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tech / sci.physics.relativity / Original Maxwell's equations and behavior of light in the Universe.

SubjectAuthor
* Original Maxwell's equations and behavior of light in the Universe.Richard Hertz
+* Re: Original Maxwell's equations and behavior of light in the Universe.JanPB
|`* Re: Original Maxwell's equations and behavior of light in the Universe.Richard Hertz
| +* Re: Original Maxwell's equations and behavior of light in the Universe.Richard Hertz
| |+* Re: Original Maxwell's equations and behavior of light in the Universe.Richard Hertz
| ||`- Re: Original Maxwell's equations and behavior of light in the Universe.Paul Alsing
| |`- Re: Original Maxwell's equations and behavior of light in the Universe.Athel Cornish-Bowden
| +* Re: Original Maxwell's equations and behavior of light in the Universe.Mikko
| |+- Re: Original Maxwell's equations and behavior of light in the Universe.Peter Kinane
| |+* Re: Original Maxwell's equations and behavior of light in the Universe.Richard Hertz
| ||+* Re: Original Maxwell's equations and behavior of light in the Universe.JanPB
| |||`- Re: Original Maxwell's equations and behavior of light in the Universe.Richard Hertz
| ||`* Re: Original Maxwell's equations and behavior of light in the Universe.Mikko
| || `* Re: Original Maxwell's equations and behavior of light in the Universe.Richard Hertz
| ||  +- Re: Original Maxwell's equations and behavior of light in theKobie Locatelli
| ||  `- Re: Original Maxwell's equations and behavior of light in the Universe.Mikko
| |`- Re: Original Maxwell's equations and behavior of light in the Universe.Thomas 'PointedEars' Lahn
| +* Re: Original Maxwell's equations and behavior of light in the Universe.JanPB
| |+* Re: Original Maxwell's equations and behavior of light in theAether Regaind
| ||`* Re: Original Maxwell's equations and behavior of light in the Universe.Mikko
| || +- Re: Original Maxwell's equations and behavior of light in the Universe.Richard Hertz
| || `* Re: Original Maxwell's equations and behavior of light in theAether Regaind
| ||  `* Re: Original Maxwell's equations and behavior of light in the Universe.Richard Hertz
| ||   `- Re: Original Maxwell's equations and behavior of light in the Universe.JanPB
| |`* Re: Original Maxwell's equations and behavior of light in theAether Regaind
| | `- Re: Original Maxwell's equations and behavior of light in the Universe.JanPB
| `* Re: Original Maxwell's equations and behavior of light in thePaul B. Andersen
|  +* Re: Original Maxwell's equations and behavior of light in the Universe.Richard Hertz
|  |`* Re: Original Maxwell's equations and behavior of light in thePaul B. Andersen
|  | `- Re: Original Maxwell's equations and behavior of light in theKobie Locatelli
|  `* Re: Original Maxwell's equations and behavior of light in the Universe.RichD
|   `- Re: Original Maxwell's equations and behavior of light in the Universe.Richard Hertz
`* Re: Original Maxwell's equations and behavior of light in the Universe.J. J. Lodder
 `* Re: Original Maxwell's equations and behavior of light in the Universe.Maciej Wozniak
  `* Re: Original Maxwell's equations and behavior of light in the Universe.J. J. Lodder
   `- Re: Original Maxwell's equations and behavior of light in the Universe.Richard Hertz

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Original Maxwell's equations and behavior of light in the Universe.

<01dc3a67-6e5e-4aa4-bcfb-7d9562ec02ffn@googlegroups.com>

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Subject: Original Maxwell's equations and behavior of light in the Universe.
From: hertz...@gmail.com (Richard Hertz)
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 by: Richard Hertz - Fri, 13 Jan 2023 23:10 UTC

The original Maxwell's equations, under the form of quaternions, had
SIX VARIABLES, being 5 of them described with 3D vectors, and the 6th.
being a scalar: electric charge density.

20 years after Maxwell's death, Heaviside (with the validation of Hertz
and Lorentz) "assassinated" the 20 quaternion equations and, using the
new vectorial algebra, gave them the form under which they are known
since then: four 3D differential equations. He got rid of the scalar electric
charge density.

When light flows across the Universe and reach Earth, it has passed by or
through an enormous amount of volumes of space where the scalar
electric charge density EXISTS.

Maxwell developed a theoretical expression for the speed of light in vacuum.
Not only that. As a gifted experimentalist, he and partners measured, in
Scottland, the values of permittivity and permeability in a giant installation
with batteries providing 3,000 Volts. He was close to obtain, in 1868, the
current FIXED speed of light, but with earthly measurements.

Questions arise:

1) Why it's assumed that such values, "for vacuum", are constant across
the infinity of the Universe?

2) Why isn't considered, in AN ELECTRIC UNIVERSE, that the speed of light
could change MANY TIMES, and in unknown ways, when it transit zones
where the scalar electric charge density HAS A ROLE TO PLAY?

Somebody?. Anybody?. Nobody?.

Scientists are dirty, lazy and go with the flow. No waves, no problems.

Re: Original Maxwell's equations and behavior of light in the Universe.

<6d35eeec-1f8a-4d4e-b1d8-54be3b905296n@googlegroups.com>

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Subject: Re: Original Maxwell's equations and behavior of light in the Universe.
From: film...@gmail.com (JanPB)
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 by: JanPB - Sat, 14 Jan 2023 06:26 UTC

On Friday, January 13, 2023 at 3:10:58 PM UTC-8, Richard Hertz wrote:
> The original Maxwell's equations, under the form of quaternions, had
> SIX VARIABLES, being 5 of them described with 3D vectors, and the 6th.
> being a scalar: electric charge density.

Maxwell didn't use quaternions. He had six 3D vectors and two scalars,
20 equations.

3D component quantities:
1. "electromagnetic momentum" F, G, H (today: vector potential A),
2. "magnetic intensity" alpha, beta, gamma (today: magnetic field H),
3. "electromotive force" P, Q, R (today: electric field E),
4. "current due to conduction" p, q, r (today: electric current density j),
5. "electric displacement" f, g, h (today: displacement field D),
6. "total current" p', q', r' (today: total current density),

scalars:
1. "quantity of free electricity" (today: charge density),
2. "electric potential" (today: same).

> 20 years after Maxwell's death, Heaviside (with the validation of Hertz
> and Lorentz) "assassinated" the 20 quaternion equations

What quaternion? I'd like to see it, sounds interesting. The equations
I've seen are just regular component equations.

