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<div style="direction: ltr;font-family: Tahoma;color: #000000;font-size: 10pt;">Andrew,<br>
<br>
To try to answer your implied question as to where the "quarter turn" came from it is from re-thinking the underlying process described by our feeble attempts to get to the nature of things using differential equations (from the perspective of an engineer or
cyberneticist).<br>
<br>
If one takes a standard, complex non-relativistic wave functions such as the travelling complex wave A e^i(kx-wt) and differentiates it with respect to space or time one obtains a similar function, but scaled by k or w and shifted by a quarter turn in phase
forwards or backwards i.e. Akie^i(kx-wt) or -Awie^i(kx-wt). <br>
<br>
In process terms this corresponds to a a scaling by k or w and a quarter turn in phase by 90 degrees (the factor of i). If one normalises to k or w (as usual) this is then just a (unitary) quarter turn in phase-space.<br>
<br>
Now one has to ask oneself if nature is doing differentials (or integrals) or if it might rather just do rotations? Aha, yes rotations seems more likely. Rotations in just what space though? Imaginary space? No that is too simple - and gets you into all sorts
of thinking problems down the line. For example if you look at the Tong reference in his Cambridge online notes (which some PhD used to try to squash Richards argument about the charged photon) you will find Tong proving that the Lorentz group (a sub group
of the Poincare group) cannot be unitary by invoking the fact that the representation of the Dirac gamma matrix algebra introduces factors corresponding to the square root of -1. He is technically correct, but the problem is inherent not in the physics but
in the mathematics he (and pretty much everyone else) have chosen to use to represent nature. They are already lost. What if nature does not have a (simple) complex dimension? What if differentials are not the best way to represent the underlying process?
For me, nature is neither complex, nor is calculus-powered. Calculus is just a tool to try to describe succinctly what is actually going on.<br>
<br>
The stuff that is the electron or the photon is always turning (turning both as a direction-change but also a change of nature (from current to field for example)). This is where field comes from guys. Just look at the equations! Just think about what is actually
happening experimentally! A quarter turn (differential order) later the stuff that was field is elsewhere (back in the current or- even more fun - manifesting as angular mometum). After four (quarter) turns comes-however-return. One is back to the starting
position. Repeat. That is your quantum. It is a quantum, not inherently and a-priori, but because nature must be inherently smooth and linear and self-sustaining to work at all.<br>
<br>
Now all I have to do is to try to explain this in the paper I'm writing in form that everyone will able to understand ...<br>
<br>
Regards,<br>
<br>
John W.<br>
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<div style="direction: ltr;" id="divRpF892803"><font face="Tahoma" color="#000000" size="2"><b>From:</b> General [general-bounces+john.williamson=glasgow.ac.uk@lists.natureoflightandparticles.org] on behalf of John Williamson [John.Williamson@glasgow.ac.uk]<br>
<b>Sent:</b> Wednesday, June 24, 2015 4:51 AM<br>
<b>To:</b> David Mathes; Nature of Light and Particles - General Discussion<br>
<b>Cc:</b> Manohar .; Nick Bailey; Anthony Booth; Ariane Mandray; Kyran Williamson<br>
<b>Subject:</b> Re: [General] Axes plots<br>
</font><br>
</div>
<div></div>
<div>
<div style="direction:ltr; font-family:Tahoma; color:#000000; font-size:10pt">Dear Chip and David,<br>
<br>
Feel free to quote me on anything - with the proviso that you do not set me up as an authority on anything. I change at least one of my minds at least once a day. Even then am in two minds about nearly everything! Further, on qunatisation, I think Andrew had
it right when he posed the question "is a bell quantised" earlier.<br>
<br>
David - to make some progress towards the way-out how about moving passages. As in ..
