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<div style="direction: ltr;font-family: Tahoma;color: #000000;font-size: 10pt;">Hi Chip and Grahame,<br>
<br>
Yes, it does take two photons. In fact though they must have the same spin (or helicity. As they are travelling in opposite directions, this then cancels in the spin zero creation of an electron positron pair.<br>
<br>
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<p class="MsoNormal"><span style="mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman"" lang="EN-US">YT you Grahame for introducing a dose of reality into the argument and asking for references. You are, as far as I know, correct
in what you say below. <br>
<br>
If there were two parts to the photon then one would see that as structure in the scattering at energies commensurate with the photon energy. This is not observed. This lack of observation of structure extends even above the electron-positron (and, as far as
is known, the muon-antimuon) pair production thresholds, at least if one restricts oneself to spin-zero scattering (spin one has three photons, and hence the complications of interpretation of a three body problem). One needs to access hadronic energy levels
before one sees structure corresponding to little hard bits of stuff on some sort of springs (forces between the bits) inside any “elementary” particles. If anyone knows differently, proper references are required.<br>
<br>
Likewise, reversing the process, one does not observe two (or more) bits within the electron (or muon), so any models positing this are, by the scientific method, simply not correct. The "two bit" hypothesis is simply contradicted by experiment. Sorry.<br>
<br>
Likewise, Wolf's earlier comment is apposite, if there are two (or more) bits,<span style="mso-spacerun:yes">
</span>they need forces holding them together. If one is going to describe this sort of stuff without just hand-waving you are anyway going to need a theory (with the bits and with the forces between them) that can be subject to test. Theories are things like
the Maxwell equations or Newtons laws, with differential equations, Lagrangian theories with contributions to action, A Hamiltonian equation, with contributions to the energy, or tensor equations of space, time and curvature, as in general relativity. This
was what was missing in Martin and my original conjecture about the electron nature and why both he and I are investigating possible extensions to theory, I in the set of differential equations posited in 2014 at Marseilles and 2015 at SPIE (and still under
development), he in extending the Bateman method in electromagnetism (amongst other things). If we want to get serious we need to move to developing theories testable by experiment, otherwise we could make up and talk about whatever we like.<br>
<br>
This is what makes solving the puzzle so interesting: there is a lot that we know about the things we are trying to describe. Any theories we come up must be consistent with known experimental facts if they are to describe reality as it is observed. Self-evidently.<br>
<br>
Regards, JGW.</span></p>
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<div id="divRpF534496" style="direction: ltr;"><font size="2" color="#000000" face="Tahoma"><b>From:</b> General [general-bounces+john.williamson=glasgow.ac.uk@lists.natureoflightandparticles.org] on behalf of Chip Akins [chipakins@gmail.com]<br>
<b>Sent:</b> Wednesday, October 11, 2017 12:55 PM<br>
<b>To:</b> 'Nature of Light and Particles - General Discussion'<br>
<b>Subject:</b> Re: [General] Fw: A composite electron?<br>
</font><br>
</div>
<div></div>
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<p class="MsoNormal"><span style="color:black">Hi Grahame</span></p>
<p class="MsoNormal"><span style="color:black"> </span></p>
<p class="MsoNormal"><span style="color:black">I think you are may be correct, in that it may take two photons to make an electron positron pair. It is clear that it would take two photons of .511MeV at least.</span></p>
<p class="MsoNormal"><span style="color:black"> </span></p>
<p class="MsoNormal"><span style="color:black">But due to the charge and spin considerations, comparing photons to electrons/positrons, it still seems that one “polarity” of each of the photons is used to form one fermion.</span></p>
<p class="MsoNormal"><span style="color:black"> </span></p>
<p class="MsoNormal"><span style="color:black">This seems to be the simplest way to explain both spin and charge of the fermions from a causal basis.</span></p>
<p class="MsoNormal"><span style="color:black"> </span></p>
<p class="MsoNormal"><span style="color:black">Chip</span></p>
<p class="MsoNormal"><span style="color:black"> </span></p>
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<p class="MsoNormal"><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"> General [mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org]
<b>On Behalf Of </b>Dr Grahame Blackwell<br>
<b>Sent:</b> Tuesday, October 10, 2017 4:49 PM<br>
<b>To:</b> Nature of Light and Particles - General Discussion <general@lists.natureoflightandparticles.org><br>
