<html><head></head><body><div style="color:#000; background-color:#fff; font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:16px"><div id="yui_3_16_0_1_1447289010706_14588"><span id="yui_3_16_0_1_1447289010706_33733">John</span></div><div id="yui_3_16_0_1_1447289010706_14589"><br></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><span style="color: rgb(0, 0, 255); font-family: Cambria;" id="yui_3_16_0_1_1447289010706_19099" class="">> Cl(1,3) </span><span style="font-family: Cambria; font-size: 16px;" id="yui_3_16_0_1_1447289010706_40415" class="">(Ed note: the correct one)</span><br></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><span style="font-family: Cambria; font-size: 16px;" id="yui_3_16_0_1_1447289010706_32623">I owe you an extra pint at the pub for this oversight. </span></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><br></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><span style="color: rgb(0, 0, 255); font-family: Cambria;" id="yui_3_16_0_1_1447289010706_60407" class="">>One can make them non-linear by doing the full product GdG for example. ... 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><br></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><span style="font-family: Cambria;" class=""><br></span></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><span style="font-family: Cambria;" class="" id="yui_3_16_0_1_1447289010706_75906">Challenging but not too difficult to do. One could accomplish setting up a proper computer model with a preparatory start in Excel and then importing the matrix to Comsol. </span></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><span style="font-family: Cambria;" class=""><br></span></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><span style="font-family: Cambria;" class="" id="yui_3_16_0_1_1447289010706_92688">Based on your paper and my goals, what I'm looking for is the nonlinear version for electroweak forces including </span><span style="font-family: Cambria; font-size: 16px;" id="yui_3_16_0_1_1447289010706_101568" class="">partial derivatives of </span><span style="font-family: Cambria; font-size: 16px;" id="yui_3_16_0_1_1447289010706_101570" class="">phase, polarization and spin. The goal would be the specifically model and simulation for testing parametric amplification. </span></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><span style="font-family: Cambria;" class=""><br></span></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><span style="font-family: Cambria;" class=""></span></div><div id="yui_3_16_0_1_1447289010706_14589" dir="ltr" class="">My deepest apologies and condolences on the straw man for the irritating and simplistic approach . </div><div dir="ltr" id="yui_3_16_0_1_1447289010706_130551" class=""><br id="yui_3_16_0_1_1447289010706_130553" class=""></div><div id="yui_3_16_0_1_1447289010706_14589" dir="ltr" class="">The naive-even-for-me strawman has passed, bereft of life, no more, ceased to be, dead, really dead, deceased, expired, off the twig, kicked the bucket...this is an ex-strawparrot, er, ex-strawman. </div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><span style="font-family: Cambria;" class=""><br></span></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><span style="font-family: Cambria;" class=""></span></div><div id="yui_3_16_0_1_1447289010706_14589" dir="ltr" class="">Guinness?</div><div id="yui_3_16_0_1_1447289010706_14589" dir="ltr" class=""><br></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><span style="font-family: Cambria;" class="" id="yui_3_16_0_1_1447289010706_130555">Best regards,</span></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><span style="font-family: Cambria;" class=""><br></span></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><span style="font-family: Cambria;" class="" id="yui_3_16_0_1_1447289010706_94907">David</span></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><span style="font-family: Cambria;" class=""><br></span></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><span style="font-family: Cambria;" class=""><br></span></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><br></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><br></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><span style="font-family: Cambria;" class=""><br></span></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><br></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><br></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><br></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><span style="font-family: Cambria;" class=""><br></span></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><span style="font-family: