The Riemann Curvature Vein of Gravitational Soliton Sensor & Gravior (Spin-2 Quanta) Quadrupole Excitations

By
Professor Kotcherlakota Lakshmi Narayana

http://trusciencetrutechnology.blogspot.com/
Dated: 23rd July 2008 at 11.30AM

keywords: Gravior, Gravitational Wave,Gravitational Soliton,
Balanced Pounding Bar detector, After-Glow,Coronal region, small signal technique,Cavitons,Quadrupole excitations, Quantum Gravity,Anttenas
Summary
The Gravitational Soliton excitation of a two-mass system of a Balanced Pounding Bar (BPB) sensor partially immersed in a liquid medium is investigated.The Gravitational Wave (G-Wave) energy translated in terms of Soliton excitation of a surface wave that would eventually dislodge,the BPB to have a free-fall has been analysed explicitly.The involved details of amplitude frequencies and other physical quantities are presented.The Lagrangian and the Equations of Motion were se up.The expression for semi-axes cone angle q subtended by the central point with the bottom circumference of the Bar has been derived.The Equation for the angle q of the BPB sensor, incorporates features of Quadrupole (Spin-2) excitations and as well the surface tension contribution to the normal mode of vibrations of the system.The two modes of vibrations(one with and other without contribution of surface tension of liquid) are found to determine the possible excitation Energy range of the system.The absorption magnitude and the cross-section of translation of G-Wave into the surface Solitary Wave excitation has been detailed out.
The free-fall is visualized by the "Gravior " Quadrupole excitation levels of BPB sensor, essentailly as a conversion of Solitary Energy to the Gravior Quantum system of Quadrupole excitations. Gravior Quanta are also Spin-2 entities and may be considered as akin to Gravitons (or like the phonons of the solid state lattice vibrations). A significant finding is that free-fall could be interpreted from a possible sequence of Gravior Quadrupole Excitation levels..The BPB sensor has been studied, by the author, to have the patent rights reserved to himself, for an advanced technological sensor based on the ideas and concepts outlined and detailed in the present model and its formulation.


I. Introduction

a) G-Waves:

Gravitational Waves (G-Waves) are thought to be small ripples moving along the space-time world lines but with the understanding that it is not possible to distinguish which parts of the space-time curvature sustain ripples and which constitute the universe at large space-time structure. [1]. Waves from a supernovae explosion in Virgo Cluster of galaxies yields about 4x10³⁸ erg/cm²/ Hz in about 0.3 seconds or 2E-03 seconds. But Supermassive objects can give out ~1E+41 to 1E+56 erg/sec with a flux at earth as 1E-03 to 1E+12 erg/sec cm². The out put power in thee form of G-Waves is 1E+30 to 1E+32 ergs/sec and flux at earth is ~ 1E-10 to 1E-12erg/sec/cm².{Ref 1 Box 36.3}. Einstein asserted that at infinitesimally small levels the metric components and gravitational perturbation propagate with the same velocity as light.It is the object of present article by me, to separate out the several effects,to a reasonable extent,to get a clear picture of G-Waves and pave the way for a Quantum Gravity Theory.


(b)Mechanism:

The mechanism of the generation of G-waves lies in its quadrupole nature. Power output factors differ between Electromagnetism and the Gravitational contributions. The later involves a 1/5th factor as contrasted of 1/20th factor suggested by Electromagnetism.The G-waves reaching earth originate from a dynamic and deformed systems, such as gravitationally collapsing entities,Black Holes, Supernovae and Pulsars. In a pulsar phase, gravitational radiation is important only when the star is deformed from axial symmetry. The deformation that involves only 1000th part of star mass could radiate 10E+13 ergs/ sec, may be the youngest pulsar of a crab nebula.
A significant point to be noted is that the off-axis directional magnetic moments beam out radio waves, light and X-ray that NASA and Japanese have extensively investigated as pulsar waves. G-waves from massive have a frequency 3000Hz and last for about 1/3 second. Impulse events, such as bursts of radiation entitled have been listed in Box 76.2 of MTW book on Gravitation [1].

