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<div style="direction:ltr; font-family:Tahoma; color:#000000; font-size:10pt">Yo David,<br>
<br>
You are in luck! Williamson has been looking at the "common threads" between these models for more than three dacades. Let me fill y'all in, mothers!<br>
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<p class="MsoNormal" style="background:white"><span style="font-family:
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"Times New Roman";color:black" lang="EN-US">John</span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
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"Times New Roman";color:black" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:black" lang="EN-US">My apologies for this late response. I'm slowly catching up
on the volumes of traffic.</span></p>
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"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:black" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:black" lang="EN-US">I find that physics is in need of roadmaps. Given all the various
types of models we have centered around the photon including both electron and spacetime, just a simple comparison between models would help. However, by using specific types of mathematical approaches such as Dirac or Weyl, there may be useful insights into
the common threads between these models.<br>
<br>
</span><span style="font-family:"Helvetica Neue";mso-fareast-font-family:
"Times New Roman";mso-bidi-font-family:"Times New Roman";color:blue" lang="EN-US">Yep. The Dirac and Weyl and Maxwell (and Williamson-van der Mark) equations can all be written : d (stuff)
= 0. All first order, linear equations.</span><span style="font-family:"Helvetica Neue";mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";color:black" lang="EN-US"></span></p>
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<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:black" lang="EN-US">When I see Dirac and Weyl, I also think particles and in particular,
Majorna. Not that this matter for linearization but the three types of particles matter as topological transformations. So linearization may not be the only approach.<br>
</span><span style="font-family:"Helvetica Neue";mso-fareast-font-family:
"Times New Roman";mso-bidi-font-family:"Times New Roman";color:blue" lang="EN-US"><br>
Look David - indeed the Dirac basis and the Weyl basis have a spinor set of solutions. We can talk about this, but a good place to start would be in UNDERSTANDING the Dirac equation and the Weyl equation in the first place. Otherwise there is little point.</span><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:black" lang="EN-US"></span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
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"Times New Roman";color:black" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:black" lang="EN-US">Also, I don't like just linearization. Yes, I use it to make experiments
work most notably Hoyle-Narlikar (linearized GRT). However, I fear I'm missing out on something by not extending the series or using exponential notation and using the full GRT. Furthermore, GRT appears inadequate at galactic distances.<br>
<br>
</span><span style="font-family:"Helvetica Neue";mso-fareast-font-family:
"Times New Roman";mso-bidi-font-family:"Times New Roman";color:blue" lang="EN-US">Hmm, of the theories above only the Maxwell (and Williamson-van-der-Mark) operate. The others have solutions
going round and round in circles very fast, over a small distance (explanation for mothers) - or spinor solutions for those who know what a spinor is. The explanation for mothers (of what a spinor is) is twofold: either it is a mathematical entity which needs
to be rotated twice before it comes back to where it started or (Williamson-van-der-Mark) it is a doubling-covering flow in some space derived (literally!) from space and time. Essentially that object, is the electron model in Martin and my seminal paper in
1997, or in the pretty pictures of the re-circulating solution of the new theory in my electron paper. Difference between the Williamson-van-der-Mark approach and the Dirac or Weyl method is that we DERIVE the spinors from the underlying mass and EM fields,
whereas they find they need a mathematical entity with those weird properties, they know-not-how.</span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:black" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:black" lang="EN-US">In that regard, Peter Rowlands work has been mentioned. I would
suggest The Theoretical Minimum (Susskind). Also, Dynamic Theory (Pharis Williams). </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:black" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:black" lang="EN-US"><a href="http://theoreticalminimum.com/">The Theoretical Minimum</a></span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Droid Serif","serif";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:black" lang="EN-US">The </span><span style="font-family:"Helvetica Neue";mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";color:black" lang="EN-US"><a href="http://theoreticalminimum.com/about"><span style="font-family:"Droid Serif","serif";color:#820000;border:none windowtext 1.0pt;
mso-border-alt:none windowtext 0cm;padding:0cm">Theoretical Minimum</span></a></span><span style="font-family:"Droid Serif","serif";mso-fareast-font-family:
"Times New Roman";mso-bidi-font-family:"Times New Roman";color:black" lang="EN-US"> is
a series of Stanford Continuing Studies courses taught by world renowned physicist </span><span style="font-family:"Helvetica Neue";
mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman";
color:black" lang="EN-US"><a href="http://theoreticalminimum.com/biography"><span style="font-family:"Droid Serif","serif";color:#820000;border:none windowtext 1.0pt;
mso-border-alt:none windowtext 0cm;padding:0cm">Leonard
Susskind</span></a></span><span style="font-family:"Droid Serif","serif";mso-fareast-font-family:
"Times New Roman";mso-bidi-font-family:"Times New Roman";color:black" lang="EN-US">. These courses collectively teach everything required to gain a basic understanding
of each area of modern physics including all of the fundamental mathematics.</span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Droid Serif","serif";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:black" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Droid Serif","serif";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US">Yes the Susskind stuff is good. I have had a go at the same
sort of thing – but it only gets you to where people are already</span><span style="font-family:"Helvetica Neue";mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";color:blue" lang="EN-US"></span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US">While the focus of this ongoing discussion has been on photon,
electron and spacetime with occasional forays into quarks and the remaining bosons, there is this nagging question about how to model neutrinos. </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US">Yeah yeah yeah.