<b>Subject:</b> [General] Fw: A composite electron?</span></p>
</div>
</div>
<p class="MsoNormal"> </p>
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<p class="MsoNormal"><span style="font-size:10.0pt; font-family:"Arial",sans-serif; color:navy">Hi Chip & All,</span></p>
</div>
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<p class="MsoNormal"> </p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt; font-family:"Arial",sans-serif; color:navy">[repeat as my first send doesn't appear to have arrived - apologies if any duplication]</span></p>
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<p class="MsoNormal"> </p>
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<p class="MsoNormal"><span style="font-size:10.0pt; font-family:"Arial",sans-serif; color:navy">Can somebody point me in the direction of experimental evidence of a single photon being split into two parts to form an electron-positron pair? I was under the
impression that such pair production takes an opposing pair of photons of requisite energy.</span></p>
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<p class="MsoNormal"> </p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt; font-family:"Arial",sans-serif; color:navy">It's my understanding that the history of this discovery goes back to Lev Landau's seminal experiments in 1934 (with his student Evgeny Lifshitz) where he identified
the fact that particle collider experiments producing such pairs always hinged on release of high-energy photons that then collided to form those pairs - collisions of photons, in my understanding, always involve more than one photon. In December of that
year - presumably based on this finding - Breit & Wheeler defined their well-documented process, which again involves collisions between opposing photons.</span></p>
</div>
<div>
<p class="MsoNormal"> </p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:10.0pt; font-family:"Arial",sans-serif; color:navy">The only practical implementation, to my knowledge, of a process whereby e-/e+ pairs have been produced from photons alone was the SLAC experiment in 1997, where
a 'Multiphoton Breit-Wheeler Process' was implemented, successively ramping up the energies of photons in a laser cavity to the point where, after around four collisions, they reached the required energies to form e-/e+ pairs on further collision with bombarding
photons.</span></p>
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<p class="MsoNormal"> </p>
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<p class="MsoNormal"><span style="font-size:10.0pt; font-family:"Arial",sans-serif; color:navy">Clearly it's possible for a photon to be split - Compton Scattering is a practical illustration in which part of a photon's energy is absorbed by a (pre-existent)
material particle to give it momentum and the rest of that photon continues on its way with reduced frequency/energy. However I know of NO situation in which a single photon has been transformed into a particle-antiparticle pair, as is being suggested below.</span></p>
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<p class="MsoNormal"> </p>
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<p class="MsoNormal"><span style="font-size:10.0pt; font-family:"Arial",sans-serif; color:navy">[As a point of detail, I find it hard to envisage how linear momentum, angular momentum and energy could all be conserved by such a happening.]</span></p>
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<p class="MsoNormal"> </p>
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<p class="MsoNormal"><span style="font-size:10.0pt; font-family:"Arial",sans-serif; color:navy">Those who are happily discussing it as if it's 'de facto', I'd be really glad of your references for same.</span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt; font-family:"Arial",sans-serif; color:navy">If no such (reliable) references exist, I'd suggest that to proceed on the basis that it IS a reality would be questionable, to say the least.</span></p>
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<p class="MsoNormal"> </p>
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<p class="MsoNormal"><span style="font-size:10.0pt; font-family:"Arial",sans-serif; color:navy">[For avoidance of doubt: Colliding two opposing photons to thus form two particles is most assuredly NOT "splitting a photon", in my book - though it IS re-apportioning
the energies & momenta of those two photons to re-cast them as particles.]</span></p>
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<p class="MsoNormal"> </p>
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<p class="MsoNormal"><span style="font-size:10.0pt; font-family:"Arial",sans-serif; color:navy">Thanks,</span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt; font-family:"Arial",sans-serif; color:navy">Grahame</span></p>
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<blockquote style="border:none; border-left:solid navy 1.5pt; padding:0in 0in 0in 4.0pt; margin-left:3.75pt; margin-top:5.0pt; margin-right:0in; margin-bottom:5.0pt">
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<p class="MsoNormal"><span style="font-size:10.0pt; font-family:"Arial",sans-serif">----- Original Message -----
