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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='font-family:"Times New Roman",serif;color:black'>Hi John<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Times New Roman",serif;color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-family:"Times New Roman",serif;color:black'>Regarding the proper computer model. How do we get started?<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Times New Roman",serif;color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-family:"Times New Roman",serif;color:black'>Chip<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Times New Roman",serif;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'>From:</span></b><span style='font-size:11.0pt'> General [mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org] <b>On Behalf Of </b>John Williamson<br><b>Sent:</b> Wednesday, November 11, 2015 7:43 PM<br><b>To:</b> davidmathes8@yahoo.com<br><b>Cc:</b> Nature of Light and Particles - General Discussion <general@lists.natureoflightandparticles.org>; Nick Bailey <nick@bailey-family.org.uk>; Anthony Booth <abooth@ieee.org>; Mark, Martin van der <martin.van.der.mark@philips.com><br><b>Subject:</b> Re: [General] SU(2) equation set<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal><span style='color:black'>Dear David,<br><br>You are not getting the point. </span><span style='color:black'><o:p></o:p></span></p><div class=MsoNormal align=center style='text-align:center'><span style='font-family:"Times New Roman",serif;color:black'><hr size=2 width="100%" align=center></span></div><p class=MsoNormal style='margin-bottom:12.0pt'><b><span style='font-family:"Tahoma",sans-serif;color:black'>From:</span></b><span style='font-family:"Tahoma",sans-serif;color:black'> <a href="mailto:davidmathes8@yahoo.com">davidmathes8@yahoo.com</a> [davidmathes8@yahoo.com]<br><b>Sent:</b> Wednesday, November 11, 2015 6:05 PM<br><b>To:</b> John Williamson<br><b>Cc:</b> Mark, Martin van der; Nature of Light and Particles - General Discussion<br><b>Subject:</b> Re: SU(2) equation set</span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>John </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Short answer - the straw man is burning. Your equation set proposed looks like Barrett's set without the conditioning. I will have to do the math to obtain compatibility using your notation, of course. </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>For the reader, the papers we are discussing include so far...</span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Williamson 2015 "Absolute relativity in classical electromagnetism: the quantisation of light"</span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> <a href="http://eprints.gla.ac.uk/110966/1/110966.pdf"><span style='color:purple'>http://eprints.gla.ac.uk/110966/1/110966.pdf</span></a></span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Barrett 2000 "Topology and the Physical Properties of Electromagnetic Fields"</span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><a href="http://redshift.vif.com/JournalFiles/Pre2001/V07NO1PDF/V07N1BAR.pdf">http://redshift.vif.com/JournalFiles/Pre2001/V07NO1PDF/V07N1BAR.pdf</a></span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>The question is whether the equation sets in these two papers are compatible or can in some way be combined. Barrett extends Maxwell's equations going so far as to use the Maxwell 20. Williamson does not use the imaginary quantities Barrett uses directly. Only U(1) X SU(2) symmetries are under discussion at present. No, SO(2) nor SU(3).</span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>I'll go back to the starting line...</span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>The collective body of EM only work so far is good enough and represented in good part by Maxwell's equations. (See Hurray 2010). One might say a good working approximation. </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>However, if one confines their work to the photon and electron, even then there are unexplained EM interactions not covered by Maxwell's equations. Aharonov-Bohm for example. </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Furthermore, there is a dichotomy in approaches. The physicist tries to get at the essence of EM or E&M, usually the simplest set as presented by nature. In order to produce predictable and repeatable results, the EM engineer needs to condition the EM in part because nature does conditioning of EM as well. </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>I'm aware there is a correlation between the Williamson equations and Barrett's EM. The loose fit does not mean causation and is certainly not a perfect fit. Some thought has been given to including Jefimenko's equations, but apparently, Barrett's and Williamson's equations will suffice for now.