Dear Robert,

Robert Stirniman wrote:

> Charles Yost wrote:
> > I have been following the comments for several days now, but the Feb. 14
> > comment by c. H. Thompson in reference to what are the fourth and fifth
> > derivatives
>
> Charles has written a wonderful and thought provoking article.
> Here are some thoughts and analysis related to this problem.

-----------------<snip>------------------------

> The second independent solution for the scalar potential
> of the oscillating electric dipole appears to be missing in
> action. I believe the second solution is the longitudinal
> wave solution.

I agree.

> It is possible to write a power series which is a second
> independent solution of the scalar wave equation for the
> oscillating electric dipole. This power series solution
> is similar in form to the second independent solution of
> the bessel equation in cylindrical coordinates. It is a
> mystery to me, why we are able to see the second independent
> solution in the cylindrical bessel equation, yet believe
> that it is not needed in a spherical coordinate system.

As if to say that there is no relation between a cylinder and a sphere.

> The second independent solution of the wave equation for
> the oscillating electrical dipole is messy and semi-divergent.
> It contains a power series of positive exponents along with
> terms related to ln(kr), and it also contains an infinite
> series of terms with negative exponents. The series of terms
> with negative exponents resembles 1/f noise, also known as
> pink noise. It is peculiar that the words "pink noise" are
> on the ECHELON watch list.

Interesting. Is white noise on the list?

> We are missing one of the solutions of the wave equation for
> the oscillating electric dipole. We are also missing both
> of the evanescent wave solutions. In effect playing
> with a quarter of a deck.

I presently consider evanescent waves to dominate in the natural environment.
Is this correct in your view? Also, have you ever examined these
concepts in light of the behaviors caused by imaginary charge?
(See, for example
http://www.physik.fu-berlin.de/~kleinert/kleiner_re232/node7.html )

> Real Waves:
> del^2(Phi) = -k^2(Phi) One solution missing.
>
> Evanescent Waves:
> del^2(Phi) = +k^2(Phi) Both solutions missing.
>
> These are linear differential equations. When we find
> all of the four independent solutions for Phi, which
> simultaneiously satisfy both of these wave equations.
> We should see a potential which satisfies the Laplacian.
>
> del^2(Phi) = 0
>
> A suggested total solution for the potential of the
> oscillating electric dipole, might look something like this:
>
> Phi = {qa/4(Pi)(e0)r^2}{cos(wt)-(ik^3r^/3!)sin(wt)}
>
> An instantaneous real electrical field due to position,
> which varies as 1/r^3, and an instantaneous, purely reactive
> (complex) electric field which is not distance dependent.
> The second part of the field is due to a source term
> related to jerk -- the time derivative of acceleration.
> The suggested reactive electric field has a cubic frequency-
> power spectrum and a formulation which is essentially similar
> to that suggested for the zero point field.

Interesting!

> What do we believe is the source of the zero point field?
> A field with a cubic frequency spectrum will require a
> source term related to jerk. No such source term currently
> exists in classical or quantum electrodynamics. We have
> source terms related to position, velocity, and acceleration
> -- i.e. terms related to +cos(wt), -sin(wt), -cos(wt). Why
> stop here?

Again, my point.

> One can see that a term related to +sin(wt),
> a jerk term, may be needed in the group of operations.

There may yet be a requirement for a similar analysis
in the 5th derivative. I consider that this could have
some implications regarding the topology of space
as related to the observed behaviors of the physical
systems.

Thanks very much for your valuable contribution!

Neil