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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink=purple style='word-wrap:break-word'><div class=WordSection1><p class=MsoNormal style='margin-right:0in'><span style='font-size:14.0pt;color:#20188C'>Jarek,<o:p></o:p></span></p><p class=MsoNormal style='margin-right:0in'><span style='font-size:14.0pt;color:#20188C'><o:p> </o:p></span></p><p class=MsoNormal style='margin-right:0in'><span style='font-size:14.0pt;color:#20188C'>So far, my focus has been on understanding the properties of the quantum vacuum, an electron, and an electron’s forces. I have been using terms such as Planck length, Planck force, impedance of spacetime, etc. Your question made me realize that there is a large body of knowledge that is currently expressed as electromagnetism equations that needs to be “translated” into the terms I have been using. For example, Section 16 of the “Electron’s forces” paper it titled “Charge conversion constant”. In this section, I propose that Planck charge (<i>Q</i><sub>p</sub>) converts to Planck length (<i>L</i><sub>p</sub>). Therefore, the charge conversion constant is <i>Q</i><sub>p</sub>/<i>L</i><sub>p</sub> </span><span style='font-size:14.0pt;font-family:"Cambria Math",serif;color:#20188C'>≈</span><span style='font-size:14.0pt;color:#20188C'> 1.16</span><span style='font-size:14.0pt;font-family:"Arial",sans-serif;color:#20188C'>ᵡ</span><span style='font-size:14.0pt;color:#20188C'>10<sup>17</sup> C/m. I have said that this length conversion is “polarized length”, not the omni-directional length of a meter stick. <o:p></o:p></span></p><p class=MsoNormal style='margin-right:0in'><span style='font-size:14.0pt;color:#20188C'><o:p> </o:p></span></p><p class=MsoNormal style='margin-right:0in'><span style='font-size:14.0pt;color:#20188C'>Your question about Gauss law makes it obvious that a lot more development of this concept is required. Terms such as “electric flux” need to be translated into properties of the quantum vacuum. This will require introducing vectors and perhaps other properties into my simplified charge conversion constant. This is a big job requiring expertise in electromagnetism. <o:p></o:p></span></p><p class=MsoNormal style='margin-right:0in'><span style='font-size:14.0pt;color:#20188C'><o:p> </o:p></span></p><p class=MsoNormal style='margin-right:0in'><span style='font-size:14.0pt;color:#20188C'>On another subject, it has been less than 2 days since I posted the information about my article to this group on </span><span style='font-size:14.0pt;color:maroon'>natureoflightandparticles.org</span><span style='font-size:14.0pt;color:#20188C'>. In the approximately 40 hours since posting the paper, it has received over 60 “reads” on ResearchGate. This is a great increase in the download rate. <o:p></o:p></span></p><p class=MsoNormal style='margin-right:0in'><span style='font-size:14.0pt;color:#20188C'><o:p> </o:p></span></p><p class=MsoNormal style='margin-right:0in'><span style='font-size:14.0pt;color:#20188C'>John<o:p></o:p></span></p><p class=MsoNormal style='margin-right:0in'><span style='font-size:14.0pt;color:#20188C'><o:p> </o:p></span></p><p class=MsoNormal style='margin-right:0in'><span style='font-size:14.0pt;color:#20188C'><o:p> </o:p></span></p><p class=MsoNormal style='margin-right:0in'><span style='font-size:14.0pt;color:#20188C'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal align=left style='margin-right:0in;text-align:left'><b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> Jarek Duda <dudajar@gmail.com> <br><b>Sent:</b> Wednesday, October 20, 2021 8:25 PM<br><b>To:</b> John Macken <john@macken.com>; Nature of Light <general@lists.natureoflightandparticles.org><br><b>Subject:</b> Re: [General] Electron's Forces<o:p></o:p></span></p></div></div><p class=MsoNormal align=left style='margin-right:0in;text-align:left'><o:p> </o:p></p><p>Dear John, <o:p></o:p></p><p>Thank you, this is the article I have looked through, but wasn't able to find the details.<o:p></o:p></p><p>We use topological mechanisms like for fluxons quantizing magnetic field in superconductor - which can be directly translated to electric charges e.g. hedgehog-like configuration (realized e.g. in liquid crystals), making Gauss law count topological charge:<o:p></o:p></p><p><img width=732 height=83 style='width:7.625in;height:.8645in' id="Picture_x0020_2" src="cid:image001.png@01D7C60D.A3B21330"><o:p></o:p></p><p><o:p> </o:p></p><p>> 2) All fundamental particles are modeled as rotating waves with Planck length amplitude and ħ/2 angular momentum. <o:p></o:p></p><p>Sounds like fluxon magnetic field quantization - to take it to point-like electric charge, we can use the above formula.