On Jul 23, 2009, at 9:43 AM, Stephen A. Lawrence wrote:
Hmm -- Horace, I had a question about a somewhat different proposal.
You have proposed that if we let two plates come together, pushed
by the
Casimir force, then slide them apart sideways, and then repeat, we can
get energy out of the cycle.
Now, I don't pretend to understand the Casimir effect at any but the
most superficial level. However, it *seems*, on the surface, a lot
like
a "push gravity" theory, in which we're being constantly bombarded by
some kind of radiation which "pushes" on all sides equally, and the
apparent gravitational field of an object is due to its shading us
from
the "global G-particle field".
The chief difference I see here is that, AFAIK, a "push gravity" field
is conservative. In fact, as I understand it, the only detectable
difference between "push gravity" and Newtonian gravity is in very
intense fields, where the "push gravity" field may "hit the rails" and
start "clipping".
As I understand it, the reason the sliding-plate thing doesn't work to
produce energy with push gravity is that the "push" comes from
impact by
particles coming from *all* *directions* over an entire hemisphere.
When we're sliding the plates apart, there is a "push" force acting on
both *edges* of the sliding plate, but the trailing edge is "partly
shaded" by the other plate. (See attachment.) Consequently the
"push"
on the leading edge is slightly larger than the "push" on the trailing
edge, and the work done sliding the plates apart ends up the same
as if
they were just pulled apart directly.
The question this brings up is, does something similar happen with the
Casimir force? Does the adjacent conductive plate reduce the
possibilities for virtual particles appearing at the trailing edge of
the plate, and hence reduce the "push" on that end, and so result
in the
need to "do work" to slide the plates apart sideways?
It may be that the fact that you can make a conductive plate
arbitrarily
thin would imply that this mechanism doesn't happen or at least
doesn't
exactly cancel the energy gained. But I don't understand the Casimir
effect, which is why I'm asking.
Nice drawing. Answering this question properly takes some work, and
a lot more knowledge than I have. But, I'll provide my viewpoint for
what it is worth. I looked for a way to answer it without spilling at
least some proprietary beans, but couldn't avoid it, so here we go ...
First, let me say that it is certainly possible to hypothesize that
the momentum exchanges of the ZPF virtual photons *is* the
gravitational force. I don't think that issue needs to be discussed
or resolved to still have a meaningful discussion of your question.
It is sufficient to note that the flux of the zero point field (ZPF)
virtual photons carry momentum and exert pressure on matter, and
that, for convenience of discussion, ZPF flux is isotropic. It is
also true that matter is essentially transparent to ZPF virtual
photons. Particles affected by receiving a virtual photon respond by
moving, and thus emit another one carrying the same momentum, unless
local conditions prevent it.
I think this is the point at which discussion and understanding of
the Casimir force can begin to take on its ordinary nature. The
Casimir effect is said to be due to the fact a virtual photon can not
be emitted in a given direction if a reflecting atom is in its path
at a distance less than its wavelength. In other words, a cavity
with a conducting metal surface prevents any wavelength virtual
photon from crossing the cavity in a particular direction if its
wavelength is longer than the path length for the virtual photon
through the cavity in that direction. If you draw a line segment
traversing the cavity, of length d, then virtual photons of
wavelength d or larger are prevented from taking that path, in either
direction. This results in an inward pressure vector along that line
segment. For convenience here, call such a line segment a "ZPF free
line". Sorry, this is my terminology only, but it will save a lot of
typing. There are many questions I have in my mind about the
consistency of all the above, but this is my understanding of the
general concepts.
Because the prevention of emission is symmetric along any ZPF free
line, it is immediately clear that no net inertial force can result
from the shaping of static matter for this purpose. Note that
inertial drives are still feasible provided the ZPF can effect
inertial mass change, and the involved changing mass is accelerated
appropriately, which is the basis of the inertial drive I proposed here:
http://mtaonline.net/~hheffner/ZPE-CasimirThrust.pdf
However, ZPF balanced forces can result within matter shaped for the
purpose, resulting in pressures, and energy can feasibly be extracted
from movement under this pressure.
Interestingly, the formulas for computing pressure along ZPF free
lines between atoms match the formulas for computing the van der
Waals retarding interaction between two atoms. It is my impression
that, for this reason, there is some doubt in some of the physics
community the ZPF exists and is the cause of the Casimir force.
OTOH, the ZPF could be the most fundamental *cause* of the van der
Walls force, the cause behind matter acting as it does to produce van
der Walls forces. Again, like the gravity issue, this doesn't need
to be discussed or resolved to understand the answer to your question.
Note that by dealing only with ZPF free lines we have changed
perspective completely, and the nature of the force computation
procedure. We no longer care about the external nature of the ZPF,
or the overall shape of the matter, when addressing forces between
conducting surfaces. We only care about nooks and crannies and
cavities that include ZPF free lines. This of course includes the
edges of parallel plates, the subject of your question. This greatly
simplifies answering the question, because we no longer have to be
concerned with rays impinging from all angles. We only need to deal
with the enclosed ZPF free lines and their lengths.
