<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_1447260730724_5967"><span id="yui_3_16_0_1_1447260730724_12051">John </span></div><div id="yui_3_16_0_1_1447260730724_5967"><span><br></span></div><div id="yui_3_16_0_1_1447260730724_5967" dir="ltr"><span id="yui_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="yui_3_16_0_1_1447260730724_5967"><span><br></span></div><div id="yui_3_16_0_1_1447260730724_5967"><span><br></span></div><div id="yui_3_16_0_1_1447260730724_5967"><span id="yui_3_16_0_1_1447260730724_12153"><font size="3" id="yui_3_16_0_1_1447260730724_12283">For the reader, the papers we are discussing include so far...</font></span></div><div id="yui_3_16_0_1_1447260730724_5967"><span><font size="3"><br></font></span></div><div id="yui_3_16_0_1_1447260730724_5967">
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<div dir="ltr" id="yui_3_16_0_1_1447260730724_12081" class=""><span id="yui_3_16_0_1_1447260730724_12083" class=""><font size="3" id="yui_3_16_0_1_1447260730724_12286">Williamson 2015 "Absolute relativity in classical electromagnetism: the
quantisation of light"</font></span></div><div dir="ltr" id="yui_3_16_0_1_1447260730724_12081" class=""><font size="3" id="yui_3_16_0_1_1447260730724_12285"><span class="" id="yui_3_16_0_1_1447260730724_12084"> </span><a rel="nofollow" shape="rect" id="yiv3919935515yui_3_16_0_1_1447211781778_4472" target="_blank" href="http://eprints.gla.ac.uk/110966/1/110966.pdf" style="color: purple;" class="">http://eprints.gla.ac.uk/110966/1/110966.pdf</a></font></div><font size="3">
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</div><div id="yui_3_16_0_1_1447260730724_5830"><br></div><div id="yui_3_16_0_1_1447260730724_5830">Barrett 2000 "<span id="yui_3_16_0_1_1447260730724_13672" class=""><font size="3" id="yui_3_16_0_1_1447260730724_13725">Topology and the Physical
Properties of Electromagnetic
Fields"</font></span></div><div id="yui_3_16_0_1_1447260730724_5830" dir="ltr"><a href="http://redshift.vif.com/JournalFiles/Pre2001/V07NO1PDF/V07N1BAR.pdf" id="yui_3_16_0_1_1447260730724_13648">http://redshift.vif.com/JournalFiles/Pre2001/V07NO1PDF/V07N1BAR.pdf</a><br></div><div id="yui_3_16_0_1_1447260730724_5830"><br></div><div id="yui_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="yui_3_16_0_1_1447260730724_5830"><br></div><div id="yui_3_16_0_1_1447260730724_5830" dir="ltr">I'll go back to the starting line...<span><br></span></div><div id="yui_3_16_0_1_1447260730724_5830" dir="ltr"><br></div><div id="yui_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="yui_3_16_0_1_1447260730724_5830" dir="ltr"><br></div><div id="yui_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="yui_3_16_0_1_1447260730724_5830" dir="ltr"><br></div><div id="yui_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="yui_3_16_0_1_1447260730724_5830" dir="ltr"><br></div><div id="yui_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="yui_3_16_0_1_1447260730724_5645" dir="ltr"><br></div><div dir="ltr" id="yui_3_16_0_1_1447260730724_5790" class=""><i id="yui_3_16_0_1_1447260730724_10007" class="">Clearly, both Williamson and Barrett sets do not cover the full Standard Model, nor were they expected to...</i><br id="yui_3_16_0_1_1447260730724_11561" class=""></div><div dir="ltr" id="yui_3_16_0_1_1447260730724_11563" class=""><i id="yui_3_16_0_1_1447260730724_11565" class=""><br id="yui_3_16_0_1_1447260730724_11567" class=""></i></div><div id="yui_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="yui_3_16_0_1_1447260730724_5645" dir="ltr"><br></div><div id="yui_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="yui_3_16_0_1_1447260730724_5645" dir="ltr"><br></div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr" class="">Ok, now to address the email...</div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr" class=""><br id="yui_3_16_0_1_1447260730724_14547" class=""></div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr" class="">John, </div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr" class=""><br id="yui_3_16_0_1_1447260730724_14551" class=""></div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr"><span style="font-family: Tahoma; font-size: 13px;" id="yui_3_16_0_1_1447260730724_14473" class="">> 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="yui_3_16_0_1_1447260730724_5645" dir="ltr"><br></div><div id="yui_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</div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr"><br></div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr">Correct me if I'm wrong, is yours U(1) EM X SU(2) spin?<br></div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr"><br></div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr">Does your formulation address EM solitons or Aharnov-Bohm?