Some errors in the math fixed. Sorry.
http://www.mtaonline.net/~hheffner/CasimirGenerator.pdf
Casimir Generator
OBJECTIVE
The purpose here is to provide a means of extracting energy upon
demand from the zero point field (ZPF), by utilization of the
Casimir force.
FUNDAMENTAL METHOD
The following method is intended to provide a means to build a nano-
scale zero point field powered generator, a true free energy generator:
(1) let two parallel conductive thin plates attract in the axis
normal to them, the y axis, gaining energy from the attraction of the
plates due to the Casimir force. Use that movement, say mechanically
or by heat generation or by conversion to electrical energy, to do
useful work.
(2) Slide the plates apart sideways, say in the x axis. This will
cost some of the energy gained by the attraction, but should cost far
less than just separating the plates while they move only on the x
axis, because the opposition to movement in the x direction from the
ZPF is based on the size of the Casimir force generated on the edges
of the plates, which is much smaller, because the Casimir force is a
1/y^4 force and the distances between any two points on the edge
related surfaces are typically much further apart than the plate
separation y.
(3) Move the now separated but still parallel plates back to the
original position by a route that avoids a separation distance
smaller than the original separation in the y axis. This should take
nominal energy. Alternatively, simply reverse the x direction
relative motion, which then repeats the energy producing y axis
motion of the plates.
(4) Repeat the cycle as fast as practical.
EXAMPLE OF IMPLEMENTATION
One means to implement this scheme at nano-scale is to make one
plate, call it the oscillating plate, a plate free to move in the y
axis, though with small angular (tilting) motion due to bending of a
supporting arm that permits this motion, be a long flexible plate
located above a rotating plate. Near the oscillating plate, and
parallel to it, provide a rotating wheel which brings into proximity
to the oscillating plate a segment of the wheel which acts as the
second plate for a Casimir attraction. A line normal to the plane of
the oscillating plate is approximately parallel to the axis of motion
of the wheel, i.e. normal to the plane of the rotating plate. The
rotating plate could be in the form of a wheel with major portions of
opposed quarters removed. By removing opposed quarters, or at least
a symmetrical group of segments, the wheel remains balanced. The
oscillating plate requires a blocking mechanism to prevent contact
between the oscillating plate and the rotating plate due to a runaway
attraction of the Casimir force. Energy from the motion of the
oscillating plate can be extracted as electrical energy by various
means. Since far less energy is required for the x axis separation
of the oscillating plate and the rotating plate than the energy
produced by their y axis attraction, some of the energy from the
motion of the oscillating plate can be used to drive the generator.
The oscillating plate returns to its starting position by spring
action, and is at the point of maximum spring displacement when
closest to the rotating plate. Multiple oscillating plates can be
used with a single wheel, and if convenient, they can be located on
opposed sides of the wheel. Either the flat side of the wheel or the
cylindrical side of the wheel can be used for the rotating plate
active surface. If the cylindrical side is used then the oscillating
plate should be curved to fit its contour.
Fig. 1 through Fig. 5 portray steps in the relative motion of the
plates of the suggested device. The oscillating plate is represented
by ooo's, the rotating plate by xxx's. For drawing convenience the y
axis is vertical in all the figures, the x axis is horizontal. The
direction of motion of the plates is shown by arrows. The
proportions chosen were merely for ease and clarity of communicating
the motions.
Fig. 1 shows a starting configuration of the repeated steps. The y
displacement between the plates is at maximum. The deflection of
the oscillating pendulum is thus maximum. As the rotating plate
moves into opposed parallel position, and plate overlap begins, the y
axis Casimir force develops between the two plates.
The Casimir force begins to move the oscillating plate toward the
rotating plate, as shown in Fig. 2, and increases as both the exposed
area increases and the y axis separation distance decreases.
