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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 Torus for:<o:p></o:p></span></p><p class=MsoNormal><img width=358 height=81 id="Picture_x0020_1" src="cid:image001.jpg@01D08652.8FADB2B0"><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'>Viewed from the Z axis:<o:p></o:p></span></p><p class=MsoNormal><img width=437 height=542 id="Picture_x0020_2" src="cid:image003.jpg@01D08652.8FADB2B0"><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'>And from the equatorial plane:<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><img width=439 height=292 id="Picture_x0020_3" src="cid:image004.jpg@01D08652.8FADB2B0"><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'>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>