Cambria;" class=""><br></span></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><span style="font-family: Cambria;" class=""><br></span></div><div id="yui_3_16_0_1_1447289010706_14590" dir="ltr"><span style="font-family: Cambria;" class=""><br></span></div><br> <blockquote style="border-left: 2px solid rgb(16, 16, 255); margin-left: 5px; margin-top: 5px; padding-left: 5px;" id="yui_3_16_0_1_1447289010706_14606"> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 16px;" id="yui_3_16_0_1_1447289010706_14605"> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 16px;" id="yui_3_16_0_1_1447289010706_14604"> <div dir="ltr" id="yui_3_16_0_1_1447289010706_20207"> <hr size="1"> <font size="2" face="Arial" id="yui_3_16_0_1_1447289010706_20208"> <b><span style="font-weight:bold;">From:</span></b> John Williamson <John.Williamson@glasgow.ac.uk><br> <b><span style="font-weight: bold;">To:</span></b> "davidmathes8@yahoo.com" <davidmathes8@yahoo.com> <br><b><span style="font-weight: bold;">Cc:</span></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><span style="font-weight: bold;">Sent:</span></b> Wednesday, November 11, 2015 5:42 PM<br> <b><span style="font-weight: bold;">Subject:</span></b> Re: [General] SU(2) equation set<br> </font> </div> <div class="y_msg_container" id="yui_3_16_0_1_1447289010706_14603"><br><div id="yiv3779983159">
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<div class="yiv3779983159MsoNormal" id="yui_3_16_0_1_1447289010706_20211"><span style="" lang="EN-US">Dear David,<br>
<br>
You are not getting the point. </span></div>
<div class="yiv3779983159MsoNormal" style="text-align:center;" align="center" id="yui_3_16_0_1_1447289010706_20214"><span style="color:black;" lang="EN-US" id="yui_3_16_0_1_1447289010706_20213">
<hr align="center" size="2" width="100%" id="yui_3_16_0_1_1447289010706_20212">
</span></div>
<div class="yiv3779983159MsoNormal" style="margin-bottom:12.0pt;"><b><span style="font-family:Tahoma;color:black;" lang="EN-US">From:</span></b><span style="font-family:Tahoma;color:black;" lang="EN-US">
davidmathes8@yahoo.com [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;" lang="EN-US"></span></div>
<div class="yiv3779983159MsoNormal" style="background:white;"><span style="color:black;" lang="EN-US">John </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;"><span style="color:black;" lang="EN-US">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></div>
<div class="yiv3779983159MsoNormal" style="background:white;"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;"><span style="color:black;" lang="EN-US">For the reader, the papers we are discussing include so far...</span></div>
<div class="yiv3779983159MsoNormal" style="background:white;"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;"><span style="color:black;" lang="EN-US">Williamson 2015 "Absolute relativity in classical electromagnetism:
the quantisation of light"</span></div>
<div class="yiv3779983159MsoNormal" style="background:white;"><span style="color:black;" lang="EN-US"> <a rel="nofollow" target="_blank" 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></div>
<div class="yiv3779983159MsoNormal" style="background:white;"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;"><span style="color:black;" lang="EN-US">Barrett 2000 "Topology and the Physical Properties of Electromagnetic
Fields"</span></div>
<div class="yiv3779983159MsoNormal" style="background:white;"><span style="color:black;" lang="EN-US"><a rel="nofollow" target="_blank" href="http://redshift.vif.com/JournalFiles/Pre2001/V07NO1PDF/V07N1BAR.pdf">http://redshift.vif.com/JournalFiles/Pre2001/V07NO1PDF/V07N1BAR.pdf</a></span></div>
<div class="yiv3779983159MsoNormal" style="background:white;"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_28152"><span style="color:black;" lang="EN-US" id="yui_3_16_0_1_1447289010706_28151">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></div>
<div class="yiv3779983159MsoNormal" style="background:white;"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_28153"><span style="color:black;" lang="EN-US">I'll go back to the starting line...</span></div>
<div class="yiv3779983159MsoNormal" style="background:white;"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_28155"><span style="color:black;" lang="EN-US" id="yui_3_16_0_1_1447289010706_28154">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></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_28156"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_28157"><span style="color:black;" lang="EN-US">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></div>
<div class="yiv3779983159MsoNormal" style="background:white;"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_28159"><span style="color:black;" lang="EN-US" id="yui_3_16_0_1_1447289010706_28158">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></div>