The point of maximum approach is shown in Fig. 3. A motion blocking
structure (not shown) stops the y axis motion of the oscillating
plate. The wheel must be rigid in comparison to the oscillating
plate, so as to maintain motion of the rotating plate only in the x
axis. The motion blocking structure requires contact between
dielectric surfaces in order to prevent a Casimir force at the point
of contact. The middle vertical line of Fig. 3 is assumed to be the
y=0 line.
When the rotating plate moves laterally away from the oscillating
plate, as shown in Fig. 4, the area exposed to the Casimir force is
reduced and thus the Casimir force is reduced and the oscillating
plate begins to return to its original position due to the spring
action associated with that plate. The increase in the y axis
separation further decreases the Casimir force.
Finally the configuration reaches that shown in Fig. 5, which is
symmetrical to Fig. 1, and thus the cycle is closed. The oscillating
plate is again at maximum displacement.
TWO PENDULUM IMPLEMENTATION
A possibly much easier design to implement consists of two
pendulums. The rotating plate is replaced by a plate on the side of
a pendulum that can vibrate only in the x direction. This x
direction moving plate is the driver plate, oriented in the x
direction like the oscillating plate, but moving only in the x
direction, and mounted on what can be called the driver pendulum
because its motion is driven by a capacitive coupling. The
oscillating plate, which moves only in the y direction, is then
called the drone plate on the drone pendulum, and its motion is
driven entirely by changes in the Casimir force as before.
Energy from the drone plate’s range of motion can be tapped
capacitively, i.e. by changes in the plate separation of a capacitor
plate mounted on the drone pendulum and a static plate.
Alternatively, the energy of the drone pendulum might be extracted in
the form of heat generation due to impact of the drone upon a motion
restriction barrier, as well as heat generated by motion of, and thus
distortion of, the drone pendulum, or in the form of sound due to the
coordinated motion of all the pendulums. However, conversion of
the drone pendulum motion to electrical energy is greatly enhanced by
the two pendulum design because all the pendulums of such a
generation system can be organized in a series plus parallel array
such that any desired voltage or current can be generated.
Significant advantages of the two pendulum system are small size,
simplicity, the ability to rapidly turn the power generated on or
off, and the ability to place the output in series to increase the
voltage generated, due to the fact all the pendulums can be driven
in synchronization by control of a single input signal used to drive
all the driver pendulums.
WHERE THE ENERGY COMES FROM
The energy for the generator comes from the zero point field, a flux
of virtual photons known to have a cubic frequency distribution.
The presence of a cavity surrounded by conductors creates the Casimir
force. The cavity excludes zero point field wavelengths larger than
the cavity dimensions. The force results from zero point radiation
having less flux through a plate coming from the direction of the
cavity. An analogy is a suction cup stuck to a piece of glass, but
not a passive cup, one with an active vacuum pump connected to it.
Once the vacuum is created between the cup and the glass the air
pressure on the outside holds the cup and glass together fiercely,
even though there is some air leakage on the sides, which has no net
force due to symmetry around the cup. However, if the cup is free to
slide sideways, say due to a lubricant, then the vacuum is easily
broken. It is well known that the energy in the Casimir case is
provided by the vacuum. The zero point field is analogous to the
vacuum pump in this case.
The incremental work dE performed by attracting the plates a small
increment dx is of the form of work times displacement:
dE = F(y) dx
where F(y) is the y axis casimir force between the two plates given by:
F(y) = A [h * c * π^2 / (240 y^4) ]
where A is the overlapped area of the plates, h is Planck’s constant,
and c is the speed of light. The incremental work is thus:
dE = A [h * c * π^2 / (240 y^4) ] dy
Except at the plate edges, there is no such work performed by plates
sliding past each other laterally in a vacuum, say in the x
direction, unless they are close enough that friction occurs.