</span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><i><span style='font-family:"Helvetica Neue";color:black'>Clearly, both Williamson and Barrett sets do not cover the full Standard Model, nor were they expected to...</span></i><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>The general strawdog thought of the two sets was more one of compatibility than one of rigor in that the equations were an rigorous EM-only attempt, but not comprehensive covering every force and instead, just confined to EM, perhaps electroweak. However, what is observed in nature is not completely covered by the Maxwell set without further clarification and extensions. </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Normally, folks would start backing up and instead of using the Maxwell 4 as defined by Heaviside, a capable engineer, they look at Maxwell's first edition and the 20 equations there. Some folks are still not satisfied and back away from the vector calculus and use quaternions. </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Ok, now to address the email...</span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>John, </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Tahoma",sans-serif;color:black'>> U(1) EM CROSS U(1) weak CROSS SU(2) spin CROSS SU(2) ln CROSS SU(2) CROSS SU(3) flavour CROSS SU(3) colour cross</span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Is this correctly stated? U(1) EM X U(1) weak X SU(2) spin X SU(2) in SU(2) X SU(3) flavour X SU(3 colour<br></span><span style='font-family:"Helvetica Neue";color:blue'><br>The standard model STARTS from putting in a load of groups. Lots and lots of them!</span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Correct me if I'm wrong, is yours U(1) EM X SU(2) spin?<br><br></span><span style='font-family:"Helvetica Neue";color:blue'>No. I do not put any group in a-priori at all! All I put in is the relativistic properties of space and time - and energy.</span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Does your formulation address EM solitons or Aharnov-Bohm?<br><br></span><span style='font-family:"Helvetica Neue";color:blue'>Yes of course. The electron solution is a soliton - look at it! Yes - Aharonov Bohm is in there and much much more. All the Aharonov Bohm stuff does is insert an eA phase change - I have a set of four coupled differential equations expressing the proper interaction of the vector potential with the spin. The full implications of all the products of the static and the dynamic are contained in Martin and my previous work on forces. Barret is not fundamental. It is a mere detail - added in the absence of any clue of what else to do. Good man - one has to try to do something.</span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>I'm thinking that Barrett's is currently U(1) EM X SU(2) phase. FWIW Barrett's goal is EM conditioning. So, polarization and spin need to be added. I've heard he is working on polarization at SU(3). Nothing published so far.<br><br></span><span style='font-family:"Helvetica Neue";color:blue'>Look, Barrett has attempted, as have others (e.g. Anderson and Arthurs), to put "spin" in as an E.A and E cross A coupling. This is just one term of a full set of field-vector products. If one takes the full set of such products in my new formalism it gives eight coupled non-linear differential equations with about a thousand terms - including all the EA terms, but lots others too. Without a proper base theory (which I hope mine is) people are stabbing in the dark..</span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>My conclusion there is an incompatibility between the Williamson and Barrett equations. But we don't seem far off.<br><br></span><span style='font-family:"Helvetica Neue";color:blue'>Damn right there is a difference! Barrett has (manfully) attempted to insert an extra term into another equation to see where it gets him. I have derived the whole set of new equations from first principles and from a deeper paradigm - by putting nothing in except space, time and energy. To be clear: No U(1) (though it comes out). No SU(2) (though it comes out). No SU(3) (though that comes out too. What I have put in is an STA for space-time. That is the Clifford-Dirac algebra Cl(1,3) (and not Cl(3,1, which is different).</span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>So it's back to basics and hard work on reconciling the two approaches.