</span></p>
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<div>
<p class="MsoNormal" style="background:#E4E4E4"><b><span style="font-size:10.0pt; font-family:"Arial",sans-serif">From:</span></b><span style="font-size:10.0pt; font-family:"Arial",sans-serif">
</span><a href="mailto:chipakins@gmail.com" title="chipakins@gmail.com" target="_blank"><span style="font-size:10.0pt; font-family:"Arial",sans-serif">Chip Akins</span></a><span style="font-size:10.0pt; font-family:"Arial",sans-serif">
</span></p>
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<div>
<p class="MsoNormal"><b><span style="font-size:10.0pt; font-family:"Arial",sans-serif">To:</span></b><span style="font-size:10.0pt; font-family:"Arial",sans-serif">
</span><a href="mailto:general@lists.natureoflightandparticles.org" title="general@lists.natureoflightandparticles.org" target="_blank"><span style="font-size:10.0pt; font-family:"Arial",sans-serif">'Nature of Light and Particles - General Discussion'</span></a><span style="font-size:10.0pt; font-family:"Arial",sans-serif">
</span></p>
</div>
<div>
<p class="MsoNormal"><b><span style="font-size:10.0pt; font-family:"Arial",sans-serif">Sent:</span></b><span style="font-size:10.0pt; font-family:"Arial",sans-serif"> Tuesday, October 10, 2017 12:22 PM</span></p>
</div>
<div>
<p class="MsoNormal"><b><span style="font-size:10.0pt; font-family:"Arial",sans-serif">Subject:</span></b><span style="font-size:10.0pt; font-family:"Arial",sans-serif"> Re: [General] A composite electron?</span></p>
</div>
<div>
<p class="MsoNormal"> </p>
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<p class="MsoNormal"><span style="color:black">Hi Richard</span></p>
<p class="MsoNormal"><span style="color:black"> </span></p>
<p class="MsoNormal"><span style="color:black">Exactly! The mere act of splitting a photon (with the requisite energy) causes each “half photon” to confine itself and the half photons become an electron/positron pair.</span></p>
<p class="MsoNormal"><span style="color:black"> </span></p>
<p class="MsoNormal"><span style="color:black">Andrew suggested in the SPIE conference we attended, that the electron was half a photon (a rectified photon is what I think he said).</span></p>
<p class="MsoNormal"><span style="color:black"> </span></p>
<p class="MsoNormal"><span style="color:black">This is part of the concept I have been trying to convey. The rest of the concept is that space is composed in a way which makes this possible. A two component tension medium. This scenario creates quantized
electric charge, as we observe. Creates mass, as we observe. Creates the spin we observe for photon and electron. Makes more energetic particles smaller particles, as we observe. And agrees with experiment regarding the velocity of electric charge, which
is much easier to conduct and less ambiguous than the current LIGO findings. </span>
</p>
<p class="MsoNormal"><span style="color:black"> </span></p>
<p class="MsoNormal"><span style="color:black">Regarding LIGO and gravity: Binary pulsars have been studied for some time. Their orbits simply do not deteriorate at the rate they would if gravity propagated at light speed. Many, who firmly believe in the
postulate of relativity that nothing can travel faster than c, have attempted to explain this away. But I have found none of these explanations to be plausible (in my opinion). The simplest explanation is the gravity is faster than light.</span></p>
<p class="MsoNormal"><span style="color:black"> </span></p>
<p class="MsoNormal"><span style="color:black">That does not mean that it is impossible for two massive bodies to generate a wave which has a phase velocity near or at light speed. That is quite possible, and perhaps even probable.</span></p>
<p class="MsoNormal"><span style="color:black"> </span></p>
<p class="MsoNormal"><span style="color:black">But back to the photon and electron. I think you are on the right track with this.</span></p>
<p class="MsoNormal"><span style="color:black"> </span></p>
<p class="MsoNormal"><span style="color:black">Chip</span></p>
<p class="MsoNormal"><span style="color:black"> </span></p>
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<p class="MsoNormal"><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"> General [</span><a href="mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org" target="_blank"><span style="font-size:11.0pt; font-family:"Calibri",sans-serif">mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org</span></a><span style="font-size:11.0pt; font-family:"Calibri",sans-serif">]
<b>On Behalf Of </b>Richard Gauthier<br>
<b>Sent:</b> Monday, October 09, 2017 11:59 PM<br>
<b>To:</b> Andrew Meulenberg <</span><a href="mailto:mules333@gmail.com" target="_blank"><span style="font-size:11.0pt; font-family:"Calibri",sans-serif">mules333@gmail.com</span></a><span style="font-size:11.0pt; font-family:"Calibri",sans-serif">><br>
<b>Cc:</b> Nature of Light and Particles - General Discussion <</span><a href="mailto:general@lists.natureoflightandparticles.org" target="_blank"><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">>;