</span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US">Imagine we did have a theory that properly modeled –the photon.
Would that be a good thing. What is it? Maxwell? WvdM?</span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US">Imagine we did have a theory that properly modeled –the electron.
Would that be a good thing. What is it? Dirac? WvdM?</span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US">Imagine we did have a theory that properly modeled –the quarks.
Would that be a good thing. What is it? QCD? WvdM?</span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US">Imagine we did have a theory that properly modeled –the neutrino.
Would that be a good thing. What is it? Weyl? WvdM??</span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US">I have put two questionmarks for the last one as I have not bothered
having a go at modeling the neutrino yet within the framework of the new theory. I think, given that the photon is 1D (rotator) the electron a 3D (three rotator) the neutrino is probably 2D (rotator) – what do you reckon?. That would make it nearly, but not
quite rest-massless Anyway the next step is to get down and dirty and not just yap about this or that model and actually do some equation solving. Reading other peoples stuff is easy. Finding new solutions to new equations is hard. We have one, and only one,
proposal within the group for a new set of differential equations of the same form as Dirac, Maxwell or Weyl. Two kinds of solution are interesting: firstly analytic solutions. I have a set of six of these in 1D (one of which is in the photon paper) and a
proposal for one in 3D (the electron) – not explicit in the paper – though it is just a conformal transformation of eq. 21 in the photon paper and I have talked about it before.</span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US">I think what is needed is a working group or two on the solution
of coupled differential equations. I think to get actual numbers out – such as the charge and the masses, I need a group with competency in the solution of differential equations using FEM (finite element methods). Finite difference methods will not hack it
– as one will need a pre-defined “grid”. Not good! I do not think it is sensible to include the whole discussion group here – as this will rapidly get technical and will lead to too much explanation. If we get anywhere we will report back!</span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US">I have a new volunteer from this group who can do this kind of
thing (Chip) and another couple I had talked to before and have brought into the group (Mayank and Joakim) there are also people outside the group who could contribute (Nick Bailey). I have worked with trying to get started on this before with Tim Drysdale
(over a period of a few years), but not sure if he is still with the group. <a name="_GoBack">
</a><span style="mso-spacerun:yes"> </span>Warning: this stuff is hard (even for just Maxwell). There is no pay – I have no funding yet – it would just be “for fun”.
<span style="mso-spacerun:yes"> </span></span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:black" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US">Anyone else with competence in numerical methods interested in
trying to find more solutions to my new field equations?</span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:black" lang="EN-US"><a href="http://phys.org/news/2015-12-nobel-winning-discovery-neutrino-oscillations-neutrinos.html">Nobel-winning
discovery of neutrino oscillations, proving that neutrinos have mass</a></span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:black" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:black" lang="EN-US">For me, this gets back to the charge-mass relationship which
appears to be a direct relationship in some case. However, it's not clear that the relationship between charge and mass is linear.</span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:black" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US">David : this statement seems a bit silly. Everything has, at
the particle level, one of a few multiples of the elementary charge. Usually +1, -1 or zero. There are, however, HUGE variations in the masses. The muon, is 207 times higher mass (6 cubed –ish) the tauon is 3477 times the mass (15 cubed –ish). There is no
linearity to charge at all – at best some sort of combinatoric cubed (as above).
