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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 W.<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'>Some of my background is in aerodynamic simulation, where I have written more than 500K lines of ‘C’ code and created one of the world’s most accurate real-time simulations of flight. Lots of use of quaternions and fluid mechanics of course.<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'>I have written code in many different languages, so practically any we choose will work for me.<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'>In order to start we will need to do as you suggest and look at the fundamentals to create a library of functions we can call as required.<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'>So if I can look at Stephen’s Python code for multiplications that would help me get a handle on how to write the division and differentiation low level code.<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'>Some personal experience and observations…<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Times New Roman",serif;color:black'>Object oriented code generally takes more time to design and runs a little slower, but it protects and manages the data and functions operating on the data as individual objects. Object oriented code generally uses more memory as well. Computation time, and memory capacity, are really critical for us because of the tremendous computational load it will take to do the simulation at any useful scale. So when we were writing flight simulation code, which had to compute all the forces and moments in real time, at about 120 times a second, we wrote it all in ‘C’. I am bringing this up because even now, when I am doing physics modeling, which is much simpler than the task at hand, I often have to wait an hour for the results from our fairly large and very fast workstations here in the office. It would be nice to create the simulation in the fastest running code we can, so that we have some hope of getting results in reasonable time, without having to rent expensive time on, or build a supercomputer.<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'>But those opinions are not as important as getting the foundation in place so we can start doing some real work in simulating particles, and interactions. Exciting stuff.<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><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'><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> Thursday, November 12, 2015 7:37 AM<br><b>To:</b> Nature of Light and Particles - General Discussion <general@lists.natureoflightandparticles.org><br><b>Cc:</b> Nick Bailey <nick@bailey-family.org.uk>; Stephen Leary <sleary@vavi.co.uk>; 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 style='margin-bottom:12.0pt'><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black'>Now we are talking.<br><br>I suggest we convene a sub-group of computer and simulation savvy folk. That should be you, me, Stephen Leary, Nick Green, Tim Drysdale (an expert in Maxwell solutions), my friend Nick Bailey and maybe Joakim, my brothers Pete and David and any others who express an interest.<br><br>I have written (big!) computer simulation software programmes in the past, but that was to do quantum electrodynamics and quantum chromodynamics and was written in FORTRAN! Not good enough for the task in hand!<br><br>Firstly need to implement a system with primitive operations which parallel the workings of the space-time algebra. Multiplications, divisions and differentiations in particular. It would be nice if such a framework existed already, but I do not think so. Stephen has written a suite in PYTHON to deal with the multiplications, which may be a start. Not sure what is best here: C++?, Python?, Something else?<br><br>Next need to devise a basis. Obvious thing is space and time and things derived from space and time. This could be the 16 Linearly independent elements or something cleverer derived from the 4-basis of space and time. I do not know how smart we can get here. I have no expertise in object-oriented code - but these methods may be useful in describing the levels of complexity required.<br><br>Following need to choose a finite element or finite difference technique, which may be tested on the subset of the Maxwell equations alone, for which there exists an extensive literature.<br><br>That is only the start!<br><br>Regards, John.<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=divRpF894111><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'> General [general-bounces+john.williamson=glasgow.ac.uk@lists.natureoflightandparticles.org] on behalf of Chip Akins [chipakins@gmail.com]<br><b>Sent:</b> Thursday, November 12, 2015 12:16 PM<br><b>To:</b> 'Nature of Light and Particles - General Discussion'<br><b>Subject:</b> Re: [General] SU(2) equation set</span><span style='font-family:"Times New Roman",serif;color:black'><o:p></o:p></span></p></div><div><div><p class=MsoNormal><span style='font-family:"Times New Roman",serif;color:black'>Hi John</span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Times New Roman",serif;color:black'> </span><span style='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?</span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Times New Roman",serif;color:black'> </span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Times New Roman",serif;color:black'>Chip</span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Times New Roman",serif;color:black'> </span><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;color:black'>From:</span></b><span style='font-size:11.0pt;color:black'> General [</span><a href="mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org"><span style='font-size:11.0pt'>mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;color:black'>] <b>On Behalf Of </b>John Williamson<br><b>Sent:</b> Wednesday, November 11, 2015 7:43 PM<br><b>To:</b> </span><a href="mailto:davidmathes8@yahoo.com"><span style='font-size:11.0pt'>davidmathes8@yahoo.com</span></a><span style='font-size:11.0pt;color:black'><br><b>Cc:</b> Nature of Light and Particles - General Discussion <</span><a href="mailto:general@lists.natureoflightandparticles.org"><span style='font-size:11.0pt'>general@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;color:black'>>; Nick Bailey <</span><a href="mailto:nick@bailey-family.org.uk"><span style='font-size:11.0pt'>nick@bailey-family.org.uk</span></a><span style='font-size:11.0pt;color:black'>>; Anthony Booth <</span><a href="mailto:abooth@ieee.org"><span style='font-size:11.0pt'>abooth@ieee.org</span></a><span style='font-size:11.0pt;color:black'>>; Mark, Martin van der <</span><a href="mailto:martin.van.der.mark@philips.com"><span style='font-size:11.0pt'>martin.van.der.mark@philips.com</span></a><span style='font-size:11.0pt;color:black'>><br><b>Subject:</b> Re: [General] SU(2) equation set</span><span style='color:black'><o:p></o:p></span></p></div></div><p class=MsoNormal><span style='color:black'> <o:p></o:p></span></p><div><p class=MsoNormal><span style='color:black'>Dear David,<br><br>You are not getting the point. <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'> </span><a href="mailto:davidmathes8@yahoo.com" target="_blank"><span style='font-family:"Tahoma",sans-serif'>davidmathes8@yahoo.com</span></a><span style='font-family:"Tahoma",sans-serif;color:black'> [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'> </span><a href="http://eprints.gla.ac.uk/110966/1/110966.pdf" target="_blank"><span style='font-family:"Helvetica Neue";color:purple'>http://eprints.gla.ac.uk/110966/1/110966.pdf</span></a><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'><a href="http://redshift.vif.com/JournalFiles/Pre2001/V07NO1PDF/V07N1BAR.pdf" target="_blank"><span style='font-family:"Helvetica Neue"'>http://redshift.vif.com/JournalFiles/Pre2001/V07NO1PDF/V07N1BAR.pdf</span></a><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'> </span><a href="mailto:davidmathes8@yahoo.com" target="_blank"><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif'>davidmathes8@yahoo.com</span></a><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black'> [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></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 </span><span style='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'> </span><span style='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. </span><span style='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'> </span><span style='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'> </span><span style='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...