This is a follow-up on a discussion on the quantum nature of Maxwell's
physical electrodynamics model. In Maxwell's model the fabric of
so-called space-time is a vortex lattice of Benard Cells (which
properly should be called Maxwell's cells...). As mention in earlier
discussion, the vortex rings of such a lattice constitutes a natural
quantum system. Each ring in the lattice has two distinct modes of
oscillation, poloidal and torroidal... If one were to cut a
'straighten out' one such ring such that it looked like,

|=========================================|
0 360

the poloidal oscillation mode is,

_ - _ _ - _ _ - _ _ - _ _ - _
|= = = = = |
- _ - - _ - - _ - - _ - - _ -

and the torroidal mode is,

= = =
|= = = = = |
= =

Clearly, both modes will tend to couple together in a harmonic
fashion.

It is well known that vortex rings couple in two distinct ways. One
leads to a coupled harmonic oscillator, and the other a static state.
These are,

- | -
o v o
- - (Static coupling)
o ^ o
- | -


- ^ -
o | o
- - (Harmonic coupling)
o ^ o
- | -

The ring lattice Maxwell envisioned and illustrated in his works was,

- --
/ \
/ \
- -- + - --
/ \ / \
/ \ / \
+ -- -- + ------ Flow up
\ / \ /
\ / \ /
-- - + -- -
/ \ / \
/ \ / \
+ -- -- +
\ / \ /
\ / \ /
- -- + - --
\ /
\ /
- --

(page 183, Ref 2)

This represents one layer of the matrix in the x-y plane. Clearly the
matrix is three dimensional, and looking at the x-z plane we'd find,


- -
/ ^ \
/ | \
- - | - -
/ ^ \ | / ^ \
/ | \ ^ / | \
| - - |
\ | / v \ | /
\ ^ / | \ ^ /
- - | - -
/ v \ | / v \
/ | \ v / | \
| - - |
\ | / ^ \ | /
\ v / | \ v /
- - | - -
\ | /
\ ^ /
- -

This configuration matches the 'static coupling' descibed above. A
statically coupled ring pair will 'blast outward' radially expanding
until restricted from doing so. This occurs when the forces of the
other such expanding rings balance. Since ring streamlines (perfectly
analogous to lines of force) cannot cross, the lattice structure is an
eneviable result. The size of a cell is defines by the basic
properties of the medium.

Well, the is the founding framework, and so far, we're just
considering basic static conditions. Each ring has the oscillation
modes identified above. Further, if one ring does oscillate in any
fashion, it MUST infulence the surrounding lattice since the lattice
is maintained but a balance in opposing forces...

This is where things become interesting...


Paul Stowe

On Sat, 30 Aug 2003 19:48:58 GMT, wrote:

This is a follow-up on a discussion on the quantum nature of Maxwell's
physical electrodynamics model. In Maxwell's model the fabric of
so-called space-time is a vortex lattice of Benard Cells (which
properly should be called Maxwell's cells...). As mention in earlier
discussion, the vortex rings of such a lattice constitutes a natural
quantum system. Each ring in the lattice has two distinct modes of
oscillation, poloidal and torroidal... If one were to cut a
'straighten out' one such ring such that it looked like,

|=========================================|
0 360

the poloidal oscillation mode is,

_ - _ _ - _ _ - _ _ - _ _ - _
|= = = = = |
- _ - - _ - - _ - - _ - - _ -

and the torroidal mode is,

= = =
|= = = = = |
= =

Clearly, both modes will tend to couple together in a harmonic
fashion.