<o:p></o:p></p><p><o:p> </o:p></p><p>>The different fundamental particles have different rotation rates, different energy and different radii. However, they all have the same wave amplitude. <o:p></o:p></p><p>Sounds like de Broglie clock E = hbar omega = m c^2, confirmed for electron: <a href="https://link.springer.com/article/10.1007/s10701-008-9225-1">https://link.springer.com/article/10.1007/s10701-008-9225-1</a><o:p></o:p></p><p><o:p> </o:p></p><p>> 3) The first order distortion of the surrounding space produced by these rotating waves scales only with wave amplitude. This distortion does not scale with frequency, with energy, or with wavelength. This common wave amplitude is the ultimate source of quantized charge. <o:p></o:p></p><p>I don't understand - maybe you could show some formula like above - showing Gauss law returning integer multiplicity of e?<o:p></o:p></p><p>Best regards,<o:p></o:p></p><p>Jarek<o:p></o:p></p><p><o:p> </o:p></p><div><p class=MsoNormal style='margin-right:0in'>On 20.10.2021 20:48, John Macken wrote:<o:p></o:p></p></div><blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><p class=MsoNormal style='margin-right:0in'><span style='font-size:14.0pt;color:#20188C'>Jarek,</span><o:p></o:p></p><p class=MsoNormal style='margin-right:0in'><span style='font-size:14.0pt;color:#20188C'> </span><o:p></o:p></p><p class=MsoNormal align=left style='margin-right:0in;text-align:left'><span style='font-size:14.0pt;color:#20188C'>You ask, “</span><span style='font-size:14.0pt'>Why Gauss law can only return integer charge?”<span style='color:#20188C'> I will restate the question as: What is the source of elementary charge <i>e </i>in particles? </span></span><o:p></o:p></p><p class=MsoNormal align=left style='margin-right:0in;text-align:left'><span style='font-size:14.0pt;color:#20188C'> </span><o:p></o:p></p><p class=MsoNormal align=left style='margin-right:0in;text-align:left'><span style='font-size:14.0pt;color:#20188C'>I think I do a good job answering this question in the paper </span><b><span style='font-size:14.0pt;font-family:"Calibri",sans-serif'>A quantum vacuum model unites an electron’s gravitational and electromagnetic forces</span></b><span style='font-size:14.0pt;color:#20188C'>. </span><o:p></o:p></p><p class=MsoNormal align=left style='margin-right:0in;text-align:left;background:white'><span style='color:black'><a href="http://www.researchgate.net/publication/353049276" target="_blank"><span style='font-size:10.5pt;font-family:inherit;border:none windowtext 1.0pt;padding:0in'>www.researchgate.net/publication/353049276</span></a></span><o:p></o:p></p><p class=MsoNormal align=left style='margin-right:0in;text-align:left'><span style='font-size:14.0pt;color:#20188C'> </span><o:p></o:p></p><p class=MsoNormal align=left style='margin-right:0in;text-align:left'><span style='font-size:14.0pt;color:#20188C'>For example, sections of the paper have titles such as: <b>Electron’s electric charge</b>, <b>What is electric charge?</b> and <b>Charge conversion constant</b>. I have to assume the fine structure constant α, but given this constant, the model predicts the electrostatic force between two electrons or two muons. </span><o:p></o:p></p><p class=MsoNormal align=left style='margin-right:0in;text-align:left'><span style='font-size:14.0pt;color:#20188C'> </span><o:p></o:p></p><p class=MsoNormal align=left style='margin-right:0in;text-align:left'><span style='font-size:14.0pt;color:#20188C'>A brief summary answer to your question can be broken down into the following points.</span><o:p></o:p></p><p class=MsoNormal align=left style='margin-right:0in;text-align:left'><span style='font-size:14.0pt;color:#20188C'>1) The quantum vacuum is modeled as a sea of vacuum fluctuations with amplitude of Planck length. </span><o:p></o:p></p><p class=MsoNormal align=left style='margin-right:0in;text-align:left'><span style='font-size:14.0pt;color:#20188C'>2) All fundamental particles are modeled as rotating waves with Planck length amplitude and </span><span style='font-size:14.0pt'>ħ<span style='color:#20188C'>/2 angular momentum. The different fundamental particles have different rotation rates, different energy and different radii. However, they all have the same wave amplitude. </span></span><o:p></o:p></p><p class=MsoNormal align=left style='margin-right:0in;text-align:left'><span style='font-size:14.0pt;color:#20188C'>3) The first order distortion of the surrounding space produced by these rotating waves scales only with wave amplitude. This distortion does not scale with frequency, with energy, or with wavelength. This common wave amplitude is the ultimate source of quantized