> 1) Why it's assumed that such values, "for vacuum", are constant across
> the infinity of the Universe?
>
> 2) Why isn't considered, in AN ELECTRIC UNIVERSE, that the speed of light
> could change MANY TIMES, and in unknown ways, when it transit zones
> where the scalar electric charge density HAS A ROLE TO PLAY?

One can assume many things. But adding tuning knobs just because is
not good science.

--
Jan

Re: Original Maxwell's equations and behavior of light in the Universe.

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Subject: Re: Original Maxwell's equations and behavior of light in the Universe.
From: hertz...@gmail.com (Richard Hertz)
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 by: Richard Hertz - Sat, 14 Jan 2023 14:21 UTC

On Saturday, January 14, 2023 at 3:26:55 AM UTC-3, JanPB wrote:
> On Friday, January 13, 2023 at 3:10:58 PM UTC-8, Richard Hertz wrote:
> > The original Maxwell's equations, under the form of quaternions, had
> > SIX VARIABLES, being 5 of them described with 3D vectors, and the 6th.
> > being a scalar: electric charge density.
> Maxwell didn't use quaternions. He had six 3D vectors and two scalars,
> 20 equations.
>
> 3D component quantities:
> 1. "electromagnetic momentum" F, G, H (today: vector potential A),
> 2. "magnetic intensity" alpha, beta, gamma (today: magnetic field H),
> 3. "electromotive force" P, Q, R (today: electric field E),
> 4. "current due to conduction" p, q, r (today: electric current density j),
> 5. "electric displacement" f, g, h (today: displacement field D),
> 6. "total current" p', q', r' (today: total current density),
>
> scalars:
> 1. "quantity of free electricity" (today: charge density),
> 2. "electric potential" (today: same).
> > 20 years after Maxwell's death, Heaviside (with the validation of Hertz
> > and Lorentz) "assassinated" the 20 quaternion equations
> What quaternion? I'd like to see it, sounds interesting. The equations
> I've seen are just regular component equations.
> > 1) Why it's assumed that such values, "for vacuum", are constant across
> > the infinity of the Universe?
> >
> > 2) Why isn't considered, in AN ELECTRIC UNIVERSE, that the speed of light
> > could change MANY TIMES, and in unknown ways, when it transit zones
> > where the scalar electric charge density HAS A ROLE TO PLAY?
> One can assume many things. But adding tuning knobs just because is
> not good science.
>
> --
> Jan

Debunk this, fucking genius:

https://www.scirp.org/journal/paperinformation.aspx?paperid=102987

"It is seen, therefore, that, if the quaternion form of Maxwell’s Electromagnetic Field Equations is used, the normal theory follows through as usual, including the more novel notions introduced in the CIA released article mentioned [5]. However, in this case the resulting scalar field turns out to be described by an equation which indicates the wave speed to be greater than that of light; that is the scalar wave is superluminal."

Re: Original Maxwell's equations and behavior of light in the Universe.

<6c35d8f9-1fff-4302-b81c-adbd0a7fccc2n@googlegroups.com>

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Subject: Re: Original Maxwell's equations and behavior of light in the Universe.
From: hertz...@gmail.com (Richard Hertz)
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 by: Richard Hertz - Sat, 14 Jan 2023 15:16 UTC

On Saturday, January 14, 2023 at 11:21:41 AM UTC-3, Richard Hertz wrote:

<snip>

> https://www.scirp.org/journal/paperinformation.aspx?paperid=102987
>
> "It is seen, therefore, that, if the quaternion form of Maxwell’s Electromagnetic Field Equations is used, the normal theory follows through as usual, including the more novel notions introduced in the CIA released article mentioned [5]. However, in this case the resulting scalar field turns out to be described by an equation which indicates the wave speed to be greater than that of light; that is the scalar wave is superluminal."

NOBODY, IN ACADEMIA, WANT TO TALK ABOUT SCALAR ENERGY THAT'S FTL.

HERE IS A MATHEMATICAL PROOF OF SUCH KIND OF WAVES. MILITARY (MAINLY RUSSIANS) ARE ON THIS.

PUTIN SAID: "BASED ON NEW PRINCIPLES OF PHYSICS".

Re: Original Maxwell's equations and behavior of light in the Universe.

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Subject: Re: Original Maxwell's equations and behavior of light in the Universe.
From: hertz...@gmail.com (Richard Hertz)
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 by: Richard Hertz - Sat, 14 Jan 2023 15:26 UTC

On Saturday, January 14, 2023 at 12:16:38 PM UTC-3, Richard Hertz wrote:
> On Saturday, January 14, 2023 at 11:21:41 AM UTC-3, Richard Hertz wrote:
>
> <snip>
> > https://www.scirp.org/journal/paperinformation.aspx?paperid=102987
> >
> > "It is seen, therefore, that, if the quaternion form of Maxwell’s Electromagnetic Field Equations is used, the normal theory follows through as usual, including the more novel notions introduced in the CIA released article mentioned [5]. However, in this case the resulting scalar field turns out to be described by an equation which indicates the wave speed to be greater than that of light; that is the scalar wave is superluminal."
> NOBODY, IN ACADEMIA, WANT TO TALK ABOUT SCALAR ENERGY THAT'S FTL.
>
> HERE IS A MATHEMATICAL PROOF OF SUCH KIND OF WAVES. MILITARY (MAINLY RUSSIANS) ARE ON THIS.
>
> PUTIN SAID: "BASED ON NEW PRINCIPLES OF PHYSICS".

I'M LAUGHING ALL THE WAY TO THE RELATIVITY CONVENTION, TO SHOVE INTO THEIR ASSES THIS COMPLETE THEORY.

LET'S TALK ABOUT LORENTZ INVARIANCE, FUCKING RETARDED!

Re: Original Maxwell's equations and behavior of light in the Universe.

<tpulrk$21ehq$1@dont-email.me>

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Subject: Re: Original Maxwell's equations and behavior of light in the Universe.
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 by: Mikko - Sat, 14 Jan 2023 16:39 UTC

On 2023-01-14 14:21:39 +0000, Richard Hertz said:

> On Saturday, January 14, 2023 at 3:26:55 AM UTC-3, JanPB wrote:

>> On Friday, January 13, 2023 at 3:10:58 PM UTC-8, Richard Hertz wrote:
>> > > The original Maxwell's equations, under the form of quaternions, had
>> > > SIX VARIABLES, being 5 of them described with 3D vectors, and the 6th.
>> > > being a scalar: electric charge density.

