EXTRACTING VACUUM ENERGY FROM THE HOMOGENEOUS ISOTROPIC UNIVERSE
Abstract
The recent report by M. Alcubierre suggests that the travel faster than the
speed of light is possible by modifying the local space time in the front
and back of the ship. Since this type of propulsion suggests the generation
of force without emission to produce action, by extrapolating this mechanism
into a terrestrial system in the homogeneous isotropic universe, it is shown
that it is possible to extract vacuum energy within the range of certain
mechanical constraint in the system.
PACS numbers : 03.30.+p, 05.90.+m, 3.65.-w
The possibility of extracting vacuum energy by using the attractive Casimir
force between metal layers has been proposed by Forward[1] in 1984. More
recently, Cole and Puthoff[2] have again raised the possibility of energy
extraction from the vacuum. He suggested a method involving a charged plasma
which could be the more practical and plentiful means for energy extraction.
His discussion included the idea of generating heat from the vacuum.
While such methods of harnessing the vacuum energy will continue to be of
importance in the field, in this paper, we suggest another method of energy
extraction from the vacuum unrelated to Casimir effect. As the Casimir force
is the manifestation of the electromagnetic zero point fields, the vacuum
seems to have other interesting properties purely from the relativistic
point of view. Recently, M. Alcubierre[3] proposed a method of hyper fast
propulsion by spacetime contraction in front of the vehicle and the
expansion behind. He suggested the motion faster than the speed of light is
possible within the framework of general relativity. However, as we know
well from our cherished law of Newtonian mechanics and special relativity,
it will take infinite amount of energy to travel faster than the speed of
light, which has been the basis for main oppositions to such ideas.
If, despite the laws of Newtonian mechanics and special relativity, there
are ways to travel faster than the speed of light within the framework of
general relativity, we may have to adopt the notion that somewhere in the
process local energy may not be conserved[5-6]. If this is indeed the case,
it should be toward the gaining side since one can not put in infinite
amount of energy for travel faster than the speed of light for a system that
moves according to Alcubierres hyper propulsion mechanism.
In fact, the idea of Alcubierre needs not necessarily be confined to the
faster than the speed of light travel by itself. Although he didnt show in
his paper the quantitative correlation between the space time distortion and
the force experienced from it, it is conceptually possible that his idea can
be applied to generate a terrestrial force by the gradual engineering of the
spacetime contraction and expansion around a vehicle. In general relativity,
free fall of an object by the gravitational force is described equivalently
as that the object is simply following the geodesic[7] toward the
successively tightly packed spacetime centering around the massive object.
In this respect, the idea of Alcubierre is not new. He isolated the concept
of the acceleration of an object toward the contracted spacetime around the
gravitating mass and applied it to the case of an artificially engineered
local spacetime distortion in the vicinity of a ship in an otherwise flat
universe.
The critical question here is how one can engineer the spacetime in the
front and back of a vehicle and create local spacetime distortion in such a
way that it can be propelled and also how one can calculate such force .
In relation to a method of propulsion, it has been shown by the author in
the previous paper[4] that a rotating hemisphere produces the shift in the
center of mass due to the relativistic mass increase effect in special
relativity. It is also shown that this shift creates the gravitational
dipole field predicted by general relativity which induces the linear force
parallel to the rotation axis. Coincidentally, the rotating hemisphere can
in fact be considered to be an example case of creating a locally asymmetric
spacetime distortion in the front and back of the rotor by special
relativistic effect associated with the asymmetry of the rotor.
The relativistic length contraction of the circumference of the rotating
hemisphere makes the spatial volume element smaller than the one in
Euclidean space depending on the tangential velocity of the mass component.
The spacetime in the wider cross sectional region of the hemisphere would be
contracted more than the one in the narrower region since the instantaneous
velocity of the mass elements is given by riw, where ri is the distance
between the symmetry axis and the point where each mass element is located,
thereby causing asymmetric spacetime distortion with respect the the center
of mass of the hemispherical rotor and this provides a case of satisfying
the Alcubierres hyper propulsion condition: the contracted spacetime in
front of the ship and the expanded one in behind, in relative terms.