<br><br></span><span style='font-family:"Helvetica Neue";color:blue'>No need to reconcile anything. Barrett is attempting to put in a little something to throw light on a deep mystery (the nature of spin). Good for him. I have no need to do this because the spin term, for me, is just a basic and necessary part of the theory of space, time and matter. I get the spin at the basic linear level - not as a non-linear product term conditioned by an extra copy of U(1). He has put in a couple of non-linear terms E.A and E x A into a linear equation (Maxwell). Martin and I have looked at non-linear equations too (see earlier work), but these are just not the set I have proposed here, which are linear. One can make them non-linear by doing the full product GdG for example. These include all of the EA terms Barrett used – but also far more. That that is far more complicated and an enormous distraction from the main thrust of what needs to be done! A thousand-plus terms in eight coupled non-linear equations. To keep track of these I think a proper computer model will be required.</span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Best</span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>David</span><span style='color:black'><o:p></o:p></span></p><div><div class=MsoNormal align=center style='text-align:center'><span style='font-family:"Times New Roman",serif;color:black'><hr size=2 width="100%" align=center></span></div><div id=divRpF504081><p class=MsoNormal style='margin-bottom:12.0pt'><b><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black'>From:</span></b><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black'> <a href="mailto:davidmathes8@yahoo.com">davidmathes8@yahoo.com</a> [davidmathes8@yahoo.com]<br><b>Sent:</b> Wednesday, November 11, 2015 6:05 PM<br><b>To:</b> John Williamson<br><b>Cc:</b> Mark, Martin van der; Nature of Light and Particles - General Discussion<br><b>Subject:</b> Re: SU(2) equation set</span><span style='font-family:"Times New Roman",serif;color:black'><o:p></o:p></span></p></div><div><div><div id="yui_3_16_0_1_1447260730724_5967"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>John <o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5967"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5967"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Short answer - the straw man is burning. Your equation set proposed looks like Barrett's set without the conditioning. I will have to do the math to obtain compatibility using your notation, of course. <o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5967"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5967"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5967"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>For the reader, the papers we are discussing include so far...<o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5967"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_12075"><div id="yui_3_16_0_1_1447260730724_12077"><div id="yui_3_16_0_1_1447260730724_12079"><div id="yui_3_16_0_1_1447260730724_12081"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Williamson 2015 "Absolute relativity in classical electromagnetism: the quantisation of light"<o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_12081"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'> <a href="http://eprints.gla.ac.uk/110966/1/110966.pdf" target="_blank" id="yiv3919935515yui_3_16_0_1_1447211781778_4472"><span style='color:purple'>http://eprints.gla.ac.uk/110966/1/110966.pdf</span></a><o:p></o:p></span></p></div></div></div></div><div id="yui_3_16_0_1_1447260730724_5830"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5830"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Barrett 2000 "Topology and the Physical Properties of Electromagnetic Fields"<o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5830"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><a href="http://redshift.vif.com/JournalFiles/Pre2001/V07NO1PDF/V07N1BAR.pdf" target="_blank">http://redshift.vif.com/JournalFiles/Pre2001/V07NO1PDF/V07N1BAR.pdf</a><o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5830"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5830"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>The question is whether the equation sets in these two papers are compatible or can in some way be combined. Barrett extends Maxwell's equations going so far as to use the Maxwell 20. Williamson does not use the imaginary quantities Barrett uses directly. Only U(1) X SU(2) symmetries are under discussion at present. No, SO(2) nor SU(3).<o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5830"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5830"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>I'll go back to the starting line...