>> Maxwell didn't use quaternions.
>
> Debunk this, fucking genius:
>
> https://www.scirp.org/journal/paperinformation.aspx?paperid=102987

That article is not useful here as it merely says "It is often claimed
that Maxwell’s electromagnetic equations were originally written in terms
of quaternions" but doesn't say whether they really were.

Mikko

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Date: Sat, 14 Jan 2023 09:13:49 -0800 (PST)
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Subject: Re: Original Maxwell's equations and behavior of light in the Universe.
From: pkin...@iol.ie (Peter Kinane)
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 by: Peter Kinane - Sat, 14 Jan 2023 17:13 UTC

On Saturday, 14 January 2023 at 16:39:19 UTC, Mikko wrote:
> On 2023-01-14 14:21:39 +0000, Richard Hertz said:
>
> > On Saturday, January 14, 2023 at 3:26:55 AM UTC-3, JanPB wrote:
>
> >> On Friday, January 13, 2023 at 3:10:58 PM UTC-8, Richard Hertz wrote:
> >> > > The original Maxwell's equations, under the form of quaternions, had
> >> > > SIX VARIABLES, being 5 of them described with 3D vectors, and the 6th.
> >> > > being a scalar: electric charge density.
>
> >> Maxwell didn't use quaternions.
> >
> > Debunk this, fucking genius:
> >
> > https://www.scirp.org/journal/paperinformation.aspx?paperid=102987
> That article is not useful here as it merely says "It is often claimed
> that Maxwell’s electromagnetic equations were originally written in terms
> of quaternions" but doesn't say whether they really were.
>
> Mikko

"PUTIN SAID: "BASED ON NEW PRINCIPLES OF PHYSICS".": Hmm!

Not directly on topic I suppose but not entirely unrelated:

New modelling of the curving of light path near a massive body:

The p, w and + of F = G*m1*(m2+(p-w))/r^2

This may serve as an analogy of gravitation “deflection”, more accurately g and p path, of light passing near a massive body.

There are two young friends who like to run to meet each other when they are in the same neighbourhood to practically express their mathematics lesson..

They want to test the speed of their approach – analogous to the g pull or attraction on one of them who has p - the g and p path.

Let’s give them good math family names: X and Y

Let’s give good math names to their respective starting points, more accurately starting points of measurement: A and B.

They have combined speed - gravitational pull - of 10mph and they have it even at their respective starting points.

All else being equal they would approach at 20mph. (m: miles).

However, X runs on a flat surface while Y runs on a decline.
This gives extra momentum (p) of 2mph to Y.
So, all else being equal, their rate of approach is 22mph.

However, Y does not wish to collide with X but pass close by.
So Y is running at a tangent (w) to the point of closest approach.

Therefore w detracts somewhat from p, the extent depending on the degree of the tangent, expressed as p-w.

The rest of the equation for the path of Y is standard.
So I include p-w: F = G*m1*(m2+(p-w))/r^2 .

But I am not quite clear whether to have p-w as + or x to m2.

https://www.amazon.com/dp/0995454876

Re: Original Maxwell's equations and behavior of light in the Universe.

<k2g79kF3svbU1@mid.individual.net>

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From: acorn...@imm.cnrs.fr (Athel Cornish-Bowden)
Newsgroups: sci.physics.relativity
Subject: Re: Original Maxwell's equations and behavior of light in the Universe.
Date: Sat, 14 Jan 2023 18:32:35 +0100
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 by: Athel Cornish-Bowden - Sat, 14 Jan 2023 17:32 UTC

On 2023-01-14 15:16:37 +0000, Richard Hertz said:

> On Saturday, January 14, 2023 at 11:21:41 AM UTC-3, Richard Hertz wrote:
>
> <snip>
>
>> https://www.scirp.org/journal/paperinformation.aspx?paperid=102987>>
>> "It is seen, therefore, that, if the quaternion form of Maxwell’s
>> Electromagnetic Field Equations is used, the normal theory follows
>> through as usual, including the more novel notions introduced in the
>> CIA released article mentioned [5]. However, in this case the resulting
>> scalar field turns out to be described by an equation which indicates
>> the wave speed to be greater than that of light; that is the scalar
>> wave is superluminal."
>
> NOBODY, IN ACADEMIA, WANT TO TALK ABOUT SCALAR ENERGY THAT'S FTL.
>
> HERE IS A MATHEMATICAL PROOF OF SUCH KIND OF WAVES. MILITARY (MAINLY
> RUSSIANS) ARE ON THIS.
>
> PUTIN SAID: "BASED ON NEW PRINCIPLES OF PHYSICS".

How much on the new crackpot scale is writing in all-caps worth?
Anyway, if he wants mathematical proof he should talk to George S.
Hammond, MS Physics, Hyannis MA.

--
Athel -- French and British, living in Marseilles for 36+ years; mainly
in England until 1987.

Re: Original Maxwell's equations and behavior of light in the Universe.

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Subject: Re: Original Maxwell's equations and behavior of light in the Universe.
From: hertz...@gmail.com (Richard Hertz)
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 by: Richard Hertz - Sat, 14 Jan 2023 18:40 UTC

On Saturday, January 14, 2023 at 1:39:19 PM UTC-3, Mikko wrote:

<snip>

> That article is not useful here as it merely says "It is often claimed
> that Maxwell’s electromagnetic equations were originally written in terms
> of quaternions" but doesn't say whether they really were.
>
> Mikko

Having any doubt about if Maxwell did write his equations in quaternions?. YES, HE DID IN 1873.
Fact-check here:

https://www.zuj.edu.jo/download/a-treatise-on-electricity-and-magnetism-vol-ii-j-c-maxwell-pdf/

A TREATISE ON ELECTRICITY AND MAGNETISM
By James Clerk Maxwell, M.A.
Vol II
Clarendon Press Series. London, MacMillan and Co
Publishers to the University of Oxford
1873

CHAPTER IX
GENERAL EQUATIONS OF THE ELECTROMAGNETIC FIELD (This Chapter start at page 227)
.....
.....
Quaternion Expressions for the Electromagnetic Equations. (This point start at page 236)

618.] In this treatise we have endeavoured to avoid any process demanding from the reader a knowledge of the Calculus of Quaternions. At the same time we have not scrupled to introduce the idea of a vector when it was necessary to do so. When we have had occasion to denote a vector by a symbol, we have used a German letter, the number of different vectors being so great that Hamilton's favourite symbols would have been exhausted at once.

