[General] SU(2) equation set

[davidmathes8 at yahoo.com]

John
> Cl(1,3)    (Ed note: the correct one)
I owe you an extra pint at the pub for this oversight. 
>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.

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. 
Based on your paper and my goals, what I'm looking for is the nonlinear version for electroweak forces including  partial derivatives of phase, polarization and spin. The goal would be the specifically model and simulation for testing parametric amplification. 
My deepest apologies and condolences on the straw man for the irritating and simplistic approach . 
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. 
Guinness?
Best regards,
David












 
      From: John Williamson <John.Williamson at glasgow.ac.uk>
 To: "davidmathes8 at yahoo.com" <davidmathes8 at yahoo.com> 
Cc: Nature of Light and Particles - General Discussion <general at lists.natureoflightandparticles.org>; Nick Bailey <nick at bailey-family.org.uk>; Anthony Booth <abooth at ieee.org>; "Mark, Martin van der" <martin.van.der.mark at philips.com> 
 Sent: Wednesday, November 11, 2015 5:42 PM
 Subject: Re: [General] SU(2) equation set
   
 <!--#yiv3779983159 _filtered #yiv3779983159 {panose-1:0 0 0 0 0 0 0 0 0 0;} _filtered #yiv3779983159 {font-family:"Cambria Math";panose-1:2 4 5 3 5 4 6 3 2 4;} _filtered #yiv3779983159 {font-family:Cambria;panose-1:2 4 5 3 5 4 6 3 2 4;} _filtered #yiv3779983159 {font-family:Tahoma;panose-1:2 11 6 4 3 5 4 4 2 4;} _filtered #yiv3779983159 {font-family:"Helvetica Neue";panose-1:2 0 5 3 0 0 0 2 0 4;}#yiv3779983159 #yiv3779983159 p.yiv3779983159MsoNormal, #yiv3779983159 li.yiv3779983159MsoNormal, #yiv3779983159 div.yiv3779983159MsoNormal {margin:0cm;margin-bottom:.0001pt;font-size:12.0pt;font-family:Cambria;}#yiv3779983159 a:link, #yiv3779983159 span.yiv3779983159MsoHyperlink {color:blue;text-decoration:underline;}#yiv3779983159 a:visited, #yiv3779983159 span.yiv3779983159MsoHyperlinkFollowed {color:purple;text-decoration:underline;}#yiv3779983159 .yiv3779983159MsoChpDefault {font-family:Cambria;} _filtered #yiv3779983159 {margin:72.0pt 90.0pt 72.0pt 90.0pt;}#yiv3779983159 div.yiv3779983159WordSection1 {}-->Dear David,

You are not getting the point. From: davidmathes8 at yahoo.com [davidmathes8 at yahoo.com]
Sent: Wednesday, November 11, 2015 6:05 PM
To: John Williamson
Cc: Mark, Martin van der; Nature of Light and Particles - General Discussion
Subject: Re: SU(2) equation setJohn  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.   For the reader, the papers we are discussing include so far... Williamson 2015 "Absolute relativity in classical electromagnetism: the quantisation of light" http://eprints.gla.ac.uk/110966/1/110966.pdf Barrett 2000 "Topology and the Physical Properties of Electromagnetic Fields"http://redshift.vif.com/JournalFiles/Pre2001/V07NO1PDF/V07N1BAR.pdf 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). I'll go back to the starting line... 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.  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.  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.  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. Clearly, both Williamson and Barrett sets do not cover the full Standard Model, nor were they expected to... 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.  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.  Ok, now to address the email... John,  > 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 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

The standard model STARTS from putting in a load of groups. Lots and lots of them! Correct me if I'm wrong, is yours U(1) EM X  SU(2) spin?

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. Does your formulation address EM solitons or Aharnov-Bohm?

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. 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.

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.. My conclusion there is an incompatibility between the Williamson and Barrett equations. But we don't seem far off.

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). So it's back to basics and hard work on reconciling the two approaches.

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. Best DavidFrom: davidmathes8 at yahoo.com [davidmathes8 at yahoo.com]
Sent: Wednesday, November 11, 2015 6:05 PM
To: John Williamson
Cc: Mark, Martin van der; Nature of Light and Particles - General Discussion
Subject: Re: SU(2) equation set

John 
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. 