</span><span style='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'> </span><span style='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"</span><span style='color:black'><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'> </span><a href="http://eprints.gla.ac.uk/110966/1/110966.pdf" target="_blank" id="yiv3919935515yui_3_16_0_1_1447211781778_4472"><span style='font-family:"Helvetica Neue";color:purple'>http://eprints.gla.ac.uk/110966/1/110966.pdf</span></a><span style='color:black'><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'> </span><span style='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"</span><span style='color:black'><o:p></o:p></span></p></div><div id="yui_3_16_0_1_1447260730724_5830"><p class=MsoNormal style='background:white'><a href="http://redshift.vif.com/JournalFiles/Pre2001/V07NO1PDF/V07N1BAR.pdf" target="_blank"><span style='font-family:"Helvetica Neue"'>http://redshift.vif.com/JournalFiles/Pre2001/V07NO1PDF/V07N1BAR.pdf</span></a><span style='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'> </span><span style='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).</span><span style='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'> </span><span style='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...</span><span style='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'> </span><span style='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. </span><span style='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'> </span><span style='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. </span><span style='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'> </span><span style='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. </span><span style='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'> </span><span style='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.</span><span style='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'> </span><span style='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='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'> </span><span style='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. </span><span style='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'> </span><span style='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. </span><span style='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'> </span><span style='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...</span><span style='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'> </span><span style='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, </span><span style='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'> </span><span style='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='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'> </span><span style='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='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'> </span><span style='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='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'> </span><span style='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='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'> </span><span style='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='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'> </span><span style='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='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'> </span><span style='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='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'> </span><span style='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</span><span style='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'> </span><span style='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</span><span style='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'> </span><span style='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'> </span><span style='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'> </span><span style='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'> </span><span style='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'> </span><span style='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'> </span><span style='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'> </span><span style='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'> </span><span style='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 <</span><a href="mailto:John.Williamson@glasgow.ac.uk" target="_blank"><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>John.Williamson@glasgow.ac.uk</span></a><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'>><br><b id="yui_3_16_0_1_1447260730724_14438">To:</b> "</span><a href="mailto:davidmathes8@yahoo.com" target="_blank"><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>davidmathes8@yahoo.com</span></a><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'>" <</span><a href="mailto:davidmathes8@yahoo.com" target="_blank"><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>davidmathes8@yahoo.com</span></a><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'>> <br><b id="yui_3_16_0_1_1447260730724_14440">Cc:</b> "Mark, Martin van der" <</span><a href="mailto:martin.van.der.mark@philips.com" target="_blank"><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>martin.van.der.mark@philips.com</span></a><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'>>; Nature of Light and Particles - General Discussion <</span><a href="mailto:general@lists.natureoflightandparticles.org" target="_blank"><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>general@lists.natureoflightandparticles.org</span></a><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'>> <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='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'> </span><span style='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.</span><span style='color:black'><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'> </span><span style='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></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'> </span><a href="mailto:davidmathes8@yahoo.com" target="_blank"><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif'>davidmathes8@yahoo.com</span></a><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black'> [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='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</span><span style='color:black'><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'> </span><span style='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.</span><span style='color:black'><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'> </span><span style='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?