This is not a typical perpetual motion scheme. All the energy in
perpetual motion schemes can typically be described in a fully closed
system in which energy can be proven to be conserved. When the
Casimir force is involved the system is not closed. The Casimir
force is due to momentum transfer from a flux of virtual photons, and
that flux flows throughout the universe. Any system utilizing that
flux can not be described as a closed system and is thus free to
obtain energy from that flux provided a means is found to break the
force symmetry. The suggested motion of parallel plates breaks this
symmetry.
SOME SIMPLIFYING DEFINITIONS
Let y be the separation between the drone and driver plater
surfaces. Let w be the x axis width of the drone plate and drive
plate. When the motion of the diver plate is in the +x direction,
then when x = -w the overlap between the two plates begins and when x
= +w the overlap between the two plates ends. When the motion of the
diver plate is in the -x direction, then when x = +w the overlap
between the two plates begins and when x = -w the overlap between the
two plates ends. The z axis size of the plates is k, and the total
area of each plate is k*w.
The area A(x) of the overlap is given by:
A(x) = k * max((w-|x|),0)
where |x| is the absolute value of x.
For the sake of simplicity, assume that the drone pendulum is
designed such that the force G(y) opposing the y direction Casimir
force F(y) is such that the displacement is a function of the area A
(x) between the plates and is such that the displacement y of the
drone, given an overlapped area A(x) is maintained as:
y = c * A(x) = c * k * max((w-|x|),0)
for some small constant c. This then alleviates the need for stop
mechanisms for the drone plate through avoiding contact between the
two by an appropriate choice of c and k.
This assumption can be carried out by making the resisting force
G(y) ~= k2 * 1/y^r
for y slightly larger than 4. The assumed force management can be
carried out if momentum effects are controlled, possibly through
forces imposed by the energy extraction mechanism.
SYMMETRY OF THE EDGE EFFECT FORCE
Note that Fig. 1 is laterally symmetric to Fig. 5. Fig. 2 is
laterally symmetric to Fig. 4. The line of this x axis lateral
symmetry lies in the center of Fig. 3, and is designated as x=0.
The y displacement of the drone plate is symmetric about the x axis,
i.e.
y = c * k * max((w-|x|),0)
Now, the geometry of the plates is symmetric about the x axis as
well. The means C(x), the x axis component of the Casimir force
between the plates, is symmetric as well, i.e.:
C(x) = -C(-x)
Since the geometry of the edges of the two plates for any two
laterally symmetric positions are symmetrical about the x = 0 line,
any Casimir force for one of those positions is equal and opposite to
that of the other. Therefore, when the energy required to overcome
any x axis Casimir effect is integrated over all x positions, i.e. C
(x) dx is integrated, it is zero for slow pendulum motions, and
should still be practically near zero even for faster pendulum
actions. The only net energy required to move the driver plate is
that which is required to bend the driver plate torsion pendulum,
which can be nominal, because it is driven primarily by spring action
of the driver torsion pendulum.
POSSIBLE DIFFICULTIES
The primary difficulty is maintaining the symmetry y = c * k * max
((w-|x|),0)
while energy is being drained from the y axis motion of the drone
plate. It is necessary to avoid hysteresis, a loss of this symmetry,
due to extracting more work out of the attraction of the plate vs the
pendulum restoration swing. The energy extraction mechanism needs to
extract energy symmetrically, equally on both parts of the swing, and
this could require active management circuits.
ooooooooooooooo
xxxxxxxxxxxxxxx -> x axis motion
Fig. 1
ooooooooooooooo | y axis motion
v
xxxxxxxxxxxxxxx -> x axis motion
Fig. 2
ooooooooooooooo
xxxxxxxxxxxxxxx -> x axis motion
Fig. 3
^
ooooooooooooooo | y axis motion
xxxxxxxxxxxxxxx -> x axis motion
Fig. 4
ooooooooooooooo
xxxxxxxxxxxxxxx -> x axis
motion
Fig. 5
Best regards,
Horace Heffner
http://www.mtaonline.net/~hheffner/
