By : Ove Tedenstig
Idungatan 37, 19 551 M{rsta
Sweden

MAXWELL's EQUATIONS OF THE ELECTROMAGNETIC FIELD


The nucleus of James Clerk Maxwell's electromagnetic theory from





1867 consist of a set of formulae which describe the behavior of


electric and magnetic field proparation. The theory was from
the beginning an "aether" or mechanical theory, but this
interpretation of electromagnetism later on was denyed.
Today only a barren shell of mathemaical formalism reaminds
which not say much of cause and source of electromagnetism.
The scientific value of these formulae therefore may be put into
question since they seem to have be overestimated in importance.

However, the most famous a

(44a) ==========================

__ _
!/ E = 0 The electric field at free
radiation from ap point source
(44b) ==========================
__ _
!/ B = 0 The magnetic field at free


(44c) ==========================

__ _ _
!/ E = -D B/Dt ( D is the partial derivative)

(44d) ==========================

__ _ 2 _
!/ B = (1/c ).D E/ Dt



DERIVING THE FORMULAE

Because of limit of space, 44a and 44b are not derived here.
However, it is a relatively easy task to get these results,
which are achived by deriving the field strength out from an
electric or magnetic point source in respect to its coordinates,
x,y and z. Therefore, we concentrate ourselves only on the two
remaining formulae, which mainly are got by vectorially
manipulating the base equation (30). (44c) is achived by taking
the time derivative of this equation, the (44d) is got by
taking the space derivative of it.


(45) ================================
_ _
_ E x v
B = ----2-- (from 30)
c
_ _
_ E x v
DB/Dt = D/Dt ( ----2---- ) =
c


__ _ 2 _ _ 2 2 __ _
!/ v/ c.(E x v ) = -v /c .( !/ x E )

__ _
For v=c DB/Dt = - !/ X E

(46) ================================================== =

__ _ __ _ _ 2
!/ x B = !/ x ( E x v/c )


__ _ _ __ _ _ __ _ _ __ _
!/ x B = DE/Dt - v( !/.E ) - (E. !/).v + E( !/.v )

!------------/ !-----------------------------------/
Result Will be zero for a non accelerating
according to point source
Maxwell


__ _ _
!/ x B = DE/Dt The result in accord with
Maxwell valid for a non
accelerating point source

================================================== ========


LIGHT AND ELECTROMAGNETIC WAVES

Beside these famous equations treated above, historically Macwell
is famous for predicting electromagnetic fields propagating in
in the same way as light in free space. The conclusions were made
on basis of comparing results from the general wave equation based
on how sound in air or mechanical waves were propagating in a medium,
air and water for instance. But the modern physics do not confess
any existence of a light bearing aether, and the contradictionary
problem in Maxwell's theories therefore still remain.

Vectorial manipulations are performed on results from (45) and (47)
as shown in below.

(48) ================================================

__ _ _
!/ x E = -DB/Dt (from 45)

__ _ 2 _
!/ x B = 1/c . D/Dt .E (from 47)


__ __ _ __2 _ __ __ _ __2 _
!/ x ( !/ x E ) ? - !/ E + !/( !/ E ) = - !/ E
__ _
( !/ E is equal to zero for a point source )


__ __ _ __ _ __ _
!/ x ( !/ x E ) = - !/(DB/Dt) = - D/Dt( !/ x B ) =

2 _ 2 2 2 _
D/Dt(1/c.D/Dt.E ) = 1/c .D /Dt .E

__ _ 2 2 2 _
- !/ E = 1/c . D /Dt .E




(49) ================================================== ===

__ _ _
!/ x E = DB/Dt (from 45)

__ _ 2 _
!/ x B = 1/c .D/Dt.E (from 47)

__ __ _ __2 _ __ __ _ __2 _
!/x( !/ x B ) = - !/ B + !/( !/ B ) = - !/ B

__ _
( !/ B is zero for a point source =


__ __ _ __ 2 _
!/ x ( !/ x B ) = !/( 1/c. D/Dt.E ) =

2 __ _ 2 2 2 _
1/c .D/Dt( !/ x E ) = 1/c . D /Dt .B

__2 _ 2 2 2 _
- !/ B = 1/c . D /Dt .B

================================================== =====


The general wave equation is written :