</span><span style='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'> </span><span style='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</span><span style='color:black'><o:p></o:p></span></p></div><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='color:black'><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 <</span><a href="mailto:John.Williamson@glasgow.ac.uk" target="_blank"><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>John.Williamson@glasgow.ac.uk</span></a><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'>><br><b>To:</b> "</span><a href="mailto:davidmathes8@yahoo.com" target="_blank"><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>davidmathes8@yahoo.com</span></a><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'>" <</span><a href="mailto:davidmathes8@yahoo.com" target="_blank"><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>davidmathes8@yahoo.com</span></a><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'>> <br><b>Sent:</b> Tuesday, November 10, 2015 8:39 PM<br><b>Subject:</b> RE: SU(2) equation set</span><span style='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'> </span><span style='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.</span><span style='color:black'><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'> </span><span style='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'> </span><a href="mailto:davidmathes8@yahoo.com" target="_blank"><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif'>davidmathes8@yahoo.com</span></a><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black'> [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='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</span><span style='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'> </span><span style='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. </span><span style='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'> </span><span style='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. </span><span style='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'> </span><span style='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. </span><span style='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'> </span><span style='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.</span><span style='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'> </span><span style='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</span><span style='color:black'><o:p></o:p></span></p></div><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='color:black'><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'> "</span><a href="mailto:davidmathes8@yahoo.com" target="_blank"><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>davidmathes8@yahoo.com</span></a><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'>" <</span><a href="mailto:davidmathes8@yahoo.com" target="_blank"><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>davidmathes8@yahoo.com</span></a><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'>><br><b>To:</b> John Williamson <</span><a href="mailto:John.Williamson@glasgow.ac.uk" target="_blank"><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>John.Williamson@glasgow.ac.uk</span></a><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'>> <br><b>Sent:</b> Tuesday, November 10, 2015 8:25 AM<br><b>Subject:</b> Re: Slide Deck</span><span style='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'> </span><span style='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</span><span style='color:black'><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'> </span><span style='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.</span><span style='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'> </span><span style='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).</span><span style='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'> </span><span style='color:black'><o:p></o:p></span></p></div><div id="yiv3919935515yui_3_16_0_1_1447171858799_10497"><p class=MsoNormal style='background:white'><a href="http://aflb.ensmp.fr/AFLB-26j/aflb26jp055.pdf" target="_blank"><span style='font-family:"Helvetica Neue"'>http://aflb.ensmp.fr/AFLB-26j/aflb26jp055.pdf</span></a><span style='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'> </span><span style='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,</span><span style='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'> </span><span style='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</span><span style='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'> </span><span style='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'> </span><span style='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'> </span><span style='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'> </span><span style='color:black'><o:p></o:p></span></p></div><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><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'> </span><span style='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 <</span><a href="mailto:John.Williamson@glasgow.ac.uk" target="_blank"><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>John.Williamson@glasgow.ac.uk</span></a><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'>><br><b>To:</b> "</span><a href="mailto:davidmathes8@yahoo.com" target="_blank"><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>davidmathes8@yahoo.com</span></a><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'>" <</span><a href="mailto:davidmathes8@yahoo.com" target="_blank"><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>davidmathes8@yahoo.com</span></a><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'>> <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='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'> </span><span style='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></span><a href="http://eprints.gla.ac.uk/110952/1/110952.pdf" target="_blank" id="yiv3919935515yui_3_16_0_1_1447211781778_4468"><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif'>http://eprints.gla.ac.uk/110952/1/110952.pdf</span></a><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black'><br></span><a href="http://eprints.gla.ac.uk/110966/1/110966.pdf" target="_blank" id="yiv3919935515yui_3_16_0_1_1447211781778_4472"><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif'>http://eprints.gla.ac.uk/110966/1/110966.pdf</span></a><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black'><br><br>Regards, John.</span><span style='color:black'><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'> </span><span style='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'> </span><a href="mailto:davidmathes8@yahoo.com" target="_blank"><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif'>davidmathes8@yahoo.com</span></a><span style='font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black'> [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='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</span><span style='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'> </span><span style='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? </span><span style='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'> </span><span style='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</span><span style='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'> </span><span style='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</span><span style='color:black'><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'> </span><span style='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'> </span><span style='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'> </span><span style='color:black'><o:p></o:p></span></p></div></div></div></blockquote></div></div></div></div></div></div></div></div></div></body></html>