Mostepanenenko and Sokolov (Dokl. Akad. Nauk SSSR, 298. 1380-1383)
provides two principles (assumptions) for simplified but accurate
practical computing using these concepts: 1. The additivity
principle, and 2. the renormalization principle.
1. The Additivity Principle:
"The dependence of the interaction potential of macrobodies on the
distance can be determined by summing the potentials of the van der
Waals retarding interaction beteen single atoms belonging to
different bodies."
2. The Renormalization Principle
"The value found for the constant of the interaction potential of the
macrobodies should be reduced by the same factor as that by which the
true constant of the interaction between flat plates of the same
materials differ from the constant obtained for them by the
additivity principle."
Beyond that, the van der Waals retarding interaction U(r) at distance
r between two individual atoms with electric and magnetic
polarizabilites a1E, a2E, a1M, and a2M, is:
U(r) = C/r^7
where:
C = (-23/Pi) ( (a1E a2E)(a1M a2M) + a1M a2M) + (7/(4 PI)) ((a1E
a2M) + (a2E a1M))
Now we get off the beaten road as I make some deductions and deal
with your question directly as best as I can.
We can differentiate the interaction potential sum to obtain a force.
The interaction potentials can be summed independently in each axis,
thus providing the ability to produce a force vector for each surface
element if desired. Note that the larger a ZPF free line, the less
wavelengths excluded, and thus the less force evolved along that
line. The smaller r is the greater the force.
I am well aware of the fringe force at the edge of capacitors and how
these are used to produce electrostatic motors. Electrostatic motors
conserve energy, so it just happens that when an edge with a small
fringe force is dragged across a wide capacitor, a lot of energy is
expended (or obtained depending on polarity) and that energy is
exactly equal to the energy stored between the plates when together
at potential. This involves the Coulomb force, which is a 1/r^2
force. I have also been aware that the Casimir force involves large
negative exponents on r, and thus the fringe force effect can not be
conservative with regard to plate effects. Further, and most
importantly, the casimir force involves only straight lines. There
are no bending E field lines to deal with.
The energy involved in plate motion with regard to the fringe force,
at least for conductive surfaces, is highly dependent on the plate
edge geometry. It is purely an effect between surfaces. While
Mostepanenenko's principles involve fudging, he says the powers of r
always come out right using his method. Therefore the method serves
well for a comparative analysis, because, in designs using the same
materials, we can ignore the material related (fudged) constant C. I
will now prove, by comparative analysis, that the lateral force on a
square plate edge is not the same as on a beveled plate edge, and
thus a net energy gain is feasible from a Casimir effect motor
provided the edges of the plates are appropriately shaped.
The following comments refer to aspects of Figure 6, Page 9 of:
http://www.mtaonline.net/~hheffner/CasimirGenerator.pdf
The following is the key to Fig. 6:
(P7,S3) - top of bottom slab
(P5,P1) - bottom of top slabs
(P5,P1,P2,P4) - sides of rectangular top plate
(P5,P1,P3,P4) - sides of beveled top plate
S1 S2 and S3 - points for van der Waals retardation calculation
(S1,S2)- ZPF free line for S1 on beveled slab to some point S2
S4,S1,S5 - angle of feasible ZPF free lines to second plate from S1
(s3,S2) - SPF free line corresponding to (S1,S2) for comparison
In Fig. 6 we are comparing two slabs, a rectangular one vs one with a
beveled edge. Now we pick any point S1 on the edge of the beveled
slab. We need to sum the potentials (or forces) from every ZPF free
line between S1 and every point S2 on the bottom slab surface. All
such ZPF free lines (S1,S2) lie within the angle S4,S1,S5. The line
(S1,S4) is parallel to the bottom slab surface, (P6,S2).
Now, for every such ZPE free line (S1,S2) there exists a unique
corresponding ZPF free line on the rectangular slab edge (P1,P2),
which shares an intersecting point S3 on the rectangular slab edge.
In every case, (S1,S2) is larger than the corresponding (S3,S2).
Because this is true for every possible point S1, the sum of the
potentials for the beveled edge are smaller than the sum of the
potentials for the rectangular slab edge. There are many ZPF lines
from the rectangular slab edge to the bottom slab which have not been
evaluated, and for which there are no corresponding ZPF free lines
from the beveled edge, but this only makes the inequality larger. In
every case of corresponding ZPF free lines, the lines make the same
angles with respect to the bottom slab, so the force vectors can be
broken into axis oriented vectors and summed without changing the
direction of the inequalities.
There are analogous arguments if the bevel goes the other way, making
an even better cavity than the rectangular slab edge.
For the above reasons, a free energy rotor can be made of blades of
parallelogram shape, with a back bevel on one side and a forward
bevel on the opposed edge, or even a squared off edge substituting
for one of the beveled edges. Since the force on the two edges is
not balanced, a net torque results without application of external
energy. This results in a free energy motor.
This also provides proof that the earlier proposed Casimir generator
principles work, provided the slab edges are beveled.
Best regards,
Horace Heffner
http://www.mtaonline.net/~hheffner/
