[Physics] Mathematical proof Maxwell's equations are incorrect?
Tom Hollings
carmam at tiscali.co.uk
Thu Apr 23 18:05:30 CEST 2020
Arend, thank you for sending me your paper on Maxwell's equations, I am always happy to receive any papers from you. As I am not very mathematical, it will take me a while to read and digest it (digest being the operative word!). It did make me think of a web page by Bernard Burchell, whom you may have heard of. He uses the minimum of mathematics, and gets his point across. There is a section on electric fields which I have linked here, you might be interested in it. http://www.alternativephysics.org/book/ElectricFields.htm
All the best,
Tom hollings
> On 23 April 2020 at 07:09 Arend Lammertink <lamare at gmail.com mailto:lamare at gmail.com > wrote:
>
>
> Dear List members,
>
> I have been studying Tesla for quite some time now and became
> convinced longitudinal waves exist and that they propagate faster than
> light. For quite some time, I have been working on the theory, which
> culminated in the attached draft paper on revision of Maxwell's
> equations. During the past week, I had a discussion about this on the
> "Theoretical Physics" LinkedIn group, which made me realise how
> important the vector Laplace equation is and believe I now have the
> mathematical proof that Maxwell's equations are incorrect. This is the
> short version of the argument:
>
> -:-
> "The Laplace operator is not some sacred physical law of the universe,
> it is a mathematical relation".
>
> Yes, it's a relation of which the correctness is pretty much
> undisputable, like 1+1=2.
>
> Equate this equation to zero and one obtains the 3D Laplace equation
> of which the solutions are the harmonic functions, which (when worked
> out) describe all possible (harmonic) wave phenomena in 3D:
>
> โยฒ๐
= โ(โยท๐
) - โร(โร๐
) = 0.
>
> This can be re-written as:
>
> -โยฒ๐
= - โ(โยท๐
) + โร(โร๐
) = 0.
>
> Then, the terms in this equation can be written out as follows:
>
> ๐= โร๐
> ฮฆ= โโ
๐
> ๐= โร๐= โร(โร๐
)
> ๐=โโฮฆ= โโ(โโ
๐
)
>
> And because of vector identities, one can also write:
>
> โร๐= 0
> โโ
๐= 0
>
> So, any given vector field ๐
can be decomposed like this into a
> rotation free component ๐ and a divergence free component ๐.
>
> There is no argument this is mathematically consistent, nor that the
> solutions to the equation -โยฒ๐
= 0 are the harmonic wave functions in
> 3D.
>
> Now compare this to Maxwell's:
>
> ๐= โโฮฆโ โ๐/โt
>
> Take the rotation at both sides of the equation and we obtain the
> Maxwell-Faraday equation:
>
> โร๐= - โ๐/โt
>
> WP: "Faraday's law of induction (briefly, Faraday's law) is a basic
> law of electromagnetism predicting how a magnetic field will interact
> with an electric circuit to produce an electromotive force (EMF)โa
> phenomenon known as electromagnetic induction."
>
> This is a circuit law, which predicts how a magnetic field will
> interact with electrons moving trough a wire. Since this involves
> moving charge carriers, which are particles, it is illogical to
> introduce this law at the medium/field modelling level. Because of the
> wave-particle duality principle, it is known that particles are
> manifestations of the EM field. So, by including this law in the
> medium/field model one introduces circular logic.
>
> Not only that, it breaks the fundamental separation of the fields into
> a divergence free component and a rotation free component.
>
> As is well known, this model eventually leads to two mutually
> exclusive theories, which cannot both be correct.
>
> In other words: what you are doing by introducing Faraday's law at
> this level in the model is you are insisting 1+1 is not 2, but
> something else.
>
> And you end up with 150+ years of trying to find additional equations
> to straighten things out, but the bottom line is: 1+1=2, NOT something
> else
>
> [...]
>
> "How does it break "the fundamental separation of the fields into a
> divergence free component and a rotation free component."? "
>
> As shown, the 3D vector Laplace equation defines two components, one
> of which is divergence free and one of which is rotation free.
>
> Since the 3D vector Laplace equaton is nothing but a 3D generalization
> of the lower dimensional Laplace equation and results in harmonic
> solutions, which is all well established undisputable math, it follows
> that the decomposition into a divergence free component and a rotation
> free component is fundamental and is therefore the only correct way to
> derive wave functions in 3D for any given vector field.
>
> There is no argument that with equating the rotation of the rotation
> free component ๐ to the time derivative of the divergence free (and
> therefore rotational) component ๐ by Maxwell results in ๐ remaining
> to be rotation free and therefore such breaks said fundamental
> separation of said components.
> -:-
>
> I have some rewriting to do of the article, because I now realize it's
> perfectly O.K. to have the primary field, which I denoted [V], as the
> null vector field, since in the Laplace equation the right side of the
> equation is also zero, so we don't have to resort to discrete math.
> So, for the time being, I included part of the discussion on LinkedIn,
> which I think you'll find interesting.
>
> In short: I believe to have found the foundation for that Theory of
> Everything scientists have been looking for for a very long time.
>
> I would love to hear your opinion about this.
>
> Best regards,
>
> Arend.
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