workshopon tests of gravity and gravitationalphysics
Venue: Cleveland
Location: Cleveland, United States
Event Date/Time: May 19, 2009 |
Description
SIR,
ABSTRACT.
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We in section (A) will propose the law of quantum gravity as ( TEST.I), that offers unification between gravity and electromagnetic interaction rendering the empirical law of Newtonian gravity as a special case as (TEST .2 ) and
similarly in section ( B ) the mathematical relation between gravitational equivalent of magnetic
field will be deduced therefrom as (TEST.3 ) and a new formula for the orbital inclination will be
presented as (TEST.4 ) ,similarly in section ( C ) the inter-relation between gravity and
time,consistent with general relativity,will be established proposing (TEST.5)and
similarly the relation for planck-time as{sqrt(h.G / c^5 )}= r.dm / p , finally in section
( D ) we will hint towards the microscopic aspects of gravity, coinciding the principles of particle physics.
SECTION ( A ).
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HERE the law of Quantum Gravity is proposed without its derivation.and (Important to
note ) that in the subsequent section ,we will verify its validity via different methods , proposing different TESTSâ€¦..and present itself as an exact quantum solution of field equations .i.e.
J . p' . g' = { dm } ^2 . { sqrt ( c^2 / v^2 - 1 ) }....(1)
WHERE J = h' / c^ 4
Here, h' = h / 2.#. with h = {6.626.(1o)^ -34}joule.sec,(Planck Constant).
and # = 22 / 7
similarly
c = 3*(1o)^8 meter/sec,(Light velocity)
Similarly p' , g' are magnitude of momentum and gravity of particle and dm is
the
differential of mass with
dm.c^2 = h' / dt,â€¦â€¦â€¦( NOTE ).This dm as meson is witnessed in Yukawa-potential theory tooâ€¦â€¦
EQUATION( I ) IS (TEST.I)
NOW working on equation (1),
i discovered ( In analogy to the coupling constant of Weak-Interaction ) that R.H.S of (1) is
equivalent to (dq'/ Y )^2
i.e. ( dq' / Y )^2 = ( dm) ^2 .{sqrt ( c^2 / v^2 - 1 )...(2)
Where Y is a lorentz-invariant parameter with dimensions as coulomb / kg.
And dq' is induced charge like differential dm .
THIS IS A NEW CONCEPT INTRODUCED HEREIN ,WE WILL VERIFY THIS IN THE FOLLOWING LINES......as a (TEST.2)
By integration and other mathematical process,equation (2) gives the result for q' as,
q' = (3.87113* 10 ^ 8 ).mvr / M....( 3 )....( BASIC THEME / TEST.2 )
For eccentricity e = 0, of orbiting objects...and the dimenssions of the constant involved
here are coulomb.second / m^2.
Here mvr is the angular momentum of orbiting object and M is
the mass of central body.
Clearly the induced charge (3) satisfies the charge conservation
principle as the angular momentum is conserved.....
By (3),we find that for m less than less than M (as the stones etc..
over earth...) q' proposed by (3) is highly negligible, that is why (we find) it
has not been detected so far.....
THUS HERE WE ,CONSEQUENTLY BY NEWLY DISCOVERED RELATION ,FORMULATE A HYPOTHESIS AS,
TOTAL CHARGE = CHARGE AT REST + INDUCED CHARGE
or Q = q + q' ......( 3 a )
TEST IN RESPECT OF PROPOSED HYPOTHESIS BY (3).
Here,Now on the basis of above results, we assume that
gravitational interaction of solar system is electromagnetic interaction as the momentum
of the orbiting objects are considerably high, meaningthereby will be observable and detectable......
SO,
F = q.E + q' v (cross)B'
where q is charge at rest ,as for originally neutral particle
q = 0 . and only induced ( as hypothesised )
charge q' in the light of (3) should exist ,thus in this case the
interaction will remain as...
