Natural Science Forum / Physics / Relativity / March 2007

Title: Frame-dragging disproves dark matter

Wanchung Hu

PhD candidate,

National Taiwan University

Correspondence should be addressed. Email: whu@jhsph.edu

Abstract
A force called spinity can be derived by the frame-dragging effect
predicted by general relativity. The spinity formula (SJm /r^2,S=2G/
c^2) is derived by the gravitational field induced by rotating mass.
Dark matter theory was proposed due to the discrepancy of virial mass
and the mass estimated by mass-to-light ratio. Considering spinity in
the deduction process, virial mass is reduced to be 2*(Rtotal*V^2)/(G
+S*R^2*ω) and closer to the mass estimated by mass-to-light ratio.
Thus, dark matter is not so important that we thought previously.
Spinity is an exciting force; its characteristics and effects should
be studied further.

Key words: frame-dragging effect, general relativity, gravity, dark
matter, spinity
PACS Nos: 95.10-a

According to the prediction of general relativity, a rotating object
will drag the space-time along with it. This is called frame-
dragging(Lense-Thirring effect). Thus, in classic physics description,
a rotating central object will generate a force to let smaller object
rotate around the central object. The field induced by the spin is
called spin field or torsion field. But, there is no formal name for
the fifth basic force. I propose to call this force-Spinity. The force
is due to “spin” of central object. The initial S can stand for
Spinity constant as well as Schwarzschild constant. The “ity” means
the force is a basic force like gravity or electricity. Below I will
discuss the new force and its effect on dark matter. According to the
Tartaglia’s and Mashhoon’s papers (translation of Lense-Thirring’s
original paper), the gravitational filed induced by spinity is given
by   :

G=SJ /r^2, S=spinity constant, J=kMR2ω(angular momentum of central
object, k=2/5 for sphere), r=distance from the center of central
object(Mass=M) to the center of the small object(Mass=m), R=central
object’s radium, ω =angular velocity of the central object, =unit
vector

We assume that the small object is rotating around the central object
in the rotating plane of the central object. The small object is
receiving the spinity force:

F= SJm /
r^2
(1)

When a smaller object is rotating around a central object in solar
system or galaxy, the formula for the small object rotation movement
is given by:

GMm/r^2+SJm/r^2 =mrW^2 , W=orbital angular velocity of the smaller
object           (2)
The spinity-to-gravity ratio is SR^2 ω/
G
(3)

The above formula doesn’t disobey Kepler’s third law of planetary
motion: r^3/T^2=constant. Spinity can solve many phenomenon observed
in the universe. Spinity can explain the swirl shape of galaxies. It
can well explain the ring formation in the rotating plane of huge
planets in solar system such as Saturn or Jupiter. It can explain why
the nine planets in our solar system are surrounding the Sun in the
same direction and same plane. It can explain why the satellites in
our solar system are surrounding the planets in the same direction and
same plane except Triton of Neptune. Uranus has special
characteristics with its 90◦ degree axis tilt. And, its ring and
satellites are still rotating in Uranus’s equator. It has been
postulated that an asteroid or comet hit Uranus and caused its axis
tilt. Spinity can bring Uranus’s ring and satellites to its new
equator plane. Gravity cannot explain the phenomenon.

Nebula theory is the dominant theory of solar system formation.
However, it faces a difficulty that Sun has only 2% angular momentum
of the total solar system and Saturn and Jupiter have the greatest
angular momentum in the solar system. Spinity can cause the angular
momentum transfer from Sun to planets surrounding it. The Kepler’s
second law points out the conservation of angular momentum in the
solar system, so our Sun rotates in a slow velocity and its spinity
can be much less than that during the initial formation of solar
system. Gravity always attracts smaller objects toward the center and
it cannot explain the rotation behavior around central object if only
gravity exists.  Spinity can explain the initial force causing the
planets rotating around the Sun. After the spinity decreases to be
much less than gravity, planets can still rotate around the Sun due to
inertia. And, gravity can prevent the planets from escaping the solar
system.

The galaxy’s total mass can be derived by two methods: virial mass and
mass-to-light ratio. Virial mass is estimated by Newton’s gravity law.
However, there is great discrepancy between the mass estimated by
virial mass and the mass estimated by mass-to-light ratio. The virial
mass is much larger than the mass from mass-to-light ratio, so
researchers proposed dark matter theory saying that there is invisible
substance contributing to the virial mass. It was estimated that
80%~90% substance of the galaxy is composed by dark matter. However,
the virial mass should be corrected if the spinity is considered.