They suggest to investigate bursts of waves from debris falling into a black hole, collisions between two black Holes, and supernovae explosions. The typical Binary Stars h-Cas,x -Boo, Sirius, Fu-46 produce a flux at earth 1.4x10E-29,6.7x10E-28,1.3x10E-24 and 7x10E-26erg/cm²/sec .Neutron stars and Black Holes of radii 10kms could produce a flux at earth of order of magnitude 2.7x1012 erg/cm²/sec[4].


c). Cosmic Rays:

It has been realized that in the source of gravitational waves, the gravitational effects are tightly interwoven with the local hydrodynamic and local plasma physics. Pulsating radio sources of pulsar can be produce cosmic rays. The total energy involved in solar flare emission is of the order 10E+31ergs in cosmic rays and 10E+27ergs in Type IV radio bursts coming out from a small area of 1E+19 cm². The flare generates about 1E+31 or 1E+32ergs in duration of time of 10³ and 10⁴ seconds. The mechanism suggested is the annihilation of magnetic field energy density (which is high near sun spots) into kinetic energy. The fields are as high as 2k to 3k Gauss over area of several million square Kms. The current required to produce a field of say 3k Gauss in a large sun spot comes to something like 1012 Amperes over an area of several million kilometers.

The microwave background at earth is received from all directions with nearly same temperature about 2.7 ⁰K and about 4E-34 gm/cm³. It's presumed to be isotropic. Gravitons and neutrinos have their temperatures red shifted in accordance with the law T ~ 1/r expansion of the Riemann Tensor and consequently today their temperature should be roughly 3⁰K.

Cosmic rays observation by Hess and Kolhorolen (1911-1913) provide that the energy density in interstellar space as about 1.0eV/cm³ or 1E-12erg/ cm³.This is within the range of energy of a star light, or a cloud of ionized interstellar gas.O.Klein and H.Alfven [5] hierarchic cosmology of matter in an asymptotically flat space-time is not consistent with the cosmic ray observations.V.F.Hess observed cosmic rays flying in a gondola balloon in Austria on August 17th, 1912 and found them to increase in intensity above the surface of earth. There exists small difference in fractional abundances of different elements in cosmic rays and the universe. The sources of these rays have been thought to contain Carbon, Silicon or Iron. These and otter primary cosmic ray particles, have energies of 1E+09eV to 1E+20eV.

With consideration of universal Microwave background the energy range extends from 1E-07 eV to 1E+20 eV. The study also indicated that power law having a negative exponent, ascertains the decrease of flux with increasing energy of the particle. The three energy intervals found are 1E+10 eV to 1E+16 eV. In the low energy region Sun plays a dominant role. The Sun is also known to emit during some solar flare events charged particles in this low energy range. These are known as Solar Cosmic rays and are found to be anisotropic. It’s also found that an Astrophysical 1E+10 eV (10GeV) electron could by interaction with weak magnetic field ~ 10 ^-6 Gauss of Galaxy can give rise to a photon of 1E -07 eV (g=12.4m. Electron of 1 GeV energy emit radio waves with wavelength of 300m to 3 cm. Crab Nebula in blue continuum
light show that 10² to 10³ GeV electrons would be harmonized and they might be existing there.G-ray and X-ray photons are much more directly associated with radio-sources (synchrotron). X-ray Sun with thermal plasma >= 1E+06 ⁰K gives an output energy of 1E+23 ergs/sec.

The magnetic fields of solar system cannot contain or confine particles with energy in excess of 1E+03 GeV/nucleon. Supernovae explosion produce 1E+49 to 1E+52 ergs in about 50 years time and thus supply 1E+40 to 1E+43 ergs/sec.It’s very interesting that even to-date certain occult philosophers in India, continue to practice the observation of what they term as cosmic flow of light during the wee hours of early mornings. They claim that they observe about seven different kinds of flows, but some occultists claim that they observe only about four of them. Question remains thus why only Microwave background of the Big Bang was observed?

