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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='color:black'>Hi Richard<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>So it is a bit more difficult to visualize exactly what is going on from the graphics with velocity.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>We increase the velocity is in steps from <b>zero through 0.9988c.</b><o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>From the Z axis the illustration looks like:<o:p></o:p></span></p><p class=MsoNormal><img width=418 height=427 id="Picture_x0020_1" src="cid:image001.jpg@01D093A5.7DFD17D0"><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Showing the reduced radius with velocity.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>But when we look at the model slightly off axis (Z axis) we see this:<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><img width=859 height=711 id="Picture_x0020_3" src="cid:image002.jpg@01D093A5.7DFD17D0"><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>So this is a set of nested electron models with different velocities, each starting from the same point (upper right of the illustration). These are drawn from an external observers frame and are not shown in the electron’s reference frame. <o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>In the electron’s reference frame we would see closure to the trajectory, but in this reference frame, the trajectory (since it is moving) is not closed.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Chip<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><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><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>Richard Gauthier<br><b>Sent:</b> Thursday, May 21, 2015 6:29 AM<br><b>To:</b> Nature of Light and Particles - General Discussion<br><b>Subject:</b> Re: [General] Electron Torus<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal>Chip,<o:p></o:p></p></div><div><p class=MsoNormal> Please correct a couple of typos in my last email. The TEQ (transluminal energy quantum) moves on the surface of a torus, not a helix. Also the first helical radius mentioned should have been Ro sqrt(2) = 1.414 Ro , not Ro sqrt(2)/2 = 1.414 Ro since sort(2)/2 = 0.707 not 1.414 . Thanks.<o:p></o:p></p></div><div><p class=MsoNormal> Richard<o:p></o:p></p></div><p class=MsoNormal><o:p> </o:p></p><div><blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><div><p class=MsoNormal>On May 20, 2015, at 6:42 PM, Richard Gauthier <<a href="mailto:richgauthier@gmail.com">richgauthier@gmail.com</a>> wrote:<o:p></o:p></p></div><p class=MsoNormal><o:p> </o:p></p><div><div><p class=MsoNormal>Chip,<o:p></o:p></p><div><p class=MsoNormal> Nice graphics!<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal> Shouldn’t the electric field lines of an electron at some distance from the electron model be pointing inward linearly towards the electron from infinity on all sides, since the electron's electric field (due to its electric charge) falls off as 1/r^2 . I don’t understand why the electric field lines appear closed in your diagrams.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal> In my original resting electron model the TEQ was a circulating negative electric charge which circulated on the surface of a helix. I called the circulating TEQ a photon-like object since it was similar to my TEQ model of a photon. I was assuming at that time that the photon in my resting electron model had spin 1, even though I had adjusted the helical radius so that the circulating TEQ generated the magnetic moment of the electron of 1 Bohr magneton, requiring a helical radius for the TEQ of Ro sqrt(2)/2 = 1.414 Ro which created the spindle torus in my model . So this was actually neither a spin 1 photon (whose radius for a resting electron would have been 2Ro, or a spin 1/2 photon, whose radius for a resting electron would be Ro, as in the 3D models that you and I generated from the moving electron equations I proposed. Since I currently prefer the model of an electron composed of a spin 1/2 circulating photon, this doesn’t generate the electron’s magnetic moment of 1 Bohr magneton. But it generates a magnetic moment more than 1/2 Bohr magneton which would be produced by a charge circulating at light speed in a simple double loop of radius Ro. I haven’t done the calculation for the magnetic moment generated by my spin 1/2 photon model of the electron, but I suspect that it would be 0.707 Bohr magneton (just a guess at this point). The calculation of this magnetic moment from the TEQ trajectory equations for a charged TEQ in the spin 1/2 photon model is relatively straightforward though.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal> By the way, have you looked at the side view of the actual TEQ trajectory at various values of v/c of the electron in the spin 1/2 photon moving-electron model that I proposed (and that you programmed and graphed in 3D to show how the model size changes as 1/gamma at various values of v/c)? The side view of the TEQ trajectory for a moving electron contains some surprises, at least for me. I thought that at high values of v/c (say 0.99 or 0.999) the TEQ would just appear from the side view to rotate helically around its reducing and increasingly more linear helical trajectory (whose trajectory reduces as 1/(gamma^2), with the TEQ’s helical radius reducing as 1/gamma. But that’s apparently not what happens. Could you check this with your 3D program? <o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal> Richard<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><div><blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><div><p class=MsoNormal>On May 19, 2015, at 8:45 AM, Chip Akins <<a href="mailto:chipakins@gmail.com">chipakins@gmail.com</a>> wrote:<o:p></o:p></p></div><p class=MsoNormal><o:p> </o:p></p><div><div><p class=MsoNormal>Hi Richard<o:p></o:p></p></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><p class=MsoNormal>If your spin 1 photon model of the electron is similar to John W and Martin’s model in that the field lines always orient with the negative end outwards (providing for charge) the estimated field distribution is similar to this illustration. (Equatorial View)<o:p></o:p></p></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><p class=MsoNormal><image001.jpg><o:p></o:p></p></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><p class=MsoNormal>(Top View from Z axis)<o:p></o:p></p></div><div><p class=MsoNormal><image002.jpg><o:p></o:p></p></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><p class=MsoNormal>(45 degree elevation view)<o:p></o:p></p></div><div><p class=MsoNormal><image004.jpg><o:p></o:p></p></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><p class=MsoNormal>Red lines represent negative ends of field lines, Blue lines represent positive, black is the transport radius, faint green line is one circulation at the transport radius.