For the reader, the papers we are discussing include so far...
Williamson 2015 "Absolute relativity in classical electromagnetism: the quantisation of light" http://eprints.gla.ac.uk/110966/1/110966.pdf
Barrett 2000 "Topology and the Physical Properties of Electromagnetic Fields"http://redshift.vif.com/JournalFiles/Pre2001/V07NO1PDF/V07N1BAR.pdf

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).
I'll go back to the starting line...

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. 
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. 
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. 
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.
Clearly, both Williamson and Barrett sets do not cover the full Standard Model, nor were they expected to...

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. 
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. 
Ok, now to address the email...
John, 
> 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

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

The standard model STARTS from putting in a load of groups. Lots and lots of them!

Correct me if I'm wrong, is yours U(1) EM X  SU(2) spin?

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.

Does your formulation address EM solitons or Aharnov-Bohm?

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.

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.

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..

My conclusion there is an incompatibility between the Williamson and Barrett equations. But we don't seem far off.

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).

So it's back to basics and hard work on reconciling the two approaches.

No need to reconcile anything. Barrett is attempting to put in a little something to throw light on a deep mystery (the nature of spin). Good for him. I have no need to do this because the spin term, for me, is just a basic and neccessary part of the theory of space, time and matter. I get the spin at the basic linear level - not as a non-linear product term conditioned by an extra copy of U(1).

Best
David








From: John Williamson <John.Williamson at glasgow.ac.uk>
To: "davidmathes8 at yahoo.com" <davidmathes8 at yahoo.com>
Cc: "Mark, Martin van der" <martin.van.der.mark at philips.com>; Nature of Light and Particles - General Discussion <general at lists.natureoflightandparticles.org>
Sent: Wednesday, November 11, 2015 5:17 AM
Subject: RE: SU(2) equation set

<!---->Dear David,

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?

Regards, John.


From: davidmathes8 at yahoo.com [davidmathes8 at yahoo.com]
Sent: Wednesday, November 11, 2015 4:50 AM
To: John Williamson
Subject: Re: SU(2) equation set

John
The straw man failed.
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?
David

From: John Williamson <John.Williamson at glasgow.ac.uk>
To: "davidmathes8 at yahoo.com" <davidmathes8 at yahoo.com>
Sent: Tuesday, November 10, 2015 8:39 PM
Subject: RE: SU(2) equation set

<!---->Hello David,

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.

Also, I see the U(1) part of what you are doing - but where is the SU(2) part?

Regards, John.


From: davidmathes8 at yahoo.com [davidmathes8 at yahoo.com]
Sent: Wednesday, November 11, 2015 3:38 AM
To: John Williamson
Subject: SU(2) equation set

John
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. 
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. 
Right now, there is confusion in notation with a conflicts in the use of A and B. 
See attached.
David

From: "davidmathes8 at yahoo.com" <davidmathes8 at yahoo.com>
To: John Williamson <John.Williamson at glasgow.ac.uk>
Sent: Tuesday, November 10, 2015 8:25 AM
Subject: Re: Slide Deck

John
Thank you. now I recall these papers this summer's work. So not that winter is begun (raining in California), I'll reread them.
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).
http://aflb.ensmp.fr/AFLB-26j/aflb26jp055.pdf

Best regards my friend,
David







From: John Williamson <John.Williamson at glasgow.ac.uk>
To: "davidmathes8 at yahoo.com" <davidmathes8 at yahoo.com>
Sent: Monday, November 9, 2015 11:14 PM
Subject: RE: Slide Deck

<!---->Hello David,

SPIE papers at:
 
http://eprints.gla.ac.uk/110952/1/110952.pdf
http://eprints.gla.ac.uk/110966/1/110966.pdf

Regards, John.


From: davidmathes8 at yahoo.com [davidmathes8 at yahoo.com]
Sent: Tuesday, November 10, 2015 5:09 AM
To: John Williamson
Subject: Slide Deck

John
Do you have a slide deck summarizing the model? 
Best
David


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