Thursday, October 10, 2013

Nuclear Quadrupole Resonance and Graviton by Professor Dr Kotcherlakota Lakshmi Narayana, 10 Oct 2013

Volume 2013 Issue No.10, Dt. 10 October 2013 Time: 09h 56mAM.
Nuclear Quadrupole Resonance and Graviton
by
Professor Dr Kotcherlakota Lakshmi Narayana,
{Retd. Prof.of Physics, SU, Kolhapur} 17-11-10, Narasimha Ashram,
Official Colony, Maharanipeta.P.O. Visakhapatnam -530002,
Mobile No. 9491902867 &  9542717723

ABSTRACT
`       An object of my work is that the Graviton of Spin-2 and Quadrupole of Spin-2 of several nuclei in the observation of the Nuclear Quadrupole Resonance experiments intrinsically involve the coupling of Gravitons with the Nuclear Quadrupole Moments. Algebraic expressions for the various spin values are listed.

INTRODUCTION
Graviton and Quadrupole Union
[Ref.1]
        It is envisaged in this paper that the Nuclear Quadrupole associated with the Nuclei in the Nuclear Quadrupole Resonance experiments, so nicely initiated by Late Prof K R Rao D.Sc. (Madras)  D.Sc.(London) at his research laboratories in Andhra University, interact with the Gravitons resulting in a spectrum of very enlarged spectral levels. The present work identifies
the association of Graviton of Spin-2 with the Quadrupole of the nucleus of Spin-2 leads to 
2 x 2 = (0 + 2 + 4) + (1 + 3)
An object of my work is that the Graviton of Spin-2 and Quadrupole of Spin-2 of several nuclei in the observation of the Nuclear Quadrupole Resonance experiments intrinsically involve the coupling of Gravitons with the Nuclear Quadrupole Moments. 
This yields a variety of spectra involving the angular momentum values ranging from +4 to -4. The intermediate values of differing symmetries can easily be envisaged by the group theoretical methods. The simple concept of just two values of +4 and -4 for the joint Nuclear Quadrupole Resonance experiments and the Graviton happens to be the simplest conjecture of positive and negative orientations along an angular momentum vector.  This is similar to projections of Spin +2 and -2 of a Graviton along a preferred axis. The other values like +3, +2, +1, 0, -1, -2, -3 are just the projections dictated by the interactions of the Graviton with the Nuclear Quadrupole resonance. Not only the experimental observations made to-date on the Nuclear Quadrupole Resonance and as well on the Gravitons need to be totally analyzed explicitly in my model for detailed work outs and presentations.
A derivation details
The expression ∂ν βν ψ = - χ ψ ------------------(1)
multiply by ∂ν βν then
∂ν ∂μ βν βμ ψ + χ ∂ν βν ψ=0 ------------------(2)
i.e. equal to
∂ν ∂μ(2*δμν - βμ βν) ψ + χ ∂ν βν ψ=0, ------------------(3)
i.e. 2∂ μ ∂ μ ψ - ∂ν ∂μ βμ βν ψ + χ ∂ν βν ψ=0. ------------------(4)
Here   ∂ν βν ψ = - χ ψ so expression becomes
2∂ μ ∂ μ ψ =  - χ ^2  ψ  +  ∂ν ∂μ βμ βν ψ, ------------------(5)
or we have 2∂ μ ∂ μ ψ = 2 χ^2  ψ , ------------------(6)
since  ∂ν ∂μ βμ βν ψ = ∂μ βμ(∂ν βν ψ)= ∂μ βμ(-χ ψ) = χ^2  ψ. ----------(7) 
We get  ∂ μ ∂ μ ψ =  χ^2  ψ  ------------------(8)
finally,
which is □^2= χ^2  ψ . ------------------(9)