<br>
<br>
Twisting passages of little maze <br>
<br>
or substituting the general "little" for something more precise (within a magnitude or three)<br>
<br>
Twisting passages of femto-maze<br>
<br>
Now we metre-magnitude monkeys are getting closer to all our models of the electron!<br>
<br>
Now lets all proceed (in an orderly fashion) onwards and upwards (and round and round in circles) to the way out of the quantum (a) maze ...<br>
<br>
Cheers, -John W.<br>
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<div id="divRpF94426" style="direction:ltr"><font face="Tahoma" color="#000000" size="2"><b>From:</b> General [general-bounces+john.williamson=glasgow.ac.uk@lists.natureoflightandparticles.org] on behalf of David Mathes [davidmathes8@yahoo.com]<br>
<b>Sent:</b> Tuesday, June 23, 2015 10:14 PM<br>
<b>To:</b> Nature of Light and Particles - General Discussion<br>
<b>Subject:</b> Re: [General] Axes plots<br>
</font><br>
</div>
<div></div>
<div>
<div style="color:#000; background-color:#fff; font-family:HelveticaNeue,Helvetica Neue,Helvetica,Arial,Lucida Grande,sans-serif; font-size:13px">
<div dir="ltr" id="yui_3_16_0_1_1435092188490_11272"><span>John, Chip and all,</span></div>
<div dir="ltr" id="yui_3_16_0_1_1435092188490_11165"><span><br>
</span></div>
<div dir="ltr" id="yui_3_16_0_1_1435092188490_11129"><span id="yui_3_16_0_1_1435092188490_11128">I view quantization as low hanging fruit and something to keep the QM people busy calculating the odds instead of playing online poker.</span></div>
<div dir="ltr" id="yui_3_16_0_1_1435092188490_11129"><span><br>
</span></div>
<div dir="ltr" id="yui_3_16_0_1_1435092188490_11129"><span id="yui_3_16_0_1_1435092188490_11343">In the London subway, there is a sign "Way out". Now normally way-out means something extra ordinary or even avant-garde.</span></div>
<div dir="ltr" id="yui_3_16_0_1_1435092188490_11129"><span><br>
</span></div>
<div dir="ltr" id="yui_3_16_0_1_1435092188490_11129"><span id="yui_3_16_0_1_1435092188490_11549">However, "Way out" is used to indicate that the path is going to be long and not merely a quick EXIT to the surface. </span></div>
<div dir="ltr" id="yui_3_16_0_1_1435092188490_11129"><span><br>
</span></div>
<div dir="ltr" id="yui_3_16_0_1_1435092188490_11129"><span id="yui_3_16_0_1_1435092188490_11657" class="" style="">I'm sure other phrases were considered. In the Tube, the path with stairs and escalators will be sort of a cross between the game Chutes and Ladders
and Colossal Cave Adventure with variations on the theme phrase of "<span class="" id="yui_3_16_0_1_1435092188490_12912" style="color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px">little maze of twisting passages</span>." </span>One
needed to draw a map to reduce the amount of repetitive moves and get out of the cave system.</div>
<div dir="ltr" id="yui_3_16_0_1_1435092188490_11129"><br>
</div>
<div dir="ltr" id="yui_3_16_0_1_1435092188490_11129">There were actually two types of caves - all alike and all different. </div>
<div dir="ltr" id="yui_3_16_0_1_1435092188490_13048"><span id="yui_3_16_0_1_1435092188490_13047" style="color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px">little maze of twisting passages, all alike </span></div>
<div dir="ltr" id="yui_3_16_0_1_1435092188490_13048"><span class="" id="yui_3_16_0_1_1435092188490_13132" style="color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px">little maze of twisting passages, all different</span><span style="color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px"><br>
</span></div>
<div dir="ltr" id="yui_3_16_0_1_1435092188490_13048"><span class="" style="color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px"><br>
</span></div>
<div dir="ltr" id="yui_3_16_0_1_1435092188490_13048"><span class="" id="yui_3_16_0_1_1435092188490_13240" style="color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px">Pay attention to detail since variants included:</span></div>
<div dir="ltr" id="yui_3_16_0_1_1435092188490_13048"><span class="" style="color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px"><br>
</span></div>