<o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5830"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5830"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>The collective body of EM only work so far is good enough and represented in good part by Maxwell's equations. (See Hurray 2010). One might say a good working approximation. <o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5830"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5830"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>However, if one confines their work to the photon and electron, even then there are unexplained EM interactions not covered by Maxwell's equations. Aharonov-Bohm for example. <o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5830"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5830"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Furthermore, there is a dichotomy in approaches. The physicist tries to get at the essence of EM or E&M, usually the simplest set as presented by nature. In order to produce predictable and repeatable results, the EM engineer needs to condition the EM in part because nature does conditioning of EM as well. <o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5830"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>I'm aware there is a correlation between the Williamson equations and Barrett's EM. The loose fit does not mean causation and is certainly not a perfect fit. Some thought has been given to including Jefimenko's equations, but apparently, Barrett's and Williamson's equations will suffice for now.<o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5790"><p class=MsoNormal style='background:white'><i><span style='font-family:"Helvetica Neue";color:black'>Clearly, both Williamson and Barrett sets do not cover the full Standard Model, nor were they expected to...</span></i><span style='font-family:"Helvetica Neue";color:black'><o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_11563"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>The general strawdog thought of the two sets was more one of compatibility than one of rigor in that the equations were an rigorous EM-only attempt, but not comprehensive covering every force and instead, just confined to EM, perhaps electroweak. However, what is observed in nature is not completely covered by the Maxwell set without further clarification and extensions. <o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Normally, folks would start backing up and instead of using the Maxwell 4 as defined by Heaviside, a capable engineer, they look at Maxwell's first edition and the 20 equations there. Some folks are still not satisfied and back away from the vector calculus and use quaternions. <o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Ok, now to address the email...<o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>John, <o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black'>> U(1) EM CROSS U(1) weak CROSS SU(2) spin CROSS SU(2) ln CROSS SU(2) CROSS SU(3) flavour CROSS SU(3) colour cross</span><span style='font-family:"Helvetica Neue";color:black'><o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Is this correctly stated? U(1) EM X U(1) weak X SU(2) spin X SU(2) in SU(2) X SU(3) flavour X SU(3 colour<br></span><span style='font-family:"Helvetica Neue";color:blue'><br>The standard model STARTS from putting in a load of groups. Lots and lots of them!</span><span style='font-family:"Helvetica Neue";color:black'><o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Correct me if I'm wrong, is yours U(1) EM X SU(2) spin?<br><br></span><span style='font-family:"Helvetica Neue";color:blue'>No. I do not put any group in a-priori at all! All I put in is the relativistic properties of space and time - and energy.</span><span style='font-family:"Helvetica Neue";color:black'><o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Does your formulation address EM solitons or Aharnov-Bohm?<br><br></span><span style='font-family:"Helvetica Neue";color:blue'>Yes of course. The electron solution is a soliton - look at it! Yes - Aharonov Bohm is in there and much much more. All the Aharonov Bohm stuff does is insert an eA phase change - I have a set of four coupled differential equations expressing the proper interaction of the vector potential with the spin. The full implications of all the products of the static and the dynamic are contained in Martin and my previous work on forces. Barret is not fundamental. It is a mere detail - added in the absence of any clue of what else to do. Good man - one has to try to do something.</span><span style='font-family:"Helvetica Neue";color:black'><o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>I'm thinking that Barrett's is currently U(1) EM X SU(2) phase. FWIW Barrett's goal is EM conditioning. So, polarization and spin need to be added. I've heard he is working on polarization at SU(3). Nothing published so far.<br><br></span><span style='font-family:"Helvetica Neue";color:blue'>Look, Barrett has attempted, as have others (e.g. Anderson and Arthurs), to put "spin" in as an E.A and E cross A coupling. This is just one term of a full set of field-vector products. If one takes the full set of such products in my new formalism it gives eight coupled non-linear differential equations with about a thousand terms - including all the EA terms, but lots others too. Without a proper base theory (which I hope mine is) people are stabbing in the dark..