EXTENDED SPIN HALF AND INTEGRAL THEORY

Madhava Rao [Ref. 2-5] adopted  
                       tμν  = ¼*(βμ  * β ν -   βν  *  βμ ) ------------------(10)
and  S μν =[ 1/(4*i)]* (βμ  * β ν -   βν  *  βμ ). ------------------(11).
He followed the works of Homi J Bhabha and acknowledged his help.
My Presentation
SPIN ½
          t2μν +  1/4 = (iSμν )2 +1/4 = - S2μν  +1/4 or S2μν  = ¼  --------------(12)
giving                                        
                                    Sμν =±1/2. ---------------------(13)
SPIN 1
We have t3μν +  tμν = (iSμν )3 + (iSμν ) = - i(Sμν )3 + (iSμν )=- (Sμν )3 + Sμν ---------(14)
or
S3 μν = Sμν so S2 μν = 1. This yields Sμν =±1 or 0.----------------------(15)
Madhavarao [Ref.4] defined the equations for spin 3/2 and 2 that yield the following results.
SPIN 3/2
Similarly for spin 3/2 we have (tμν +3/2)* (tμν +1/2)* (tμν -1/2) (tμν -3/2)=0 ---(16)
 gives t4μν - 5/2* t2μν + 9/16  =0 .----------------------------------------(17)
solve(t4μν - 5/2* t2μν + 9/16 ) 
ans = -3/2 ;    -1/2  ;  1/2  ;     3/2.   -------------------------------------(18)
Explicit values for spin 3/2.
Similarly evaluated for spin 3/2 
 (iSμν +3/2)* (iSμν +1/2)* (iSμν -1/2)( (iSμν -3/2)=0 ----------------(19)
gives  S4μν + 5/2* S2μν +9/16  =0 for the spin 3/2.
solve(S4μν + 5/2* S2μν +9/16 )  yields
ans =     -i/2;         i/2;    -(3*i)/2;     (3*i)/2.--------------------------(20)
SPIN 2
For spin 2 we have (iSμν +2)* (iSμν +1)* (iSμν )* (iSμν -1)( (iSμν -2)=0 -----(21)
gives S5μν + 5* S3μν + 4 * Sμν  =0 -----------------------------------(22)
for the spin-2 .
Evaluation yields by Mathlab
solve(S5μν + 5* S3μν + 4 * Sμν ) yields
ans =    0 ;     -i ;    i;  -2*i;   2*i------------------------------------(23)
 These involve imaginary quantity  i.
The expressions for (tμν +2)* (tμν +1)* (tμν )* (tμν -1)( (tμν -2)=0---------------(24)
 yields t5μν  -  5 * t3μν + 4 * tμν =0 . -------------------------(25)
solve(t5μν    -  5 * t3μν+ 4 * tμν)
ans =  -2 ;   -1;    0 ;    1;  2 . ----------------------------------(26)
Explicit values for Spin 2.
This is the desired expressive values of Spin 2 projections from +2 to -2.
Next we extend the formalism to study the higher spins explicitly:
My Work
SPIN 5/2
Similarly evaluated for spin 5/2 
(iSμν +5/2)* (iSμν +3/2)* (iSμν +1/2)* (iSμν-1/2)* (iSμν-3/2)*( iSμν-5/2) =0 ---(27)
gives S6μν + 35/4 * S4μν + 259/16 * S2μν + 225/64=0------------------(28)