<li class="" id="yui_3_16_0_1_1435092188490_13239" style="margin-bottom:0.1em; color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px">
Little maze of twisting passages</li><li class="" id="yui_3_16_0_1_1435092188490_13238" style="margin-bottom:0.1em; color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px">
Little maze of twisty passages</li><li class="" id="yui_3_16_0_1_1435092188490_13237" style="margin-bottom:0.1em; color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px">
Little twisty maze of passages</li><li class="" id="yui_3_16_0_1_1435092188490_13236" style="margin-bottom:0.1em; color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px">
Maze of little twisting passages</li><li class="" id="yui_3_16_0_1_1435092188490_13235" style="margin-bottom:0.1em; color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px">
Maze of little twisty passages</li><li class="" id="yui_3_16_0_1_1435092188490_13234" style="margin-bottom:0.1em; color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px">
Maze of twisting little passages</li><li class="" id="yui_3_16_0_1_1435092188490_13233" style="margin-bottom:0.1em; color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px">
Maze of twisty little passages</li><li class="" id="yui_3_16_0_1_1435092188490_13274" style="margin-bottom:0.1em; color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px">
Twisting little maze of passages</li><li class="" id="yui_3_16_0_1_1435092188490_13232" style="margin-bottom:0.1em; color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px">
Twisting maze of little passages</li><li class="" id="yui_3_16_0_1_1435092188490_13231" style="margin-bottom:0.1em; color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px">
Twisty little maze of passages
<div dir="ltr" id="yui_3_16_0_1_1435092188490_13048" class="" style=""><span class="" style="color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px"></span></div>
</li><li class="" id="yui_3_16_0_1_1435092188490_13275" style="margin-bottom:0.1em; color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px">
Twisty maze of little passages
<div dir="ltr" id="yui_3_16_0_1_1435092188490_13048"><span class="" style="color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px"><br>
</span></div>
<div dir="ltr" id="yui_3_16_0_1_1435092188490_13048"><span class="" id="yui_3_16_0_1_1435092188490_13313" style="color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px">Way out is sufficient for me even if at times it's a double entendre.</span></div>
<div dir="ltr" id="yui_3_16_0_1_1435092188490_13048"><span class="" style="color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px"><br>
</span></div>
<div dir="ltr" id="yui_3_16_0_1_1435092188490_13048"><span class="" style="color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px">Best</span></div>
<div dir="ltr" id="yui_3_16_0_1_1435092188490_13048"><span class="" style="color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px"><br>
</span></div>
<div dir="ltr" id="yui_3_16_0_1_1435092188490_13048"><span class="" style="color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px">David</span></div>
<div dir="ltr" id="yui_3_16_0_1_1435092188490_13048"><span class="" style="color:rgb(37,37,37); font-family:sans-serif; font-size:14px; line-height:22px"><br>
</span></div>
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<font id="yui_3_16_0_1_1435092188490_11027" face="Arial" size="2"><b><span style="font-weight:bold">From:</span></b> Chip Akins <chipakins@gmail.com><br>
<b><span style="font-weight:bold">To:</span></b> 'Nature of Light and Particles - General Discussion' <general@lists.natureoflightandparticles.org>
<br>
<b><span style="font-weight:bold">Sent:</span></b> Tuesday, June 23, 2015 11:48 AM<br>
<b><span style="font-weight:bold">Subject:</span></b> Re: [General] Axes plots<br>
</font></div>
<div class="y_msg_container" id="yui_3_16_0_1_1435092188490_11071"><br>
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<div class="yiv4566296506MsoNormal" id="yui_3_16_0_1_1435092188490_11076"><span style="color:black">Hi John</span></div>
<div class="yiv4566296506MsoNormal" id="yui_3_16_0_1_1435092188490_11079"><span style="color:black"> </span></div>