Whenever therefore, a German letter is used it denotes a Hamiltonian vector, and indicates not only its magnitude but its direction.

The constituents of a vector are denoted by Roman or Greek letters.
The principal vectors which we have to consider are:

The radius vector of a point.
The electromagnetic momentum at a point 2
The magnetic induction
The (total) electric current
The electric displacement...
Symbol of Vector. Constituents..........
..............

ENJOY.

Re: Original Maxwell's equations and behavior of light in the Universe.

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Subject: Re: Original Maxwell's equations and behavior of light in the Universe.
From: pnals...@gmail.com (Paul Alsing)
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 by: Paul Alsing - Sat, 14 Jan 2023 20:00 UTC

On Saturday, January 14, 2023 at 7:26:54 AM UTC-8, Richard Hertz wrote:

> I'M LAUGHING ALL THE WAY TO THE RELATIVITY CONVENTION, TO SHOVE INTO THEIR ASSES THIS COMPLETE THEORY.
>
> LET'S TALK ABOUT LORENTZ INVARIANCE, FUCKING RETARDED!

https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcSc7vLbnwI64Prwsh4eX4v5ciuv71_r3DtYcg&usqp=CAU

Re: Original Maxwell's equations and behavior of light in the Universe.

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Subject: Re: Original Maxwell's equations and behavior of light in the Universe.
From: film...@gmail.com (JanPB)
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 by: JanPB - Sun, 15 Jan 2023 05:35 UTC

On Saturday, January 14, 2023 at 6:21:41 AM UTC-8, Richard Hertz wrote:
> On Saturday, January 14, 2023 at 3:26:55 AM UTC-3, JanPB wrote:
> > On Friday, January 13, 2023 at 3:10:58 PM UTC-8, Richard Hertz wrote:
> > > The original Maxwell's equations, under the form of quaternions, had
> > > SIX VARIABLES, being 5 of them described with 3D vectors, and the 6th..
> > > being a scalar: electric charge density.
> > Maxwell didn't use quaternions. He had six 3D vectors and two scalars,
> > 20 equations.
> >
> > 3D component quantities:
> > 1. "electromagnetic momentum" F, G, H (today: vector potential A),
> > 2. "magnetic intensity" alpha, beta, gamma (today: magnetic field H),
> > 3. "electromotive force" P, Q, R (today: electric field E),
> > 4. "current due to conduction" p, q, r (today: electric current density j),
> > 5. "electric displacement" f, g, h (today: displacement field D),
> > 6. "total current" p', q', r' (today: total current density),
> >
> > scalars:
> > 1. "quantity of free electricity" (today: charge density),
> > 2. "electric potential" (today: same).
> > > 20 years after Maxwell's death, Heaviside (with the validation of Hertz
> > > and Lorentz) "assassinated" the 20 quaternion equations
> > What quaternion? I'd like to see it, sounds interesting. The equations
> > I've seen are just regular component equations.
> > > 1) Why it's assumed that such values, "for vacuum", are constant across
> > > the infinity of the Universe?
> > >
> > > 2) Why isn't considered, in AN ELECTRIC UNIVERSE, that the speed of light
> > > could change MANY TIMES, and in unknown ways, when it transit zones
> > > where the scalar electric charge density HAS A ROLE TO PLAY?
> > One can assume many things. But adding tuning knobs just because is
> > not good science.
> >
> > --
> > Jan
> Debunk this, fucking genius:
>
> https://www.scirp.org/journal/paperinformation.aspx?paperid=102987

Maxwell originally wrote his equations in the component form, as
I described. He later tried to put them in quaternion form. This is fine
although the modern differential form is even more succinct: just
two equations.

> "It is seen, therefore, that, if the quaternion form of Maxwell’s Electromagnetic Field Equations is used, the normal theory follows through as usual, including the more novel notions introduced in the CIA released article mentioned [5]. However, in this case the resulting scalar field turns out to be described by an equation which indicates the wave speed to be greater than that of light; that is the scalar wave is superluminal."

Yeah, yeah, whatever.

--
Jan

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Subject: Re: Original Maxwell's equations and behavior of light in the Universe.
From: film...@gmail.com (JanPB)
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 by: JanPB - Sun, 15 Jan 2023 05:36 UTC

On Saturday, January 14, 2023 at 10:40:39 AM UTC-8, Richard Hertz wrote:
> On Saturday, January 14, 2023 at 1:39:19 PM UTC-3, Mikko wrote:
>
> <snip>
> > That article is not useful here as it merely says "It is often claimed
> > that Maxwell’s electromagnetic equations were originally written in terms
> > of quaternions" but doesn't say whether they really were.
> >
> > Mikko
> Having any doubt about if Maxwell did write his equations in quaternions?.. YES, HE DID IN 1873.

He did and it wasn't particularly impressive. Many equations in physics and
mathematics can be written in many ways.

--
Jan

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From: hertz...@gmail.com (Richard Hertz)
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 by: Richard Hertz - Sun, 15 Jan 2023 12:36 UTC

On Sunday, January 15, 2023 at 2:36:58 AM UTC-3, JanPB wrote:
> On Saturday, January 14, 2023 at 10:40:39 AM UTC-8, Richard Hertz wrote:

<snip>

> > Having any doubt about if Maxwell did write his equations in quaternions?. YES, HE DID IN 1873.

> He did and it wasn't particularly impressive. Many equations in physics and
> mathematics can be written in many ways.

Only a self-entitled IGNORANT cretin like YOU can write such stupid comment, fucking relativist/PIC programmer (like Paul).

Who the fuck do you believe that you are, that you found Maxwell's work "not particularly impressive"?, DISGRACE of a human being?

Maxwell't "Treatise on Electricity and Magnetism" (1,100+ pages, two volumes) is such an IMPRESSIVE and FUNDAMENTAL work
that it CREATED, SINGLE-HANDEDLY, the science of electromagnetism that changed the world forever since its publication.

As a complete framework on E&M, this monumental work served as a UNIQUE and MANDATORY reference on the new science for
the NEXT 50 YEARS AND BEYOND.

But a DESPICABLE ANT like you dare to make such comment, being you NOBODY? Having you done NOTHING in your miserable life?

You don't even worth the effort of spitting in your silly face, and even less punching into your face, so you have to breathe by your asshole.

Retarded kazharian polish.

Re: Original Maxwell's equations and behavior of light in the Universe.