charge. </span><o:p></o:p></p><p class=MsoNormal align=left style='margin-right:0in;text-align:left'><span style='font-size:14.0pt;color:#20188C'>4) This explanation requires the manual insertion of α<sup>1/2</sup> to be exact. Therefore, it is incomplete. However, it generates the surprising connection between the electron’s electrostatic force and the electron’s gravitational force. </span><o:p></o:p></p><p class=MsoNormal align=left style='margin-right:0in;text-align:left'><span style='font-size:14.0pt;color:#20188C'> </span><o:p></o:p></p><p class=MsoNormal align=left style='margin-right:0in;text-align:left'><span style='font-size:14.0pt;color:#20188C'>John</span><o:p></o:p></p><p class=MsoNormal style='margin-right:0in'><span style='font-size:14.0pt;color:#20188C'> </span><o:p></o:p></p><p class=MsoNormal style='margin-right:0in'><span style='font-size:14.0pt;color:#20188C'> </span><o:p></o:p></p><p class=MsoNormal style='margin-right:0in'><span style='font-size:14.0pt;color:#20188C'> </span><o:p></o:p></p><p class=MsoNormal style='margin-right:0in'><span style='font-size:14.0pt;color:#20188C'> </span><o:p></o:p></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal align=left style='margin-right:0in;text-align:left'><b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> Jarek Duda </span><a href="mailto:dudajar@gmail.com"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'><dudajar@gmail.com></span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> <br><b>Sent:</b> Wednesday, October 20, 2021 1:24 AM<br><b>To:</b> </span><a href="mailto:general@lists.natureoflightandparticles.org"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>general@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>; </span><a href="mailto:john@macken.com"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>john@macken.com</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'><br><b>Subject:</b> Re: [General] Electron's Forces</span><o:p></o:p></p></div></div><p class=MsoNormal align=left style='margin-right:0in;text-align:left'> <o:p></o:p></p><p>Dear John,<o:p></o:p></p><p>Thank you, personally I am mostly interested in models of electrons - in your paper I see "quantized wave-based electron model", " An electron’s core is a rotating wave in the universal <br>field."<o:p></o:p></p><p>While I deeply agree with both statements, I don't see the details - especially for the most important: charge quantization -<b> why Gauss law can only return integer charge?</b><o:p></o:p></p><p>With Manfried Faber we get it by interpreting curvature of some deeper e.g. unitary vector field, this way Gauss law counts topological charge - getting built in charge quantization.<o:p></o:p></p><p>Such view is also used in liquid crystals, for which they get long-range e.g. Coulomb-like interactions: <a href="https://www.nature.com/articles/s41598-017-16200-z">https://www.nature.com/articles/s41598-017-16200-z</a><o:p></o:p></p><p>Here is how I would like to get 3 leptons (slides: <a href="https://www.dropbox.com/s/9dl2g9lypzqu5hp/liquid%20crystal%20particles.pdf">https://www.dropbox.com/s/9dl2g9lypzqu5hp/liquid%20crystal%20particles.pdf</a> - Coulomb between such charges, Klein-Gordon for phase as twist of the long axis):<o:p></o:p></p><p><img border=0 width=594 height=212 style='width:6.1875in;height:2.2083in' id="Picture_x0020_1" src="cid:image002.png@01D7C60D.A3B21330"><o:p></o:p></p><p> <o:p></o:p></p><p>Is it close to your explanation of electric charge quantization?<o:p></o:p></p><p>With best regards,<o:p></o:p></p><p>Jarek Duda<o:p></o:p></p><p> <o:p></o:p></p><div><p class=MsoNormal style='margin-right:0in'>W dniu 20.10.2021 o 03:15, John Macken pisze:<o:p></o:p></p></div><blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><p class=MsoNormal style='margin-right:0in;background:white'><span style='font-size:14.0pt;color:#111111;background:white'>Hello Chandra and All,</span><o:p></o:p></p><p class=MsoNormal style='margin-right:0in;background:white'><span style='font-size:14.0pt;color:#111111;background:white'> </span><o:p></o:p></p><p class=MsoNormal style='margin-right:0in;background:white'><span style='font-size:14.0pt;color:#111111;background:white'>I used to be an active member of this discussion group. However, when everyone else seemed to be attempting to construct electrons out of photons, my participation stopped. Now that I see the discussion has broadened, I would like to participate again. </span><o:p></o:p></p><p class=MsoNormal style='margin-right:0in;background:white'><span style='font-size:14.0pt;color:#111111;background:white'> </span><o:p></o:p></p><p class=MsoNormal style='margin-right:0in;background:white'><span style='font-size:14.0pt;color:#111111;background:white'>I have been developing a model of an electron and the quantum vacuum for about 20 years. I started by characterizing the physical properties of the quantum vacuum. This led to a wave-based model of an electron. This model successfully generates an electron’s approximate energy, inertia and de Broglie wave characteristics. However, then something unexpected happened. The electron model also created two types of disturbances in the surrounding quantum vacuum. The first order effect was found to correspond to the electron’s electric/magnetic field. The much weaker, second order effect was found to correspond to the electron’s gravitational field.