(50) =============================

__2 2 2 2
!/ Y = 1/v . D /Dt . Y

==================================

The mathematical structure of (48),(49) and (50) is the same
and it was this mathematical equivalency which gave Maxwell
the idea of light being a medium carried wave. Since then many
experiments have been perfomed by light, clearly showing that
no active light aether do exist. Only the mathematical
equivalency reamin intact.

NILS BÖRJESSON wrote:
Since then many
experiments have been perfomed by light, clearly showing that
no active light aether do exist.

Many experiments have proved that empty space is not empty.
"A rose by any other name ..."
--
73, Cecil http://www.w5dxp.com

On Sun, 10 Sep 2006 10:54:20 +0000, Cecil Moore wrote:

NILS BÖRJESSON wrote:
[quoted text muted]

Many experiments have proved that empty space is not empty. "A rose by any
other name ..."

Did your radios stop working? ;-)

Barnard Peters wrote:
Cecil Moore wrote:
Many experiments have proved that empty space is not empty. "A rose by any
other name ..."

Did your radios stop working? ;-)

They *would* stop working if empty space were really
empty. Call it what you will, "aether" or something
else. Radio waves cannot propagate through absolute
nothing. There really *is* something there. The
assumptions about the characteristics of aether were
wrong but that doesn't mean it doesn't exist.
--
73, Cecil http://www.w5dxp.com

Cecil Moore wrote:
Barnard Peters wrote:

Cecil Moore wrote:

Many experiments have proved that empty space is not empty. "A rose
by any
other name ..."


Did your radios stop working? ;-)


They *would* stop working if empty space were really
empty. Call it what you will, "aether" or something
else. Radio waves cannot propagate through absolute
nothing. There really *is* something there. The
assumptions about the characteristics of aether were
wrong but that doesn't mean it doesn't exist.


Cecil, when I first started reading this group, I gained a lot of respect
for you. As time went by, I even tried to justify some of your arguments and
adopt them as my own. Some were successful, some were not.

As more time went by, I lost a lot of the respect I had for you. I think it
was because I became more educated.

Now you make the statement above. Dammit! Have you not heard of the
Michelson-Morley experiment? Does it mean nothing to you?

Bye.

John

On Sun, 10 Sep 2006 22:48:06 GMT, John - KD5YI
wrote:

Now you make the statement above. Dammit! Have you not heard of the
Michelson-Morley experiment? Does it mean nothing to you?

Hi John,

In those same years of declining respect, you should have noticed that
indignation counts for no more than logic nor historical precedent.

Dark matter (and Dark energy) is something I've been on about here for
a number of years, and the scientific community estimates it
constitutes a significant portion to the bulk of the Universe - I
don't recall their last guess (it is variable, certainly), but it
verges on 60% - 80%.

However, its presence says nothing about wave mechanics and can only
come to bear on the familiar terms of permittivity and permeability
which light (and RF) happily coexists with. If Dark matter did
interfere such that it offered an Æther, it would, of course conform
to your and our understanding of Michelson-Morley that it must offset
the speed. That, or it is always neutral. Now, Dark matter being
neutral necessarily invalidates its state of being an Æther.

Cap'n Jack
"Helmsman, why aren't we making progress?"

Davy Jonz
"No wind skipper"

Cap'n Jack
"Nonsense, 80% of atmosphere is air!"

Davy Jonz
"Beggin' your pardon, skipper, but It wouldn't seem to be the 80%
that is behind our sails, sir."

Cap'n Jack
"The cat of tall-tales against your back for such bilge, sailor.
Your assumptions about the characteristics of wind are
wrong but that doesn't mean it doesn't exist and we should be
moving!"