<tq0sto$2bpb8$1@dont-email.me>

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From: mikko.le...@iki.fi (Mikko)
Newsgroups: sci.physics.relativity
Subject: Re: Original Maxwell's equations and behavior of light in the Universe.
Date: Sun, 15 Jan 2023 14:52:08 +0200
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 by: Mikko - Sun, 15 Jan 2023 12:52 UTC

On 2023-01-14 18:40:36 +0000, Richard Hertz said:

> On Saturday, January 14, 2023 at 1:39:19 PM UTC-3, Mikko wrote:
>
> <snip>
>
>> That article is not useful here as it merely says "It is often claimed>
>> that Maxwell’s electromagnetic equations were originally written in
>> terms> of quaternions" but doesn't say whether they really were.>> Mikko
>
> Having any doubt about if Maxwell did write his equations in
> quaternions?. YES, HE DID IN 1873.
> Fact-check here:
>
> https://www.zuj.edu.jo/download/a-treatise-on-electricity-and-magnetism-vol-ii-j-c-maxwell-pdf/
>
>
>
> A TREATISE ON ELECTRICITY AND MAGNETISM
> By James Clerk Maxwell, M.A.
> Vol II
> Clarendon Press Series. London, MacMillan and Co
> Publishers to the University of Oxford
> 1873
>
>
> CHAPTER IX
> GENERAL EQUATIONS OF THE ELECTROMAGNETIC FIELD (This Chapter start at page 227)
> ....
> ....
> Quaternion Expressions for the Electromagnetic Equations. (This point
> start at page 236)
>
> 618.] In this treatise we have endeavoured to avoid any process
> demanding from the reader a knowledge of the Calculus of Quaternions.
> At the same time we have not scrupled to introduce the idea of a vector
> when it was necessary to do so. When we have had occasion to denote a
> vector by a symbol, we have used a German letter, the number of
> different vectors being so great that Hamilton's favourite symbols
> would have been exhausted at once.
>
> Whenever therefore, a German letter is used it denotes a Hamiltonian
> vector, and indicates not only its magnitude but its direction.
>
> The constituents of a vector are denoted by Roman or Greek letters.
> The principal vectors which we have to consider are:
> The radius vector of a point.
> The electromagnetic momentum at a point 2
> The magnetic induction
> The (total) electric current
> The electric displacement...
> Symbol of Vector. Constituents..........
> .............
>
> ENJOY.

That text does not really use quaternions. In the article 618 some vectors
are introduced that could be used to make equations simpler. These are pure
vectors, with zero scalar part, so there are quaternions only in the same
sense as real numbers are quaternions. But one who only uses real numbers
is not said to use quaternions. Quaternions are also mentioned earlier in
the text but not really used.

Mikko

Re: Original Maxwell's equations and behavior of light in the Universe.

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From: paul.b.a...@paulba.no (Paul B. Andersen)
Newsgroups: sci.physics.relativity
Subject: Re: Original Maxwell's equations and behavior of light in the
Universe.
Date: Sun, 15 Jan 2023 13:56:39 +0100
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 by: Paul B. Andersen - Sun, 15 Jan 2023 12:56 UTC

Den 14.01.2023 15:21, skrev Richard Hertz:
>
> Debunk this, fucking genius:
>
> https://www.scirp.org/journal/paperinformation.aspx?paperid=102987
>
> "It is seen, therefore, that, if the quaternion form of Maxwell’s Electromagnetic Field Equations is used, the normal theory follows through as usual, including the more novel notions introduced in the CIA released article mentioned [5]. However, in this case the resulting scalar field turns out to be described by an equation which indicates the wave speed to be greater than that of light; that is the scalar wave is superluminal."
>

The more novel notions in the CIA released article [5] "Star wars now":

https://www.cia.gov/readingroom/docs/CIA-RDP96-00788R001900680015-3.pdf

There is no end to what these "scalar-waves" can do.
They are undetectable and can penetrate anything, yet
they are very powerful and can cause a nuclear blast
to occur within an underground complex, or a complex
within a mountain.

"Star wars now" indeed! :-D

So are these "scalar waves" used now?
Yes. They can even cure any disease!

https://www.spooky2scalar.com/what-are-scalar-waves/

"It has been confirmed that scalar waves can stimulate
a twenty-fold cell growth in human immune system cells.
What’s more, scalar waves can increase the energy covalent
level of every single hydrogen atom in the body, and that’s
important due to hydrogen bonds holding DNA together."

Buy this, and you will live forever:
https://www.spooky2scalar.com/product/spooky2-scalar-essential-kit/

Only $2500!

But they are kind of honest:
https://www.spooky2scalar.com/scalar/

"The Unique Features of Spooky2 Scalar.
Most so-called scalar devices use the placebo effect.
However, the fields produced by Spooky2 Scalar are strong.
We use analog circuitry to ensure a pure signal, and
the signal can be either molecular or frequency modulated
using low or high frequencies."

Gullible people may not know what the "placebo effect" is.
But lawyers do, so don't try to sue them if the scalar waves
don't cure you!

--
Paul

https://paulba.no/

Re: Original Maxwell's equations and behavior of light in the Universe.

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Subject: Re: Original Maxwell's equations and behavior of light in the Universe.
From: hertz...@gmail.com (Richard Hertz)
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 by: Richard Hertz - Sun, 15 Jan 2023 13:04 UTC

On Sunday, January 15, 2023 at 9:52:11 AM UTC-3, Mikko wrote:

<snip>

> That text does not really use quaternions. In the article 618 some vectors
> are introduced that could be used to make equations simpler. These are pure
> vectors, with zero scalar part, so there are quaternions only in the same
> sense as real numbers are quaternions. But one who only uses real numbers
> is not said to use quaternions. Quaternions are also mentioned earlier in
> the text but not really used.
>
> Mikko

MAXWELL CLEARLY WROTE THAT, IN HIS TREATISE, HE AVOIDED THE BURDEN OF USING QUATERNIONS, FOR THE READER'S SAKE,
DUE TO ITS COMPLEXITY.

HIS GOALS, WRITING THE MONUMENTAL TREATISE ON ELECTRICITY AND MAGNETISM, WAS TO TEACH TO THE WORLD WHAT WAS
KNOWN IN 1871 ABOUT SUCH SCIENCE. THE TREATISE ALSO SERVES AS A GUIDE TO THE HISTORY OF THE NEW SCIENCE, WITH
DUE CREDIT TO HUNDRED OF SCIENTISTS THAT WORKED ON THE FIELD.