while t6μν-35/4* t4μν+259/16* t2μν-225/64=0---------(29)
SPIN 3
Evaluated for spin 3
we have t7μν-14* t5μν+49* t3μν-36* tμν=0--------------------(30)
with  S7μν + 14 * S5μν + 49 * S3μν + 36* Sμν =0----------------------(31)
SPIN 7/2
Evaluated for spin 7/2
we have
t8μν-84/4* t6μν-1974/16*t4μν- 12916/64 * t2μν + 11025/256=0---(32)
S8μν + 84 /4* S6μν -1974/16 * S4μν + 12916/64*S2μν +11025/286=0.-------------(33)
SPIN 4
I study the spin 4 system in view of findings in the paper Ref.1. The object of the present work is to examine the Spin 4 system thoroughly to arrive at a possible link between the spin 4 and the Quadrupole Resonances data.[Ref.1]
(tμν +4) (tμν +3) (tμν +2)* (tμν +1)* (tμν )* (tμν -1) (tμν -2)( tμν -3)( tμν -4)=0 -----(34)
That yields the algebraic expression,
t9μν -13* t7μν +36* t5μν -16* t7μν +16*13* t5μν  -16*36* t3μν- t7μν
 +13* t5μν  -36* t3μν  +16* t5μν  -16*36* t3μν  +16*13* tμν =0; ----------(35)
simplifying we get,
t9μν-30* t7μν+273* t5μν-820* t3μν+576* tμν =0; ----------------------(36)
The roots of it are
roots (t9μν-30* t7μν+273* t5μν-820* t3μν+576* tμν);
----------(37)
In Mathlab we get for spin 4
Solve (tμν *( t2μν -16)*( t2μν -9)*( t2μν -4)*( t2μν -1))----------------------(38)
roots as ans = -4 ; -3; -2; -1;  0;  1;  2;  3;  4--------------------------(39)
Or solve(t9μν-30* t7μν+273* t5μν-820* t3μν+576* tμν);------(40)
gives roots as  0, -1,1,-2, 2,-3, 3,-4, 4.--------------------------(41)
PRESENT WORK AND EQUATIONS OF GRAVITY
The equation for realization of the possible values of Spin 4 gravity is
             t9μν-30* t7μν+273* t5μν-820* t3μν+576* tμν-------------(42)
This may be considered also as a product given by
                         (t5μν  -  5 * t3μν + 4 * tμν)*( t4μν  -  25 * t2μν + 144 )-----------(43)
of spin 2 the first expression and the additional terms factor
                                       (t2μν  -  9)*(t2μν-16).-------------------------------------(44)
But the product of two Spin 2 expressions is given as
                         t10μν-10* t8μν+33* t6μν-40* t4μν+16* t2μν =0 -------------(45)
                       solve(t^10-10*t^8+33*t^6-40*t^4+16*t^2)
                                ans =  -2,  -2, -1, -1,  0,  0,  1,  1,  2,  2
Ratio of (45) with (42) gives
                          (t5μν  -  5 * t3μν + 4 * tμν)/ (t2μν  -  9)*(t2μν-16)-----------------(46)
              i.e. equal to (t5μν  -  5 * t3μν + 4 * tμν)/ (t4μν  - 25*t2μν + 144)