II.Plasma Solitons:

Interaction of EM waves in gaseous plasmas immersed in magnetic fields was the subject of experimental observations by Rao et al [5]. After a pulsed hot gas discharge akin to magneto plasma of afterglow, due to self-modulation, the energy state of the gaseous plasma changes. Each wave packet propagates in slightly different plasma than the previous one Rao et al[5]. Momentum transfer collision between light and heavy constituents of plasma, in certain conditions, hinders energy transfer. The energy of particle in this situation grows in between collisions. During after glow of the beam-treated plasma, this modulation of plasma density exists in the form of density wells and bunches. Rao et al [5] have given
details of how the EM energy is transferred into kinetic energy of a charged constituent of plasma confinement gets altered, with concomitant collision frequency changes. The wave bunches propagate along the magnetic field without spreading. Width of individual pulse comprises the wave packet. Non-linear wave packets due to cross-modulation Rao et al[5] propagation speeds depend on their amplitudes.In a stable equilibrium set between the effects of non-linearity and dispersion and during that phase a part of initial disturbance is converted into escaping soliton. Wave packets could convert to the stable soliton state with increasing amplitude and decreasing size just when the packet size exceeds the Debye radius.The cavitons found by Rao et.al.[5]have a size of the order of several Debye radii.The life time of sustenance of cavitons has been reported as much more than the collapse time of a Longmuir effect. The plasma density oscillations with the cavitons,of course, has been found to go with the double or multiple excitation frequencies of EM waves. Discrete character of the small signal amplitudes realized in the experiments performed by Rao et al[5] is finer than the conventional spectroscopy spectra of scattered EM waves, especially in the regions where the cavitons exist. The EM wave treated plasma during the afterglow led to observation of plasma density cavitons and bunches, which correlate with the bunches of KVNRao et al[5]. These bunches can travel considerable distances along the magnetic field without spreading. It is this feature that suggests the soliton formations.

Energy characteristic of gravitational soliton produced in a solar disturbed condition (not necessarily near a sun spot) I found it to be of the order of 0.286J. The angular frequency involved has the range from 39.51rad/s to about 55.882rad/sec. The two masses involved are m₁=M (39)=0.39Kg and m₂=M(55)= 0.195Kg.


III.Gravitational Plasma:

Chandrasekhar thought of a gravitational force separates the light and heavy charged constituents of a star coronal region. But the contention of the present author is that these separations become oscillatory and produce in turn a gravitational soliton. This idea is the spinal concept of the new formulation and model given in the present article. The EM soliton energy gets absorbed in the generation of gravitational solitons.


IV. DETECTORS:

Joseph Weber [7] gave the limit of Cosmic flux of G-Waves as <>2/sec/Hz at frequency 3.1 E-04 Hz. Dyson[8] stated that an elastic solid to have a response amplitude 2E-17 cm which is too small relative to seismic noise. The fundamental quadrupole modes of earth and Moon are found to be 54m and 15 m respectively. The Earth-Moon system separation as a G-Wave detector gives the limit of mass of G-Wave as <10e-13>3 . Weber used Al bar of 153cms length and diameter 66cm and weight 1.4E+06g, suspended by a wire and decoupled totally from its surroundings effects. He found that 1660Hz could be excited due to G-Waves.
Douglass[9] by a vibrating bar detector of arbitrary shape sought to have a range of fundamental frequencies that could be excited by G-Waves. Waves from Pulsars and from SuperNovae in other galaxies, were thought to become well registered with advent of new detectors. Waves from a massive star collapse suggested to be detectable, with sensors to gauze changes in vibration amplitudes of
order <= 1E-15cm in the time scale of 0.1 to 0.3 secs.G-Waves interact not only with matter but also with EM waves etc and so devices are suggested to exploit these interactions. In 1986 Weber[7] gave an article on gravitational antennas and search for gravitational radiation. Identification of gravitational radiation in terms of G-Waves seems to be a theme of research to provide vital information about the Universe. Dynamic space-time curvature measurement is sought to give development of antennas for Einstein’s G-Wave detection. People have accepted the curvature of space-time as the geometrical machinery behind the gravitation phenomenon. . A simple xx component of tide producing acceleration is given by

R^x_0x0 =w²= 4*p*r/3

with
w as the angular velocity of a moving particle, r being the density of planet. This formula implies the need of
two masses to measure a reasonable local affect of gravitation. The non-local physics is determined by the generation of gravitational field that could be obtained by solving the Einstein’s equations.


