<html><head><meta http-equiv="Content-Type" content="text/html charset=windows-1252"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><div class=""></div><div class="">It’s nice to show this helical trajectory in a different color, superimposed on the trajectory of the particular photon model such as the TEQ model, moving along this trajectory, for the relativistic electron in the 3D graphic, preferably one 3D graphic for each electron velocity so the graphic doesn’t look so complicated with many different electron velocities combined in a single diagram.</div><div class=""> Richard</div><br class=""><div><blockquote type="cite" class=""><div class="">On May 21, 2015, at 7:32 PM, Richard Gauthier <<a href="mailto:richgauthier@gmail.com" class="">richgauthier@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><meta http-equiv="Content-Type" content="text/html charset=iso-8859-1" class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><div class="">Chip,</div><div class=""> I see the problem. The formula that I now think best represents the electron (which is the formula that I plotted in 3D versus velocity in my graphics program) is the one that is composed of a circulating spin 1/2 photon of amplitude Ro, not a spin 1 photon that is in the formula you just sent that has amplitude 2Ro. The formula for using the spin 1/2 photon is one of the two that I sent before (which corresponds to circulation on a horn torus)</div><div class="">:</div><div class=""></div></div><span id="cid:A2674E21-DF20-43E3-BCB9-2242CFB13C14@hsd1.ca.comcast.net"><PastedGraphic-5.pdf></span><meta http-equiv="Content-Type" content="text/html charset=windows-1252" class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><div class=""></div><div class=""><br class=""></div><div class="">so a factor of 2 and one of .5 needs to be removed from your x, y and z coordinates if we are to be on the same page. The “else” formula is not needed because it is included in your “if” statement in the case of v=0 (or VelocityC*c=0)</div><div class=""><br class=""></div><div class=""><br class=""></div><br class=""><div class=""><blockquote type="cite" class=""><div class="">On May 21, 2015, at 4:41 PM, Chip Akins <<a href="mailto:chipakins@gmail.com" class="">chipakins@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><span style="" class="">Can we check the formula once more?<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><span style="" class="">Here is the MATLAB code if you would like to take a look.<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><span style="font-size: 10pt; font-family: 'Courier New';" class="">y=1/sqrt(1-(VelocityC^2/c^2));</span><span style="font-family: 'Courier New';" class=""><o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><span style="font-size: 10pt; font-family: 'Courier New';" class="">X(ii)=Roc*(1/y^2+(2/y)*cosd(.5*y*c*t/Roc))*cosd(y*c*t/Roc);</span><span style="font-family: 'Courier New';" class=""><o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><span style="font-size: 10pt; font-family: 'Courier New';" class="">Y(ii)=Roc*(1/y^2+(2/y)*cosd(.5*y*c*t/Roc))*sind(y*c*t/Roc);<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><span style="font-family: 'Courier New';" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><span style="font-size: 10pt; font-family: 'Courier New'; color: blue;" class="">if</span><span style="font-size: 10pt; font-family: 'Courier New';" class=""><span class="Apple-converted-space"> </span>RefFrame == Observer</span><span style="font-family: 'Courier New';" class=""><o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><span style="font-size: 10pt; font-family: 'Courier New';" class=""> Z(ii)=((2*Roc)/y)*sind(.5*y*c*t/Roc)+(VelocityC*c*t);</span><span style="font-family: 'Courier New';" class=""><o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><span style="font-size: 10pt; font-family: 'Courier New'; color: blue;" class="">else</span><span style="font-family: 'Courier New';" class=""><o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><span style="font-size: 10pt; font-family: 'Courier New';" class=""> Z(ii)=((2*Roc)/y)*sind(.5*y*c*t/Roc);</span><span style="font-family: 'Courier New';" class=""><o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><span style="font-size: 10pt; font-family: 'Courier New'; color: blue;" class="">end</span></div></div></blockquote></div><br class=""></div></div></blockquote></div><br class=""></body></html>