73's
Richard Clark, KB7QHC

John - KD5YI wrote:
Now you make the statement above. Dammit! Have you not heard of the
Michelson-Morley experiment? Does it mean nothing to you?

Michelson-Morley didn't know about relativity and quantum
mechanics. Things have changed. Space is NOT empty. Mass
has been created from empty space. Particles have been
detected winking in and out of existence in empty space.

Methinks you have fallen into the trap of thinking that man
has discovered all the knowledge there is to be discovered.
Almost everything you think you know as true will be proved
false in the next 1000 years.
--
73, Cecil http://www.w5dxp.com

Richard Clark wrote:
On Sun, 10 Sep 2006 22:48:06 GMT, John - KD5YI
wrote:


Now you make the statement above. Dammit! Have you not heard of the
Michelson-Morley experiment? Does it mean nothing to you?


Hi John,

In those same years of declining respect, you should have noticed that
indignation counts for no more than logic nor historical precedent.

Dark matter (and Dark energy) is something I've been on about here for
a number of years, and the scientific community estimates it
constitutes a significant portion to the bulk of the Universe - I
don't recall their last guess (it is variable, certainly), but it
verges on 60% - 80%.

However, its presence says nothing about wave mechanics and can only
come to bear on the familiar terms of permittivity and permeability
which light (and RF) happily coexists with. If Dark matter did
interfere such that it offered an Æther, it would, of course conform
to your and our understanding of Michelson-Morley that it must offset
the speed. That, or it is always neutral. Now, Dark matter being
neutral necessarily invalidates its state of being an Æther.

Cap'n Jack
"Helmsman, why aren't we making progress?"

Davy Jonz
"No wind skipper"

Cap'n Jack
"Nonsense, 80% of atmosphere is air!"

Davy Jonz
"Beggin' your pardon, skipper, but It wouldn't seem to be the 80%
that is behind our sails, sir."

Cap'n Jack
"The cat of tall-tales against your back for such bilge, sailor.
Your assumptions about the characteristics of wind are
wrong but that doesn't mean it doesn't exist and we should be
moving!"

73's
Richard Clark, KB7QHC


Hi, Richard -

Did you say something relevant?

73,
John

Cecil Moore wrote:

Almost everything you think you know as true will be proved
false in the next 1000 years.

Especially if you're Howard Dean. :-)

de AC6XG

John - KD5YI wrote:
Richard Clark wrote:

On Sun, 10 Sep 2006 22:48:06 GMT, John - KD5YI
wrote:


Now you make the statement above. Dammit! Have you not heard of the
Michelson-Morley experiment? Does it mean nothing to you?



Hi John,

In those same years of declining respect, you should have noticed that
indignation counts for no more than logic nor historical precedent.

Dark matter (and Dark energy) is something I've been on about here for
a number of years, and the scientific community estimates it
constitutes a significant portion to the bulk of the Universe - I
don't recall their last guess (it is variable, certainly), but it
verges on 60% - 80%.
However, its presence says nothing about wave mechanics and can only
come to bear on the familiar terms of permittivity and permeability
which light (and RF) happily coexists with. If Dark matter did
interfere such that it offered an Æther, it would, of course conform
to your and our understanding of Michelson-Morley that it must offset
the speed. That, or it is always neutral. Now, Dark matter being
neutral necessarily invalidates its state of being an Æther.

Cap'n Jack
"Helmsman, why aren't we making progress?"

Davy Jonz
"No wind skipper"

Cap'n Jack
"Nonsense, 80% of atmosphere is air!"

Davy Jonz
"Beggin' your pardon, skipper, but It wouldn't seem to be the 80%
that is behind our sails, sir."

Cap'n Jack
"The cat of tall-tales against your back for such bilge, sailor.
Your assumptions about the characteristics of wind are
wrong but that doesn't mean it doesn't exist and we should be
moving!"

73's
Richard Clark, KB7QHC



Hi, Richard -

Did you say something relevant?

73,
John

Relatively speaking, I think he did.