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
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 [Ref.6-8] 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 software
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);
[[0,1],[1,1],[2,1],[3,1[4,1],[-4,1],[-3,1],[-2,1],[-1,1]] ----------(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
Mathematics
We may mathematically describe the finding as
QPV spin 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
Spontaneous
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
QPV spin 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.
ADDENDUM
Prof K R Rao a tribute Photo0188
REFERENCES
1a. 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
1b.
“Manorama : Tell Me Why”, Issue. 2013 Volume.7, No.6,
“Why is K. R.
Rao considered a pioneer in NQR Spectroscopy?
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Time: 19h20mP.M.” Some Experimental Investigations on Nuclear Quadrupole Resonance and
Graviton “ by Professor Dr Kotcherlakota
Lakshmi Narayana,
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