Martin Rivas <</span><a href="mailto:martin.rivas@ehu.es" target="_blank"><span style="font-size:11.0pt; font-family:"Calibri",sans-serif">martin.rivas@ehu.es</span></a><span style="font-size:11.0pt; font-family:"Calibri",sans-serif">>; David Hestenes <</span><a href="mailto:Hestenes@asu.edu" target="_blank"><span style="font-size:11.0pt; font-family:"Calibri",sans-serif">Hestenes@asu.edu</span></a><span style="font-size:11.0pt; font-family:"Calibri",sans-serif">>;
robert hudgins <</span><a href="mailto:hudginswr@msn.com" target="_blank"><span style="font-size:11.0pt; font-family:"Calibri",sans-serif">hudginswr@msn.com</span></a><span style="font-size:11.0pt; font-family:"Calibri",sans-serif">><br>
<b>Subject:</b> Re: [General] A composite electron?</span></p>
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<p class="MsoNormal"> </p>
<p class="MsoNormal">Hello Andrew and all,</p>
<div>
<p class="MsoNormal"> </p>
<div>
<p class="MsoNormal"> De Broglie proposed his 2 spin-1/2 particle photon idea (not sure if he also had a model for this) in the early 30’s in his book "La Physique Nouvelle et les Quanta” (available free at
<a href="http://archive.org" target="_blank">archive.org</a>) and in English translation as "<a href="https://www.amazon.com/gp/product/B0007G309U/ref=oh_aui_detailpage_o00_s00?ie=UTF8&psc=1" target="_blank"><span style="font-size:10.0pt; font-family:"Arial",sans-serif; color:#0066C0; text-decoration:none">The
revolution in physics: A non-mathematical survey of quanta</span></a>”, available at <a href="http://Amazon.com" target="_blank">Amazon.com</a>. With the help of Google Translate (slightly edited) I give below what de Broglle wrote on this (p. 277-278 in the
French edition):</p>
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<p class="MsoNormal"> </p>
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<pre><span style="font-family:inherit; color:#212121" lang="EN">From these general remarks, we have concluded that, in order to constitute a theory of the photon, we must first use a relativistic form of wave mechanics comprising elements of symmetry due to polarization and, secondly, introduce something to differentiate the photon from the other particles. The first part of this program is realized immediately by using the theory of the electron of Dirac that we studied previously. We know that Dirac's theory is relativistic and that it contains elements of symmetry with a marked kinship with those of the polarization of light. Nevertheless, it was not sufficient to suppose that the photon is a particle of negligible mass obeying the equations of the Dirac theory, for the model of the photon thus obtained would have, so to speak, only half the symmetry of the real photon; moreover, it would, like the electron, apparently obey Fermi statistics and could not be annihilated in the photoelectric effect. We need something more.</span></pre>
<pre><span style="font-family:inherit; color:#212121" lang="EN">This something more, we tried to introduce on the assumption that the photon is constituted not of a Dirac particle, but of two. It can be realized that these two particles or half-photons must be complementary to each other in the same sense as the positive electron is complementary to the negative electron in Dirac</span><span style="font-family:"Times New Roman",serif; color:#212121">’</span><span style="font-family:inherit; color:#212121" lang="EN">s hole theory. Such a pair of complementary particles is liable to annihilate itself by contact with matter and yielding all its energy, and this perfectly accounts for the chracteristics of the photoelectric effect. Moreover, the photon then being constituted by two elementary particles with spin h/4pi must obey Bose-Einstein statistics, as required by the accuracy of Planck's law for black-body radiation. Finally, this photon model makes it possible to define an electromagnetic field linked to the probability of annihilation of the photon, a field which obeys Maxwell</span><span style="font-family:"Times New Roman",serif; color:#212121">’</span><span style="font-family:inherit; color:#212121" lang="EN">s equations and possesses all the characteristics of the electromagnetic light wave. Although it is still premature to pronounce definitively on the value of this attempt, it is indisputable that it leads to interesting results and that it heavily draws attention to the properties of symmetry of complementary particles whose existence, suggested by the Dirac theory, was verified by the discovery of the positive electron.</span></pre>
<pre> </pre>
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<div>
<p class="MsoNormal">So what I have called in the past a spin-1/2 charged photon I now think should be called a spin-1/2 charged half-photon, since two of them (one positive and one negative) would move in a double helix to form a spin 1 photon which helps
generate electromagnetic waves. This renaming should also solve the semantic problem of the name of this superluminal charged spin-1/2 particle , which I would no longer consider to be a variety of photon, since it would take two of them to make a photon.
