned out, as a Y-component aspires in zero under the law 1/R^{6} (the first composed) and 1/R^{7} (the second composed).
As we see, the gravitational waves created by an oscillating gravitational dipole with removal from a source, aspire in zero not more slowly than 1/R^{6}.
9. The gravitational waves created by the thermal movement a crystal lattice of atoms
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Let us have an atom of a crystal lattice there is nobody a solid body, at a temperature other than absolute zero. Such atom will fluctuate, about average situation. We will carry out the plane, through a point of supervision and the line along which there is a fluctuation of atom in a crystal lattice. We will direct axis Y through the line of fluctuation of atom, and the beginning of coordinates it is compatible to average situation. Let amplitude of the maximum deviation be equal α.
We look for a gravitational field in this plane in a point, with coordinates (x, y). Let in some time point the atom is in a point +α.
Then the size of the gravitational field intensity in a point with coordinates (x, y), m created by atom with a weight, it will be equal:
(205)
(206)
(207)
where R - that is a distance from an average point of oscillation of atom to a supervision point.
Moving in the opposite direction, the atom will pass an average point after a while. In this case, intensity of a gravitational field in a point with coordinates (x, y) and the gravitational field created by an oscillating source with a mass of m will be:
(208)
(209)
When (through certain time) the atom hits the nail-α, we will receive the new size of the gravitational field intensity in a point with coordinates (x, y), the gravitational field created by an oscillating source with a mass of m:
(210)
(211)
We will define how the gravitational field created by a source in a point +α differs from the field created by a source in an average point (0):
(212)
(213)
where
(214)
We will replace expression in degree 3/2 with too expression in degree 1 increased by the three first the member of decomposition of a square root in a row Taylor.
(215)
Then, having rejected δ^{6}, the bracket in (212) will correspond:
(216)
Also the bracket in (213) will similarly correspond:
(217)
Then, at δ < < 1, the equation (212) will correspond:
(218)
On axis X, coordinate x will be made even to R, as a result will be:
(219)
We will similarly deal with Y component
(220)
On axis Y, the coordinate of y will be made even to R; as a result we will receive two components which are differently aspiring to zero:
(221)
The first member of expression (221) will aspire to zero, quicker than the second member therefore, considering and (219), since a certain distance, he will remain only:
(222)
(223)
We have received the gravitational wave extended along an axis of fluctuation of atom, amplitude
(224)
In the directions other than a fluctuation axis, it is necessary to increase by a cosine of the angle between the direction and an axis of fluctuation of atom:
(225)
As we see, 1/R^{2} gives easing with distance of the most gravitational field, 1/R more the gravitational wave gives, and as a result it turns out 1/R^{3}. - This slowest decrease of amplitude of the gravitational waves with distance to a source created by elementary particles and atoms and molecules of substance of the Universe consisting of them.
With growth of absolute temperature of substance, will increase, and amplitude of the gravitational waves created by his atoms. Obviously, registration of gravitational waves by means of solid bodies, at least, requires cooling of these bodies (and also the bodies surrounding them) up to the temperatures, near absolute to zero. But also at the same time there is very good chance to catch gravitational waves from the passing car or other moving subject. Also there is a stream of the electronic neutrinos passing through installation, but it can be separated on the frequency of the accepted signal.
10. The gravity waves of elementary particles
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Any rotating couple of elementary particles, forces of the electromagnetic nature connected among themselves, creates in space around itself gravitational waves with a frequency (f) equal to rotation frequency (or the doubled rotation frequency in case of couple of identical elementary particles), and the wavelength determined:
where λ - is the wavelength, v_{gr} - is the speed of distribution of gravitational waves.
Gravitational waves are created by also any rotating molecule of substance consisting of several atoms (which is at a temperature other than absolute zero), and also the molecular connections of electronic neutrinos forming “dark substance” of the Universe (also at not a zero temperature). On the rotation termination, the radiation of the gravitational waves (created by rotation of pair of gravitational masses) is stops (before emergence of new rotation, from interaction with the elementary particle which has flown by nearby or for other reason).