When the glalaxy is rotating in the same plane, the virial mass can be
derived by:

Virial theorem: dG/dt= ΣF*r+2Ek=0
-2Ek=ΣF*r(Virial theorem is effective in a forever bound system like
galaxy,dt=∞)
Mtotal=N*m,

dUs(spinity energy)=F*ds=F*r*dθ=τ*dθ=-SJj dθ/r
(Extra work is needed when moving smaller object from inner orbit to
outer orbit. Because the spinity energy in outer orbit is greater than
the spinity energy in inner orbit like the gravitational potential
energy, there is a minus sign in spinity energy formula. When r=∞,
spinity energy=0; spinity energy is negative at any finite r)

ΣF*r=-0.5*{(G*N^2*m^2)/Rtotal+(S*N^2*m^2*R^2*ω)/Rtotal}
                              =-0.5(G*Mtotal^2+S*Mtotal^2*R^2*ω)/
Rtotal

Kinetic energy(Ek)=0.5*N*m*V^2
                             =0.5*Mtotal*V^2

Virial theom: Ek=-0.5 ΣF*r

0.5*Mtotal*V^2=+0.25*(G*Mtotal^2+S*Mtotal^2* R^2*ω)/Rtotal

Virial mass: Mtotal=2*(Rtotal*V^2)/(G
+S*R^2*ω)                                                       (4)

Compared to original Virial mass: Mtotal=2*(Rtotal*V^2)/G

the effect of spinity. Thus, virial mass can be more similar with the
mass from mass-to-light ratio. From the above formula(2)(3), we can
predict the S(spinity constant) value. Because the spinity in solar
system is much less than gravity, we can predict spinity constant by
calculating the nine planets’ movement. The predicted S(spinity
constant) should be less than 10^-22. If we use S=10^-26 for
calculating the virial mass for Milky Way galaxy, the denominator can
be much more increased. (G=6.67*10^-11 Nm^2Kg^-2,R=6*10^19m for
central bulge diameter of Milky Way galaxy, ω=10^-16circle/sec for
angular velocity of Milky Way galaxy). All the values are from
http://www.wikipedia.org. For the case of Uranus, Uranus’s satellites
can receive 10^13 to 10^15   Newton spinity force from Uranus in
current Uranus’s angular momentum with S=10^-26. If we assume S=10^-26
to calculate the spinity received by Sun from Milky Way galactic
nuclear, the spinity is 10^7 N greater than gravity of all the
rotating stars in Milky Way galaxy due to the spinity-to-gravity
ratio. Thus, stars in galaxy can have enough force to maintain their
rotational velocity. When the spinity constant is greater than 10^-33,
the virial mass can be greatly decreased. The importance of dark
matter should be decreased. Dark matter theory is proposed due to the
discrepancy of predicted galaxy rotation curve and observed galaxy
rotation curve as shown in Fig. 1. In predicted galaxy rotation curve,
rotation velocity should be decreased while the distance increased
like our solar system. However, the rotation velocity can be
maintained if we consider the effect of spinity. When the spinity
energy of galaxy is decreased to much less than gravity, the galaxy
rotation curve will fall to fit predicted galaxy rotation curve like
our solar system. When the the galaxy nuclear in a wide diameter spins
fast and the angular momentum of central nuclear is still huge, there
is still enough spinity force to maintain high rotational velocity for
galaxy. Thus, dark matter theory’s importance is decreased.

Based on previous studies, the spinity constant is predicted to be
equal to Schwarzschild constant:2G/c^2   . The value is 1.5*10^-27,
which fails in the range between 10^-22  to 10^-33. If the prediction
is correct, spinity is 106 greater than gravity on stars rotating in
Milky Way galaxy. And, virial mass of Milky Way galaxy should be 106
less than original predicted virial mass. This provides further
evidence supporting my hypothesis. However, the actual spinity
constant needs to be proved by delicate experiments. Although
Newtonian force needs dark matter, general relativity doesn’t require
the need of dark matter. Previous two studies pointed out the dark
matter is unnecessary under the framework of general relativity  .
Spinity can well explain many phenomenons in our home-Earth. Spinity
can explain why retrograde satellites are more difficult to make than
prograde satellites because retrograde satellites need to overcome the
spinity of Earth. Flight from America to Japan takes longer time than
flight from Japan to America, because retrograde flight needs to
overcome our Earth’s spinity. In summary, spinity is an exciting
force, and its characteristics and effects need to be studied
further.

References
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