On Aug 1, 2009, at 6:13 AM, Stephen A. Lawrence wrote:
Thanks, Horace, this was enlightening.
Is it fair to say that,
a) The Casimir force is a surface phenomenon, unlike most common
forces,
which act on the body of the material, including all the forces
mentioned below in (b);
Again, I'm no expert, and there are many inconsistencies in my own
mind about all this. I have many questions myself. I think it is
more correct to say, especially in the case of metals, it is an
effect between surfaces, because it is an effect between atoms, the
effect being the exclusion of ZPF virtual photons in the intervening
line segment. However, in the case of metal conductors, apparently
it is an effect between surfaces in any practical sense under
Mostepanenenko's method, given that the metal atoms are packed side-
by side and share conduction bands. I take it that within the metal
itself there are very small voids and thus much smaller wavelengths
are excluded, but there is no net force on the overall body of metal
from these voids to be considered, only an improved adhesion of the
atoms. I should say that Mostepanenenko does in fact explicitly limit
his method to forces between atoms *on separate bodies*. This I
assume because (1) forces between atoms of a single body only result
in stress or strain within that body and (2) his primary goal was to
compute the Casimir force between bodies, e.g. two spheres or a
sphere and a plane. It is not clear to me that the effect between
dielectrics is totally a surface effect, but I would think it would
not be a deep effect. I could be all wrong about this.
b) The net Casimir force which acts on a body due to the presence of
more than one "shading" object is *not* related to the force due to
each
individual "shading" object by linear superposition, unlike EM forces,
Newtonian gravity, and push gravity (in the low-strength limit);
This is one of those things I do not fully understand, but here is my
thinking anyway. Suppose two atoms A and B lie on a line of length
L. The line segment (A,B) then constitutes a ZPF free line, i.e. a
line segment on which all ZPF wavelengths longer than the length of
(A,B) are excluded. We now interject atom C in the middle of (A,B).
This creates intervals (A,C) and and (C,B) each of length L/2.
Suppose A, B and C all exist in or are separate bodies. Now, in the
initial case, wavelengths greater than L are excluded from (A,B). In
the second case, wavelengths greater than (L/2) are excluded from
(A,C) and (C,B). However, this does not change a thing with regards
to wavelengths larger than L already being excluded from (A,B). The
imposition of C merely excludes the *additional* wavelengths between
L and L/2. In this sense superposition of a kind occurs.
Now, suppose A is inside a body and C is on the surface of the body,
and B is on the surface of an independent body. The fact A exists in
a colinear fashion with C and B is irrelevant to computing the
wavelengths excluded on the line between B and C. The forces between
bodes thus end up being computable as between-surface effects.
Beyond that, there is the question of when an effect becomes
dismissible as second order. In the Coulomb world the potential
between point charges is linear with distance. In the Casimir force
world the potential between atoms is 1/r^7. Two atoms at 2r distance
have (1/2)^6 = 1/64 force effect of the same two at r distance. Even
for a one atom thick plane "plate" surface, the fringe effect is
small compared to a Coulomb fringe effect.
I'm not sure, but the above may be complicated immensely if relative
motion is involved. The doppler shift doesn't change photon speed,
but it changes photon momentum and wavelength. My impression is that
virtual photons are absorbed and emitted by matter. If matter is in
relative motion, then then a frequency shift should occur, and thus a
virtual photon momentum shift should occur, and thus a force change
should occur. A body moving away should downshift the ZPF field in
its "shadow", thus making the ZPF anisotropic in its shadow.
I think it is certain that any device which can obtain momentum or
energy from the ZPF must leave a ZPF shadow, but given that the ZPF
is isotropic, the shadow may take a spherical form, i.e. be in the
form of a radial gradient in the ZPF flux magnitude.
and for these reasons, and most particularly due to (b), the Casimir
force is also *not* conservative, unlike the other common forces
mentioned in (b)?
I don't know that the Casimir force is a force in the same sense as
the Coulomb force or gravity, even though it is carried by the
Coulomb force messenger particle. It is more like a force from the
wind, and thus its energy is available for tapping, or at least has
an identifiable source. The technical problem is it blows every
direction at once. Unlike the wind, it is carried by entities with
wave properties, and is strictly the result of these wave properties.
If we were bathed in isotropic light, we would not question the
availability of energy, though it might have to be extracted by
Carnot independent means, in other words by quantum means, the
photoelectric effect. With the Casimir force the only apparent means
of manipulation at the moment is the exclusion of large wavelengths
from cavities, and this has proven difficult to utilize. Still, any
system utilizing externally originating virtual photon 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
which is due to the isotropy of the flux.
Linear superposition is what allows us to conclude from the
conservative
nature of single-particle E and B fields that the action of
arbitrarily
complex E and B fields must also be conservative, of course, and the
fact that the Casimir force doesn't follow this is remarkable.
That to me means it is not a fundamental force like the Coulomb force
or gravity, it is a manifestation of the wavelike nature of the force
carrier particles of such forces.
Horace Heffner wrote:
[ snip parts I didn't comment on ]
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.
Don't follow this particular paragraph's conclusion, which *seems*
to be
saying that because it's higher power than 1/r^2, it can't be
conservative. But perhaps I misunderstood this.
You have my intent right. The point is that for plates at any given
separation r, far less fringe area is involved significantly in the
fringe for the Casimir force than for the Coulomb force, wherever you
set the limit on "significant". It was a poor choice of words on my
part to say I was "aware ... the fringe force can not be
conservative." I merely deduced (assumed!?) such and wrote it up in:
http://www.mtaonline.net/~hheffner/CasimirGenerator.pdf
in 2008. I summarized this (inadequately) as "... because the
Casimir force is a 1/y4 force
and the distances between any two points on the edge related surfaces
are typically
much further apart than the plate separation y."
Just because it's higher power than r^2 doesn't imply it's not
conservative, does it? Surely, for instance, a 1/r^12 force can be
represented by a potential field going as k/r^11, can it not?
But in any case this has no bearing on what you said both earlier and
later, which made it seem clear the Casimir force should, indeed,
*not*
be conservative.
I think the problem here is that the Casimir force is not a
fundamental force. It doesn't have a potential field.
Further, and most importantly, the casimir
force involves only straight lines. There are no bending E field
lines
to deal with.
Right -- I think this is a direct consequence of the fact that it
doesn't obey the law of superposition. The E field consists of
nothing
but straight lines, also, at some fundamental level, but when we
superpose several sources which all produce "straight lines" with
magnitudes varying along the lines, the *sum* of those lines is a
bunch
of curves.
Yes, the E field is actually a genuine vector field, and it has a
genuine potential field. The Casimir force is not like that.
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.
Very nice! Nice demonstration that the force isn't conservative,
and I
like the rotor, which leaves the plates at fixed separation and
just has
one of them spin -- it's a lot more convincing (to me) than general
assertions that we can bring the plates together along one path and
separate them by sliding along a different, longer, path.
Thanks!
From a practical standpoint I still like the vibrating plate
approach because I think it can be implemented much more easily with
existing chip fabrication technology than things involving rotors. I
think vibrating plates should have a much longer lifetime as well. I
wish I were up to speed on a good 3D rendering system on my Mac. The
shape of the "pendulums" I have in mind is difficult to describe in
words only, and the text is already over tedious due to a lack of
good figures.
I should also say that I hope it is obvious that I'm not totally
convinced I have all this right!
Best regards,
Horace Heffner
http://www.mtaonline.net/~hheffner/