Such a photon model could easily generate an electron-positron pair when near an atomic nucleus that absorbs excess momentum (creating two rest masses) and splits a sufficiently energetic photon into an e-p pair. Comments? </p>
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<p class="MsoNormal">On Oct 2, 2017, at 5:20 AM, Andrew Meulenberg <<a href="mailto:mules333@gmail.com" target="_blank">mules333@gmail.com</a>> wrote:</p>
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<p class="MsoNormal" style="margin-bottom:12.0pt">Dear Folks,</p>
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<p class="MsoNormal">The composite electron model has a history of which I was not aware. From mid-right column of page 4 of (free access):</p>
<div>
<div>
<p class="MsoNormal" style="margin-bottom:12.0pt"><a href="https://www.omicsonline.org/open-access/" target="_blank">https://www.omicsonline.org/open-access/</a><b>the-last-challenge-of-modern-physics</b>-2090-0902-1000217.php?aid=87682</p>
<div style="margin-left:30.0pt">
<p class="MsoNormal" style="margin-bottom:12.0pt"><span class="gmail-fontstyle0">Louis de Broglie elaborated a most promising hypothesis to help</span><br>
<span class="gmail-fontstyle0">explain these special characteristics of the photon [7]. Having analyzed</span><br>
<span class="gmail-fontstyle0">them in light of the verifed aspects of the various pertaining theories,</span><br>
<span class="gmail-fontstyle0">he eventually concluded that the only way for an electromagnetic</span><br>
<span class="gmail-fontstyle0">photon to satisfy at the same time Bose-Einstein's statistic and Planck's</span><br>
<span class="gmail-fontstyle0">law, and to perfectly explain the photoelectric e</span><span class="gmail-fontstyle0"><span style="font-family:"Cambria Math",serif">ff</span>ect while obeying</span><br>
<span class="gmail-fontstyle0">Maxwell's equations and conforming to the symmetry property of</span><br>
<span class="gmail-fontstyle0">complementary corpuscles in Dirac's Hole Theory, would be for it to</span><br>
<span class="gmail-fontstyle0">be made not of one corpuscle, but of two corpuscles, or half-photons,</span><br>
<span class="gmail-fontstyle0">that would be complementary, like the electron is complementary to</span><br>
<span class="gmail-fontstyle0">the positron in Dirac's Hole Theory [15].</span><br>
<br>
<span class="gmail-fontstyle0">This conclusion mandates the association of charges (possibly</span><br>
<span class="gmail-fontstyle0">unsigned) to each half-photon, and consequently to the photon itself, ...</span>
<br>
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<p class="MsoNormal"><span class="gmail-fontstyle0">7. Michaud A (2016) On De Broglie’s Double-particle Photon Hypothesis. J Phys</span><br>
<span class="gmail-fontstyle0">Math 7: 153.</span> <br>
<br>
<span class="gmail-fontstyle0">15. De Broglie L (1937) New physics and quanta, Flammarion, 2</span><span class="gmail-fontstyle0"><span style="font-size:4.0pt">nd
</span>1993 new</span><br>
<span class="gmail-fontstyle0">Preface.</span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt">This would imply that, historically, the Nature of Light is even more curious than most of us thought.</p>
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<p class="MsoNormal">Andrew M.</p>
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<p class="MsoNormal">On Mon, Sep 25, 2017 at 5:24 PM, Richard Gauthier <<a href="mailto:richgauthier@gmail.com" target="_blank">richgauthier@gmail.com</a>> wrote:</p>
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<p class="MsoNormal" style="">Hello Martin (and all),</p>
<p class="MsoNormal" style=""> Thank you for this summary of your CC-CM approach to a moving particle such as an electron. My approach to modeling an electron is quite similar to yours, except that in my approach the CC (center of charge) is the position
of a light-speed spin-1/2 charged quantum particle that I call a choton. It is in circular motion in a resting electron and moves helically in a moving electron. The linear momentum of the choton in a resting electron is Po=mc=2.73x10^-22 kg m/s = 0.511 MeV/c
(and its energy is mc^2= 0.511 MeV) and this momentum mc circles with radius Ro= L-compton/4pi = hbar/2mc = 1.93x10^-13m at the zitterbewegung frequency f-zitt=2mc^2/h. The choton’s average position as the choton circles around is what you call the CM (center
of mass). In a resting electron the choton (at the position CC) and the CM are separated by the distance Ro, with the choton circling around its CM at the zitter frequency. Due to its circular motion with its changing momentum direction, the choton appears
