[NewCandle] that which reacteth not and is clear

[Horace Heffner]

On Feb 26, 2008, at 4:54 AM, Nick Reiter wrote:
>
> Where I tend to fall short in brainpower is the
> understanding of how different surface geometries
> alter the Casimir force.  The calculation for parallel
> conducting surfaces is classic, and understandable to
> me.  I've never seen the modified formula for force
> between spheres, though I've been told there is one.
> (The generally used geometry for demonstrating the
> Casimir force seems to be a planar surface and a
> spherical probe on a load cell or AFM stylus.)

Well, my understanding of the situation is minimal, so at least there  
should not be much difficulty communicating it!  8^)

There is a formula for the force between spheres, but I don't have it  
or know where to get it.  I could derive one, but it would be highly  
suspect and probably wrong.  Having said that, within a lattice of  
such spheres, the following might be used as a very rough approximation:

F  =(h*c*Pi/(480*s^4))*(Pi*(s/2)^2)

where s is the separation distance between sphere centers.

The reason I say this is the action area for the spheres is A =  
Pi*r^2 = (Pi*(s/2)^2).  Between planes with separation distance s,  
the Casimir pressure is given by:

P  =(h*c*Pi/(480*s^4))

(See http://en.wikipedia.org/wiki/Casimir_effect)

So, we get the approximation F = pressure * area = P*A.

It is very interesting, that despite the fact the Casimir pressure is  
a 1/r^4 phenomenon, the inter-atomic force is merely a 1/s^2  
phenomenon, because (1/s^4)*(s^2) = 1/s^2.

Let me think out loud about all this, and then take some thoughts to  
maybe wild conclusions ...

SOME BACKGROUND

Now, the pressure is a result of *excluding* certain wavelengths.   
The amount of zero point radiation (energy) at a given wavelength is  
proportional to 1/lambda^3, which results in a pressure that is  
proportional to 1/r^4.  To determine the pressure involved it is  
necessary, from every angle of incidence, every ray path, to estimate  
the wavelength of radiation excluded, and integrate the energy and  
force for excluding that wavelength (where the force is based on the  
momentum transfer assumed for the external incoming virtual photon  
flux excluded AFAIK.)

This all gives us some good feel for what happens to inter-sphere  
pressure as the size of the spheres decreases. Every  space, every  
exclusion zone, between the spheres shrinks in proportion to the  
sphere size.  This is true regardless the packing factor involved.   
Assuming a constant packing factor, thus know the inter-sphere force  
increases as 1/r^2 for the spheres of radius r.  We know the external  
pressure for some volume of spheres in fixed geometry (and thus fixed  
surface area) thus increases as 1/r^4, and we can roughly approximate  
those values using the above formulae for F and P.

The (I think virtual) photon flux is uniform in all directions.   
Applying uniform pressure to a mass seems to have not much utility.  
It strikes me as strange that physicists would think excluding the  
virtual photons from some volume would reduce gravitational mass.  It  
only reduces inertial mass.  Gravity is carried by the graviton.   
What is useful is being able to reduce or increase inertial mass very  
fast.  It then is possible to selectively create directional  
centrifugal force, and thus an infinite Isp inertial drive.

AN INERTIAL DRIVE

What is needed for the subject method is a spongy compressible medium  
for the aluminum spheres, and then a piezo to drive the compression/ 
expansion in synchronization with a strong centrifugal force  
generating rotation.  A liquid or solid or even gas medium for the  
spheres could work for this, and gas, being compressible, may be  
viable, depending on particle size and type, and gas pressure (the  
higher the pressure the more sound conductivity and speed).  If you  
can vibrate the stuff enough, even vacuum might work, but that has  
its own problems. The problem separating very small spheres (or any  
shape particle) is probably overcoming the van der Vaals forces, so a  
highly compressible medium might play a significant role in  
eliminating that problem by avoiding the need to break surface  
contact altogether, plus it can carry sound energy.

If the sphere separation can be varied from in-contact to not in- 
contact, through the expansion of the intervening medium, then the  
packing factor itself will be non-linear, and the Casimir pressure  
will thus also become *far* more non-linear.  If there is anything at  
all to the notion that inertia is a result of the zero point field,  
then the inertia of the medium should vary as the Casimir pressure is  
varied.

Instead of rotating the medium (to make a centrifuge) for which the  
inertial mass is to be varied, it can be vibrated in a special way.   
The vibration needs to provide a smooth inertial reversal at one end  
of the cycle and a strong jerk at the other.  The material in the  
strong jerk will be compressed, and thus its inertial mass reduced.  
The transducer signal for that can be generated by using a flyback  
transformer driver technique.


A DIFFERENT APPROACH BASED ON A DIFFERING MODEL - FREE ELECTRON DENSITY

Here's another thought.  Across some temperature and/or pressure  
ranges some materials convert from conducting to non-conducting.  It  
is the conduction band electrons that can exclude the ZPF from a  
volume. It may be more effective to manipulate conductivity, or even  
superconductivity, rather than particle separation, in order to  
controllably exclude the ZPF.   Superconductivity is quickly but  
momentarily destroyed by application of high frequency or even a  
short duration pulse.   It should be possible to employ a coordinated  
sound and electromagnetic signal to an appropriate mass to create an  
inertial drive, with the inertial mass increasing EM pulse applied in  
the same half of each sonic cycle, when the included lattice points  
experience acceleration in the direction opposed to the desired force  
direction.