</span><span style='font-family:"Helvetica Neue";color:black'><o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>My conclusion there is an incompatibility between the Williamson and Barrett equations. But we don't seem far off.<br><br></span><span style='font-family:"Helvetica Neue";color:blue'>Damn right there is a difference! Barrett has (manfully) attempted to insert an extra term into another equation to see where it gets him. I have derived the whole set of new equations from first principles and from a deeper paradigm - by putting nothing in except space, time and energy. To be clear: No U(1) (though it comes out. No SU(2) (though it comes out. No SU(3) (though that comes out too. What I have put in is an STA for space-time. That is the Clifford-Dirac algebra Cl(1,3) (and not Cl(3,1, which is different).</span><span style='font-family:"Helvetica Neue";color:black'><o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>So it's back to basics and hard work on reconciling the two approaches.<br><br></span><span style='font-family:"Helvetica Neue";color:blue'>No need to reconcile anything. Barrett is attempting to put in a little something to throw light on a deep mystery (the nature of spin). Good for him. I have no need to do this because the spin term, for me, is just a basic and neccessary part of the theory of space, time and matter. I get the spin at the basic linear level - not as a non-linear product term conditioned by an extra copy of U(1).</span><span style='font-family:"Helvetica Neue";color:black'><o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Best<o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>David<o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5645"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><blockquote style='border:none;border-left:solid #1010FF 1.5pt;padding:0in 0in 0in 4.0pt;margin-left:3.75pt;margin-top:3.75pt;margin-bottom:5.0pt' id="yui_3_16_0_1_1447260730724_5644"><div id="yui_3_16_0_1_1447260730724_5643"><div id="yui_3_16_0_1_1447260730724_5642"><div id="yui_3_16_0_1_1447260730724_5641"><div class=MsoNormal align=center style='text-align:center;background:white'><span style='font-family:"Helvetica Neue";color:black'><hr size=1 width="100%" align=center></span></div><p class=MsoNormal style='background:white'><b id="yui_3_16_0_1_1447260730724_14436"><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'>From:</span></b><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'> John Williamson <<a href="mailto:John.Williamson@glasgow.ac.uk">John.Williamson@glasgow.ac.uk</a>><br><b id="yui_3_16_0_1_1447260730724_14438">To:</b> "<a href="mailto:davidmathes8@yahoo.com">davidmathes8@yahoo.com</a>" <<a href="mailto:davidmathes8@yahoo.com">davidmathes8@yahoo.com</a>> <br><b id="yui_3_16_0_1_1447260730724_14440">Cc:</b> "Mark, Martin van der" <<a href="mailto:martin.van.der.mark@philips.com">martin.van.der.mark@philips.com</a>>; Nature of Light and Particles - General Discussion <<a href="mailto:general@lists.natureoflightandparticles.org">general@lists.natureoflightandparticles.org</a>> <br><b id="yui_3_16_0_1_1447260730724_14442">Sent:</b> Wednesday, November 11, 2015 5:17 AM<br><b>Subject:</b> RE: SU(2) equation set</span><span style='font-family:"Helvetica Neue";color:black'><o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5684"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p><div id=yiv3919935515><div id="yui_3_16_0_1_1447260730724_5686"><div id="yui_3_16_0_1_1447260730724_5685"><p class=MsoNormal style='background:white'><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black'>Dear David,<br><br>Mu. "Putting things in" in a symptom of the current disease in physics. The first question is anyway:which SU(2)? The standard model plonks in lots of them .. spin. isospin, lepton number ... loads more. It also sticks in a U(1) and a couple of SU(3)'s (that of "colour" and "flavour"). it is often stated that the standard model is U(1) CROSS SU(2) CROSS SU(3). Not so, It is more like U(1) EM CROSS U(1) weak CROSS SU(2) spin CROSS SU(2) ln CROSS SU(2) CROSS SU(3) flavour CROSS SU(3) colour cross ... Each time you plonk in another a-priori "group" you add levels of complexity to the starting point, such that the standard model as it stands has about 50 of them. Also, putting in any group a-priori then removes the possibility of explaining where the group has come from. Any time any experimentalist finds a new symmettry - whammo - some daft theorist whacks it in as a starting point. One does not want to stick them in - one wants to derive them. I get SU(2) spin out, already. Why would I ever, then, want to put it in?<br><br>Regards, John.