to be acted on by a centripetal force Fc=dp/dt = w Po = w-zitt Po = 0.424 N , where w-zitt (omega-zitt) = 2 mc^2/hbar = 1.55 x 10^21 rad/sec. The choton’s centripetal acceleration A-cent in this circular motion in a resting electron is A-cent = r w^2 = Ro
(w-zitt)^2 = 4.66x10^29 m/s^2. My article “Derivation of the inertial mass m=Eo/c^2 of an electron composed of a circling spin-1/2 charge photon” at <a href="https://richardgauthier.academia.edu/research%23papers" target="_blank">https://richardgauthier.academia.edu/research#papers</a> (4<sup>th</sup> article)
also shows that the above circling choton (spin-1/2 charged photon) has an inertial mass m = Eo/c^2 = 0.511MeV/c^2 derived from its circling momentum mc=Eo/c.</p>
<p class="MsoNormal" style=""> When no external force (besides the apparent 0.424 N central force) acts on the choton, the moving electron model moves longitudinally with velocity
<b>v</b> and with momentum <b>p</b>=gamma m<b>v</b>. The choton circulates with its longitudinal momentum component P-long = gamma mv, which is the electron’s linear momentum, and with a transverse momentum component P-trans = Po = mc. Using the Pythagorean
equation, this gives the choton’s total momentum directed along its helical trajectory as P-total^2 = P-long^2 + P-trans^2 = (gamma mv)^2 + (mc)^2 = (gamma mc)^2, or P-total = gamma mc. The choton’s corresponding total energy is E-total = P-total c = gamma
mc^2, which is the same as a relativistic electron’s total energy. </p>
<h4 style="margin-right:0in; margin-bottom:9.0pt; margin-left:0in"><span style="font-weight:normal"> When an external electric field
</span>E<span style="font-weight:normal"> acts on the circulating choton, the choton (with its inertial mass m=0.511 MeV/c^2) is accelerated by a net force
</span>Fnet<span style="font-weight:normal"> equal to the rapidly rotating centripetal force
</span>Fc<span style="font-weight:normal">= 0.424 N plus the external force </span>
F<span style="font-weight:normal">=-e</span>E. <span style="font-weight:normal">The total force on the choton is
</span>Fnet<span style="font-weight:normal"> = </span>Fc<span style="font-weight:normal"> + e</span>E
<span style="font-weight:normal">= m </span>a-total <span style="font-weight:normal">
in the non-relativistic case or </span>Fnet<span style="font-weight:normal"> = d</span>p-total<span style="font-weight:normal">/dt in the relativistic case. The choton’s helical motion (the motion of the CC) will be changed by the external electric field
</span>E <span style="font-weight:normal">acting on the choton, and the choton’s CM (average position) will be affected accordingly, and move in the direction of the applied external force
</span>E<span style="font-weight:normal">.</span></h4>
<h4 style="margin-right:0in; margin-bottom:9.0pt; margin-left:0in"><span style="font-weight:normal"> There are also quantum mechanical features of the above motion. As the choton changes its helical trajectory due to the applied electric field
</span>E<span style="font-weight:normal">, the choton’s transverse momentum component P-trans = mc adjusts its orientation so that P-trans continues to be transverse to the choton’s new longitudinal motion with its new longitudinal component velocity
</span>v’ <span style="font-weight:normal">(the new electron velocity). In this way the calculated spin of the choton electron model continues to be Ro x Po = hbar/2 and the Pythogorean momentum relation continues to be P-total^2 = P-long^2 + P-trans^2 (which
is mathematically equivalent to the relativistic energy-momentum equation E^2 = p^2 c^2 +m^2 c4). Further information on the spin-1/2 charged photon model is at “Electron’s are spin 1/2 charged photons generating the de Broglie wavelength” at
</span><a href="https://richardgauthier.academia.edu/research#papers" target="_blank"><span style="font-weight:normal">https://richardgauthier.academia.edu/research#papers</span></a><span style="font-weight:normal"> (19<sup>th</sup> article).</span></h4>
<h4 style="margin-right:0in; margin-bottom:9.0pt; margin-left:0in"><span style="font-weight:normal"> In summary, the choton electron model does not need to be a rigid body to maintain the relation between CC and CM. All forces (including the apparent centripetal
force F-cent) act on the choton (at the CC), which has its own inertial mass, producing the choton’s acceleration and average center of mass position CM. </span></h4>
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<p class="MsoNormal">with warm regards,</p>
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<p class="MsoNormal"> Richard</p>
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