F = q'. v (cross)B'
or
F = q' v B'.Sin p ,
for nearly circular orbit eccentricity e = o and Sin p = 1.
so
F = q' v B'............ (4)
where B' is magnetic flux density of central body around which q' is orbiting.
and B' = { V.E / c^2 } with E = k.Q' / r^2.
and c is velocity of light.
similarly k = 9* 10^ 9,(Coulomb-Constant).
HERE capital V and E represent velocity and electric intensity of central
body respectively.
Thus equation (4) now takes the form as...
F = q' v.V.kQ' / c^2 .r^2.......( 5 ).
Now we test the equation ( 3 ) for the case of moon and earth via equation (5).
FOR that, using the same newly discovered relation by (3) , the induced charge of earth Q' will be as...
Q' = (3.87113* 10^8). MVR / M^
similarly here MVR is the angular momentum of earth around the SUN.
and M^ is the mass of central body. i.e. SUN.
Now by putting moon charge q' and earth charge Q' in (5), we get as
F={3.87113*10^8 *mvr / M}.(v).{Vk /c^2.r^2}.{ 3.87113*10^8 *MVR/ M^}
or
F={14.98564*10^16 .k.v^2 .V^2 .r.R / c^2 .MM^ }.{Mm / r^2 }..(5)
Here v is moon-velocity, capital V is earth-velocity, M is earth mass , M^ is
sun mass,r is moon-earth distance, R is earth-sun distance, K is
coulomb constant and c is the velocity of light..........
Now putting these ( exact ) values in the first
bracket of (5), we find that it equals to 6.673 * 10^ -11, which is
the value of gravitational constant G ( which appears as a compound one, as with the deviation from circular orbit the value of G shall slightly vary , namely it is not an original constant).
SO,
F = 6.673*10^ -11 .{ Mm / r^2 }....(5)
THUS our proposed relation ( 3 ) and hypothesis ( 3a ) both stand
verified.....Meaningtherteby that it is actually the electromagnetic interaction
that manifests itself as chargeless gravitational interaction , as due to the non-detection of induced charge, as it remains hidden due to the extreme smallnessâ€¦
As the deduction (3) , from equation ( 1 ).i.e. the proposal for
quantum gravity law , is verified as it provides the way for the Unification of
gravitational and electromagnetic interaction and renders the( empirical relation)
of
Newtonian gravity as mathematical derivation ...........THUS equation (3) is TEST.2(verified).
SECTION ( B ).( TEST.3)
DEDUCTION OF GRAVITATIONAL EQUIVALENT OF MAGNETIC FEILD.
------
WE know that by the ' equivalence principle ' of general relativity gravity is
termed as acceleration........
SO by equation ( 4 ), We will here establish the mathematical and measurable relation for gravitational equivalent of magnetic feild as,(which has been recently detected in Autria)
F = m.g = q'.v.B.........( 6 )
Using the value of q' from equation ( 3 ), we get,
m.g = { 3.87113 * 10 ^8 }.m.v^2 .r.B / M^......( 7 ).
WE know that v^2 = G.M / r .
Using this equation ( 7 ) becomes as,
g = { 3.87113* 10 ^8 }.G.B , where G = 6.673 * 10 ^ -11
OR, g = { 2.58321 * 10 ^ -2 } .B..........( 8 ).
Here dimenssions of the constant involved are ampere.meter / kg .
In equation ( 8 ) g is acceleration ( gravity ) and B is the magnetic flux density produced by the acceleration.......
THIS results of equation ( 8 ) can be tallied with the
experiments by ACCELERATOR....or it is a testable prediction of the proposal too.....importantly inviting as TEST.3.....
SECTION. (B.1 ).( TEST.4)
FORMULA FOR ORBITAL INCLINATION.
------------
WE using (3), arrive at the very important formula
of orbital inclination ' $ ' angle of orbitting object w. r. t the
central body equator from the afore-mentioned unification.i.e
$ = { arc-cos +_ GMT^2 / 4.(pi)^2 .r^3 }.....(9).....for ' e ' nearly equal to
zero......the formula has two
roots,as the sign refers to the side of inclination............
Here $ is orbital inclination angle w.r.t. {equator of central body}.
and pi = 22 / 7, G is gravitational constant, M is
mass of central body......