<div class="yiv3779983159MsoNormal" style="background:white;"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_21440"><span style="color:black;" lang="EN-US" id="yui_3_16_0_1_1447289010706_21439">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></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_21441"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_21444"><i id="yui_3_16_0_1_1447289010706_21443"><span style="color:black;" lang="EN-US" id="yui_3_16_0_1_1447289010706_21442">Clearly, both Williamson and Barrett sets do not cover the
full Standard Model, nor were they expected to...</span></i><span style="color:black;" lang="EN-US"></span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_21445"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_21447"><span style="color:black;" lang="EN-US" id="yui_3_16_0_1_1447289010706_21446">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></div>
<div class="yiv3779983159MsoNormal" style="background:white;"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_28161"><span style="color:black;" lang="EN-US" id="yui_3_16_0_1_1447289010706_28160">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></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_14600"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_28162"><span style="color:black;" lang="EN-US">Ok, now to address the email...</span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_28163"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_28164"><span style="color:black;" lang="EN-US">John, </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_28165"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;"><span style="font-family:Tahoma;color:black;" lang="EN-US">> 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;" lang="EN-US"></span></div>
<div class="yiv3779983159MsoNormal" style="background:white;"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_14615"><span style="color:black;" lang="EN-US">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="color:blue;" lang="EN-US" id="yui_3_16_0_1_1447289010706_14614"><br>
The standard model STARTS from putting in a load of groups. Lots and lots of them!</span><span style="color:black;" lang="EN-US"></span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_14612"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_14610"><span style="color:black;" lang="EN-US" id="yui_3_16_0_1_1447289010706_14611">Correct me if I'm wrong, is yours U(1) EM X SU(2) spin?<br>
<br>
</span><span style="color:blue;" lang="EN-US" id="yui_3_16_0_1_1447289010706_14609">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;" lang="EN-US"></span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_28167"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;"><span style="color:black;" lang="EN-US">Does your formulation address EM solitons or Aharnov-Bohm?<br>
<br>
</span><span style="color:blue;" lang="EN-US">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;" lang="EN-US"></span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_14636"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_15742"><span style="color:black;" lang="EN-US" id="yui_3_16_0_1_1447289010706_15741">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="color:blue;" lang="EN-US" id="yui_3_16_0_1_1447289010706_28186">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;" lang="EN-US"></span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_29277"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_15744"><span style="color:black;" lang="EN-US" id="yui_3_16_0_1_1447289010706_29279">My conclusion there is an incompatibility between the Williamson
and Barrett equations. But we don't seem far off.<br>
<br>
</span><span style="color:blue;" lang="EN-US" id="yui_3_16_0_1_1447289010706_16856">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;" lang="EN-US"></span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_16855"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_15765"><span style="color:black;" lang="EN-US">So it's back to basics and hard work on reconciling the two
approaches.<br>
<br>
</span><span style="color:blue;" lang="EN-US" id="yui_3_16_0_1_1447289010706_15764">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;" lang="EN-US"></span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_17972"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_19092"><span style="color:black;" lang="EN-US">Best</span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_30402"><span style="color:black;" lang="EN-US"> </span></div>
<div class="yiv3779983159MsoNormal" style="background:white;" id="yui_3_16_0_1_1447289010706_21452"><span style="color:black;" lang="EN-US" id="yui_3_16_0_1_1447289010706_59298">David</span></div>