V.BPB Sensor:

The ancient Indians believed that a simple apparatus can be used to detect the gravitational impact during the period of an off-set of solar eclipse. The experimental set up they have used consisted of balancing a pounding bar (BPB) of length about 1.8m and diameter of 5 cm, which was made to stand erect in a bucket full of water.The free fall of the bar ,due toan impact of the gravitational affect of the Sun,following the off-set of Solar Total eclipse, was considered as an indication of the influence of the Sun’s power(Shakti).

This simple experiment,of course, is akin to the two-masses vibratory detector responding to linearly polarized G-Wave, but differs from what are termed as Weber Bar detectors. Various Types of mechanical detectors have been reviewed by MTW[1] who assert the role of concept of cross-section in the flux utilization of G-Wave energy by the detector.

An overview of detectors for which concept of cross-section is useless have been given by Press and Thorne[10].Bandwidth Press and Thorne[10].Bandwidth of antenna and coupling of antenna to the displacement sensor and noise considerations have been emphasized in the futuristic detector/sensor scenario for detecting and monitoring the G-Waves.
It is a more of thoughtful exercise by the present author to see how bandwidth concept can be neatly incorporated in the detailed analysis
of the free-fall of pounding bar sensor used by the ancient Indian astro-panchang pundits.

VI.The BPB Sensor Details:

See the Fig.1 and Fig.2 for the details of the “Balanced Pounding Bar" Sensor. The distance above the surface of the water is decided by the buoyancy and gravity forces balancing the pounding bar in the bucket of water. The BPB sensor differs from Weber bar in the sense that we have two different mass entities involved. The BPB could be thought to akin to alight structure with lumped masses, but important difference is that we have a G-Wave impact that knocks of the sensor to have a free fall. The Bar is not bound rigid to the bottom surface of the bucket of water, but is maintained just balanced. This is ingenuity of the ancient BPB sensor used by the astro-panchang pundits. The two degrees of freedom of BPB system is visualized by the author. The restoring forces of the two masses m1 and m2 differ since the m2 mass is a result of immersion in water. The Lagrangian has been constructed and the equation of motion for the semi-apex cone angle of the BPB sensor has been obtained.
(See Fig.1 and Fig.2 for details).The distances r1 and r2 that depict the horizontal natural vibration are sufficient to formulate the Lagrangian of the BPB sensor and derive an equation for the semi-apex cone angle. The radius r of the bar is 0.025m.

In this method of analysis of BPB sensor an advantage is gained by involving the water surface (along with its surface tension properties) to be subjected to a solitary wave absorption and concomitant excitation. A LASER experimental technique may be a simple way to asses the extent of depths and heights involved of the solitary wave excitation. But analytical approach seems to be more sound and useful to determine the characteristic features of the BPB sensor.

VII. GRAVITATIONAL RADIUS OF BPB Sensor:

Sensor usefulness is its cross-section for absorbing G-Wave energy. The steady-state solution of the Equation of Motion of the sensor gives an expression for j (refer Fig.2).Note that we use b for the projection of Quadrupole [11] semi-major axis on the sensor’s axis.

The driving force, of course, since Spin-2 nature of G-Waves[1] entity (1/2)*w²*A₀ represents the tidal acceleration quantity i.e. related to the Riemann Curvature Components, produced by the Soliton Wave. The gravitational radius of BPB sensor is 2*M=4.6Kg * 0.74E-28 cm/g=1.702E-25 cm which is three order’s of magnitude less than that of a Weber bar detector.