It is well known that vortex rings couple in two distinct ways. One
leads to a coupled harmonic oscillator, and the other a static state.
These are,

- | -
o v o
- - (Static coupling)
o ^ o
- | -


- ^ -
o | o
- - (Harmonic coupling)
o ^ o
- | -

The ring lattice Maxwell envisioned and illustrated in his works was,

- --
/ \
/ \
- -- + - --
/ \ / \
/ \ / \
+ -- -- + ------ Flow up
\ / \ /
\ / \ /
-- - + -- -
/ \ / \
/ \ / \
+ -- -- +
\ / \ /
\ / \ /
- -- + - --
\ /
\ /
- --

(page 183, Ref 2)

This represents one layer of the matrix in the x-y plane. Clearly the
matrix is three dimensional, and looking at the x-z plane we'd find,


- -
/ ^ \
/ | \
- - | - -
/ ^ \ | / ^ \
/ | \ ^ / | \
| - - |
\ | / v \ | /
\ ^ / | \ ^ /
- - | - -
/ v \ | / v \
/ | \ v / | \
| - - |
\ | / ^ \ | /
\ v / | \ v /
- - | - -
\ | /
\ ^ /
- -

This configuration matches the 'static coupling' descibed above. A
statically coupled ring pair will 'blast outward' radially expanding
until restricted from doing so. This occurs when the forces of the
other such expanding rings balance. Since ring streamlines (perfectly
analogous to lines of force) cannot cross, the lattice structure is an
eneviable result. The size of a cell is defines by the basic
properties of the medium.

Well, the is the founding framework, and so far, we're just
considering basic static conditions. Each ring has the oscillation
modes identified above. Further, if one ring does oscillate in any
fashion, it MUST infulence the surrounding lattice since the lattice
is maintained but a balance in opposing forces...

This is where things become interesting...


Paul Stowe

Oops, typos & ..., forgot to include references.

Refs:

1. "On the Physical Lines of Force" J. C. Maxwell, 1861-62
2. "Maxwell on the Electromagnetic Field, A Guided Study",
T. K. Simpson, Rutger University Press - 1997

wrote in message
...
| On Sat, 30 Aug 2003 19:48:58 GMT, wrote:
|
| This is a follow-up on a discussion on the quantum nature of Maxwell's
| physical electrodynamics model. In Maxwell's model the fabric of
| so-called space-time is a vortex lattice of Benard Cells (which
| properly should be called Maxwell's cells...). As mention in earlier
| discussion, the vortex rings of such a lattice constitutes a natural
| quantum system. Each ring in the lattice has two distinct modes of
| oscillation, poloidal and torroidal... If one were to cut a
| 'straighten out' one such ring such that it looked like,
|
| |=========================================|
| 0 360
|
| the poloidal oscillation mode is,
|
| _ - _ _ - _ _ - _ _ - _ _ - _
| |= = = = = |
| - _ - - _ - - _ - - _ - - _ -
|
| and the torroidal mode is,
|
| = = =
| |= = = = = |
| = =
|
| Clearly, both modes will tend to couple together in a harmonic
| fashion.
|
| It is well known that vortex rings couple in two distinct ways. One
| leads to a coupled harmonic oscillator, and the other a static state.
| These are,
|
| - | -
| o v o
| - - (Static coupling)
| o ^ o
| - | -
|
|
| - ^ -
| o | o
| - - (Harmonic coupling)
| o ^ o
| - | -
|
| The ring lattice Maxwell envisioned and illustrated in his works was,
|
| - --
| / \
| / \
| - -- + - --
| / \ / \
| / \ / \
| + -- -- + ------ Flow up
| \ / \ /
| \ / \ /
| -- - + -- -
| / \ / \
| / \ / \
| + -- -- +
| \ / \ /
| \ / \ /
| - -- + - --
| \ /
| \ /
| - --
|
| (page 183, Ref 2)
|
| This represents one layer of the matrix in the x-y plane. Clearly the
| matrix is three dimensional, and looking at the x-z plane we'd find,
|
|
| - -
| / ^ \
| / | \
| - - | - -
| / ^ \ | / ^ \
| / | \ ^ / | \
| | - - |
| \ | / v \ | /
| \ ^ / | \ ^ /
| - - | - -
| / v \ | / v \
| / | \ v / | \
| | - - |
| \ | / ^ \ | /
| \ v / | \ v /
| - - | - -
| \ | /
| \ ^ /
| - -
|
| This configuration matches the 'static coupling' descibed above. A
| statically coupled ring pair will 'blast outward' radially expanding
| until restricted from doing so. This occurs when the forces of the
| other such expanding rings balance. Since ring streamlines (perfectly
| analogous to lines of force) cannot cross, the lattice structure is an
| eneviable result. The size of a cell is defines by the basic
| properties of the medium.
|
| Well, the is the founding framework, and so far, we're just
| considering basic static conditions. Each ring has the oscillation
| modes identified above. Further, if one ring does oscillate in any
| fashion, it MUST infulence the surrounding lattice since the lattice
| is maintained but a balance in opposing forces...
|
| This is where things become interesting...
|
|
| Paul Stowe
|
| Oops, typos & ..., forgot to include references.
|
| Refs:
|
| 1. "On the Physical Lines of Force" J. C. Maxwell, 1861-62
| 2. "Maxwell on the Electromagnetic Field, A Guided Study",
| T. K. Simpson, Rutger University Press - 1997