ANALYSIS
      
The two “Spin 2” association for the Quadrupole (QP) and the Spin 2 Graviton explicitly is given by
                              QP : 2, 1, 0, -1, -2 and Graviton : 2, 1, 0, -1, -2
results in about (9) : 4,3,2,1,0,-1,-2,-3,-4 plus about (7) : 3,2,1,0,-1,-2,-3 plus
about (3) : 0, -1, 1 plus the left over Zero spins numbering about (6): 0,0,0,0,0,0 totaling as 9+7+3+6=25.
              
   Here 4,3,2,1,0,-1,-2,-3,-4 describes Spin 4 (I expect Graviton and QP) and 3,2,1,0,-1,-2,-3 describes spin 3 while 0, -1, 1 describes spin 1.




Of these we expect only +4 and -4 to really survive to describe the joint spin structure of graviton and QP. However, a careful analysis shows that a spin zero survives. Physics ascribes it as the basic reference point in the spin diagram given in Fig.1.

New Maths
We may mathematically describe the finding as
                      QPVspin 2  Θ  spin 3 Θ spin 1 Θ six spin 0 = Spin 4
 where V is a product and Θ is a subtraction symbols. This happens to be a new
formulation as a spin structure that can easily be extended to higher spin values.

QUESTION OF MASS
       Spontneous symmetry breaking that happened after 10-11s after Big Bang about 13.82 billion years ago, unleashed to new particles of different masses attributed to Higgs field which is an invisible field of energy pervading the universe. Tiniest disturbances in this field form the Higgs bosons. Higgs mechanism forms the process of mass.  Coupling at greater strengths gives more mass retarding the motion of particle. The model gave bottom quark found in 1977, W and Z bosons in 1983 by UA1 and UA2 experiments, top quark in 1995, and tau neutrino lepton in 2000. The largest Hadron Collider a 4.3km wide atom smasher near Geneva Switzerland, found in July 2012, spotted possible first hints of Higgs boson. Big bang released sea of energy symmetrical, but 10-11s later symmetry violated and broken due to fluctuations in the field of energy, its repercussions could impart mass to some matter and force particles formation. Higgs boson is a ripple, in the quantum field of with some average potential energy with smallest ripple of it termed as a particle. On July 4, 2012, ATLAS and CMS detectors spotted first hints of Higgs-boson-like particle. In January 2013 CERN announced particle found as Higgs boson.

COMMENT
            Mass and the quantum particles seem to go hand in hand with the particles and waves exhibiting dual nature. Graviton has a mass is questioned very much.

CONCLUSIONS
           
                                                We may mathematically describe the finding as
                      QPVspin 2  Θ  spin 3 Θ spin 1 Θ six spin 0 = Spin 4
 where V is a product and Θ is a subtraction symbols. This happens to be a new
formulation as a spin structure that can easily be extended to higher spin values. The equation for realization of the possible values of Spin 4 gravity is
             t9μν-30* t7μν+273* t5μν-820* t3μν+576* tμν with all possible integral values for spin from -4 to +4. Of these we expect only +4 and -4 to really survive to describe the joint spin structure of graviton and QP. However, a careful analysis shows that a spin zero survives. Physics ascribes it as the basic reference point in the spin diagram. A thorough look into physics of elementary particles envisages that the new particles of different masses attributed to Higgs field which is an invisible field of energy pervading the universe seems to be doubtful.

ACKNOWLEDGMENT
                      The author is greatly indebted to Late Prof K. R. Rao, D.Sc. (Madras) D.Sc. (London) for his continuous zeal in promoting the outstanding research work at AU, Waltair (1932-1972) covering the entire Electromagnetism Spectrum from Cosmic Rays to the Radio waves during the years of his unselfish and devoted research in several branches and exceptional devotion in care-taking the youngsters to achieve glory and comfortable positions at several institutions in India and abroad.
    

REFERENCES
  1. trusciencetrutechnology@blogspot.com, Volume 2013 Issue No.4, Dt. 16 April 2013 Time: 19h 20m P.M. “Some Experimental Investigations on Nuclear Quadrupole Resonance and Graviton”, by Professor Dr Kotcherlakota Lakshmi Narayana, {Retd. Prof. of Physics, SU, Kolhapur} 17-11-10, Narasimha Ashram,
Official Colony, Maharanipeta.P.O. Visakhapatnam -530002,
Mobile No. 9491902867 &  9542717723
2         B. S. Madha Rao, J.of the Mysore University, Section Ā Mathematics, “commutation rules related to particles of spin half and one”, Vol.III, Part X, pp.59-63,1942.
3         B. S. Madhava Rao, “ Commutation rules for Matrices related to particles of Higher Spins”,
The Proceedings of the Indian Academy of Sciences,  Vol.XV,  No.3, Sec. A. 1942.
4         B. S. Madha Rao, J.of the Mysore University, Section B Mathematics,
 “commutation rules related for particles of higher spin”,
Vol.VI, Part V, pp.57-62, July 24, 1945.
5         B. S. Madhava Rao, V. R. Thiruvenkatachar, K. Venkatachaliengar,
 “Algebra related to elementary particles of spin 3/2”,
 Proc. of the Royal Society, A, volume 187, 1946.
6         Homi J. Bhabha, Curr.Sci.Vol.14, pp.89-90, 1945
7         Homi J. Bhabha, Rev. Mod. Phys. 1945

8         Homi J. Bhabha, Proc. of Ind. Acad. of Sciences, Vol.21, pp.241-264, 1945

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