The next crucial question is if the force calculated from the center of mass
shift of the hemispherical rotor[4] would truly represent the force produced
by the corresponding spacetime distortion. The metric of spacetime used by
Alcubierre[3] is a fictitious one that was employed only for the purpose of
giving an example to show that the travel faster than the speed of light is
possible within the framework of general relativity. It bears no direct
relation to a practical propulsion method. However, his argument clearly
gives an impetus on the conclusion that the rotating hemisphere will
actually be accelerated toward the open side of the hemispherical shell.
The method of deriving the linear force shown in the paper by using the
center of mass shift and the centrifugal force may look rather unusual.
However, the force contains all the informations regarding the degree of
spacetime distortion which must depend on the center of mass shift drc that
is again a function of the radius R, the angular frequency w and the
relativistic factor c^2. More sophisticated calculations may give a
different constant multiplication factor but not the different power
combinations of R, w and c. The dimensional restrictions on this force is
rather strict and it doesn=D5t give much freedom for choice of the power
combination. The linear force is given by
=46(linear)=3Dpi*mw^4R^3/(48squareroot(2/3)c^2)
for wR/c< < 1, which could have been derived purely from the dimensional
deduction within the variation of the constant multiplication factor, where
R is the radius of the hemispherical shell, m the mass and w the angular
frequency of the rotor respectively.
Once the rotational motion of an object which is axisymmetric yet asymmetric
with respect to the center of mass is shown to create the asymmetric
spacetime distortion and the corresponding force is given by the above
expression, the next step of designing the system and extracting unlimited
local energy is straight forward. The force can be used to rotate the wheel
to generate torque and the torque can again be used to turn the generator
and produce electricity.
It is noted that there exists one important constraint in this process. The
dipole rotors have to overcome the resisting force acting against changing
its own angular momentum in the process of rotating the wheel in which the
axis of the rotors are attached firmly at the end of the arms in the wheel
and overcoming this resisting force will require energy to be drawn from the
system. The energy generated by the dipole rotor must be greater than the
energy required to change its own angular momentum for positive energy
production.
To understand the mechanism of energy production by the gravitational dipole
moment in analogy with the electromagnetic phenomenon, consider the behavior
of an electric dipole moment placed in a sparsely populated uniform charge
cloud in a nonconducting spherical shell for an example. It is assumed that
the charges stay fixed in space in their original position so that they do
not form or develop clusters by themselves. The dipole would be accelerated
toward certain direction depending on its initial position and the
orientation of its polarity. In this case, the kinetic energy of the dipole
is provided by the electrostatic potential field pervading the inner sphere
resulting from the distribution of the charges not by the energy produced
and radiated from the dipole moment via Newtons third law of motion.
An object falling from the sky by the attractive gravitational force of the
earth is following the geodesic toward the contracted spacetime according to
general relativity. The falling object gains kinetic energy as it travels.
The gravitational dipole moment generated by the center of mass shift placed
in an environment of the sparsely populated matter in the universe will
behave exactly the same way as the electric dipole moment would. Only with
one exception of the fact that there is no center in the homogeneous
isotropic universe. As long as the strength of the dipole moment is
maintained as protected by the angular momentum conservation law, the
rotating hemisphere will follow the self created spacetime distortion and
the kinetic energy will increase no matter where the initial position of the
dipole moment would be. In fact the system only requires the existence of
the centrifugal force4 which has been conjectured by Mach to be caused by
the influence of the rest of the universe filled with matter as we observe
it today. What Alcubierre has shown us in his paper is one of the pioneering
attempts to generalize the motion in an artificially created, locally
distorted spacetime.
One can summarize the above arguments as following:
* 1. The rotating hemisphere creates more contracted spacetime in the
larger cross sectional region relative to the smaller side due to the
relativistic length contraction of the circumferences.
* 2. This satisfies Alcubierres hyper drive condition.
* 3. The linear force experienced by this spacetime distortion can be
calculated from the consideration of the center of mass shift and the
centrifugal force which depend on the angular frequency w and the
radius R of the rotating hemisphere.