Yes, I come up with something very similar to this when attempting to
model the EM vacuum as a "spin matrix" comprised of "virtual" e+e- pairs.
To my amazement, everything works out very well if "vacuum charge" is
sqrt(hbar*c) in gaussian units or sqrt(eps0*hbar*c) in SI units. To me,
one of the main features of what you present is that all the vacuum
oscillators are indeed *coupled* instead of uncoupled. And effect each
other producing an equilibrium state.

FrediFizzx

:
This is a follow-up on a discussion on the quantum nature of Maxwell's
physical electrodynamics model. In Maxwell's model the fabric of
so-called space-time is a vortex lattice of Benard Cells (which
properly should be called Maxwell's cells...).

That simply isn't so. Benard cells are formed in systems which a thermal
gradient exists over the entire system and which is bounded by a
containers having only certain aspect ratios for fluids with particular
densities, all of which are interrelated. Maxwell's equations do not
describe them, nor is your description of the cells as hexagonal complete.
The types of cells you get depends upon a number of factors, including the
shape of the container, and the boundary conditions on the surfaces, in
addition to the factors already mentioned.

Your pictures are nice, however, your description of what maxwell
envisioned, doesn't accurately depict benard cells.


The ring lattice Maxwell envisioned and illustrated in his works was,

- --
/ \
/ \
- -- + - --
/ \ / \
/ \ / \
+ -- -- + ------ Flow up
\ / \ /
\ / \ /
-- - + -- -
/ \ / \
/ \ / \
+ -- -- +
\ / \ /
\ / \ /
- -- + - --
\ /
\ /
- --

(page 183, Ref 2)

This represents one layer of the matrix in the x-y plane. Clearly the
matrix is three dimensional,

Clearly it not three-dimesional, or at least not in the sense that all
three dimensions are equivalent. The directions in the x-y plane are not
equivalent to the z-direction. The circulation in the z-direction results
from two suraces parallel to the x-y plane shown which are a fixed
distance apart in the z-direction and maintained at a fixed temperatures
so that a thermal gradient exists between the surfaces. This determines
the cell size in the x-y plane (assuming you also employ the correct
boundary conditions for the two surfaces). The critical wavelength which
corresponds to the cell-size in the x-y plane, for example, is about
2*sqrt(2) d, where d is the z-spacing. The eigenvalues are 2*sqrt(2) d/n.

In addition, the hexagonal cells typically form in containers with open
tops. In closed containers, the cells form concentric rings (for containers
that are right-circular cylinders).

and looking at the x-z plane we'd find,


- -
/ ^ \
/ | \
- - | - -
/ ^ \ | / ^ \
/ | \ ^ / | \
| - - |
\ | / v \ | /
\ ^ / | \ ^ /
- - | - -
/ v \ | / v \
/ | \ v / | \
| - - |
\ | / ^ \ | /
\ v / | \ v /
- - | - -
\ | /
\ ^ /
- -

This configuration matches the 'static coupling' descibed above. A
statically coupled ring pair will 'blast outward' radially expanding
until restricted from doing so. This occurs when the forces of the
other such expanding rings balance. Since ring streamlines (perfectly
analogous to lines of force) cannot cross, the lattice structure is an
eneviable result. The size of a cell is defines by the basic
properties of the medium.