Wavelength of resonance radiation is 4.8E05 Km. i.e. about 0.07*Rs, where Rs is the Sun radius. This is very interesting and significant finding unlike only 200Km for a Weber Bar detector. This is seven orders of magnitude lesser than of a Weber Bar ratio. The Q value is 39.51 that give the fraction of the energy dissipated per radian of oscillation. I expect the soliton impact would resonate with the BPB sensor device which I term as G-sharp resonance. (Soldiers marching over a suspended bridge is another example of a sharp resonance.) Conversion to Quadrupole excitation makes it resemble a flat resonance.


VIII.Quadrupole Excitations:

The obtained body Quadrupole moment for the excitation is found to be 0.315 m2. Conversion of gravitational soliton surface disturbance to a gravitational Quadrupole excitation is the main concept of the phenomenon that I proposed in this article. The incoming incident flux T^GW is found to be 0.02J/cm²/sec. I am happy to state that the amplitude of driving force of the conversion is of magnitude A₀=113.6 which is a constant, for the said experimental set up. But with w₂=55.9 rad/sec A₀=80.33.Technically speaking in terms of the two modes of vibrations of the BPB sensor the magnitudes of the Quadrupole moments are 0.123 Kg. m² and 0.061 Kg. m².

Quadrupole gravitational excitation define here as “trace-free part of the second moment of the mass distribution of BPB sensor” (See Ref[1] page 977) with a distinction of it being specified in terms of the ellipsoid of the semi-major (a) and semi-minor (b=c) axes. (Refer the Fig.1)

Ambiguity in the notation has been avoided adopting the analogy off investigations made earlier by the author [11].
It is well known that deformation of the Sun, i.e. Solar Oblateness or Quadrupole Moment causes shift in perihelion of Mercury and the dimensionless parameter is J₂. For Sun it is <= 3E-05 as per 1972 experiments. IX.GRAVIOR:

The energy packets that constitute the Soliton get involved succinctly in a Quadrupole mode of excitation, obviously it differs from a fluid model,
in the sense that the former has about 1000 times more energy than the later. This is indeed, a feature of the present theory that soliton interaction would lead to a Quadrupole excitation that dislodges the buoyant balanced system of the pounding bar in the water filled bucket.

The release of some Graviors of Spin-2 of excitation energy, in quantum units (n+5/2)*h/ (2*p)
*w_gr with integral n could be a feasible proposition. This idea triggers several alternate theories and options of understanding the Quadrupole Gravitational Excitations.h/ (2*p) *w_gr defines a uniform spacing of the Quadrupole excitations. And so essentially quantum field theory has been found out in this formulation. The order of magnitude of h/ (2*p) *w_gr is derived using the normal mode of vibrations of BPB sensor to be in the range 4.2E-33 to about
5.9E-33 ergs. The number of Graviors involved is from 4.9E+31 to about 6.9E+31 depending on the normal mode of vibration of the BPB sensor.




X. CONCLUSION:

The theory proposed here envisages that cross-section plays an important role in the sense that the amplitude of gravitational force gets modified as the inverse square of the normal mode of vibration of BPB sensor.This would off-set all Newtonian gravitational effects and results a free-fall of the Pounding bar. Thus incoming flux as felt in terms of the curvature of the space-time has something to do with the square of the normal modes of vibrations of the system.Sensor absorbs energy from the G-Wave which in turn is essentially determined by the product of amplitude square times the cross-section offered by the BPB sensor. So the theory is strong in the sense that the incoming flux of G-Waves as sensed by the BPB sensor is solely due to the square of the amplitude of G-Wave.The range of natural mode of vibrations of BPB sensor hence sets the limit for the Quadrupole excitation of Graviors, by virtue of absorbed energy and curvature of space-time in a free-fall situation.

