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</head><body><p>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. <a href="http://www.alternativephysics.org/book/ElectricFields.htm">http://www.alternativephysics.org/book/ElectricFields.htm</a></p><p><br></p><p>All the best,</p><p>Tom hollings</p><p><br></p><blockquote type="cite">On 23 April 2020 at 07:09 Arend Lammertink <<a href="mailto:lamare@gmail.com">lamare@gmail.com</a>> wrote:<br><br><br>Dear List members,<br><br>I have been studying Tesla for quite some time now and became<br>convinced longitudinal waves exist and that they propagate faster than<br>light. For quite some time, I have been working on the theory, which<br>culminated in the attached draft paper on revision of Maxwell's<br>equations. During the past week, I had a discussion about this on the<br>"Theoretical Physics" LinkedIn group, which made me realise how<br>important the vector Laplace equation is and believe I now have the<br>mathematical proof that Maxwell's equations are incorrect. This is the<br>short version of the argument:<br><br>-:-<br>"The Laplace operator is not some sacred physical law of the universe,<br>it is a mathematical relation".<br><br>Yes, it's a relation of which the correctness is pretty much<br>undisputable, like 1+1=2.<br><br>Equate this equation to zero and one obtains the 3D Laplace equation<br>of which the solutions are the harmonic functions, which (when worked<br>out) describe all possible (harmonic) wave phenomena in 3D:<br><br> ∇²𝐅= ∇(∇·𝐅) - ∇×(∇×𝐅) = 0.<br><br>This can be re-written as:<br><br> -∇²𝐅= - ∇(∇·𝐅) + ∇×(∇×𝐅) = 0.<br><br>Then, the terms in this equation can be written out as follows:<br><br> 𝐀= ∇×𝐅<br> Φ= ∇⋅𝐅<br> 𝐁= ∇×𝐀= ∇×(∇×𝐅)<br> 𝗘=−∇Φ= −∇(∇⋅𝐅)<br><br>And because of vector identities, one can also write:<br><br> ∇×𝗘= 0<br> ∇⋅𝐁= 0<br><br>So, any given vector field 𝐅 can be decomposed like this into a<br>rotation free component 𝗘 and a divergence free component 𝐁.<br><br>There is no argument this is mathematically consistent, nor that the<br>solutions to the equation -∇²𝐅= 0 are the harmonic wave functions in<br>3D.<br><br>Now compare this to Maxwell's:<br><br> 𝗘= −∇Φ− ∂𝐀/∂t<br><br>Take the rotation at both sides of the equation and we obtain the<br>Maxwell-Faraday equation:<br><br> ∇×𝗘= - ∂𝐁/∂t<br><br>WP: "Faraday's law of induction (briefly, Faraday's law) is a basic<br>law of electromagnetism predicting how a magnetic field will interact<br>with an electric circuit to produce an electromotive force (EMF)—a<br>phenomenon known as electromagnetic induction."<br><br>This is a circuit law, which predicts how a magnetic field will<br>interact with electrons moving trough a wire. Since this involves<br>moving charge carriers, which are particles, it is illogical to<br>introduce this law at the medium/field modelling level. Because of the<br>wave-particle duality principle, it is known that particles are<br>manifestations of the EM field. So, by including this law in the<br>medium/field model one introduces circular logic.<br><br>Not only that, it breaks the fundamental separation of the fields into<br>a divergence free component and a rotation free component.<br><br>As is well known, this model eventually leads to two mutually<br>exclusive theories, which cannot both be correct.<br><br>In other words: what you are doing by introducing Faraday's law at<br>this level in the model is you are insisting 1+1 is not 2, but<br>something else.<br><br>And you end up with 150+ years of trying to find additional equations<br>to straighten things out, but the bottom line is: 1+1=2, NOT something<br>else<br><br>[...]<br><br>"How does it break "the fundamental separation of the fields into a<br>divergence free component and a rotation free component."? "<br><br>As shown, the 3D vector Laplace equation defines two components, one<br>of which is divergence free and one of which is rotation free.<br><br>Since the 3D vector Laplace equaton is nothing but a 3D generalization<br>of the lower dimensional Laplace equation and results in harmonic<br>solutions, which is all well established undisputable math, it follows<br>that the decomposition into a divergence free component and a rotation<br>free component is fundamental and is therefore the only correct way to<br>derive wave functions in 3D for any given vector field.<br><br>There is no argument that with equating the rotation of the rotation<br>free component 𝗘 to the time derivative of the divergence free (and<br>therefore rotational) component 𝐁 by Maxwell results in 𝗘 remaining<br>to be rotation free and therefore such breaks said fundamental<br>separation of said components.<br>-:-<br><br>I have some rewriting to do of the article, because I now realize it's<br>perfectly O.K. to have the primary field, which I denoted [V], as the<br>null vector field, since in the Laplace equation the right side of the<br>equation is also zero, so we don't have to resort to discrete math.<br>So, for the time being, I included part of the discussion on LinkedIn,<br>which I think you'll find interesting.<br><br>In short: I believe to have found the foundation for that Theory of<br>Everything scientists have been looking for for a very long time.<br><br>I would love to hear your opinion about this.<br><br>Best regards,<br><br>Arend.<br>_______________________________________________<br>Physics mailing list<br><a href="mailto:Physics@tuks.nl">Physics@tuks.nl</a><br><a href="http://mail.tuks.nl/cgi-bin/mailman/listinfo/physics" rel="noopener" target="_blank">http://mail.tuks.nl/cgi-bin/mailman/listinfo/physics</a></blockquote></body></html>