That is not really true. There is a relationship between the cell
size and the properties of the medium, given in terms of the rayleigh
number as a function of a dimensionless parameter related to the
distance between the two x-y surfaces held at different temperatures
across a distance in the z-direction. The cell size is found by
minimizing the rayleigh number with respect to this parameter. If
you separate the properties of the fluid from the container dimensions,
then for a given fluid. the cells size is determined by the dimensions
of the container in the z-direction.

Well, the is the founding framework, and so far, we're just
considering basic static conditions. Each ring has the oscillation
modes identified above. Further, if one ring does oscillate in any
fashion, it MUST infulence the surrounding lattice since the lattice
is maintained but a balance in opposing forces...

This is where things become interesting...

That may be, but so far it doesn't describe E&M.

On Sat, 30 Aug 2003 14:43:43 -0700, "FrediFizzx"
wrote:

wrote in message
.. .
On Sat, 30 Aug 2003 19:48:58 GMT, wrote:

This is a follow-up on a discussion on the quantum nature of Maxwell's
physical electrodynamics model. In Maxwell's model the fabric of
so-called space-time is a vortex lattice of Benard Cells (which
properly should be called Maxwell's cells...). As mention in earlier
discussion, the vortex rings of such a lattice constitutes a natural
quantum system. Each ring in the lattice has two distinct modes of
oscillation, poloidal and torroidal... If one were to cut a
'straighten out' one such ring such that it looked like,

|=========================================|
0 360

the poloidal oscillation mode is,

_ - _ _ - _ _ - _ _ - _ _ - _
|= = = = = |
- _ - - _ - - _ - - _ - - _ -

and the torroidal mode is,

= = =
|= = = = = |
= =

Clearly, both modes will tend to couple together in a harmonic
fashion.

It is well known that vortex rings couple in two distinct ways. One
leads to a coupled harmonic oscillator, and the other a static state.
These are,

- | -
o v o
- - (Static coupling)
o ^ o
- | -


- ^ -
o | o
- - (Harmonic coupling)
o ^ o
- | -

The ring lattice Maxwell envisioned and illustrated in his works was,

- --
/ \
/ \
- -- + - --
/ \ / \
/ \ / \
+ -- -- + ------ Flow up
\ / \ /
\ / \ /
-- - + -- -
/ \ / \
/ \ / \
+ -- -- +
\ / \ /
\ / \ /
-- - + -- -
\ /
\ /
- --

(page 183, Ref 2)

This represents one layer of the matrix in the x-y plane. Clearly the
matrix is three dimensional, and looking at the x-z plane we'd find,


- -
/ ^ \
/ | \
- - | - -
/ ^ \ | / ^ \
/ | \ ^ / | \
| - - |
\ | / v \ | /
\ ^ / | \ ^ /
- - | - -
/ v \ | / v \
/ | \ v / | \
| - - |
\ | / ^ \ | /
\ v / | \ v /
- - | - -
\ | /
\ ^ /
- -

This configuration matches the 'static coupling' descibed above. A
statically coupled ring pair will 'blast outward' radially expanding
until restricted from doing so. This occurs when the forces of the
other such expanding rings balance. Since ring streamlines (perfectly
analogous to lines of force) cannot cross, the lattice structure is an
eneviable result. The size of a cell is defines by the basic
properties of the medium.

Well, the is the founding framework, and so far, we're just
considering basic static conditions. Each ring has the oscillation
modes identified above. Further, if one ring does oscillate in any
fashion, it MUST infulence the surrounding lattice since the lattice
is maintained but a balance in opposing forces...

This is where things become interesting...

Refs:

1. "On the Physical Lines of Force" J. C. Maxwell, 1861-62
2. "Maxwell on the Electromagnetic Field, A Guided Study",
T. K. Simpson, Rutger University Press - 1997

Paul Stowe

Yes, I come up with something very similar to this when attempting
to model the EM vacuum as a "spin matrix" comprised of "virtual"
e+e- pairs.

