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<p>Dear John, <br>
</p>
<p>Thank you, this is the article I have looked through, but wasn't
able to find the details.</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:</p>
<p><img src="cid:part1.kYjjU8Ua.ca8e92Bp@gmail.com" alt=""
width="731" height="83"></p>
<p><br>
</p>
<p>> 2) All fundamental particles are modeled as rotating waves
with Planck length amplitude and ħ/2 angular momentum. <br>
</p>
<p>Sounds like fluxon magnetic field quantization - to take it to
point-like electric charge, we can use the above formula.<br>
</p>
<p><br>
</p>
<p>>The different fundamental particles have different rotation
rates, different energy and different radii. However, they all
have the same wave amplitude. <br>
</p>
<p>Sounds like de Broglie clock E = hbar omega = m c^2, confirmed
for electron:
<a class="moz-txt-link-freetext" href="https://link.springer.com/article/10.1007/s10701-008-9225-1">https://link.springer.com/article/10.1007/s10701-008-9225-1</a></p>
<p><br>
</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. <br>
</p>
<p>I don't understand - maybe you could show some formula like above
- showing Gauss law returning integer multiplicity of e?<br>
</p>
<p>Best regards,</p>
<p>Jarek</p>
<p><br>
</p>
<div class="moz-cite-prefix">On 20.10.2021 20:48, John Macken wrote:<br>
</div>
<blockquote type="cite"
cite="mid:009b01d7c5e3$1a3bbe50$4eb33af0$@macken.com">
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<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;text-align:left"
align="left"><span style="font-size:14.0pt;color:#20188C">You
ask, </span><span style="font-size:14.0pt;color:#20188C">“</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? <o:p></o:p></span></span></p>
<p class="MsoNormal" style="margin-right:0in;text-align:left"
align="left"><span style="font-size:14.0pt;color:#20188C"><o:p> </o:p></span></p>
<p class="MsoNormal" style="margin-right:0in;text-align:left"
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><span
style="font-size:14.0pt;color:#20188C"><o:p></o:p></span></p>
<p class="MsoNormal"
style="margin-right:0in;text-align:left;background:white"
align="left"><span style="color:black"><a
href="http://www.researchgate.net/publication/353049276"
target="_blank" moz-do-not-send="true"><span
style="font-size:10.5pt;font-family:inherit;border:none
windowtext 1.0pt;padding:0in">www.researchgate.net/publication/353049276</span></a></span><span
style="font-size:10.5pt;font-family:Roboto;color:#111111"><o:p></o:p></span></p>
<p class="MsoNormal" style="margin-right:0in;text-align:left"
align="left"><span style="font-size:14.0pt;color:#20188C"><o:p> </o:p></span></p>
<p class="MsoNormal" style="margin-right:0in;text-align:left"
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. <o:p></o:p></span></p>
<p class="MsoNormal" style="margin-right:0in;text-align:left"
align="left"><span style="font-size:14.0pt;color:#20188C"><o:p> </o:p></span></p>
<p class="MsoNormal" style="margin-right:0in;text-align:left"
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.<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-right:0in;text-align:left"
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. <o:p></o:p></span></p>
<p class="MsoNormal" style="margin-right:0in;text-align:left"
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;font-family:"Cambria
Math",serif;color:#20188C">ħ</span><span
style="font-size:14.0pt;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. <o:p></o:p></span></p>
<p class="MsoNormal" style="margin-right:0in;text-align:left"
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. <o:p></o:p></span></p>
<p class="MsoNormal" style="margin-right:0in;text-align:left"
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.
<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-right:0in;text-align:left"
align="left"><span style="font-size:14.0pt;color:#20188C"><o:p> </o:p></span></p>
<p class="MsoNormal" style="margin-right:0in;text-align:left"
align="left"><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>
<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"
style="margin-right:0in;text-align:left" 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 <a class="moz-txt-link-rfc2396E" href="mailto:dudajar@gmail.com"><dudajar@gmail.com></a> <br>
<b>Sent:</b> Wednesday, October 20, 2021 1:24 AM<br>
<b>To:</b> <a class="moz-txt-link-abbreviated" href="mailto:general@lists.natureoflightandparticles.org">general@lists.natureoflightandparticles.org</a>;
<a class="moz-txt-link-abbreviated" href="mailto:john@macken.com">john@macken.com</a><br>
<b>Subject:</b> Re: [General] Electron's Forces<o:p></o:p></span></p>
</div>
</div>
<p class="MsoNormal" style="margin-right:0in;text-align:left"
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"
moz-do-not-send="true" class="moz-txt-link-freetext">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"
moz-do-not-send="true" class="moz-txt-link-freetext">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 style="width:6.1875in;height:2.2083in"
id="Picture_x0020_1"
src="cid:part2.qXY6V2j7.4jwTtRw4@gmail.com" class=""
width="594" height="212" border="0"><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" moz-do-not-send="true"><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" style="margin-right:0in;text-align:left"
align="left"><span
style="font-size:11.0pt;font-family:"Calibri",sans-serif"><br>
<br>
<o:p></o:p></span></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" moz-do-not-send="true" class="moz-txt-link-freetext">dudajar@gmail.com</a><o:p></o:p></pre>
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<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/" moz-do-not-send="true" class="moz-txt-link-freetext">http://th.if.uj.edu.pl/~dudaj/</a><o:p></o:p></pre>
</div>
</blockquote>
<pre class="moz-signature" cols="72">--
dr Jarosław Duda
Institute of Computer Science and Computer Mathematics,
Jagiellonian University, Cracow, Poland
<a class="moz-txt-link-freetext" href="http://th.if.uj.edu.pl/~dudaj/">http://th.if.uj.edu.pl/~dudaj/</a></pre>
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