<div style="font-family:Times New Roman;color:#000000;font-size:16px;" id="yui_3_16_0_1_1447289010706_21450">
<hr tabindex="-1">
<div style="direction:ltr;" id="yiv3779983159divRpF504081"><font face="Tahoma" color="#000000" size="2"><b>From:</b> davidmathes8@yahoo.com [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<br>
</font><br>
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<div style="color:#000;background-color:#fff;font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:16px;">
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5967"><span id="yiv3779983159yui_3_16_0_1_1447260730724_12051">John </span></div>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5967"><span><br>
</span></div>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5967" dir="ltr"><span id="yiv3779983159yui_3_16_0_1_1447260730724_14213">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></div>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5967"><span><br>
</span></div>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5967"><span><br>
</span></div>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5967"><span id="yiv3779983159yui_3_16_0_1_1447260730724_12153"><font id="yiv3779983159yui_3_16_0_1_1447260730724_12283" size="3">For the reader, the papers we are discussing include so far...</font></span></div>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5967"><span><font size="3"><br>
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<div dir="ltr" id="yiv3779983159yui_3_16_0_1_1447260730724_12081" class="yiv3779983159"><span id="yiv3779983159yui_3_16_0_1_1447260730724_12083" class="yiv3779983159"><font id="yiv3779983159yui_3_16_0_1_1447260730724_12286" size="3">Williamson 2015 "Absolute relativity in classical electromagnetism: the quantisation of light"</font></span></div>
<div dir="ltr" id="yiv3779983159yui_3_16_0_1_1447260730724_12081" class="yiv3779983159"><font id="yiv3779983159yui_3_16_0_1_1447260730724_12285" size="3"><span class="yiv3779983159" id="yiv3779983159yui_3_16_0_1_1447260730724_12084"> </span><a rel="nofollow" shape="rect" id="yiv3779983159yui_3_16_0_1_1447211781778_4472" target="_blank" href="http://eprints.gla.ac.uk/110966/1/110966.pdf" class="yiv3779983159" style="color:purple;">http://eprints.gla.ac.uk/110966/1/110966.pdf</a></font></div>
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<div id="yiv3779983159yui_3_16_0_1_1447260730724_5830"><br>
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<div id="yiv3779983159yui_3_16_0_1_1447260730724_5830">Barrett 2000 "<span id="yiv3779983159yui_3_16_0_1_1447260730724_13672" class="yiv3779983159"><font id="yiv3779983159yui_3_16_0_1_1447260730724_13725" size="3">Topology and the Physical Properties of Electromagnetic Fields"</font></span></div>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5830" dir="ltr"><a rel="nofollow" target="_blank" href="http://redshift.vif.com/JournalFiles/Pre2001/V07NO1PDF/V07N1BAR.pdf" id="yiv3779983159yui_3_16_0_1_1447260730724_13648">http://redshift.vif.com/JournalFiles/Pre2001/V07NO1PDF/V07N1BAR.pdf</a><br>
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<div id="yiv3779983159yui_3_16_0_1_1447260730724_5830"><br>
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<div id="yiv3779983159yui_3_16_0_1_1447260730724_5830" dir="ltr">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).</div>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5830"><br>
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<div id="yiv3779983159yui_3_16_0_1_1447260730724_5830" dir="ltr">I'll go back to the starting line...<span><br>
</span></div>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5830" dir="ltr"><br>
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<div id="yiv3779983159yui_3_16_0_1_1447260730724_5830" dir="ltr">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. </div>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5830" dir="ltr"><br>
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<div id="yiv3779983159yui_3_16_0_1_1447260730724_5830" dir="ltr">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. </div>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5830" dir="ltr"><br>
</div>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5830" dir="ltr">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. </div>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5830" dir="ltr"><br>
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<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr">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.</div>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr"><br>
</div>