READ CAREFULLY, BECAUSE HE HAD DEVELOPED HIS EQUATIONS 7 YEARS BEFORE, USING QUATERNIONS. THE TREATISE IS BEYOND
HIS FAMOUS EQUATIONS FOR "LIGHT", AND COMPREHEND EVERYTHING THAT WAS KNOWN BY THEN.

Quaternion Expressions for the Electromagnetic Equations. (This point start at page 236)

"618.] In this treatise we have endeavoured to avoid any process demanding from the reader a knowledge of the Calculus of Quaternions. At the same time we have not scrupled to introduce the idea of a vector when it was necessary to do so. When we have had occasion to denote a vector by a symbol, we have used a German letter, the number of different vectors being so great that Hamilton's favourite symbols would have been exhausted at once.

Whenever therefore, a German letter is used it denotes a Hamiltonian vector, and indicates not only its magnitude but its direction."

Re: Original Maxwell's equations and behavior of light in the Universe.

<a91f5d6d-d338-4237-91ce-ac7f1d965d0cn@googlegroups.com>

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Subject: Re: Original Maxwell's equations and behavior of light in the Universe.
From: hertz...@gmail.com (Richard Hertz)
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 by: Richard Hertz - Sun, 15 Jan 2023 13:05 UTC

On Sunday, January 15, 2023 at 9:56:42 AM UTC-3, Paul B. Andersen wrote:
> Den 14.01.2023 15:21, skrev Richard Hertz:
> >
> > Debunk this, fucking genius:
> >
> > https://www.scirp.org/journal/paperinformation.aspx?paperid=102987
> >
> > "It is seen, therefore, that, if the quaternion form of Maxwell’s Electromagnetic Field Equations is used, the normal theory follows through as usual, including the more novel notions introduced in the CIA released article mentioned [5]. However, in this case the resulting scalar field turns out to be described by an equation which indicates the wave speed to be greater than that of light; that is the scalar wave is superluminal."
> >
> The more novel notions in the CIA released article [5] "Star wars now":
>
> https://www.cia.gov/readingroom/docs/CIA-RDP96-00788R001900680015-3.pdf
>
> There is no end to what these "scalar-waves" can do.
> They are undetectable and can penetrate anything, yet
> they are very powerful and can cause a nuclear blast
> to occur within an underground complex, or a complex
> within a mountain.
>
> "Star wars now" indeed! :-D
>
> So are these "scalar waves" used now?
> Yes. They can even cure any disease!
>
> https://www.spooky2scalar.com/what-are-scalar-waves/
>
> "It has been confirmed that scalar waves can stimulate
> a twenty-fold cell growth in human immune system cells.
> What’s more, scalar waves can increase the energy covalent
> level of every single hydrogen atom in the body, and that’s
> important due to hydrogen bonds holding DNA together."
>
> Buy this, and you will live forever:
> https://www.spooky2scalar.com/product/spooky2-scalar-essential-kit/
>
> Only $2500!
>
> But they are kind of honest:
> https://www.spooky2scalar.com/scalar/
>
> "The Unique Features of Spooky2 Scalar.
> Most so-called scalar devices use the placebo effect.
> However, the fields produced by Spooky2 Scalar are strong.
> We use analog circuitry to ensure a pure signal, and
> the signal can be either molecular or frequency modulated
> using low or high frequencies."
>
> Gullible people may not know what the "placebo effect" is.
> But lawyers do, so don't try to sue them if the scalar waves
> don't cure you!
>
> --
> Paul
>
> https://paulba.no/

Tesla knew.

Re: Original Maxwell's equations and behavior of light in the Universe.

<tq0ukq$2btsp$1@dont-email.me>

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From: be...@cliietik.oo (Kobie Locatelli)
Newsgroups: sci.physics.relativity,sci.physics,sci.math
Subject: Re: Original Maxwell's equations and behavior of light in the
Universe.
Date: Sun, 15 Jan 2023 13:21:31 -0000 (UTC)
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 by: Kobie Locatelli - Sun, 15 Jan 2023 13:21 UTC

Richard Hertz wrote:

>> Mikko
>
> MAXWELL CLEARLY WROTE THAT, IN HIS TREATISE, HE AVOIDED THE BURDEN OF
> USING QUATERNIONS, FOR THE READER'S SAKE, DUE TO ITS COMPLEXITY.

not true. Quaternions are simpler, but */_exhibits_singularities_/*, hence
useless for the continuum of Maxwell.

Re: Original Maxwell's equations and behavior of light in the Universe.

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From: paul.b.a...@paulba.no (Paul B. Andersen)
Newsgroups: sci.physics.relativity
Subject: Re: Original Maxwell's equations and behavior of light in the
Universe.
Date: Sun, 15 Jan 2023 14:30:32 +0100
Organization: A noiseless patient Spider
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 by: Paul B. Andersen - Sun, 15 Jan 2023 13:30 UTC

Den 15.01.2023 14:05, skrev Richard Hertz:
> On Sunday, January 15, 2023 at 9:56:42 AM UTC-3, Paul B. Andersen wrote:
>> Den 14.01.2023 15:21, skrev Richard Hertz:
>>>
>>> Debunk this, fucking genius:
>>>
>>> https://www.scirp.org/journal/paperinformation.aspx?paperid=102987
>>>
>>> "It is seen, therefore, that, if the quaternion form of Maxwell’s Electromagnetic Field Equations is used, the normal theory follows through as usual, including the more novel notions introduced in the CIA released article mentioned [5]. However, in this case the resulting scalar field turns out to be described by an equation which indicates the wave speed to be greater than that of light; that is the scalar wave is superluminal."
>>>
>> The more novel notions in the CIA released article [5] "Star wars now":
>>
>> https://www.cia.gov/readingroom/docs/CIA-RDP96-00788R001900680015-3.pdf
>>
>> There is no end to what these "scalar-waves" can do.
>> They are undetectable and can penetrate anything, yet
>> they are very powerful and can cause a nuclear blast
>> to occur within an underground complex, or a complex
>> within a mountain.
>>
>> "Star wars now" indeed! :-D
>>
>> So are these "scalar waves" used now?
>> Yes. They can even cure any disease!
>>
>> https://www.spooky2scalar.com/what-are-scalar-waves/
>>
>> "It has been confirmed that scalar waves can stimulate
>> a twenty-fold cell growth in human immune system cells.
>> What’s more, scalar waves can increase the energy covalent
>> level of every single hydrogen atom in the body, and that’s
>> important due to hydrogen bonds holding DNA together."
>>
>> Buy this, and you will live forever:
>> https://www.spooky2scalar.com/product/spooky2-scalar-essential-kit/
>>
>> Only $2500!
>>
>> But they are kind of honest:
>> https://www.spooky2scalar.com/scalar/
>>
>> "The Unique Features of Spooky2 Scalar.
>> Most so-called scalar devices use the placebo effect.
>> However, the fields produced by Spooky2 Scalar are strong.
>> We use analog circuitry to ensure a pure signal, and
>> the signal can be either molecular or frequency modulated
>> using low or high frequencies."
>>
>> Gullible people may not know what the "placebo effect" is.
>> But lawyers do, so don't try to sue them if the scalar waves
>> don't cure you!
>>
>> --
>> Paul
>>
>> https://paulba.no/
>
> Tesla knew.
>

Quite.
He invented scalar energy.
Much used today:

https://universe-inside-you.com/orgone-energy/

--
Paul

https://paulba.no/

Re: Original Maxwell's equations and behavior of light in the Universe.

