[General] SU(2) equation set

Fri Nov 13 07:27:37 PST 2015

Hi Al

I couldn’t agree more.

One thing that observations of the principles of physics has illustrated for me is that the problems all boil down to very basic and easy to understand starting principles.  

In this way I agree very much with John Archibald Wheeler when he said…“It is my opinion that everything must be based on a simple idea. And it is my opinion that this idea, once we have finally discovered it, will be so compelling, so beautiful, that we will say to one another, “yes, how could it have been any different?””

There are some questions which might help us in this quest…

When it is difficult and complex to really get the basic concepts to start with, is it likely we are on the right path?  

Are we really explaining the concepts well? Or is it rather that we MUST manufacture artificially complex solutions in order to keep the basis we trust to be correct? 

Have we done our job and tested and questioned the foundations upon which we are building?

Can we expect to build the correct theory from the existing foundations? Or is it the foundations which are preventing our further understanding? 

Is it errors in the foundations which has caused the stagnation in physics? 

Is it possible that the proposed solutions are so complex simply because they are wrong? And again, are they wrong because we have misunderstood some of the foundational principles of nature?

Is it possible that when we do understand correctly the basic principles of nature, that the solutions will be much easier, paradox free, coherent, and quite unified?  I think the answer to this question is a resounding yes.

This is not to say that any specific theory is wrong.  But it is at least a healthy approach to attempt to keep us well founded in our quest. But it takes work.

Chip

From: General [mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.org] On Behalf Of af.kracklauer at web.de
Sent: Friday, November 13, 2015 8:41 AM
To: general at lists.natureoflightandparticles.org
Cc: Stephen Leary <sleary at vavi.co.uk>; Mark, Martin van der <martin.van.der.mark at philips.com>; Nature of Light and Particles - General Discussion <general at lists.natureoflightandparticles.org>; pete at leathergoth.com; David Williamson <david.williamson at ed.ac.uk>; Nicholas Bailey <Nicholas.Bailey at glasgow.ac.uk>
Subject: Re: [General] SU(2) equation set

Hi:

If I may, I'd like to stick a word here in.  For the record (as is said): I'm not up to speed, although I've given it a once-over.  

In the past, goofy, incomplete, mystical Physics theories have resulted from faulty or contradictory or inapproporate (and usually also covert-implicit) input.  Then the theory get developed, embelished, expanded, partially verified and what not until its "too big to fail"!  An antidote for this syndrom is FIRST to produce a proposal or schimatic "for dummies."  One that "your mother could understand."  It's hard to produce these things, because one has to return to a stage of understanding, so as to speak to a 'dummy' on his level. that the typical proponent has long left behind.  But the great advantage is that, it is hard to fudge the basic inputs on the basis of known, but sophisticated knowledge, information that in principle should not be referenced or input at the initial level, so as to keep the logic clean.

If this step is ommited, and you are very lucky (at first!), you may find yourself way, way, out on the limb with a lot of *** on your face!

For what it is worth, Al   

Gesendet: Freitag, 13. November 2015 um 14:57 Uhr
Von: "John Williamson" <John.Williamson at glasgow.ac.uk <mailto:John.Williamson at glasgow.ac.uk> >
An: "Nicholas Bailey" <Nicholas.Bailey at glasgow.ac.uk <mailto:Nicholas.Bailey at glasgow.ac.uk> >
Cc: "Stephen Leary" <sleary at vavi.co.uk <mailto:sleary at vavi.co.uk> >, "David Williamson" <david.williamson at ed.ac.uk <mailto:david.williamson at ed.ac.uk> >, "Nature of Light and Particles - General Discussion" <general at lists.natureoflightandparticles.org <mailto:general at lists.natureoflightandparticles.org> >, "pete at leathergoth.com <mailto:pete at leathergoth.com> " <pete at leathergoth.com <mailto:pete at leathergoth.com> >, "Mark, Martin van der" <martin.van.der.mark at philips.com <mailto:martin.van.der.mark at philips.com> >
Betreff: Re: [General] SU(2) equation set

Dear everyone,

Chip - your background is ideal. I always tell my aero students (I teach them a maths course) - that they will have a better skill set than physicists or mathematicians for solving differential equations because fluid mechanics is (relatively) hard, compared to mere Maxwell or QM (even relativistic QM!). Also the algebra (The space-time algebra (STA)- Cl(1,3)) is a kind of 4D extension of the quaternion algebra (which it contains as a sub-algebra). This is not to say it will be easy for you - there are concepts in there which will still make your head explode.