<div dir="ltr" id="yiv3779983159yui_3_16_0_1_1447260730724_5790" class="yiv3779983159"><i id="yiv3779983159yui_3_16_0_1_1447260730724_10007" class="yiv3779983159">Clearly, both Williamson and Barrett sets do not cover the full Standard Model, nor were they expected to...</i><br id="yiv3779983159yui_3_16_0_1_1447260730724_11561" class="yiv3779983159">
</div>
<div dir="ltr" id="yiv3779983159yui_3_16_0_1_1447260730724_11563" class="yiv3779983159"><i id="yiv3779983159yui_3_16_0_1_1447260730724_11565" class="yiv3779983159"><br id="yiv3779983159yui_3_16_0_1_1447260730724_11567" class="yiv3779983159">
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<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr">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. </div>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr"><br>
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<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr">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. </div>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr"><br>
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<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr" class="yiv3779983159">Ok, now to address the email...</div>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr" class="yiv3779983159"><br id="yiv3779983159yui_3_16_0_1_1447260730724_14547" class="yiv3779983159">
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<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr" class="yiv3779983159">John, </div>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr" class="yiv3779983159"><br id="yiv3779983159yui_3_16_0_1_1447260730724_14551" class="yiv3779983159">
</div>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr"><span id="yiv3779983159yui_3_16_0_1_1447260730724_14473" class="yiv3779983159" style="font-family:Tahoma;font-size:13px;">> 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><br>
</div>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr"><br>
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<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr">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>
<font color="0000FF"><br>
The standard model STARTS from putting in a load of groups. Lots and lots of them!</font><br>
</div>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr"><br>
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<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr">Correct me if I'm wrong, is yours U(1) EM X SU(2) spin?<br>
<br>
<font color="0000FF">No. I do not put any group in a-priori at all! <font color="0000FF">
All I put in is the <font color="0000FF">relat<font color="0000FF">i</font>vistic properties of space and time - and energy.</font></font></font><br>
</div>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr"><br>
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<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr">Does your formulation address EM solitons or Aharnov-Bohm?<br>
<br>
<font color="0000FF">Yes of course. The electron solution is a soliton - look at it!
<font color="0000FF">Y</font>es - Aharonov Bohm is in there and much much more. All the Aharonov Bohm stuff does is insert a<font color="0000FF">n eA</font> phase change - I have a set of four coupled differential equations expressing the proper interaction
of the vector potential with t<font color="0000FF">he spin</font>. The full implications of all the products of the static and the dynamic are contained in Martin and my previous work on forces.
<font color="0000FF">Barret is not fundamental. It</font> 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<font color="0000FF">.</font><br>
</font></div>
<font color="0000FF"></font>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr"><br>
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<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr">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>
<font color="0000FF">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.
<font color="0000FF">Without a proper base theory (which I hope mine is) p</font>eople are stabbing in the dark<font color="0000FF">.</font>.<br>
</font></div>
<font color="0000FF"></font>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr"><br>
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<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr">My conclusion there is an incompatibility between the Williamson and Barrett equations. But we don't seem far off.<br>
<br>
<font color="0000FF">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 -
b<font color="0000FF">y</font> putting nothing in except space, time and energy. To be clear: N<font color="0000FF">o</font> 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.