<o:p></o:p></p></div><div><p class=MsoNormal>Photon field amplitude is shown as a cosine function of wavelength/2.<o:p></o:p></p></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><p class=MsoNormal>Chip<o:p></o:p></p></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><div><p class=MsoNormal><b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>From:</span></b><span class=apple-converted-space><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> </span></span><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>General [<a href="mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org">mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org</a>]<span class=apple-converted-space> </span><b>On Behalf Of<span class=apple-converted-space> </span></b>Richard Gauthier<br><b>Sent:</b><span class=apple-converted-space> </span>Tuesday, May 05, 2015 10:06 AM<br><b>To:</b><span class=apple-converted-space> </span>Nature of Light and Particles - General Discussion<br><b>Subject:</b><span class=apple-converted-space> </span>Re: [General] Electron Torus</span><o:p></o:p></p></div></div></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><p class=MsoNormal>Chip,<o:p></o:p></p></div><div><div><p class=MsoNormal> Perfect! It would also be good to have the pair of tori seen an an angle from above their ‘equator’ to get a more 3-D quality.<o:p></o:p></p></div></div><div><div><p class=MsoNormal> Richard<o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div><div><blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><div><div><p class=MsoNormal>On May 5, 2015, at 6:07 AM, Chip Akins <<a href="mailto:chipakins@gmail.com"><span style='color:purple'>chipakins@gmail.com</span></a>> wrote:<o:p></o:p></p></div></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><div><div><p class=MsoNormal>Hi Richard<o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal>How do these look?<o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal><image003.png><o:p></o:p></p></div></div><div><div><p class=MsoNormal><image001.jpg><o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal>Chip<o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal><b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>From:</span></b><span class=apple-converted-space><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> </span></span><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>General [<a href="mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org"><span style='color:purple'>mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org</span></a>]<span class=apple-converted-space> </span><b>On Behalf Of<span class=apple-converted-space> </span></b>Richard Gauthier<br><b>Sent:</b><span class=apple-converted-space> </span>Monday, May 04, 2015 1:18 PM<br><b>To:</b><span class=apple-converted-space> </span>Nature of Light and Particles - General Discussion<br><b>Subject:</b><span class=apple-converted-space> </span>Re: [General] Electron Torus</span><o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><div><p class=MsoNormal>Hi Chip,<o:p></o:p></p></div></div><div><div><div><p class=MsoNormal> The radius of the circle in the horn torus (spin 1/2 photon model) should visually be (since it is actually) 1/2 of the radius of the circle in the spindle torus (spin 1 photon model) -- the spin 1/2 photon model is smaller than the spin 1 photon model. Thanks! And could you perhaps show the energy quantum trajectory in a different color that the torus background so the trajectory stands out better?<o:p></o:p></p></div></div></div><div><div><div><p class=MsoNormal> Richard<o:p></o:p></p></div></div></div></div><div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><div><p class=MsoNormal>On Mon, May 4, 2015 at 10:42 AM, Chip Akins <<a href="mailto:chipakins@gmail.com" target="_blank"><span style='color:purple'>chipakins@gmail.com</span></a>> wrote:<o:p></o:p></p></div></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0in;margin-bottom:5.0pt'><div><div><div><div><p class=MsoNormal>Hi Richard<o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal><image004.png><o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal><image005.png><o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal>Chip<o:p></o:p></p></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><div><div><p class=MsoNormal><b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>From:</span></b><span class=apple-converted-space><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> </span></span><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>General [mailto:</span><a href="mailto:general-bounces%2Bchipakins" target="_blank"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:purple'>general-bounces+chipakins</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>=</span><a href="mailto:gmail.com@lists.natureoflightandparticles.org" target="_blank"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:purple'>gmail.com@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>]<span class=apple-converted-space> </span><b>On Behalf Of<span class=apple-converted-space> </span></b>Richard Gauthier<br><b>Sent:</b><span class=apple-converted-space> </span>Monday, May 04, 2015 12:19 PM<br><b>To:</b><span class=apple-converted-space> </span>Nature of Light and Particles - General Discussion<br><b>Subject:</b><span class=apple-converted-space> </span>Re: [General] Electron Torus</span><o:p></o:p></p></div></div></div></div><div><div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><p class=MsoNormal>Hi Chip,<o:p></o:p></p></div></div><div><div><div><p class=MsoNormal> Thanks. And finally, the vertical ovals of the tori should be circles because the circulating quantum has the same radius in the vertical and horizontal directions.