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From: be...@cliietik.oo (Kobie Locatelli)
Newsgroups: sci.physics.relativity,sci.physics,sci.math
Subject: Re: Original Maxwell's equations and behavior of light in the
Universe.
Date: Sun, 15 Jan 2023 14:07:12 -0000 (UTC)
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 by: Kobie Locatelli - Sun, 15 Jan 2023 14:07 UTC

Paul B. Andersen wrote:

>> Tesla knew.
>
> Quite. He invented scalar energy. Much used today:

wonderful, not watch the nazi khazar zelenske, shamelessly visiting
americaa, with a visible nazi swastika on his chest. That fork is a nazi
fork, the fork of satan. More proof that the americans are the nazi beasts
of the earth. Smaller than the chinese, another capitalist beasts, eating
dogs, cats and I don't want to enum the most significant, I wish I never
know. So kill the chinese satanists beast, america, not the europe.

deep nazis in EU.

A message for the Dutch PM Mark Rutte no Nazies in the Ukraine check your
own party!
https://%62%69%74%63%68%75%74%65.com/%76%69%64%65%6f/ZWcRo77LRFEY

US lawmaker proposes putting Zelensky's bust in US Congress
https://%62%69%74%63%68%75%74%65.com/%76%69%64%65%6f/70ihbAlCbrIN

Kadyrov Humiliates America In Interview With Western Propagandist
https://%62%69%74%63%68%75%74%65.com/%76%69%64%65%6f/BVA8272wp3Q0

German Journalist Anna Lipp "Germany Is Now A Dictatorship"
https://%62%69%74%63%68%75%74%65.com/%76%69%64%65%6f/QVgxwb2zeOKJ

Re: Original Maxwell's equations and behavior of light in the Universe.

<1994036.oMNUckLgyt@PointedEars.de>

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From: PointedE...@web.de (Thomas 'PointedEars' Lahn)
Newsgroups: sci.physics.relativity
Subject: Re: Original Maxwell's equations and behavior of light in the Universe.
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 by: Thomas 'Pointed - Mon, 16 Jan 2023 03:59 UTC

Mikko wrote:

> On 2023-01-14 14:21:39 +0000, Richard Hertz said:
>> On Saturday, January 14, 2023 at 3:26:55 AM UTC-3, JanPB wrote:
>>> On Friday, January 13, 2023 at 3:10:58 PM UTC-8, Richard Hertz wrote:
>>> > > The original Maxwell's equations, under the form of quaternions, had
>>> > > SIX VARIABLES, being 5 of them described with 3D vectors, and the
>>> > > 6th. being a scalar: electric charge density.
>>> Maxwell didn't use quaternions.
>>
>> Debunk this, fucking genius:
>>
>> https://www.scirp.org/journal/paperinformation.aspx?paperid=102987
>
> That article is not useful here as it merely says "It is often claimed
> that Maxwell’s electromagnetic equations were originally written in terms
> of quaternions" but doesn't say whether they really were.

It is at least possible that James Clerk Maxwell did that in 1861 as William
Rowan Hamilton introduced quaternions in 1843, and Maxwell learned of
quaternions from his correspondence with P. G. Tait.

Maxwell’s treatise is available for free, so there is no point in
complaining when you could find out yourself easily.

PointedEars
--
Q: Where are offenders sentenced for light crimes?
A: To a prism.

(from: WolframAlpha)

Re: Original Maxwell's equations and behavior of light in the Universe.

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From: nos...@de-ster.demon.nl (J. J. Lodder)
Newsgroups: sci.physics.relativity
Subject: Re: Original Maxwell's equations and behavior of light in the Universe.
Date: Mon, 16 Jan 2023 10:25:36 +0100
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 by: J. J. Lodder - Mon, 16 Jan 2023 09:25 UTC

Richard Hertz <hertz778@gmail.com> wrote:

> The original Maxwell's equations, under the form of quaternions, had
> SIX VARIABLES, being 5 of them described with 3D vectors, and the 6th.
> being a scalar: electric charge density.
>
> 20 years after Maxwell's death, Heaviside (with the validation of Hertz
> and Lorentz) "assassinated" the 20 quaternion equations and, using the
> new vectorial algebra, gave them the form under which they are known
> since then: four 3D differential equations. He got rid of the scalar electric
> charge density.

Right. And Heaviside and Lorentz between them also invented
Heaviside-Lorentz units.
In these units Maxwell's equation take their simplest possible form.

In this form it is immediately obvious
that c can be eliminated completely from the Maxwell-Lorentz equations
by a suitable choice of units, (we can put c=1)
because in H-L units c only occurs in the combination ct.
(so also only as v/c)

But natural units are beyond your understanding,

Jan

Re: Original Maxwell's equations and behavior of light in the Universe.

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Subject: Re: Original Maxwell's equations and behavior of light in the Universe.
From: maluwozn...@gmail.com (Maciej Wozniak)
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 by: Maciej Wozniak - Mon, 16 Jan 2023 09:52 UTC

On Monday, 16 January 2023 at 10:25:39 UTC+1, J. J. Lodder wrote:
> Richard Hertz <hert...@gmail.com> wrote:
>
> > The original Maxwell's equations, under the form of quaternions, had
> > SIX VARIABLES, being 5 of them described with 3D vectors, and the 6th.
> > being a scalar: electric charge density.
> >
> > 20 years after Maxwell's death, Heaviside (with the validation of Hertz
> > and Lorentz) "assassinated" the 20 quaternion equations and, using the
> > new vectorial algebra, gave them the form under which they are known
> > since then: four 3D differential equations. He got rid of the scalar electric
> > charge density.
> Right. And Heaviside and Lorentz between them also invented
> Heaviside-Lorentz units.
> In these units Maxwell's equation take their simplest possible form.