Th<font color="0000FF">at is the Clifford-Dirac algebra Cl(1,3) (and not Cl<font color="0000FF">(3,1, which is different).</font></font></font><br>
</div>
<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr"><br>
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<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr">So it's back to basics and hard work on reconciling the two approaches.<br>
<br>
<font color="0000FF">No need to reconcile anything. Barrett i<font color="0000FF">s</font> 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).<br>
</font></div>
<font color="0000FF"></font>
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<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr">Best</div>
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<div id="yiv3779983159yui_3_16_0_1_1447260730724_5645" dir="ltr">David</div>
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<blockquote id="yiv3779983159yui_3_16_0_1_1447260730724_5644" style="border-left:2px solid rgb(16,16,255);margin-left:5px;margin-top:5px;padding-left:5px;">
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<div id="yiv3779983159yui_3_16_0_1_1447260730724_5642" style="font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:16px;">
<div dir="ltr" id="yiv3779983159yui_3_16_0_1_1447260730724_5641">
<hr id="yiv3779983159yui_3_16_0_1_1447260730724_9954" size="1">
<font id="yiv3779983159yui_3_16_0_1_1447260730724_5683" face="Arial" size="2"><b id="yiv3779983159yui_3_16_0_1_1447260730724_14436"><span id="yiv3779983159yui_3_16_0_1_1447260730724_14435" style="font-weight:bold;">From:</span></b> John Williamson <John.Williamson@glasgow.ac.uk><br>
<b id="yiv3779983159yui_3_16_0_1_1447260730724_14438"><span id="yiv3779983159yui_3_16_0_1_1447260730724_14437" style="font-weight:bold;">To:</span></b> "davidmathes8@yahoo.com" <davidmathes8@yahoo.com>
<br>
<b id="yiv3779983159yui_3_16_0_1_1447260730724_14440"><span id="yiv3779983159yui_3_16_0_1_1447260730724_14439" style="font-weight:bold;">Cc:</span></b> "Mark, Martin van der" <martin.van.der.mark@philips.com>; Nature of Light and Particles - General Discussion <general@lists.natureoflightandparticles.org>
<br>
<b id="yiv3779983159yui_3_16_0_1_1447260730724_14442"><span id="yiv3779983159yui_3_16_0_1_1447260730724_14441" style="font-weight:bold;">Sent:</span></b> Wednesday, November 11, 2015 5:17 AM<br>
<b><span style="font-weight:bold;">Subject:</span></b> RE: SU(2) equation set<br>
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Dear David,<br clear="none">
<br clear="none">
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 clear="none">
<br clear="none">
Regards, John.<br clear="none">
<div class="yiv3779983159qtdSeparateBR"><br>
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<div class="yiv3779983159yqt3992645398" id="yiv3779983159yqt11989">
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<hr tabindex="-1" id="yiv3779983159yui_3_16_0_1_1447260730724_14364">
<div id="yiv3779983159divRpF961264" style="direction:ltr;"><font id="yiv3779983159yui_3_16_0_1_1447260730724_14363" face="Tahoma" color="#000000" size="2"><b>From:</b> davidmathes8@yahoo.com [davidmathes8@yahoo.com]<br clear="none">
<b>Sent:</b> Wednesday, November 11, 2015 4:50 AM<br clear="none">
<b>To:</b> John Williamson<br clear="none">
<b>Subject:</b> Re: SU(2) equation set<br clear="none">
</font><br clear="none">
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<div id="yiv3779983159yui_3_16_0_1_1447260730724_11982">
<div id="yiv3779983159yui_3_16_0_1_1447260730724_11981" style="color:#000;background-color:#fff;font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:16px;">
<div id="yiv3779983159yui_3_16_0_1_1447260730724_11980"><span>John</span></div>
<div id="yiv3779983159yui_3_16_0_1_1447216954511_3107"><span><br clear="none">
</span></div>
<div id="yiv3779983159yui_3_16_0_1_1447216954511_3102"><span>The straw man failed.</span></div>
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<div id="yiv3779983159yui_3_16_0_1_1447216954511_3101"><span id="yiv3779983159yui_3_16_0_1_1447216954511_3100">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></div>