Here's a stunning thought (pun intended). If conduction band  
electrons can exclude the ZPF, then free electrons should be able to  
do the same. A gas/plasma could be vibrated with a strong ionizing  
pulse applied at one end of the vibration cycle, say the jerk end of  
a cycle as specified above, when maximum acceleration is occurring,  
so as to increase free electron density then, and thus reduce  
inertial mass then.


A CONDUCTION BAND ELECTRON DENSITY BASED INERTIAL DRIVE

The Casimir force, i.e. Casimir pressure, is supposedly created by  
exclusion of zero point field (ZPF) photons from a volume by means of  
at least partially enclosing the volume by conductive surfaces.  The  
theory of gravimagnetism [1] provides justification for asserting  
that the zero point field is carried by virtual photons, not real  
photons.  A stochastically varying flux of virtual photons is  
identical in effect to a stochastically varying electromagnetic near  
field.  Especially at wavelengths less than the diameter of an atom,  
a zero point field comprised of virtual photons should couple far  
better to free electrons, or conduction band electrons, than to  
orbital electrons. This then provides an explanation for why  
conductors can substantially exclude the zero point field from a  
volume when dielectrics can not.

It has been theorized that the zero point field is responsible for  
inertia.  [2] [3]  It is thus reasonable to conclude that exclusion  
of the ZPF from a volume will reduce the inertia of that volume to  
the degree the excluded photons account for the inertia of the  
affected mass.  It is therefore reasonable to conclude that an  
exceptionally high concentration of conduction band electrons, excess  
electrons, within a conductor will reduce inertia of the metal atoms  
in proximity to those excess electrons.  It is similarly reasonable  
to conclude that a thin dielectric between such ZPF excluding  
electrodes will not have a significant effect on the ZPF between the  
electrodes because such a dielectric has no conduction bands. The  
inertia of such a bounded dielectric should be affected to the extent  
the excluded ZPF photons are responsible for its inertia.

The Casimir pressure, is highly non-linear. [4]  It might thus be  
concluded that simply moving a concentration of conduction band  
electrons from one side of a conductive film to the other will  
provide a net decrease in inertial mass for material screened from  
the ZPF by that conductor.  Similarly, increasing the negative charge  
of a conductor should provide a decrease in inertial mass of the  
conductor itself.  Far more importantly, increasing the density of a  
conductor plate surface charge increases the threshold frequency of  
the excluded photons.  This means the ZPF effects on matter between  
between two plates is dramatically, nonlinearly, increased by placing  
a surface charge on the plates.  Fortunately, this does not mean the  
plates bounding a material must contain a net charge to affect the  
inertia of the material, only that one or the other or each of the  
plate surfaces contain a high electron density.

 From the above deductions, it appears applying an alternating  
current to a capacitor on a rotating device, in phase with the  
rotation, should provide a net thrust. However, sonic vibration can  
provide a high atomic acceleration, and much higher momentum transfer  
repetition rate, and can readily stress material to extremes. It is  
therefore suggested that an inertial drive might be constructed from  
a multilayer capacitor which is sonically energized in phase with an  
AC charge current.  The objective is to have maximal plate charge  
during the times of maximal acceleration in the direction opposed to  
the desired direction of thrust.

Note that the orientation of the capacitor plates with respect to the  
sound direction is not necessarily important, unless piezoelectric  
effects of the included dielectric is present.  Such an piezoelectric  
effect might even be used to produce the desired plate surface charge.

It is important that the sonic wavelength is long compared to the  
dimension of the smallest segment of capacitor for which the charge  
is controllable.  This is because the charge must be present only  
during acceleration in a single direction.  The capacitor should be  
neutralized at other times.   This indicates the probable need for  
construction of a miniature array of capacitors, each charged and  
discharged in very short cycles in synchronization with sound wave  
transversals.  It is also important to design the sound transducer,  
if it is indeed separate from the inertial drive capacitor, such that  
undesirable inertial effects, i.e. net force canceling effects,  are  
not inadvertently generated.


[1] Horace Heffner, 2007,”Gravimagnetics”,
http://mtaonline.net/~hheffner/FullGravimag.pdf

[2] Reuda and Haisch,"Gravity and the quantum vacuum inertia  
hypothesis",Ann. Phys. (Leipzig) 14, No. 8, 479 – 498 (2005):
http://www.calphysics.org/articles/gravity_arxiv.pdf

[3].  B. Haisch, A. Rueda, and H. E. Puthoff. "Physics of the Zero- 
Point Field: Implications for Inertia, Gravitation and Mass," Spec.  
in Sci. and Technology 20, 99 (1997):
http://www.earthtech.org/publications/spec_sci_tech.pdf

[4] Wikipedia article on the Casimir Effect:
http://en.wikipedia.org/wiki/Casimir_effect


Horace Heffner
http://www.mtaonline.net/~hheffner/