So does Roger Penrose (see Twistor theory). I was always dismayed
by the fact that Penrose NEVER referenced or gave credit to Maxwell.

To my amazement, everything works out very well if "vacuum charge"
is sqrt(hbar*c) in gaussian units or sqrt(eps0*hbar*c) in SI units.
To me, one of the main features of what you present is that all the
vacuum oscillators are indeed *coupled* instead of uncoupled. And
effect each other producing an equilibrium state.

Yep, now try seeing what happens when you send a wave pulse thru the
region...

Second, flip the orientation of just one ring, what happens???

Paul Stowe

:
On Sun, 31 Aug 2003 19:04:26 -0000,
(Bilge) wrote:

boundary conditions for the two surfaces). The critical wavelength which
corresponds to the cell-size in the x-y plane, for example, is about
2*sqrt(2) d, where d is the z-spacing. The eigenvalues are 2*sqrt(2) d/n.
^^^^^^^^^^^


It is interesting that with multiple layers (rather than 2) the
eigenvlaue is 2*sqrt(3)(2pi)^2 ~= 137...

2*sqrt(2) d/n

:

So does Roger Penrose (see Twistor theory). I was always dismayed
by the fact that Penrose NEVER referenced or gave credit to Maxwell.

Maxwell never described anything resembling twistors. Twistors
are a spinor fields in a minkowski space and maxwell never dreamt
the existence of spinors. I have the text on twistors by huggett
and tod and I can't see from anything in that test how maxwell
would have earned any special credit beyond that which he is
universally acknowledged.

wrote in message
...
On Sun, 31 Aug 2003 19:04:26 -0000,
SNIP


Again, you take the Bernard Cell analogy way to far. Clearly neither
I nor Maxwell was claiming that the universe existed between two
plates held at a thermal gradient... The refernce to Bernard Cells
is/was to should that, like Maxwell predicted, ring vortices (the
so-called vortex sponge) align in a lattice (a psuedo solid).

SNIP

Does this imply that the ("solid") ether of Lorentz is in fact that of
Maxwell?

Harald

Harry wrote in message
...

wrote in message
...
On Sun, 31 Aug 2003 19:04:26 -0000,
SNIP


Again, you take the Bernard Cell analogy way to far. Clearly neither
I nor Maxwell was claiming that the universe existed between two
plates held at a thermal gradient... The refernce to Bernard Cells
is/was to should that, like Maxwell predicted, ring vortices (the
so-called vortex sponge) align in a lattice (a psuedo solid).

SNIP

Does this imply that the ("solid") ether of Lorentz is in fact that of
Maxwell?

Neither Lorentz nor Maxwell used a 'solid' aether.

greywolf42
ubi dubium ibi libertas

Harry wrote in message
...

"greywolf42" wrote in message
...

Harry wrote in message
...

wrote in message
...
On Sun, 31 Aug 2003 19:04:26 -0000,
SNIP


Again, you take the Bernard Cell analogy way to far. Clearly
neither
I nor Maxwell was claiming that the universe existed between two
plates held at a thermal gradient... The refernce to Bernard Cells
is/was to should that, like Maxwell predicted, ring vortices (the
so-called vortex sponge) align in a lattice (a psuedo solid).

SNIP

Does this imply that the ("solid") ether of Lorentz is in fact that
of
Maxwell?

Neither Lorentz nor Maxwell used a 'solid' aether.

greywolf42
ubi dubium ibi libertas


You always come with interesting comments!
Do you have a reference for me?
Thanks in advance!


For Maxwell's model, see "On Physical Lines of Force", Philosophical
Magazine, Vol XXI, XXIII; 1862, Maxwell. (You'll probably need to get a
copy from a large University Library, as it's not a popular item.) The
University of California at Berkeley Library can make a copy for you and
mail it.

For Lorentz' work, I'd suggest the easiest source is Lorentz' 1904 work
"Electromagnetic Phenomena in a System Moving with Any Velocity less than
that of Light." Found in "The Principle of Relativity", Dover, first
published 1952. This book also includes several other original works, and
is well worth the money.

greywolf42
ubi dubium ibi libertas