<o:p></o:p></span></p><div><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black'><o:p> </o:p></span></p></div><div id=yiv3919935515yqt11989><div id="yui_3_16_0_1_1447260730724_11983"><div class=MsoNormal align=center style='text-align:center;background:white'><span style='font-family:"Times New Roman",serif;color:black'><hr size=2 width="100%" align=center id="yui_3_16_0_1_1447260730724_14364"></span></div><div id=yiv3919935515divRpF961264><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><b><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black'>From:</span></b><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black'> <a href="mailto:davidmathes8@yahoo.com">davidmathes8@yahoo.com</a> [davidmathes8@yahoo.com]<br><b>Sent:</b> Wednesday, November 11, 2015 4:50 AM<br><b>To:</b> John Williamson<br><b>Subject:</b> Re: SU(2) equation set</span><span style='font-family:"Times New Roman",serif;color:black'><o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_11982"><div id="yui_3_16_0_1_1447260730724_11981"><div id="yui_3_16_0_1_1447260730724_11980"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>John<o:p></o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447216954511_3107"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447216954511_3102"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>The straw man failed.<o:p></o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447216954511_3108"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447216954511_3101"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Let me approach this from a different direction. Just for the record, I'm not interested in writing a paper. I'm simply interested in getting to SU(2). How would you add SU(2) to your current equation set?<o:p></o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447216954511_3096"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447216954511_3096"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>David<o:p></o:p></span></p></div><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><br><br><o:p></o:p></span></p><blockquote style='border:none;border-left:solid #1010FF 1.5pt;padding:0in 0in 0in 4.0pt;margin-left:3.75pt;margin-top:3.75pt;margin-bottom:5.0pt'><div id="yiv3919935515yui_3_16_0_1_1447216954511_3045"><div id="yiv3919935515yui_3_16_0_1_1447216954511_3044"><div id="yiv3919935515yui_3_16_0_1_1447216954511_3043"><div class=MsoNormal align=center style='text-align:center;background:white'><span style='font-family:"Helvetica Neue";color:black'><hr size=1 width="100%" align=center></span></div><p class=MsoNormal style='background:white'><b><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'>From:</span></b><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'> John Williamson <<a href="mailto:John.Williamson@glasgow.ac.uk">John.Williamson@glasgow.ac.uk</a>><br><b>To:</b> "<a href="mailto:davidmathes8@yahoo.com">davidmathes8@yahoo.com</a>" <<a href="mailto:davidmathes8@yahoo.com">davidmathes8@yahoo.com</a>> <br><b>Sent:</b> Tuesday, November 10, 2015 8:39 PM<br><b>Subject:</b> RE: SU(2) equation set</span><span style='font-family:"Helvetica Neue";color:black'><o:p></o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447216954511_3097"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p><div id=yiv3919935515><div id="yiv3919935515yui_3_16_0_1_1447216954511_3099"><div id="yiv3919935515yui_3_16_0_1_1447216954511_3098"><p class=MsoNormal style='background:white'><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black'>Hello David,<br><br>Had a look at the equations but I think there is a problem as you are kind of putting things in twice. The vector potential appears in my equations as a vector - you are also putting it in as a complex number - which both expands the algebra and confuses the situation as you are using two different dimensions for the same quantity. I think the same problem exist (by the look of it) for the Barret formulation itself. There is a similar problem in Dirac QM which, famously, led Dirac into the mists of confusion as well.<br><br>Also, I see the U(1) part of what you are doing - but where is the SU(2) part?<br><br>Regards, John.<o:p></o:p></span></p><div><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black'><o:p> </o:p></span></p></div><div id=yiv3919935515yqt71629><div id="yiv3919935515yui_3_16_0_1_1447216954511_3109"><div class=MsoNormal align=center style='text-align:center;background:white'><span style='font-family:"Times New Roman",serif;color:black'><hr size=2 width="100%" align=center></span></div><div id=yiv3919935515divRpF343849><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><b><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black'>From:</span></b><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black'> <a href="mailto:davidmathes8@yahoo.com">davidmathes8@yahoo.com</a> [davidmathes8@yahoo.com]<br><b>Sent:</b> Wednesday, November 11, 2015 3:38 AM<br><b>To:</b> John Williamson<br><b>Subject:</b> SU(2) equation