<div class="yiv4566296506MsoNormal" id="yui_3_16_0_1_1435092188490_11080"><span style="color:black">Very well said!!!</span></div>
<div class="yiv4566296506MsoNormal" id="yui_3_16_0_1_1435092188490_11081"><span style="color:black"> </span></div>
<div class="yiv4566296506MsoNormal" id="yui_3_16_0_1_1435092188490_11082"><span style="color:black">May I cite you regarding this statement?</span></div>
<div class="yiv4566296506MsoNormal"><span style="color:black"> </span></div>
<div class="yiv4566296506MsoNormal" id="yui_3_16_0_1_1435092188490_11084"><span id="yui_3_16_0_1_1435092188490_11083" style="font-size:10.0pt">There is a disease which I do not fully understand which seems to have infected nearly every physicist living and
most for about the last hundred years. That is the desire to "quantise" everything from the beginning. It seems to me that, if you do that, you lose the possibility of finding out why things are quantised all. You are already lost. Ok it is kind of nice to
put in something that you observe experimentally as an axiom, I suppose. Poor choice if you want to understand the origins of quantisation though.<br clear="none">
<br clear="none">
</span><span style="color:black">Chip</span></div>
<div class="yiv4566296506MsoNormal" id="yui_3_16_0_1_1435092188490_11085"><span style="color:black"> </span></div>
<div class="yiv4566296506MsoNormal" id="yui_3_16_0_1_1435092188490_11086"><span style="color:black"> </span></div>
<div class="qtdSeparateBR"><br>
<br>
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<div class="yiv4566296506MsoNormal" id="yui_3_16_0_1_1435092188490_11088"><b><span style="font-size:11.0pt">From:</span></b><span id="yui_3_16_0_1_1435092188490_11087" style="font-size:11.0pt"> General [mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org]
<b>On Behalf Of </b>John Williamson<br clear="none">
<b>Sent:</b> Tuesday, June 23, 2015 1:33 PM<br clear="none">
<b>To:</b> David Mathes; Nature of Light and Particles - General Discussion<br clear="none">
<b>Cc:</b> Nick Bailey; Anthony Booth; Manohar .; Ariane Mandray<br clear="none">
<b>Subject:</b> Re: [General] Axes plots</span></div>
</div>
</div>
<div class="yiv4566296506MsoNormal"> </div>
<div id="yui_3_16_0_1_1435092188490_11092">
<div class="yiv4566296506MsoNormal" id="yui_3_16_0_1_1435092188490_11091"><span id="yui_3_16_0_1_1435092188490_11093" style="font-size:10.0pt">Could not agree more.
<br clear="none">
<br clear="none">
There is far far more unknown than known for all of us collectively. Further, any of our competences is dwarfed by those of all of us.<br clear="none">
<br clear="none">
I see it now. Seuss was right all along (as always) and we need to go onto that new alphabet!<br clear="none">
<br clear="none">
Gonna use it in the new paper ... watch this space ...<br clear="none">
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Cheers,<br clear="none">
<br clear="none">
John.</span></div>
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<div class="yiv4566296506MsoNormal" style="margin-bottom:12.0pt"><b><span style="font-size:10.0pt">From:</span></b><span style="font-size:10.0pt"> David Mathes [davidmathes8@yahoo.com]<br clear="none">
<b>Sent:</b> Tuesday, June 23, 2015 4:16 PM<br clear="none">
<b>To:</b> John Williamson; Nature of Light and Particles - General Discussion<br clear="none">
<b>Cc:</b> Nick Bailey; Anthony Booth; Manohar .; Ariane Mandray<br clear="none">
<b>Subject:</b> Re: [General] Axes plots</span><span style="color:black"></span></div>
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<div class="yiv4566296506MsoNormal" style="background:white"><span style="font-size:10.0pt">John,</span></div>
</div>
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<div class="yiv4566296506MsoNormal" style="background:white"><span style="font-size:10.0pt"> </span></div>
</div>
<div id="yiv4566296506yui_3_16_0_1_1435068835254_10921">
<div class="yiv4566296506MsoNormal" style="background:white"><span style="font-size:10.5pt">"It's high time you were shown</span><span style="font-size:10.0pt"></span></div>
</div>
<div id="yiv4566296506yui_3_16_0_1_1435068835254_10921">