</div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr"><br></div><div id="yui_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.</div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr"><br></div><div id="yui_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.</div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr"><br></div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr">So it's back to basics and hard work on reconciling the two approaches.</div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr"><br></div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr">Best</div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr"><br></div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr">David</div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr"><br></div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr"><br></div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr"><br></div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr"><br></div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr"><br></div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr"><br></div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr"><br></div><div id="yui_3_16_0_1_1447260730724_5645" dir="ltr"><br></div> <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_1447260730724_5644"> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 16px;" id="yui_3_16_0_1_1447260730724_5643"> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 16px;" id="yui_3_16_0_1_1447260730724_5642"> <div dir="ltr" id="yui_3_16_0_1_1447260730724_5641"> <hr size="1" id="yui_3_16_0_1_1447260730724_9954"> <font size="2" face="Arial" id="yui_3_16_0_1_1447260730724_5683"> <b id="yui_3_16_0_1_1447260730724_14436"><span style="font-weight:bold;" id="yui_3_16_0_1_1447260730724_14435">From:</span></b> John Williamson <John.Williamson@glasgow.ac.uk><br> <b id="yui_3_16_0_1_1447260730724_14438"><span style="font-weight: bold;" id="yui_3_16_0_1_1447260730724_14437">To:</span></b> "davidmathes8@yahoo.com" <davidmathes8@yahoo.com> <br><b id="yui_3_16_0_1_1447260730724_14440"><span style="font-weight: bold;" id="yui_3_16_0_1_1447260730724_14439">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="yui_3_16_0_1_1447260730724_14442"><span style="font-weight: bold;" id="yui_3_16_0_1_1447260730724_14441">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> </font> </div> <div class="y_msg_container" id="yui_3_16_0_1_1447260730724_5684"><br><div id="yiv3919935515"><style type="text/css"></style><div id="yui_3_16_0_1_1447260730724_5686">
<div style="direction:ltr;font-family:Tahoma;color:#000000;font-size:10pt;" id="yui_3_16_0_1_1447260730724_5685">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="qtdSeparateBR"><br><br></div><div class="yiv3919935515yqt3992645398" id="yiv3919935515yqt11989"><div style="font-family:Times New Roman;color:#000000;font-size:16px;" id="yui_3_16_0_1_1447260730724_11983">
<hr tabindex="-1" id="yui_3_16_0_1_1447260730724_14364">
<div id="yiv3919935515divRpF961264" style="direction:ltr;"><font face="Tahoma" color="#000000" size="2" id="yui_3_16_0_1_1447260730724_14363"><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">
</div>
<div></div>
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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;" id="yui_3_16_0_1_1447260730724_11981">
<div id="yui_3_16_0_1_1447260730724_11980"><span>John</span></div>
<div id="yiv3919935515yui_3_16_0_1_1447216954511_3107"><span><br clear="none">
</span></div>
<div id="yiv3919935515yui_3_16_0_1_1447216954511_3102"><span>The straw man failed.</span></div>
<div id="yiv3919935515yui_3_16_0_1_1447216954511_3108"><span><br clear="none">
</span></div>
<div id="yiv3919935515yui_3_16_0_1_1447216954511_3101"><span id="yiv3919935515yui_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>
<div id="yiv3919935515yui_3_16_0_1_1447216954511_3096"><span><br clear="none">
</span></div>
<div id="yiv3919935515yui_3_16_0_1_1447216954511_3096"><span>David</span></div>
<br clear="none">
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<font id="yiv3919935515yui_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>
<div class="yiv3919935515y_msg_container" id="yiv3919935515yui_3_16_0_1_1447216954511_3097"><br clear="none">
<div id="yiv3919935515"><style type="text/css">
#yiv3919935515 #yiv3919935515
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<div id="yiv3919935515yui_3_16_0_1_1447216954511_3098" style="direction:ltr;font-family:Tahoma;color:#000000;font-size:10pt;">
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="yiv3919935515qtdSeparateBR"><br clear="none">
