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<p>Dear John,<br>
</p>
<p>Vacuum is, among others, a medium for interactions, e.g.
long-range: electromagnetism and gravity, the former has charge
quantization in Gauss law.<br>
</p>
<p>It seems there is also third long-range: quantum phase/pilot
wave, required for quantum phenomena like Mach-Zehnder
interference, produced due to de Broglie clock/zitterberwegung.</p>
<p><br>
</p>
<p>Wanting to understand vacuum, the simplest scenario seems pair
creation:</p>
<p>energy -> electron + positron, with 1/r Coulomb energy
dependence.</p>
<p>Charge quantization is constraint of Gauss law, which allows to
explain e.g. <b>why we cannot create half-electron this way?</b><br>
</p>
<p><br>
</p>
<p>Personally I know only this topological quantization mechanism -
making that Gauss law counts topological charge. Do you maybe have
any hint for an alternative?</p>
<p>Best,</p>
<p>Jarek</p>
<p>ps. Getting 1/r Coulomb energy dependence is nontrivial, but
realizable e.g. in liquid crystals. Below is field of minus-plus
pair of topological charges, integrating energy density of the
field, we get e.g. V(r)~1/r long-range interaction for such
charges:<br>
</p>
<p><img src="cid:part1.RmEOdHb0.5V3sRo0y@gmail.com" alt=""
width="671" height="153"></p>
<p><br>
</p>
<p><br>
</p>
<div class="moz-cite-prefix">W dniu 21.10.2021 o 20:36, John Macken
pisze:<br>
</div>
<blockquote type="cite"
cite="mid:00fc01d7c6aa$8dd1dd00$a9759700$@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"><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"
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 8:25 PM<br>
<b>To:</b> John Macken <a class="moz-txt-link-rfc2396E" href="mailto:john@macken.com"><john@macken.com></a>; Nature
of Light
<a class="moz-txt-link-rfc2396E" href="mailto:general@lists.natureoflightandparticles.org"><general@lists.natureoflightandparticles.org></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, 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 style="width:7.625in;height:.8645in"
id="Picture_x0020_2"
src="cid:part2.g09yoF1b.Nfnk0zJO@gmail.com" class=""
width="732" height="83"><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"
moz-do-not-send="true" class="moz-txt-link-freetext">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" 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">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" style="margin-right:0in;text-align:left"
align="left"><span style="font-size:14.0pt;color:#20188C"> </span><o:p></o:p></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><o:p></o:p></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><o:p></o:p></p>
<p class="MsoNormal" style="margin-right:0in;text-align:left"
align="left"><span style="font-size:14.0pt;color:#20188C"> </span><o:p></o:p></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. </span><o:p></o:p></p>
<p class="MsoNormal" style="margin-right:0in;text-align:left"
align="left"><span style="font-size:14.0pt;color:#20188C"> </span><o:p></o:p></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.</span><o:p></o:p></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. </span><o:p></o:p></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">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" 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. </span><o:p></o:p></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. </span><o:p></o:p></p>
<p class="MsoNormal" style="margin-right:0in;text-align:left"
align="left"><span style="font-size:14.0pt;color:#20188C"> </span><o:p></o:p></p>
<p class="MsoNormal" style="margin-right:0in;text-align:left"
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"
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 </span><a href="mailto:dudajar@gmail.com"
moz-do-not-send="true"><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"
moz-do-not-send="true"><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" moz-do-not-send="true"><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" 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:part3.DN49KbfD.FcghusBh@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>
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<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>
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<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>
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<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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