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</o:shapelayout></xml><![endif]--></head><body lang=EN-GB link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US'>Chip:<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US'>Thanks for the work so far on this. It sounds like it’s amazingly difficult to simulate something so simple. I’m not sure what to suggest, other than <i>where the wave is, space is curved</i>. So another wave going over it follows a curved path. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US'>Maybe the surface is a problem, but maybe there’s an opportunity there. You know there’s a wave gif on Wikipedia, see <a href="http://commons.wikimedia.org/wiki/File:Deep_water_wave.gif">this</a> and <a href="http://en.wikipedia.org/wiki/Wind_wave">this</a> . If you could emulate that but with the wave going round a waterworld, then when you make the circumference smaller, you should get to a point where the rotational motion of the wave matches the rotational motion of the red-dot test particles. That might be interesting. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><img border=0 width=390 height=256 id="_x0000_i1030" src="cid:image006.gif@01D08BC3.60146FA0"></span><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US'> <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US'>Regards<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US'>John D<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0cm 0cm 0cm'><p class=MsoNormal><b><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri",sans-serif'>From:</span></b><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri",sans-serif'> General [mailto:general-bounces+johnduffield=btconnect.com@lists.natureoflightandparticles.org] <b>On Behalf Of </b>Chip Akins<br><b>Sent:</b> 10 May 2015 13:47<br><b>To:</b> 'Nature of Light and Particles - General Discussion'<br><b>Subject:</b> Re: [General] Electron<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Arial",sans-serif;color:black'>Hi John D<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Arial",sans-serif;color:black'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Arial",sans-serif;color:black'>There is some computational difficulty in modeling the waves as you have requested, but I have not given up. We can do this but it is taking more time than I had imagined.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Arial",sans-serif;color:black'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Arial",sans-serif;color:black'>I am able to model a confined wave and provide a surface plot.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><img border=0 width=600 height=575 id="Picture_x0020_1" src="cid:image001.png@01D08BC1.F55D5D30"></span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial",sans-serif;color:black'><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Arial",sans-serif;color:black'>And then I am able to rotate a wave to be from a different direction (using quaternion rotation), and add it to the surface plot.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Arial",sans-serif;color:black'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US><img border=0 width=528 height=478 id="_x0000_i1026" src="cid:image002.png@01D08BC1.F55D5D30"></span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial",sans-serif;color:black'><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Arial",sans-serif;color:black'>The problem is that the second wave is not traveling through disturbed space yet in my model, but rather is like the first, traveling through undisturbed space. When space is disturbed, the second wave must travel farther than the first due to the disturbances, which may cause the effects you have mentioned. Now I have to realistically quantify the amount of displacement in space caused by the first wave in order to recalculate the second wave with accurate displacement effects.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Arial",sans-serif;color:black'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Arial",sans-serif;color:black'>This initial simulation is assuming a first wave which is already present and a second wave then impinging upon the first. Later we can get into simultaneous wave interaction.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Arial",sans-serif;color:black'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Arial",sans-serif;color:black'>A surface plot has an x and y location and a magnitude in this model. I now need to recalculate the magnitude values based on the propagation of the second wave over the first, and sum the magnitudes which occur as this result. This grid is 720 X 720 in x and y. The first wave velocity is c through flat space (so c in the x, y plane), the second wave velocity will be c through the disturbances caused by the first wave (so c in the x, y, plane plus the disturbance in the z direction).<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Arial",sans-serif;color:black'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Arial",sans-serif;color:black'>Any clever insights or suggestions are welcome.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Arial",sans-serif;color:black'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Arial",sans-serif;color:black'>Chip<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:black'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0cm 0cm 0cm'><p class=MsoNormal><b><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri",sans-serif'>From:</span></b><span lang=EN-US 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>] <b>On Behalf Of </b>John Duffield<br><b>Sent:</b> Thursday, April 30, 2015 2:36 PM<br><b>To:</b> 'Nature of Light and Particles - General Discussion'<br><b>Subject:</b> Re: [General] Electron<o:p></o:p></span></p></div></div><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Chip:<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Yes, I do envisage a 3D model. I was thinking a 2D model would be simple place to start, and didn’t want to be too demanding. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>I wasn’t proposing that the two waves <i>diffract</i> one another, but instead <i>displace</i> one another. Light is displacement current, see <a href="http://mag.digitalpc.co.uk/olive/ode/physicsworld/LandingPage/LandingPage.aspx?href=UEhZU1dvZGUvMjAxMC8wOS8wMQ..&pageno=MzM.&entity=QXIwMzMwMA..&view=ZW50aXR5">Taming light at the nanoscale</a>. Think of a big oceanic swell wave, then mentally freeze it. Then send an ordinary ocean wave towards it. The latter rides up the swell wave. In doing this, it changes direction. It is displaced. Once it gets to the top it goes down the other side and continues on its way as if nothing happened, so you might think the two waves didn’t interact. But they did. One wave changed the direction of the other. Do this with two 511keV electromagnetic waves and each is displaced into itself, and then displaces its own path into a closed path, forever. In terms of an experiment see <a href="http://en.wikipedia.org/wiki/Two-photon_physics">gamma-gamma pair production</a> and the <a href="http://en.wikipedia.org/wiki/Breit%E2%80%93Wheeler_process">Breit-Wheeler</a> process, which was done indirectly at SLAC in 1997. There is no magic to this, the only tool in the box is light, and angular momentum is conserved. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>For background reading check out Maxwell and <a href="http://en.wikipedia.org/wiki/Displacement_current#History_and_interpretation">displacement current</a> wherein “light consist of transverse undulations”, along with <a href="http://www.compumag.org/jsite/images/stories/newsletter/ICS-99-06-2-Hammond.pdf">Percy Hammond</a> who said “we conclude that the field describes the curvature that characterizes the electromagnetic interaction”. People think a gravity is all about curved space, but it isn’t, it’s all about inhomogeneous space. So what’s curved space all about? Electromagnetism! Check out <a href="https://www.google.co.uk/#q=electromagnetic+geometry&spell=1">electromagnetic geometry</a>. In an electromagnetic wave the curvature goes one way <i>then</i> the other, like my grid picture of potential. But when the wave goes round a tight twisted double loop, you end up with an all-round curvature, one way <i>or</i> the other. It’s chiral, in 3D, but we can come on to that. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><img border=0 width=480 height=163 id="_x0000_i1027" src="cid:image003.jpg@01D08BC1.F55D5D30"><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Regards<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>John D<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0cm 0cm 0cm'><p class=MsoNormal><b><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri",sans-serif'>From:</span></b><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri",sans-serif'> General [<a href="mailto:general-bounces+johnduffield=btconnect.com@lists.natureoflightandparticles.org">mailto:general-bounces+johnduffield=btconnect.com@lists.natureoflightandparticles.org</a>] <b>On Behalf Of </b>Chip Akins<br><b>Sent:</b> 30 April 2015 14:18<br><b>To:</b> 'Nature of Light and Particles - General Discussion'<br><b>Subject:</b> Re: [General] Electron<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><span lang=EN-US style='color:black'>Hi John D<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:black'>Do you envision a 3D model which is a 3D grid of space with your prescribed wave propagating through the 3D mesh? Or are you suggesting a 2D wave representation?<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:black'>Are you proposing that two EM waves interact to diffract each other? Has this ever been seen in experiment?<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:black'>I suspect that a strong source of angular momentum <b>must also be present</b> in order to catalyze electron-positron pair production (like when gamma rays strike an atomic nucleus). So I think this means the waves will otherwise just pass through each other and <b>the conditions for confinement will not exist, absent this additional source of angular momentum</b>.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:black'>Chip<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='color:black'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0cm 0cm 0cm'><p class=MsoNormal><b><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri",sans-serif'>From:</span></b><span lang=EN-US 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>] <b>On Behalf Of </b>John Duffield<br><b>Sent:</b> Thursday, April 30, 2015 2:12 AM<br><b>To:</b> 'Nature of Light and Particles - General Discussion'<br><b>Subject:</b> Re: [General] Electron<o:p></o:p></span></p></div></div><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Martin:<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>No probs re mass and gravity. It’s good to talk. And if there was never any confusion, and we all agreed about everything, whatever would we talk about?<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>David:<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>I don’t have any issues with the horn torus or spindle-sphere torus. In a previous email I’ve referred to “inflating” the ring torus through these stages. See Adrian Rossiter’s </span><span lang=EN-US><a href="http://www.antiprism.com/album/860_tori/index.html"><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif'>antiprism</span></a></span><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'> for torus animations. See Martin’s picture below? Look at the cut end, it’s a bit like a slice of onion. Mentally add more onion rings around those that are already there, and the torus gets more and more spherical. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><img border=0 width=328 height=272 id="Picture_x0020_2" src="cid:image004.jpg@01D08BC1.F55D5D30" alt="cid:image001.jpg@01D08318.6E155550"></span><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>There is no charge at the centre. The charge is the twist, the winding, the knottedness, the vorticity. Undo it with the opposite twist, and instead of two field variations going round at c looking like standing fieldall, you’ve got two field variations moving linearly at c.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Chip:<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Is there any chance you could animate a wave in space, like this?<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><img border=0 width=640 height=157 id="Picture_x0020_3" src="cid:image005.gif@01D08BC1.F55D5D30" alt="cid:image002.gif@01D08318.6E155550"></span><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>It’s a bit like a wave in a rubber mat, or a seismic wave. Only this is a wave of electromagnetic four-potential. The spatial derivative of this gives the sinusoidal electric waveform, and the time-derivative gives the sinusoidal magnetic waveform. See the horizontal lines? Where the tilt is steepest the electric sine wave is highest. Where the tilting is fastest is where the magnetic sine wave is highest. L</span><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#666666'>ook at </span><span lang=EN-US><a href="http://en.wikipedia.org/wiki/Electromagnetic_radiation"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#0033CC'>electromagnetic radiation</span></a></span><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#666666'> on Wiki. Read the </span><span lang=EN-US><a href="http://en.wikipedia.org/wiki/Electromagnetic_radiation#Derivation_from_electromagnetic_theory"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>Derivation >From Electromagnetic Theory</span></a></span><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#666666'> </span><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F4E79'>section, and you’ll see this: <em><span style='font-family:"Calibri",sans-serif'>“the curl operator on one side of these equations results in first-order spatial derivatives of the wave solution, while the time-derivative on the other side of the equations, which gives the other field, is first order in time”</span></em>. </span><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F4E79'>After that I’d be very interested in an animation where two such waves pass each other and displace each other’s path, so much so that each wave ends up moving through itself. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Regards<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>John D<o:p></o:p></span></p></div></body></html>