The free-fall is visualized by the Gravior Quadrupole excitation levels of BPB sensor essentially as a conversion of Solitary wave energy to the Gravior Quantum system of Quadrupole excitations.
BR>

Fig.3 Professor Kotcherlakota lakshmi Narayana in the center with some foreign delegates at a Conference held in nagpur University during the 1980s






XI. ACKNOWLEDGMENT:

The author is deeply indebted to Late Prof. K. Rangadhama Rao D.Sc.(Madras) D.Sc.(London) for selecting him to join the CSIR Scheme N0.44 entitled” Nuclear Quadrupole Moments” at JVD College of Science & Technology, Andhra University, Waltair (See Ref 12) as a Junior Research Fellow( during the years 1961-1964) at his laboratories. The author also expresses his gratitude to him for the inspiration and constant guidance provided.

Fig.4 K.Rangadhama Rao C.S.I.R Scheme (1960-1972) presentation

XII. REFERENCES:
[1].
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(b).See Also Ref [5] given below: "Discovery stellar core collapse events using Satellite-born RF detectors, (Type II core stellar collapse )"
Astrophysics Space Science Vol.314, p.275-279 (2008)
MEMP =1E+43 ergs during the time of 2mS
at l= 100KHz Antenna of about 1 meter Intensity at distance pof R=1light Year (ly) is L=500/(R*R)W/m². Sensitivity of Antenna 7E-17 W/m² with R=2.69E+09 ly.
(c). Solar system Radio Astronomy Ed.J. J.Aarans, Plenum Press (1965)
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b)The Polar Aurora by Stormer Oxford Press Ltd (1955)
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This paper adopted Plasma Wave described by soliton-like terms
arcSech (-T/t_d) *arcCosh (t/t_d)
where T, t and t_d are duration of soliton-like profile, time variable and the damping constant.
The later is characterizes the collisions.
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O.Klein, H.Alfven, “Hierarchy Cosmology of matter in an asymptotically flat-space-time”, Ark.Fys, Vol.23, p87-194, (1962)
[5] K.V.Narasinga Rao et al, ” Interaction of Microwaves in gaseous Plasmas Immersed in Magnetic Fields”,
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[6] S.Chandrsekhar, book on “PLASMA”, CPU
[7]. Joseph Weber “Gravitational Antennas and the search for Gravitational Radiation” p.1-77, Sir Arthur Eddington Centenary Symposium”
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[11]
a) K.L.Narayana et al,” Molecular Quadrupole of N₂ and O₂“, Shivaji University Journal Vol.6, p.32, 1973
b) K.L.Narayana “The Uranium Quadrupole moment based on a Dual ore fissionable Model” Current Science Vol.38. p.261. (1966)
c).K.L.Narayana, " On Nuclear Quadrupole Resonance in TiCl ₂ and CrCl₂ crystals" J.Chem.Phys.Vol.43, No.8, p.2916 (1963)
d).K.L.Narayana “Quadrupolar Binding of Gravitational free Quarks”, GR-10 Conf. Univ.of Padov, Institute di Fisica, “G.Galilei”, Italy.
e) K.L.Narayana et al, "On Nuclear Quadrupole Coupling Constants of Chlorine isotopes and Dipole moment of Br Cl ^35,37 Molecules", Indian Journal of Physics, Vol.37, No.5, p.261 May 1963.
[12] K.Rangadhama Rao et al, No.44, C.S.I.R Scheme entitled “Nuclear Quadrupole Moments” p.89 Phys.Conf. and Symposium on Solid State Physics, I.I.Sc, Bangalore, 1-3 Feb. 1960
[13] Occultists: The author had a very brief talk, during Oct 1975, with one late “Rasa Swamy”(Samadhi now in Divi Place of Godavari river) who
was an expert on Himalayas Medicinal Plants and who told me that he visited Germany 22 times to work with some firms. He was also an expert in
solidifying metals like mercury using some juices of plant materials, but I was at that time was not interested. The other living occultists whom the
author had a privilege to meet, in Yr.2004 is Dr. Cherravoori Sri Rama Sarma of Gauthami Vidhya peetam, Rajahmundry,Phone.08832460148 and
his son Ch.K.Padmanabham, their ideas to establish a research centre on occult science was in vain to-date.