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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><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'>The first model, simple line drawing, equal time steps, accelerated toward the right, from 0 to .9 c, in steps of .1 c.<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'>Representing:</span> <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><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
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</v:shape><![endif]--><![if !vml]><img width=239 height=90 src="cid:image002.jpg@01D0863D.CA0310F0" align=left hspace=12 v:shapes="Picture_x0020_1"><![endif]><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'><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'><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'>Starting from the left showing 0 velocity, and incrementing toward the right to .9 c.<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'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'><img width=490 height=433 id="Picture_x0020_2" src="cid:image005.jpg@01D0863D.CA0310F0"></span><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'>Radius decreases, frequency increases, 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'>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> 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<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal>Chip and all,<o:p></o:p></p></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><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>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></body></html>