<div class="yiv4566296506MsoNormal" style="background:white"><span style="font-size:10.5pt">That you really don't know</span><span style="font-size:10.0pt"></span></div>
</div>
<div id="yiv4566296506yui_3_16_0_1_1435068835254_10921">
<div class="yiv4566296506MsoNormal" style="background:white"><span style="font-size:10.5pt">All there is to be known."</span><span style="font-size:10.0pt"></span></div>
</div>
<div id="yiv4566296506yui_3_16_0_1_1435068835254_10921">
<div class="yiv4566296506MsoNormal" style="background:white"><span style="font-size:10.0pt"> </span></div>
</div>
<div id="yiv4566296506yui_3_16_0_1_1435068835254_10921">
<div class="yiv4566296506MsoNormal" style="background:white"><span style="font-size:10.5pt">"In the places I go there are things that I see</span><span style="font-size:10.0pt"></span></div>
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<div class="yiv4566296506MsoNormal" style="background:white"><span style="font-size:10.5pt">That I never could spell if I stopped with the Z.</span><span style="font-size:10.0pt"></span></div>
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<div class="yiv4566296506MsoNormal" style="background:white"><span style="font-size:10.5pt">I'm telling you this 'cause you're one of my friends.</span><span style="font-size:10.0pt"></span></div>
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<div class="yiv4566296506MsoNormal" style="background:white"><span style="font-size:10.5pt">My alphabet starts where your alphabet ends!"</span><span style="font-size:10.0pt"></span></div>
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<div class="yiv4566296506MsoNormal" style="background:white"><span style="font-size:10.0pt">From Seuss, T.G. "On Beyond Zebra" 1955 </span></div>
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<div class="yiv4566296506MsoNormal" style="background:white"><span style="font-size:10.0pt">David</span></div>
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<div class="yiv4566296506MsoNormal" style="background:white"><b><span style="font-size:10.0pt">From:</span></b><span style="font-size:10.0pt"> John Williamson <<a rel="nofollow" shape="rect" href="mailto:John.Williamson@glasgow.ac.uk" target="_blank">John.Williamson@glasgow.ac.uk</a>><br clear="none">
<b id="yiv4566296506yui_3_16_0_1_1435068835254_11198">To:</b> Nature of Light and Particles - General Discussion <<a rel="nofollow" shape="rect" href="mailto:general@lists.natureoflightandparticles.org" target="_blank">general@lists.natureoflightandparticles.org</a>>
<br clear="none">
<b>Cc:</b> Nick Bailey <<a rel="nofollow" shape="rect" href="mailto:nick@bailey-family.org.uk" target="_blank">nick@bailey-family.org.uk</a>>; Anthony Booth <<a rel="nofollow" shape="rect" href="mailto:abooth@ieee.org" target="_blank">abooth@ieee.org</a>>;
Manohar . <<a rel="nofollow" shape="rect" href="mailto:manohar_berlin@hotmail.com" target="_blank">manohar_berlin@hotmail.com</a>>; Ariane Mandray <<a rel="nofollow" shape="rect" href="mailto:ariane.mandray@wanadoo.fr" target="_blank">ariane.mandray@wanadoo.fr</a>>;
David Mathes <<a rel="nofollow" shape="rect" href="mailto:davidmathes8@yahoo.com" target="_blank">davidmathes8@yahoo.com</a>>
<br clear="none">
<b>Sent:</b> Tuesday, June 23, 2015 3:50 AM<br clear="none">
<b>Subject:</b> RE: [General] Axes plots</span><span style=""></span></div>
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<div class="yiv4566296506MsoNormal" style="background:white"><span style=""> </span></div>
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<div class="yiv4566296506MsoNormal" style="background:white"><span style="font-size:10.0pt">Dear David and Andrew,<br clear="none">
<br clear="none">
There is a disease which I do not fully understand which seems to have infected nearly every physicist living and most for about the last hundred years. That is the desire to "quantise" everything from the beginning. It seems to me that, if you do that, you
lose the possibility of finding out why things are quantised all. You are already lost. Ok it is kind of nice to put in something that you observe experimentally as an axiom, I suppose. Poor choice if you want to understand the origins of quantisation though.<br clear="none">