The simplest doesn't mean the wisest, poor halfbrain,
and if you replace both sides totally by 1 - and get 1=1 -
it will be even simpler.

Re: Original Maxwell's equations and behavior of light in the Universe.

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From: AetherRe...@invalid.com (Aether Regaind)
Newsgroups: sci.physics.relativity
Subject: Re: Original Maxwell's equations and behavior of light in the
Universe.
Date: Mon, 16 Jan 2023 15:36:00 +0000
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 by: Aether Regaind - Mon, 16 Jan 2023 15:36 UTC

> On Saturday, January 14, 2023 at 3:26:55 AM UTC-3, JanPB wrote:
> Maxwell didn't use quaternions. He had six 3D vectors and two scalars,
> 20 equations.
>
> 3D component quantities:
> 1. "electromagnetic momentum" F, G, H (today: vector potential A),
> 2. "magnetic intensity" alpha, beta, gamma (today: magnetic field H),
> 3. "electromotive force" P, Q, R (today: electric field E),
> 4. "current due to conduction" p, q, r (today: electric current
density j),
> 5. "electric displacement" f, g, h (today: displacement field D),
> 6. "total current" p', q', r' (today: total current density),
>
> scalars:
> 1. "quantity of free electricity" (today: charge density),
> 2. "electric potential" (today: same).
>
> What quaternion? I'd like to see it, sounds interesting. The equations
> I've seen are just regular component equations.
>
> Maxwell originally wrote his equations in the component form, as
> I described. He later tried to put them in quaternion form. This is fine
> although the modern differential form is even more succinct: just
> two equations.
>
> --
> Jan
>

Richard Hertz is right, in that Maxwell's 1879 treatise uses quaternions.

See the section: "Quaternion Expressions for the Electromagnetic
Equations" in:
https://en.wikisource.org/wiki/A_Treatise_on_Electricity_and_Magnetism/Part_IV/Chapter_IX

The vectors he refers to are HAMILTONIAN VECTORS, a.k.a, quaternions.

i, j, k in the treatise are the Hamiltonian bases and are not the unit
vectors of vector algebra, though they are very similar in operation. See:
https://en.wikipedia.org/wiki/Quaternion#Multiplication_of_basis_elements

In particular:
A*B (quaternion product) = (ax*i + ay*j + az*k)*(bx*i + by*j + bz*k) =
-A⋅B + A⨯B (vector products)

Similary for a quaternion field:
σ = X*i + Y*j + Z*k

∇*σ = -∇⋅σ + ∇⨯σ [again LHS is a quaternion product, RHS is in
equivalent vector products]

Maxwell gives a crash course on QUATERNION CALCULUS in the very
beginning of his treatise:
https://en.wikisource.org/wiki/A_Treatise_on_Electricity_and_Magnetism/Preliminary

Relevant sections are:
On the Relation of Physical Quantities to Directions in Space.
On the effect of the operator ∇ on a [Hamiltonian] vector function.

All this is pretty interesting given that Maxwell wrote this in 1879,
while the common impression is that Maxwell struggled with 18 vector
components and had no idea of the power [notational succinctness] of
vector calculus which was invented much later by Heaviside and Gibbs.
Quaternion calculus is even more succinct as it combines both the scalar
and vector products in one multiplication operator.

Re: Original Maxwell's equations and behavior of light in the Universe.

<tq3qve$2p5s3$1@dont-email.me>

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From: AetherRe...@invalid.com (Aether Regaind)
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Subject: Re: Original Maxwell's equations and behavior of light in the
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Date: Mon, 16 Jan 2023 15:39:00 +0000
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 by: Aether Regaind - Mon, 16 Jan 2023 15:39 UTC

JanPB:
> On Saturday, January 14, 2023 at 3:26:55 AM UTC-3, JanPB wrote:
> Maxwell didn't use quaternions. He had six 3D vectors and two scalars,
> 20 equations.
>
> 3D component quantities:
> 1. "electromagnetic momentum" F, G, H (today: vector potential A),
> 2. "magnetic intensity" alpha, beta, gamma (today: magnetic field H),
> 3. "electromotive force" P, Q, R (today: electric field E),
> 4. "current due to conduction" p, q, r (today: electric current density j),
> 5. "electric displacement" f, g, h (today: displacement field D),
> 6. "total current" p', q', r' (today: total current density),
>
> scalars:
> 1. "quantity of free electricity" (today: charge density),
> 2. "electric potential" (today: same).
>
> What quaternion? I'd like to see it, sounds interesting. The equations
> I've seen are just regular component equations.
>
> Maxwell originally wrote his equations in the component form, as
> I described. He later tried to put them in quaternion form. This is fine
> although the modern differential form is even more succinct: just
> two equations.
>
> --
> Jan

Richard Hertz is right in that, Maxwell's 1879 treatise uses quaternions.

See the section: "Quaternion Expressions for the Electromagnetic
Equations" in:
https://en.wikisource.org/wiki/A_Treatise_on_Electricity_and_Magnetism/Part_IV/Chapter_IX

The vectors he refers to are HAMILTONIAN VECTORS, a.k.a, quaternions.

i, j, k in the treatise are the Hamiltonian bases and are not the unit
vectors of vector algebra, though they are very similar in operation. See:
https://en.wikipedia.org/wiki/Quaternion#Multiplication_of_basis_elements

In particular:
A*B (quaternion product) = (ax*i + ay*j + az*k)*(bx*i + by*j + bz*k) =
-A⋅B + A⨯B (vector products)

Similarly for a quaternion field:
σ = X*i + Y*j + Z*k

∇*σ = -∇⋅σ + ∇⨯σ [again LHS is a quaternion product, RHS is in
equivalent vector products]

Maxwell gives a crash course on QUATERNION CALCULUS in the very
beginning of his treatise:
https://en.wikisource.org/wiki/A_Treatise_on_Electricity_and_Magnetism/Preliminary

Relevant sections are:
On the Relation of Physical Quantities to Directions in Space.
On the effect of the operator ∇ on a [Hamiltonian] vector function.

All this is pretty interesting given that Maxwell wrote this in 1879,
while the common impression is that Maxwell struggled with 18 vector
components and had no idea of the power [notational succinctness] of
vector calculus which was invented much later by Heaviside and Gibbs.
Quaternion calculus is even more succinct as it combines both the scalar
and vector products in one multiplication operator.

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