In a macrocosm, gravitational waves are created also by any rotating asymmetric material object, and single gravitational waves are created by any moving material object. Gravitational waves of material objects of a macrocosm represent the sum of gravitational waves of elementary particles of which this object consists.
When declare to us detection of gravitational waves from the objects which are at the distances exceeding one billion light years and in too time don’t notice gravitational waves from the terrestrial sources which are at distances about a kilometer, the first question which arises: but whether the tale played with “Higgs boson” already in relation to gravitation repeats.
Having learned to register gravitational waves of different frequencies, to define the direction from where they have come, the mankind will open for itself the new world inaccessible in the 20th century - the world of gravitational waves.
11. Gravitational waves, black holes, and LIGO (Laser Interferometer Gravitational-Wave Observatory)
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In February, 2016 there was a message which alarmed the planet. Quote (and two subsequent) from Wikipedia: “on 11 February 2016 LIGO and Virgo collaborations announced the discovery of gravitational waves that occurred on 14 September 2015 in the installations of LIGO, the detected signal came from the merger of two black holes with masses of 36 and 29 solar masses at a distance of about 1.3 billion light years from Earth, with three solar masses left for radiation.”
That “black hole” is from the world of mathematical tales, I have already shown, but not everyone can read Russian or want to use a translator, and continue to repeat the failed tales, passing them off as science.
Will try to figure it out and understand.
1. Quote: “LIGO consists of two observatories in Livingston, Louisiana) and in Hanford (Washington), remote from each other at 3002 miles. Because the speed of propagation of gravitational waves is expected to equal the speed of light, this distance gives a difference of 10 milliseconds, which will determine the direction to the source of the registered signal.”
Question: from which it follows that the propagation speed of gravitational waves must be equal to the speed of light? - Approval of the General theory of relativity albert Einstein - this statement is one of the theories of gravity, and dozens of them. The gravitational field of General relativity exists in the framework of this theory, and how and what it creates in nature. If not elementary particles create it, then is what?
If the gravitational fields of General relativity to create fictional black holes that are the same field and creates - then the question is: what is cause and what is effect? Or maybe the gravitational field of General relativity creates a fabulous “dark matter”? - The gravitational field does not exist in nature by itself - physics has found its sources. If the gravitational field the General theory of relativity there is no source (able to create this field), so in nature there is no this field, or anything else we don’t know, but then you can invent whatever comes to mind, and then to give their own opinion of the scientific data.
Propagation of gravitational waves in space and the propagation of electromagnetic waves in space are two different physical processes, due to the different properties of space through which they propagate. From physics there is no compelling reason (in addition to the wishes of some authors and their supporters) to argue that the speed of propagation of these different physical processes are required to match. Hence: difference in time of arrival of the gravity signals to determine the direction to the source.
2. Quote: “the Main element of each Observatory is l-shaped system consisting of two four-kilometer-long shoulders with a high vacuum inside. Inside this system installs a modified Michelson interferometer, each arm of which is with mirror made of quartz glass are formed resonators, Fabry-Perot, these mirrors are to special are the suspension of the test masses, the distance between which changes came a gravitational wave. She extends one shoulder and at the same time shortens the second.”
The last statement is false. The impact of gravitational waves on each of the arms depends on the direction to the source. This may lead to different change of the length of each arm, and sometimes the same. There is a direction along which the device cannot detect gravitational waves, because of the sameness of changing the lengths of both shoulders. Is any direction lying in the plane passing through the center of the spectrometer at an angle of 45 degrees to each of his shoulders. In this plane is a lie in the beam splitter that distributes the light flux from the laser between the shoulders.
3. Quote: “the laser Beam first passes through a one-way mirror which passes the beam from the laser and reflects the beam returning from the interferometer, thus being recirculated power and allowing instead of 750-kilowatt laser to use a 200-watt. Then the beam enters the interferometer and is split by the beam splitter into two beams, each of which is sent to the appropriate arm of the interferometer and passes the Fabry-Perot about 280 times, repeatedly reflected at the end and beginning of the shoulder, which greatly improves the sensitivity of the interferometer. Then the rays of the two shoulders are formed in the photo detector, and the difference between them causes a current change in the detector”. This information is necessary for understanding the operation of the interferometer.