First of these is: the quaternion algebra is a division algebra (technically a division ring). The STA is not. This is both a problem and a solution. It is a problem in that there are limits where differentiation explodes. It is a solution in that division has implicit scalings (for which we need Martin and my paper on division) which allow (sorry -force!) extra constraints which are required - as the Maxwell equations alone) are under-constrained. Same is true for ordinary QM by the way - as one needs (at least) an extra external normalisation condition. Note, for example, that my eq 21 does not contain one - it is self-quantised.

Coming back to the code. I'm delighted that you professionals don't really seem to mind on which platform it runs. My preference would be for Python, or failing that something I could, at least read, like C. Object-oriented stuff makes my poor old head hurt!

Hmm on speed ... fast is good of course, but I think i would rather it was clever. What I am looking for is generating solutions to the particle spectrum. I have an analytic solutions for the photon, and a candidate one for the electron and the positron.  This would allow for testing of the numerical program in those cases. In the first instance a numerical system would look to parallel these.

What is needed further is a model for the quarks (I think I know how to do this, as I talked about first at CYBCOM 2008) and the interactions between them. Also one needs a model for the neutrinos - and how they propagate. Martin and I have some ideas for this - but there is room for (a lot of) development here. The best thing would be to get all of us into a room and not come out till we had a specification. I think we need a week in the first instance. Starting with me and Martin teaching you about how things work! Despite the existing papers, email back and forwards is just going to be inadequate

To brass tacks: a good starting point (even better than Stephen's code - as it is more extensive) for the algebra input is Martin's 16 by 16 matrix.

The second thing is a sharing of the division algebra paper (are we ready for this Martin?). This is a second-level thing though - and not needed for the first steps in the photon solution.

Anyway Stephen and Martin - this is down to you guys to decide whether or not (and how much) of this stuff you want to make public.

The next is the development of a proper "grid". A merely spatial (xyz) grid is not going to hack this. Indeed, it will be counter productive since it imposes a form which is just too simple (and one is already lost). What the 4-vector differential actually DOES (in terms of process - per differential) is transform a set of eight even terms (the fields, root-mass and quadrivector) to a set of odd terms (the currents and the angular momenta) and vice -versa. The constraint here is that the process must be UNITARY.  This means going to transformations (in terms of process) from an eight degree of freedom system to another eight degree of freedom system, using unitary differential transformations. 8D to 8D then. Not for the faint-hearted! Any "motion" or "oscillation" is really a transformation between these sets. I have invented a mathematics to try to think about this, based on fundamental process. I cannot email it to you as it is symbolic. It could be implemented (I think) as a process in a program. I anyway do not want to just "give it away", publically. Best method to teach it in the first instance is on a whiteboard!

The final step, however, is that everything must project back onto a grid on which one can measure it. That is 3D space and time - the basis set.

That is it. The process should parallel the process observed in reality - and project onto the basis of what may be measured. Hopefully, then, what is observed parallels what is simulated.