To determine the mechanical constraint for positive local energy production
following the above discussion, consider a device which has the shape of a
large scale classic wind speedometer with four arms of equal length attached
perpendicular to the main axis horizontally stretched 90 degree to each
other. The axis of four rotating hemispheres are attached at the end of each
arms perpendicular to both the main axis and the arms respectively. The
purpose of the argument is to show that there exists a condition that
positive energy is produced in this system above certain minimum angular
frequency of the dipole rotor despite certain anticipated frictional energy
losses.
Consider an infinitesimal distance dS=3Drdq traveled by the rotor due to the
force exerted on the dipole due to the space time distortion. Assuming that
all the dipole generators and other moving components in the device are
massless except one dipole which is activated and massive and also that the
force exerted on the dipole is given by the component of the centrifugal
force in the direction of the center of mass shift,[4] the amount of work
performed during the infinitesimal travel is given by
=46*dS=3D(pi*mw^4R^3/(48squareroot(2/3)c^2))Rdq
assuming wR/c< < 1, where R and w are the radius and angular speed of the
hemispherical rotor respectively and r the length of the arms and dq the
infinitesimal angular rotation the arms have experienced. Since the dipole
moment has non zero angular momentum by itself, it requires energy to change
the direction of the dipole moment. This energy is given by
tdq=3D(dL/dt)dq=3DW(2/3)mR^2wdq
where W is the angular frequency of the main axis in the system. Even with
the assumption that all the frictional energy loss can be eliminated
completely, this is the fundamental low limit of the energy loss required to
make up by the force exerted on the dipole. The output energy must be
greater than this energy loss, so that the condition
(pi*mw^4R^3/(48squareroot(2/3)c^2))Rdq > W(2/3)mR^2wdq
must be satisfied, which gives
w^3Rr/(8.3 c^2) > W
for the hemispherical shell type rotor for wR/c< < 1. This clearly
demonstrates that the system is capable of producing positive energy. For
any combinations of R, r, w, there always exists non zero W, which means the
positive energy production. The W sets the maximum available angular
frequency for given R, r and w. In a normal stabilized energy production
mode, the W slows down and maintains the smaller value than the one given by
the above condition depending on how much energy is drawn from the system.
The total amount of energy produced depends on the sixth power of the
angular frequency w and on the second power of r and R respectively.
REFERENCES
1 R. L. Forward, Phys. Rev. B 30, 1700 (1984)
2 Daniel C. Cole and H. E. Puthoff, Phys. Rev. E 48, 1562 (1993)
3 M. Alcubierre, Class. and Quantum Grav. 11, L73 (1994)
4 E.J. Jeong, [Rotating Hemisphere: Center of Mass Shift] Preprint
5 A. Einstein, Sitzungsber. Preuss. Akad. Wiss. Phys. Math. K1, 688 (1916);
154
(1918).
6 E. Noether, Nachr. Ges. Wiss. Goettingen 2, 235(1918) ; J. G. Fletcher,
Rev. Mod.
Phys. 32, 65(1960) ; R. Wald, J. Math. Phys. 31, 2378 (1990) ; Dongsu Bak,
D.
Cangemi, and R. Jackiw, Phys. Rev. D. 49, 5173 (1994)
7 C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation (Freeman, San
=46rancisco,
1973)
Generated Energy Form : Pure Electricity with No Heat Exchanger
Possible Equipment Size : Commercial Air Conditioner Unit For Domestic
Use, Portable
Key Technologies Required : Ultra Precision Balancing and Highly
Tensile Material
Possible Applications : From Domestic to Industry and Interstellar
Travel
Pollution : None
Mode of Operation : Completely Mechanical
Possible Cause of Break Down : Fracture of The Rotor due to Metal
Fatigue
Durability : Permanent ( Use Magnetically Levitated Bearing )
* Patent Title: Unlimited Energy Production By Dipole Gravity
* U.S. Patent File Number: 08/519450,
* PTO Filing Date: Aug. 25 1995
* Applicant: Eue Jin Jeong Ph. D.
* e-mail address: ejeong@bga.com
* Developers and Investors Inquiries should be addressed to the above
e-mail address
Half of the Patent Right Will be Shared with Ambitious Developer Who Will
Participate From Research to The Final Product
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