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<div id="yiv3779983159yui_3_16_0_1_1447216954511_3096"><span>David</span></div>
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<font id="yiv3779983159yui_3_16_0_1_1447216954511_3047" face="Arial" size="2"><b><span style="font-weight:bold;">From:</span></b> John Williamson <John.Williamson@glasgow.ac.uk><br clear="none">
<b><span style="font-weight:bold;">To:</span></b> "davidmathes8@yahoo.com" <davidmathes8@yahoo.com>
<br clear="none">
<b><span style="font-weight:bold;">Sent:</span></b> Tuesday, November 10, 2015 8:39 PM<br clear="none">
<b><span style="font-weight:bold;">Subject:</span></b> RE: SU(2) equation set<br clear="none">
</font></div>
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Hello David,<br clear="none">
<br clear="none">
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 clear="none">
<br clear="none">
Also, I see the U(1) part of what you are doing - but where is the SU(2) part?<br clear="none">
<br clear="none">
Regards, John.<br clear="none">
<div class="yiv3779983159qtdSeparateBR"><br clear="none">
<br clear="none">
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<div class="yiv3779983159yqt8670471533" id="yiv3779983159yqt71629">
<div id="yiv3779983159yui_3_16_0_1_1447216954511_3109" style="font-family:Times New Roman;color:#000000;font-size:16px;">
<hr tabindex="-1">
<div id="yiv3779983159divRpF343849" style="direction:ltr;"><font id="yiv3779983159yui_3_16_0_1_1447216954511_3110" face="Tahoma" color="#000000" size="2"><b>From:</b> davidmathes8@yahoo.com [davidmathes8@yahoo.com]<br clear="none">
<b>Sent:</b> Wednesday, November 11, 2015 3:38 AM<br clear="none">
<b>To:</b> John Williamson<br clear="none">
<b>Subject:</b> SU(2) equation set<br clear="none">
</font><br clear="none">
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<div></div>
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<div id="yiv3779983159yui_3_16_0_1_1447216954511_3111" style="color:#000;background-color:#fff;font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:16px;">
<div id="yiv3779983159yui_3_16_0_1_1447211781778_3751">John</div>
<div id="yiv3779983159yui_3_16_0_1_1447211781778_3751"><br clear="none">
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<div id="yiv3779983159yui_3_16_0_1_1447211781778_3751">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. </div>
<div id="yiv3779983159yui_3_16_0_1_1447211781778_3751"><br clear="none">
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<div dir="ltr" id="yiv3779983159yui_3_16_0_1_1447211781778_3751">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. </div>
<div id="yiv3779983159yui_3_16_0_1_1447211781778_3751"><br clear="none">
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<div id="yiv3779983159yui_3_16_0_1_1447211781778_3751">Right now, there is confusion in notation with a conflicts in the use of A and B. </div>
<div id="yiv3779983159yui_3_16_0_1_1447211781778_3751"><br clear="none">
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<div id="yiv3779983159yui_3_16_0_1_1447211781778_3751">See attached.</div>
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<div id="yiv3779983159yui_3_16_0_1_1447211781778_3751">David</div>
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<font id="yiv3779983159yui_3_16_0_1_1447211781778_4488" face="Arial" size="2"><b><span style="font-weight:bold;">From:</span></b> "davidmathes8@yahoo.com" <davidmathes8@yahoo.com><br clear="none">
<b><span style="font-weight:bold;">To:</span></b> John Williamson <John.Williamson@glasgow.ac.uk>
<br clear="none">
<b><span style="font-weight:bold;">Sent:</span></b> Tuesday, November 10, 2015 8:25 AM<br clear="none">
<b><span style="font-weight:bold;">Subject:</span></b> Re: Slide Deck<br clear="none">
</font></div>
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<div id="yiv3779983159yui_3_16_0_1_1447171858799_10495"><span>John</span></div>
<div id="yiv3779983159yui_3_16_0_1_1447171858799_10496"><span><br clear="none">