</span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:black" lang="EN-US">Best</span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:black" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:black" lang="EN-US">David</span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:black" lang="EN-US"> </span></p>
<p class="MsoNormal" style="background:white"><span style="font-family:
"Helvetica Neue";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:blue" lang="EN-US">Cheers, John W.</span></p>
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<b id="yui_3_16_0_1_1449854796467_31335"><span id="yui_3_16_0_1_1449854796467_31334" style="font-weight:bold">From:</span></b> John Williamson <John.Williamson@glasgow.ac.uk><br>
<b><span style="font-weight:bold">To:</span></b> "af.kracklauer@web.de" <af.kracklauer@web.de>
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<b><span style="font-weight:bold">Cc:</span></b> Nick Bailey <nick@bailey-family.org.uk>; "Mark, Martin van der" <martin.van.der.mark@philips.com>; "general@lists.natureoflightandparticles.org" <general@lists.natureoflightandparticles.org>; Ariane Mandray <ariane.mandray@wanadoo.fr>;
"pete@leathergoth.com" <pete@leathergoth.com>; David Williamson <david.williamson@ed.ac.uk><br>
<b><span style="font-weight:bold">Sent:</span></b> Thursday, November 26, 2015 8:01 PM<br>
<b><span style="font-weight:bold">Subject:</span></b> [General] 21st century linear, first order theories. Are there any others?<br>
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<div class="yiv3903682786MsoNormal" style=""><span style="font-family:Tahoma; color:black" lang="EN-US">Dear all,</span></div>
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<span id="yui_3_16_0_1_1449854796467_30775" style="font-family:Tahoma; color:black" lang="EN-US">I’m just writing a paper on the new linear set of differential equations I proposed last year and want to compare it to similar work in the 21<sup>st</sup> century,
or fairly recently at least. I usually like to read a couple of papers before breakfast (thanks for keeping me supplied guys – especially David John D and Al) – but I’m just drawing a blank here. What should I be looking at?</span></div>
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<span id="yui_3_16_0_1_1449854796467_30734" style="font-family:Tahoma; color:black" lang="EN-US">To be specific:
<span style=""> </span>is anyone aware of any other equations which have been proposed this century or in the second half of last century which can be written in the linear first-order form d (something) = 0?</span></div>
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<span id="yui_3_16_0_1_1449854796467_30736" style="font-family:Tahoma; color:black" lang="EN-US">For reference, what comes to mind in the early twentieth are the Dirac equation and the Weyl equation. There were other guys playing with things around then, but
my mind has gone blank (Eddington?). Shroedinger’s, of course, has second order derivatives (though, as Dieks has argued it has first order features imported though the adoption of the de Broglie relation – and I am going to refer to that). I’m also not talking
about further work on Dirac or Maxwell such as that by Hestenes or using the Bateman method on the Maxwell equations (of which the most advanced work, in my view, is that of Martin which he and I will review over the Christmas “vacation”). I’m talking about
proper, basic, first order equations of light, matter or anything else.</span></div>
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<span id="yui_3_16_0_1_1449854796467_30738" style="font-family:Tahoma; color:black" lang="EN-US">David – you were proposing I write a review of comparable work (and I am delighted that you are going to review the various electron models!) – but I’m talking
here about linear theories expressed in (vector) differential form, not about any specific model within them. Tony … your stuff is brilliant but second order – anything else you are aware of?<span style="">
</span>Nick … Pask’s stuff was brilliant too – did he express anything new in linear equations? Also, of course, not referring to work on such perturbative theories as QED and non-perturbative stuff such as QCD, most of the “standard model” and the various
string theories. Chip, Albrecht, Richard ... you have been looking at lots of electron and photon models - anything there? Joakim, Adam, Mayank ... anything caught your attention? Chandra, Al, Martin … anything on light beyond Maxwell or in “quantum entanglement”?
Michael M, David, Viv … anything out there in space?</span></div>
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<span id="yui_3_16_0_1_1449854796467_30760" style="font-family:Tahoma; color:black" lang="EN-US">Maybe I’m being stupid at this time in the morning and more things will come to me after another cup of coffee, but I’m drawing a blank here.<span style="">
</span>Any further suggestions would be helpful!</span></div>
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<span style="font-family:Tahoma; color:black" lang="EN-US">Regards, John.</span></div>
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