set</span><span style='font-family:"Times New Roman",serif;color:black'><o:p></o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447216954511_3112"><div id="yiv3919935515yui_3_16_0_1_1447216954511_3111"><div id="yiv3919935515yui_3_16_0_1_1447211781778_3751"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>John<o:p></o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447211781778_3751"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447211781778_3751"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>As a raw draft I've combined the Williamson equations with Barrett equations to produce a framework for a U(1) X SU(2) version. <o:p></o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447211781778_3751"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447211781778_3751"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>The general approach has been to use the Williamson notation since the primary focus is on electron modeling regardless of whether the photonic electron or quanta electron are used. Also, these equations remain to vetted properly and represent a working framework instead of a full matrix with appropriate interpretation. <o:p></o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447211781778_3751"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447211781778_3751"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Right now, there is confusion in notation with a conflicts in the use of A and B. <o:p></o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447211781778_3751"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447211781778_3751"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>See attached.<o:p></o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447211781778_3751"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447211781778_3751"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>David<o:p></o:p></span></p></div><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><br><br><o:p></o:p></span></p><blockquote style='border:none;border-left:solid #1010FF 1.5pt;padding:0in 0in 0in 4.0pt;margin-left:3.75pt;margin-top:3.75pt;margin-bottom:5.0pt'><div id="yiv3919935515yui_3_16_0_1_1447211781778_3994"><div id="yiv3919935515yui_3_16_0_1_1447211781778_3993"><div id="yiv3919935515yui_3_16_0_1_1447211781778_4486"><div class=MsoNormal align=center style='text-align:center;background:white'><span style='font-family:"Helvetica Neue";color:black'><hr size=1 width="100%" align=center></span></div><p class=MsoNormal style='background:white'><b><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'>From:</span></b><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'> "<a href="mailto:davidmathes8@yahoo.com">davidmathes8@yahoo.com</a>" <<a href="mailto:davidmathes8@yahoo.com">davidmathes8@yahoo.com</a>><br><b>To:</b> John Williamson <<a href="mailto:John.Williamson@glasgow.ac.uk">John.Williamson@glasgow.ac.uk</a>> <br><b>Sent:</b> Tuesday, November 10, 2015 8:25 AM<br><b>Subject:</b> Re: Slide Deck</span><span style='font-family:"Helvetica Neue";color:black'><o:p></o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447211781778_3992"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p><div id=yiv3919935515><div id="yiv3919935515yui_3_16_0_1_1447211781778_3991"><div id="yiv3919935515yui_3_16_0_1_1447211781778_3990"><div id="yiv3919935515yui_3_16_0_1_1447171858799_10495"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>John<o:p></o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447171858799_10496"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447171858799_10497"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Thank you. now I recall these papers this summer's work. So not that winter is begun (raining in California), I'll reread them.<o:p></o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447171858799_10497"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447171858799_10497"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Barrett did have extensions to Maxwell-Heaviside equations. I'm wondering if a similar treat can be extended to your additional set of four and the consequences thereof. SU(2), no SU(3).