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<div id="yiv3779983159yui_3_16_0_1_1447171858799_10497">Thank you. now I recall these papers this summer's work. So not that winter is begun (raining in California), I'll reread them.</div>
<div id="yiv3779983159yui_3_16_0_1_1447171858799_10497"><br clear="none">
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<div id="yiv3779983159yui_3_16_0_1_1447171858799_10497">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).</div>
<div id="yiv3779983159yui_3_16_0_1_1447171858799_10497"><br clear="none">
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<div dir="ltr" id="yiv3779983159yui_3_16_0_1_1447171858799_10497"><a rel="nofollow" shape="rect" id="yiv3779983159yui_3_16_0_1_1447171858799_12694" target="_blank" href="http://aflb.ensmp.fr/AFLB-26j/aflb26jp055.pdf">http://aflb.ensmp.fr/AFLB-26j/aflb26jp055.pdf</a><br clear="none">
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<div id="yiv3779983159yui_3_16_0_1_1447171858799_10497">Best regards my friend,</div>
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<div id="yiv3779983159yui_3_16_0_1_1447171858799_10497">David</div>
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<font id="yiv3779983159yui_3_16_0_1_1447171858799_13235" face="Arial" size="2"><b id="yiv3779983159yui_3_16_0_1_1447171858799_13274"><span id="yiv3779983159yui_3_16_0_1_1447171858799_13273" style="font-weight:bold;">From:</span></b> John Williamson <John.Williamson@glasgow.ac.uk><br clear="none">
<b><span style="font-weight:bold;">To:</span></b> "davidmathes8@yahoo.com" <davidmathes8@yahoo.com>
<br clear="none">
<b><span style="font-weight:bold;">Sent:</span></b> Monday, November 9, 2015 11:14 PM<br clear="none">
<b id="yiv3779983159yui_3_16_0_1_1447171858799_13276"><span id="yiv3779983159yui_3_16_0_1_1447171858799_13275" style="font-weight:bold;">Subject:</span></b> RE: Slide Deck<br clear="none">
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Hello David,<br clear="none">
<br clear="none">
SPIE papers at:<font id="yiv3779983159yui_3_16_0_1_1447211781778_4470" face="Tahoma" color="black" size="2"><span dir="ltr" id="yiv3779983159yui_3_16_0_1_1447211781778_4469" style="font-size:10pt;"><br clear="none">
<br clear="none">
<a rel="nofollow" shape="rect" id="yiv3779983159yui_3_16_0_1_1447211781778_4468" target="_blank" href="http://eprints.gla.ac.uk/110952/1/110952.pdf">http://eprints.gla.ac.uk/110952/1/110952.pdf</a><br clear="none">
<a rel="nofollow" shape="rect" id="yiv3779983159yui_3_16_0_1_1447211781778_4472" target="_blank" href="http://eprints.gla.ac.uk/110966/1/110966.pdf">http://eprints.gla.ac.uk/110966/1/110966.pdf</a><br clear="none">
<br clear="none">
Regards, John.</span></font><br clear="none">
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<div class="yiv3779983159yqt8981336933" id="yiv3779983159yqt04806">
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<hr tabindex="-1">
<div id="yiv3779983159divRpF276520" style="direction:ltr;"><font id="yiv3779983159yui_3_16_0_1_1447211781778_4474" face="Tahoma" color="#000000" size="2"><b>From:</b> davidmathes8@yahoo.com [davidmathes8@yahoo.com]<br clear="none">
<b>Sent:</b> Tuesday, November 10, 2015 5:09 AM<br clear="none">
<b>To:</b> John Williamson<br clear="none">
<b>Subject:</b> Slide Deck<br clear="none">
</font><br clear="none">
</div>
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<div id="yiv3779983159yui_3_16_0_1_1447130421153_7312"><span>John</span></div>
<div id="yiv3779983159yui_3_16_0_1_1447130421153_7311"><span><br clear="none">
</span></div>
<div id="yiv3779983159yui_3_16_0_1_1447130421153_7311"><span id="yiv3779983159yui_3_16_0_1_1447211781778_4687">Do you have a slide deck summarizing the model? </span></div>
<div id="yiv3779983159yui_3_16_0_1_1447130421153_7311"><span><br clear="none">
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<div id="yiv3779983159yui_3_16_0_1_1447130421153_7311"><span>Best</span></div>
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<div id="yiv3779983159yui_3_16_0_1_1447130421153_7311"><span>David</span></div>
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