Both drawings are taken from Wikipedia.
4. Quote: “the parameters of the event
The shape of the signal matches with the prediction of General relativity for the merger of two black holes with masses 36(+5-4) and 29(+4-4) sun. Resulting black hole has a mass of 62(+4-4) the mass of the Sun and the parameter of rotation a = 0,67(+0,05-0,07). Rejected for tenths of a second in a fusion energy - the equivalent of 3(+0,5-0,5) solar masses.
The location of the source
Distance to source was calculated from the comparison of emitted power, evaluation of which give black hole masses, and the measured signal amplitude - 10^{-21}. Distance was equal to roughly 1.3 billion light years (410(+160-180) MPC, redshift z = 0,09(+0,03-0,04)).
The direction to the source of the signal is determined using the time difference of the signal passing through the detectors. With only the two LIGO detectors, this difference in time can only determine the angle between the direction of propagation of the signal and a straight line connecting the detectors. This sets the cone, the surface of which may be the source. The sky map of the possible area of origin looks like a thin ring - ring thickness is smaller, the smaller the measurement error. The signal delay was 6.9(+0,5-0,4) ms, it is possible to calculate that the source of the signal GW150914 lies on the cone target which is directed in the southern celestial hemisphere. Additional consideration of the polarization of gravitational waves and the relative position of the two antennas with respect to the alleged source on the basis of the ratio of the signal amplitudes allows you to further narrow the scope. The map of the sky is a region where the source signal is a Crescent with an area of 140 square degrees (50% chance) or 590 sq. degrees (with 90% probability). If you have three detectors that are not located on one straight line could significantly increase the accuracy of determining the coordinates of the source.”
4.1. Fabulous black holes, contrary to Classical electrodynamics, the law of conservation of energy and gravitation theory of elementary particles - their existence in nature is impossible.
4.2. On this screenshot the readings of detectors of the interferometers, we see not a single pulse, and the oscillatory process, tear-off at high frequency. This can be observed with vibrational or rotational system, where during each cycle selected some (not decreasing) the value of the energy. When all the energy is exhausted, the process stops.
4.3. The question of how, and which bear in themselves the gravitational wave energy is yet to be seen.
4.4. The distance to the source and the direction to it - all these unproven assumptions, the investigation to one theory of gravity.
4.5. Compare the amplitude of gravitational waves from pairs of rotating gravitational sources with masses of 36 and 29 solar masses, located at a distance of 1.3 billion light years with an amplitude of gravitational waves from a pair of rotating terrestrial sources of gravitation with masses of 36 and 29 grams located in the middle between the two interferometers ( i.e. the distance is 1501 km). The orientation of the plane of rotation will correspond to the maximum radiation in the direction of the interferometers.
The mass of the sun is equal to: 1.9891•10^{33} grams, 1 light year is equal to: 9.4605281•10^{12} km 1.3 billion light-years is: 1.22987•10^{22} km. And now you can remember the formula (187) defines the amplitude of the gravitational waves a pair of rotating objects from the distance from the source, and we will see the 1/R^{4}. The end result is that the amplitude of gravitational waves from rotating a pair of massive gravitational sources is weaker than the amplitude of the gravitational waves rotating pair of terrestrial sources, more than 10^{42} times. And while these devices do not learn reliably to register gravitational waves from terrestrial sources, confidence in their ability to register gravitational waves from rotating sources in other galaxies will be zero.
To identify the true direction to the source of the gravitational waves will have to build another shoulder straight down is to introduce another orthogonal axis, and to learn how to accurately measure the length of each shoulder separately.
LIGO with Virgo can get a Nobel prize in physics, pushing through the science officials from Stockholm right solution, but it will be another wrong decision of the Nobel Committee for physics. Time a science fair ended together with the era in which HONOR was a fundamental principle. It’s the time of cutting of grants for “scientific” research. But at all times the existence of physics there are people for whom science is the meaning of life.
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Vladimir Gorunovich |