<br clear="none">
Andrew, then, raises an important point. Why not a continuum indeed? I think the proper answer lies in the relationship between things - not in the things themselves. Things inter-act. Charge is, at root, (at least an invitation to) an inter-action.<br clear="none">
<br clear="none">
Imagine a bunch of such inter-actors in a (universe sized) box. They do what they do. They inter-act. Now imagine some of them are bigger, faster, better inter-actors. It turns out that the universal law that big is small and small is large makes these the
little guys. Small, loud and shrill. They throw out their stuff to all and sundry - losing energy (and hence getting bigger) in the process. The stuff they throw out is more likely to find the (bigger) quiet ones - hence shrinking them. Meanwhile (being small)
they do not get a lot of stuff back. In time, if you have enough inter-actors then all tend to the same size and potency. Apparent uniformity (quantisation) is then just a result of thermodynamic exchange.<br clear="none">
<br clear="none">
Discuss!<br clear="none">
<br clear="none">
Regards, John W.<br clear="none">
<br clear="none">
P.S. Spin is different!</span></div>
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<b><span style="font-size:10.0pt">From:</span></b><span style="font-size:10.0pt"> General [general-bounces+john.williamson=glasgow.ac.uk@lists.natureoflightandparticles.org] on behalf of Andrew Meulenberg [mules333@gmail.com]<br clear="none">
<b>Sent:</b> Tuesday, June 23, 2015 11:28 AM<br clear="none">
<b>To:</b> Nature of Light and Particles - General Discussion<br clear="none">
<b>Cc:</b> Nick Bailey; Anthony Booth; Manohar .; Ariane Mandray; David Mathes<br clear="none">
<b>Subject:</b> Re: [General] Axes plots</span><span style="color:black"></span></div>
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<div class="yiv4566296506MsoNormal" style="margin-bottom:12.0pt; background:white">
<span style="color:black">Dear John W. and all,</span></div>
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<span style="color:black">If you start with a circularly-polarized photon, give it one full twist per wavelength (to 'unwind' it), and then close it at any point, could you not create the out-going
<b>E</b>-field that we attribute to the electron or positron? However, since there is no reason to join the twisted photon only at integer wavelengths, then the electron would not have fixed properties. The only thing fixed would be the amount of twist per
wavelength. What causes the photon twist in any of the models and, if the above model is correct, why don't we have particles with a continuum of charge (and spin?) values?</span></div>
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<div class="yiv4566296506MsoNormal" style="background:white"><span style="color:black">Andrew</span></div>
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<span style="color:black">__________________________________</span></div>
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<div class="yiv4566296506MsoNormal" style="background:white"><span style="color:black">On Tue, Jun 23, 2015 at 12:19 AM, John Williamson <<a rel="nofollow" shape="rect" href="mailto:John.Williamson@glasgow.ac.uk" target="_blank">John.Williamson@glasgow.ac.uk</a>>
wrote:</span></div>
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<div class="yiv4566296506MsoNormal" style="background:white"><span style="font-size:10.0pt">Here are some using a set of axes, as in the POS paper circulated earlier<br clear="none">
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Torfieldrock just shows three views of a positron. <br clear="none">
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Torfieldsinglemin0.4 is just a simple double loop. Not too busy.<br clear="none">
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Trockrevert is similar to the first, but with a glass torus.<br clear="none">
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Cheers, John.</span></div>
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