[General] SU(2) equation set

Chip Akins chipakins at gmail.com
Thu Nov 12 07:11:10 PST 2015


Hi John W.

 

Some of my background is in aerodynamic simulation, where I have written
more than 500K lines of 'C' code and created one of the world's most
accurate real-time simulations of flight. Lots of use of quaternions and
fluid mechanics of course.

 

I have written code in many different languages, so practically any we
choose will work for me.

 

In order to start we will need to do as you suggest and look at the
fundamentals to create a library of functions we can call as required.

 

So if I can look at Stephen's Python code for multiplications that would
help me get a handle on how to write the division and differentiation low
level code.

 

Some personal experience and observations.

Object oriented code generally takes more time to design and runs a little
slower, but it protects and manages the data and functions operating on the
data as individual objects. Object oriented code generally uses more memory
as well. Computation time, and memory capacity, are really critical for us
because of the tremendous computational load it will take to do the
simulation at any useful scale. So when we were writing flight simulation
code, which had to compute all the forces and moments in real time, at about
120 times a second, we wrote it all in 'C'.  I am bringing this up because
even now, when I am doing physics modeling, which is much simpler than the
task at hand, I often have to wait an hour for the results from our fairly
large and very fast workstations here in the office. It would be nice to
create the simulation in the fastest running code we can, so that we have
some hope of getting results in reasonable time, without having to rent
expensive time on, or build a supercomputer.

 

But those opinions are not as important as getting the foundation in place
so we can start doing some real work in simulating particles, and
interactions.  Exciting stuff.

 

Chip

 

 

 

From: General
[mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.
org] On Behalf Of John Williamson
Sent: Thursday, November 12, 2015 7:37 AM
To: Nature of Light and Particles - General Discussion
<general at lists.natureoflightandparticles.org>
Cc: Nick Bailey <nick at bailey-family.org.uk>; Stephen Leary
<sleary at vavi.co.uk>; Mark, Martin van der <martin.van.der.mark at philips.com>
Subject: Re: [General] SU(2) equation set

 

Now we are talking.

I suggest we convene a sub-group of computer and simulation savvy folk. That
should be you, me, Stephen Leary, Nick Green, Tim Drysdale (an expert in
Maxwell solutions), my friend Nick Bailey and maybe Joakim, my brothers Pete
and David and any others who express an interest.

I have written (big!) computer simulation software programmes in the past,
but that was to do quantum electrodynamics and quantum chromodynamics and
was written in FORTRAN! Not good enough for the task in hand!

Firstly need to implement a system with primitive operations which parallel
the workings of the space-time algebra. Multiplications, divisions and
differentiations in particular.  It would be nice if such a framework
existed already, but I do not think so. Stephen has written a suite in
PYTHON to deal with the multiplications, which may be a start. Not sure what
is best here: C++?, Python?, Something else?

Next need to devise a basis. Obvious thing is space and time and things
derived from space and time. This could be the 16 Linearly independent
elements or something cleverer derived from the 4-basis of space and time. I
do not know how smart we can get here. I have no expertise in
object-oriented code - but these methods may be useful in describing the
levels of complexity required.

Following need to choose a finite element or finite difference technique,
which may be tested on the subset of the Maxwell equations alone, for which
there exists an extensive literature.

That is only the start!

Regards, John.

  _____  

From: General
[general-bounces+john.williamson=glasgow.ac.uk at lists.natureoflightandparticl
es.org] on behalf of Chip Akins [chipakins at gmail.com]
Sent: Thursday, November 12, 2015 12:16 PM
To: 'Nature of Light and Particles - General Discussion'
Subject: Re: [General] SU(2) equation set

Hi John

 

Regarding the proper computer model.  How do we get started?

 

Chip

 

From: General [
<mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.
org>
mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.o
rg] On Behalf Of John Williamson
Sent: Wednesday, November 11, 2015 7:43 PM
To:  <mailto:davidmathes8 at yahoo.com> davidmathes8 at yahoo.com
Cc: Nature of Light and Particles - General Discussion <
<mailto:general at lists.natureoflightandparticles.org>
general at lists.natureoflightandparticles.org>; Nick Bailey <
<mailto:nick at bailey-family.org.uk> nick at bailey-family.org.uk>; Anthony Booth
< <mailto:abooth at ieee.org> abooth at ieee.org>; Mark, Martin van der <
<mailto:martin.van.der.mark at philips.com> martin.van.der.mark at philips.com>
Subject: Re: [General] SU(2) equation set

 

Dear David,

You are not getting the point. 

  _____  

From:  <mailto:davidmathes8 at yahoo.com> 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>
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>
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

 

David

  _____  

From:  <mailto:davidmathes8 at yahoo.com> 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>
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>
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 < <mailto:John.Williamson at glasgow.ac.uk>
John.Williamson at glasgow.ac.uk>
To: " <mailto:davidmathes8 at yahoo.com> davidmathes8 at yahoo.com" <
<mailto:davidmathes8 at yahoo.com> davidmathes8 at yahoo.com> 
Cc: "Mark, Martin van der" < <mailto:martin.van.der.mark at philips.com>
martin.van.der.mark at philips.com>; Nature of Light and Particles - General
Discussion < <mailto:general at lists.natureoflightandparticles.org>
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:  <mailto:davidmathes8 at yahoo.com> 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 < <mailto:John.Williamson at glasgow.ac.uk>
John.Williamson at glasgow.ac.uk>
To: " <mailto:davidmathes8 at yahoo.com> davidmathes8 at yahoo.com" <
<mailto: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:  <mailto:davidmathes8 at yahoo.com> 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: " <mailto:davidmathes8 at yahoo.com> davidmathes8 at yahoo.com" <
<mailto:davidmathes8 at yahoo.com> davidmathes8 at yahoo.com>
To: John Williamson < <mailto:John.Williamson at glasgow.ac.uk>
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>
http://aflb.ensmp.fr/AFLB-26j/aflb26jp055.pdf

 

Best regards my friend,

 

David

 

 

 

 

 

 


  _____  


From: John Williamson < <mailto:John.Williamson at glasgow.ac.uk>
John.Williamson at glasgow.ac.uk>
To: " <mailto:davidmathes8 at yahoo.com> davidmathes8 at yahoo.com" <
<mailto: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/110952/1/110952.pdf
 <http://eprints.gla.ac.uk/110966/1/110966.pdf>
http://eprints.gla.ac.uk/110966/1/110966.pdf

Regards, John.

 


  _____  


From:  <mailto:davidmathes8 at yahoo.com> 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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