<br clear="none">
</div>
<div class="yiv3919935515yqt8670471533" id="yiv3919935515yqt71629">
<div id="yiv3919935515yui_3_16_0_1_1447216954511_3109" style="font-family:Times New Roman;color:#000000;font-size:16px;">
<hr tabindex="-1">
<div id="yiv3919935515divRpF343849" style="direction:ltr;"><font id="yiv3919935515yui_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">
</div>
<div></div>
<div id="yiv3919935515yui_3_16_0_1_1447216954511_3112">
<div id="yiv3919935515yui_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="yiv3919935515yui_3_16_0_1_1447211781778_3751">John</div>
<div id="yiv3919935515yui_3_16_0_1_1447211781778_3751"><br clear="none">
</div>
<div id="yiv3919935515yui_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="yiv3919935515yui_3_16_0_1_1447211781778_3751"><br clear="none">
</div>
<div dir="ltr" id="yiv3919935515yui_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="yiv3919935515yui_3_16_0_1_1447211781778_3751"><br clear="none">
</div>
<div id="yiv3919935515yui_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="yiv3919935515yui_3_16_0_1_1447211781778_3751"><br clear="none">
</div>
<div id="yiv3919935515yui_3_16_0_1_1447211781778_3751">See attached.</div>
<div id="yiv3919935515yui_3_16_0_1_1447211781778_3751"><br clear="none">
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<div id="yiv3919935515yui_3_16_0_1_1447211781778_3751">David</div>
<br clear="none">
<blockquote id="yiv3919935515yui_3_16_0_1_1447211781778_3989" style="border-left:2px solid rgb(16,16,255);margin-left:5px;margin-top:5px;padding-left:5px;">
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<font id="yiv3919935515yui_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>
<div class="yiv3919935515y_msg_container" id="yiv3919935515yui_3_16_0_1_1447211781778_3992">
<br clear="none">
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<div id="yiv3919935515yui_3_16_0_1_1447211781778_3990" style="color:#000;background-color:#fff;font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:16px;">
<div id="yiv3919935515yui_3_16_0_1_1447171858799_10495"><span>John</span></div>
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<div id="yiv3919935515yui_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>
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<div id="yiv3919935515yui_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>
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<div dir="ltr" id="yiv3919935515yui_3_16_0_1_1447171858799_10497"><a rel="nofollow" shape="rect" id="yiv3919935515yui_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="yiv3919935515yui_3_16_0_1_1447171858799_10497">Best regards my friend,</div>
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<div id="yiv3919935515yui_3_16_0_1_1447171858799_10497">David</div>
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<font id="yiv3919935515yui_3_16_0_1_1447171858799_13235" face="Arial" size="2"><b id="yiv3919935515yui_3_16_0_1_1447171858799_13274"><span id="yiv3919935515yui_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>
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<b><span style="font-weight:bold;">Sent:</span></b> Monday, November 9, 2015 11:14 PM<br clear="none">
<b id="yiv3919935515yui_3_16_0_1_1447171858799_13276"><span id="yiv3919935515yui_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">
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SPIE papers at:<font id="yiv3919935515yui_3_16_0_1_1447211781778_4470" face="Tahoma" color="black" size="2"><span dir="ltr" id="yiv3919935515yui_3_16_0_1_1447211781778_4469" style="font-size:10pt;"><br clear="none">
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<a rel="nofollow" shape="rect" id="yiv3919935515yui_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="yiv3919935515yui_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">
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Regards, John.</span></font><br clear="none">
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<div id="yiv3919935515divRpF276520" style="direction:ltr;"><font id="yiv3919935515yui_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">
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<div id="yiv3919935515yui_3_16_0_1_1447130421153_7312"><span>John</span></div>
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<div id="yiv3919935515yui_3_16_0_1_1447130421153_7311"><span id="yiv3919935515yui_3_16_0_1_1447211781778_4687">Do you have a slide deck summarizing the model? </span></div>
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<div id="yiv3919935515yui_3_16_0_1_1447130421153_7311"><span>Best</span></div>
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