<o:p></o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447171858799_10497"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447171858799_10497"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><a href="http://aflb.ensmp.fr/AFLB-26j/aflb26jp055.pdf" target="_blank">http://aflb.ensmp.fr/AFLB-26j/aflb26jp055.pdf</a><o:p></o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447171858799_10497"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447171858799_10497"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Best regards my friend,<o:p></o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447171858799_10497"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447171858799_10497"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>David<o:p></o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447171858799_10497"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447171858799_12521"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447171858799_13230"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447171858799_13231"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p><div id="yui_3_16_0_1_1447260730724_12093"><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id=yiv3919935515yqt92965><blockquote style='border:none;border-left:solid #1010FF 1.5pt;padding:0in 0in 0in 4.0pt;margin-left:3.75pt;margin-top:3.75pt;margin-bottom:5.0pt'><div id="yiv3919935515yui_3_16_0_1_1447171858799_12868"><div id="yiv3919935515yui_3_16_0_1_1447171858799_12867"><div id="yiv3919935515yui_3_16_0_1_1447171858799_13236"><div class=MsoNormal align=center style='text-align:center;background:white'><span style='font-family:"Helvetica Neue";color:black'><hr size=1 width="100%" align=center></span></div><p class=MsoNormal style='background:white'><b id="yiv3919935515yui_3_16_0_1_1447171858799_13274"><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'>From:</span></b><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'> John Williamson <<a href="mailto:John.Williamson@glasgow.ac.uk">John.Williamson@glasgow.ac.uk</a>><br><b>To:</b> "<a href="mailto:davidmathes8@yahoo.com">davidmathes8@yahoo.com</a>" <<a href="mailto:davidmathes8@yahoo.com">davidmathes8@yahoo.com</a>> <br><b>Sent:</b> Monday, November 9, 2015 11:14 PM<br><b id="yiv3919935515yui_3_16_0_1_1447171858799_13276">Subject:</b> RE: Slide Deck</span><span style='font-family:"Helvetica Neue";color:black'><o:p></o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447171858799_12866"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p><div id=yiv3919935515><div id="yiv3919935515yui_3_16_0_1_1447171858799_12865"><div id="yiv3919935515yui_3_16_0_1_1447171858799_12864"><p class=MsoNormal style='background:white'><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black'>Hello David,<br><br>SPIE papers at:<br> <br><a href="http://eprints.gla.ac.uk/110952/1/110952.pdf" target="_blank" id="yiv3919935515yui_3_16_0_1_1447211781778_4468">http://eprints.gla.ac.uk/110952/1/110952.pdf</a><br><a href="http://eprints.gla.ac.uk/110966/1/110966.pdf" target="_blank" id="yiv3919935515yui_3_16_0_1_1447211781778_4472">http://eprints.gla.ac.uk/110966/1/110966.pdf</a><br><br>Regards, John.<o:p></o:p></span></p><div id="yiv3919935515yui_3_16_0_1_1447211781778_4473"><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black'><o:p> </o:p></span></p></div><div id=yiv3919935515yqt04806><div id="yiv3919935515yui_3_16_0_1_1447171858799_12863"><div class=MsoNormal align=center style='text-align:center;background:white'><span style='font-family:"Times New Roman",serif;color:black'><hr size=2 width="100%" align=center></span></div><div id=yiv3919935515divRpF276520><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><b><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black'>From:</span></b><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black'> <a href="mailto:davidmathes8@yahoo.com">davidmathes8@yahoo.com</a> [davidmathes8@yahoo.com]<br><b>Sent:</b> Tuesday, November 10, 2015 5:09 AM<br><b>To:</b> John Williamson<br><b>Subject:</b> Slide Deck</span><span style='font-family:"Times New Roman",serif;color:black'><o:p></o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447171858799_12862"><div id="yiv3919935515yui_3_16_0_1_1447171858799_12861"><div id="yiv3919935515yui_3_16_0_1_1447130421153_7312"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>John<o:p></o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447130421153_7311"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447130421153_7311"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Do you have a slide deck summarizing the model? <o:p></o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447130421153_7311"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447130421153_7311"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>Best<o:p></o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447130421153_7311"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447130421153_7311"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'>David<o:p></o:p></span></p></div></div></div></div></div></div></div></div></div></div></div></blockquote></div></div></div></div><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div></div></div></blockquote></div></div></div></div></div></div></div><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div></div></div></blockquote></div></div></div></div></div></div></div><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-family:"Helvetica Neue";color:black'><o:p> </o:p></span></p></div></div></div></blockquote></div></div></div></div></div></body></html>