T and r are ( sidereal ) time period and orbital radius ( usually semi-major axis)
respectively.
CLEARLY, kepler third law appears to be the special case of this formula for $ = o,
Equation (9) can very easily be verified using data on the site.i.e. .en.wikipedia/org/wiki/planet.
SECTION ( C ). (TEST.5)
---------------------------------
UNIFIED RELATION FOR GRAVITY AND TIME ETC.....
Here at this juncture we would like to caste light via
proposed 'Quantum Gravity Law' of equation ( 1 ) on the
unification of gravity and time.i.e.
Now as conidering the R.H.S of the equation (1) as Lorentz-Invariant that ubequently verified by (5)â€¦.
CONSEQUENTLY, L.H.S of ( 1 ) must be lorentz-invariant.i.e.
p' .g' = p .g
or
p.g = p'.g' ..........( 6 ).
Where p' and g' are relative momentum and gravity of particle w.r.t velocity,
But we (by special relativity) know that p' = p / sqrt{1- v^2 /c^2 }
and t' = t / sqrt{1-v^2 /c^2}
Thus by these two equations ( 6 ) takes the form as,
g.t = g'.t'.......( 7 ).
This must too be lorentz-invariant, meaningthereby that
d (g.t) / dv = 0..........( 8 )
Now the dimenssions of equation ( 7 ) are definitely of some velocity, So satisfying the
condition of lorentz-invariance this only suggests equation ( 7 ) as,
g.t = c ........( 9 ), where c is the
velocity of light,
or, t = c / g , meaningthereby that gravity slows down the '
time ' as proposed by ' General-Relativity'.....
Thus equation ( 9 ) establishes direct inter-relation between gravity and time.............and
offering towards the relativistic aspect of gravity in the following manner too....
as,
g.t = c .........( 9 ).
Or, g.t = g'.t'
but we know that, t' = t / sqrt{1-v^2 / c^2 }
so
g' = g . sqrt{1-v^2/ c^2 }
or
g' = G.m / r^2 .sqrt{ 1- v^2 / c^2 }......( 10 )â€¦(TEST.5 ).i.e. gravity is inversely proportional to velocityâ€¦
or
g' =G.m / r^2.{1- v^2 / 2. c^2..+..+..+..infinity }.
This is the relativistic aspect of gravity,undiscovered uptill now as for clearly
because of lower velocities, SO for very higher velocities , considerable difference is here predicted........
SECTION(C.I ).( PLANCK-TIME )
NOTE..Using (11) and (18) for equation (1), we get as,
J^ . p. v. m / r^2 = { dm }^2 , where r is radius of particle
and J^ = h'. G / c ^5 ,
OR , r. dm / p = sqrt { h'.G / c^5 }.....( 19 ).
The R.H.S of equation is ' Planck-time '.........THUS the equation (1).i.e. proposal for
quantum gravity includes/ demystifies and inter-relates the ' planck-time ' with the
perimeters of particle......MORESO the unification proposal should introduce the compound constant .i.e. the composition ' of relativity constant 'c' , gravity constant G ,and
quantum constant 'h'.......and same case appears in the above equation
which clearly introduces this CONSTANT as J ^ = h'.G / c^ 5 .
SECTION ( D ).
MICROSCOPIC ANALYSIS OF GRAVITY.
Quantum law of gravity is the law , which can be put into the theories of particle ( quantum ) physics........
For that we know that, wave-length = h / p, where p is momentum of particle, by De Broglie hypothesis....
NOW in equation ( 1 ), substituting wave-length in place of momentum of
particle and employing wave equations , we can easily analyse the behaviour and effects of microscopic particles/ waves.......Similarly by equation
(11), we can TEST the gravity of particle moving with very high velocitiesâ€¦..
CONCLUSION.
THE proposal for quantum gravity.i.e. unification of gravity and electromagnetic interaction offers different TESTS for its validityâ€¦.
OR in other word the proposal (1) can be termed to be the exact ( quantum) solution of the field equations as only single feature of the broader main proposal.