<o:p></o:p></p></div></div></div><div><div><div><p class=MsoNormal> Richard<o:p></o:p></p></div></div></div><div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><div><div><div><p class=MsoNormal>On May 4, 2015, at 9:32 AM, Chip Akins <<a href="mailto:chipakins@gmail.com" target="_blank"><span style='color:purple'>chipakins@gmail.com</span></a>> wrote:<o:p></o:p></p></div></div></div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div><div><div><div><div><p class=MsoNormal>Hi Richard<o:p></o:p></p></div></div></div><div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div></div><div><div><div><p class=MsoNormal>Thank you.<o:p></o:p></p></div></div></div><div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div></div><div><div><div><p class=MsoNormal>Here you go:<o:p></o:p></p></div></div></div><div><div><div><p class=MsoNormal><image001.png><o:p></o:p></p></div></div></div><div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div></div><div><div><div><p class=MsoNormal><image002.png><o:p></o:p></p></div></div></div><div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div></div><div><div><div><p class=MsoNormal>Chip<o:p></o:p></p></div></div></div><div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div></div><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><div><div><div><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;color:purple'>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, May 04, 2015 10:43 AM<br><b>To:</b> Nature of Light and Particles - General Discussion<br><b>Subject:</b> Re: [General] Electron Torus</span><o:p></o:p></p></div></div></div></div></div><div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div></div><div><div><div><p class=MsoNormal>Hi Chip,<o:p></o:p></p></div></div></div><div><div><div><div><p class=MsoNormal> Both tori should be symmetrical above and below the z-axis and center on z=0.<o:p></o:p></p></div></div></div></div><div><div><div><div><p class=MsoNormal> Richard<o:p></o:p></p></div></div></div></div><div><div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div></div><div><blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><div><div><div><div><p class=MsoNormal>On May 4, 2015, at 8:16 AM, Chip Akins <<a href="mailto:chipakins@gmail.com" target="_blank"><span style='color:purple'>chipakins@gmail.com</span></a>> wrote:<o:p></o:p></p></div></div></div></div><div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div></div><div><div><div><div><div><p class=MsoNormal>Hi Richard<o:p></o:p></p></div></div></div></div><div><div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div></div></div><div><div><div><div><p class=MsoNormal><image001.jpg><o:p></o:p></p></div></div></div></div><div><div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div></div></div><div><div><div><div><p class=MsoNormal>Viewed from the Z axis:<o:p></o:p></p></div></div></div></div><div><div><div><div><p class=MsoNormal><image002.jpg><o:p></o:p></p></div></div></div></div><div><div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div></div></div><div><div><div><div><p class=MsoNormal>And from the equatorial plane:<o:p></o:p></p></div></div></div></div><div><div><div><div><p class=MsoNormal><image003.jpg><o:p></o:p></p></div></div></div></div><div><div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div></div></div><div><div><div><div><p class=MsoNormal>Chip<o:p></o:p></p></div></div></div></div><div><div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div></div></div><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><div><div><div><div><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;color:#954F72'>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> Sunday, May 03, 2015 11:07 PM<br><b>To:</b> Nature of Light and Particles - General Discussion<br><b>Subject:</b> Re: [General] position</span><o:p></o:p></p></div></div></div></div></div></div><div><div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div></div></div><div><div><div><div><div><p class=MsoNormal>Chip and all,<o:p></o:p></p></div></div></div></div></div><div><div><div><div><div><p class=MsoNormal> Here are some equations that relate to the modeling of a circulating photon as an electron. The second and third set include my own model of the photon. The first set doesn’t require a particular model for the photon, except as mentioned below. The first model is the one that generates the de Broglie wavelength as explained in my article mentioned below.<o:p></o:p></p></div></div></div></div></div><div><div><div><div><div><p class=MsoNormal> <o:p></o:p></p></div></div></div></div></div><div><div><div><div><div><p class=MsoNormal>1. Here is the set of parametric equations for the helical trajectory of double-looping photon that models a free electron, and whose circular radius for a resting electron is Ro=hbar/2mc. The speed of the photon along this trajectory is always c. The longitudinal or z-component of the photon’s speed is the electron’s velocity v along the z-axis. The frequency of the photon around the helical axis is proportional to the circulating photon/electron's energy E=gamma mc^2. The distance of the photon’s helical trajectory from the z-axis for an electron whose speed is v, is proportional to 1/gamma^2. This equation is in my article “The electron is a charged photon with the de Broglie wavelength”. This equation does not include a particular model of the photon, but assumes that the photon follows the relations c=f lambda, E=hf and p=h/lambda. Both helicities of the helical trajectory are given.<o:p></o:p></p></div></div></div></div></div><div><div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Helvetica",sans-serif'>_______________________________________________<br>If you no longer wish to receive communication from the Nature of Light and Particles General Discussion List at </span><a href="mailto:richgauthier@gmail.com" target="_blank"><span style='font-size:9.0pt;font-family:"Helvetica",sans-serif;color:#954F72'>richgauthier@gmail.com</span></a><span style='font-size:9.0pt;font-family:"Helvetica",sans-serif'><br><a href="</span><a href="http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/richgauthier%40gmail.com?unsub=1&unsubconfirm=1" target="_blank"><span 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