</span><o:p></o:p></p><p class=MsoNormal style='margin-right:0in;background:white'><span style='font-size:14.0pt;color:#111111;background:white'> </span><o:p></o:p></p><p class=MsoNormal style='margin-right:0in;background:white'><span style='font-size:14.0pt;color:#111111;background:white'>Since this single model was creating both forces, the model was predicting how an electron’s quantum mechanical properties should unify the electron’s gravitational and electromagnetic forces. Usually, the goal of an electron model is to explain known electron properties. This model was going further and predicting there should be previously unknown fundamental relationships between the electron’s electrostatic force and the electron’s gravitational force. This appears to be quantum gravity generated on the scale of electrons rather than the scale of black holes.</span><o:p></o:p></p><p class=MsoNormal style='margin-right:0in;background:white'><span style='font-size:14.0pt;color:#111111;background:white'> </span><o:p></o:p></p><p class=MsoNormal style='margin-right:0in;background:white'><span style='font-size:14.0pt;color:#111111;background:white'>These predictions have now been proven correct without requiring new experiments. The details of this model and the proofs of the predictions are in the technical paper titled:<i> </i><b>A quantum vacuum model unites an electron’s gravitational and electromagnetic forces</b><i>.</i> This paper is currently under review by a physics journal. The preprint is available at the link below: </span><span style='font-size:14.0pt;color:black'>It has received about 1400 “reads” on ResearchGate in about 3 months.</span><o:p></o:p></p><p class=MsoNormal style='margin-right:0in;background:white'><span style='font-size:14.0pt;color:black'> </span><o:p></o:p></p><p class=MsoNormal style='margin-right:0in;background:white'><span style='color:black'><a href="http://www.researchgate.net/publication/353049276" target="_blank"><span style='font-size:14.0pt;border:none windowtext 1.0pt;padding:0in'>www.researchgate.net/publication/353049276</span></a></span><o:p></o:p></p><p class=MsoNormal style='margin-right:0in;background:white'><span style='font-size:14.0pt;color:#111111;background:white'> </span><o:p></o:p></p><p class=MsoNormal style='margin-right:0in'><span style='font-size:14.0pt;color:#111111;background:white'> </span><o:p></o:p></p><p class=MsoNormal style='margin-right:0in'><span style='font-size:14.0pt;color:#111111;background:white'>John Macken</span><o:p></o:p></p><p class=MsoNormal style='margin-right:0in'><span style='font-size:14.0pt'> </span><o:p></o:p></p><p class=MsoNormal align=left style='margin-right:0in;text-align:left'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'><br><br><br></span><o:p></o:p></p><pre>_______________________________________________<o:p></o:p></pre><pre>If you no longer wish to receive communication from the Nature of Light and Particles General Discussion List at <a href="mailto:dudajar@gmail.com">dudajar@gmail.com</a><o:p></o:p></pre><pre><a href=<a href="http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/dudajar%40gmail.com?unsub=1&unsubconfirm=1">"http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/dudajar%40gmail.com?unsub=1&unsubconfirm=1"</a>><o:p></o:p></pre><pre>Click here to unsubscribe<o:p></o:p></pre><pre></a><o:p></o:p></pre></blockquote><pre>-- <o:p></o:p></pre><pre>dr Jarosław Duda<o:p></o:p></pre><pre>Institute of Computer Science and Computer Mathematics,<o:p></o:p></pre><pre>Jagiellonian University, Cracow, Poland<o:p></o:p></pre><pre><a href="http://th.if.uj.edu.pl/~dudaj/">http://th.if.uj.edu.pl/~dudaj/</a><o:p></o:p></pre></blockquote><pre>-- <o:p></o:p></pre><pre>dr Jarosław Duda<o:p></o:p></pre><pre>Institute of Computer Science and Computer Mathematics,<o:p></o:p></pre><pre>Jagiellonian University, Cracow, Poland<o:p></o:p></pre><pre><a href="http://th.if.uj.edu.pl/~dudaj/">http://th.if.uj.edu.pl/~dudaj/</a><o:p></o:p></pre></div></body></html>