That brings me to a second question. Are we going to make the code and the process public or private? If private, under the "ownership" of what body? There are a few considerations here. Firstly, I noted recently that there is a prize for the solutions of a set of problems in mathematics - the Clay prizes. Solve one, win a million (dollars - i think). I got fairly excited, because I thought I may be able to solve one of them with (aspects of) the new maths. I phoned Nick Bailey for help - and he and I had a session last Saturday. Upshot of that was - no - probably cannot solve it in short order - partly because the way the question is formulated is on an un-realistic basis. Best that can be hoped for is to suggest "oracle" like solutions to particular practical problems.  Another problem has to do with the "momentum gap" in Yang-Mills theories. Again - cannot solve this directly (as Yang-Mills - though close to the truth - are themselves unphysical - in my view) - but should be able to solve the ACTUAL underlying problem - so (morally) should win that one (if we can do it)). Also, if we have code modelling both light and matter, one can begin to think about simulating molecules and crystals - and hence inventing new materials, devices and systems. That can be very lucrative!

My usual feeling is that all code should be open - but if there is serious money to be made down the line, which we could put into a foundation for the support and training of young international scientists, for example, then I would like to do that.

Anyway - the good news is that Hilbert once said that physics was getting to hard for the physicists. If we can solve one or two of the Clay prizes that will tend to show that maths just got too hard for the mathematicians!

Regards, John.

  _____  

From: Nicholas Bailey
Sent: Friday, November 13, 2015 11:21 AM
To: John Williamson
Cc: Nature of Light and Particles - General Discussion; Mark, Martin van der; Stephen Leary; Joakim Pettersson
Subject: Re: [General] SU(2) equation set

Do you want it to be fast?

Python is fast (and fun!) to write but slow to run. Although actually, not that slow.  <http://percival-music.ca/artifastring/> Artifastring, a modal physical model written by my ex-postgrad in C++ as the engine behind  <http://percival-music.ca/vivi.html> Vivi, the virtual violinist, actually ran faster when bound to Python than when linked to a larger C++ program! I didn't look into why. Curious.

Anyway, if you want fast, I'd write in C++ with as much built-in operator overloading as you can so that you can read your own code. You can test that to hell, then pull it in to Python using  <http://www.swig.org/> swig or  <https://riverbankcomputing.com/software/sip/intro> sip.

Alternatively, I suppose one could think of starting with Python and extending the functionality of a numeric module such as  <http://www.numpy.org/> numpy.

The other advantage of having at least the possibility of running C++ instead of Python is that Python doesn't support threads (because of the  <https://www.jeffknupp.com/blog/2012/03/31/pythons-hardest-problem/> Global Intepreter Lock problem) and if you want to do real heavy duty number crunching on multiple cores, you'd best use C++ with  <http://www.boost.org/> boost or something like that. Boost is proposed to be included in the standard library in C++17 anyway.

Nick/.

On Thursday 12 November 2015 13:37:03 John Williamson wrote:

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?

Hi John and Martin,

I am thrilled with the opportunities now when John has raised the funding question and Chip finally took a dive into the math and calculus!
Hope it stays at that level or continues to the next!

Some things I believe I could be most helpful with in your work are listed below. Tell me what to do and I will work free on it a few hours a week, odd week numbers. I could also offer my services more intensively as a consultant if that is an option. My normal tariff is 850 SEK/h (pretty standard in Sweden) and I only charge for productive time (not setting up tools, training, coffe-breaks etc). Likewise goes for my collegues at Join Business and Technology AB where there are few people that already work with FEM modeling and simulations regularly.

1.	simpy/numpy Python framework for interactive calculus:
2.	https://github.com/joakimbits/Quflow-and-Perfeco-tools/blob/master/lib/algebra.py (outdated now but I can fix it to work in Python 3)
3.	Ejs Java framework for interactive 2D-3D simulations (and a clever web interface): http://www.um.es/fem/EjsWiki/Main/ExamplesLorentzForce
4.	Usage of DX12 or its up-coming open-source derivates to make rough FEM/numeric calculations on arbitary gpu/cpu platforms.
5.	I could also bring my dual quad-core 32GB RAM server online if it helps.

Which calculus framework are you experimenting with today? I used to work in Mathematica, Matlab and Mathcad but nowadays I use Python or Jython for pretty much everything.

Best regards,
/Joakim 

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

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