[General] SU(2) equation set

Tue Nov 17 11:21:19 PST 2015

Perhaps http://fqxi.org/community/forum/topic/2585 may help. They fund projects.

     On Tuesday, November 17, 2015 2:00 AM, John Williamson <John.Williamson at glasgow.ac.uk> wrote:

 #yiv8784497291 #yiv8784497291 -- _filtered #yiv8784497291 {font-family:Times;panose-1:2 0 5 0 0 0 0 0 0 0;} _filtered #yiv8784497291 {panose-1:0 0 0 0 0 0 0 0 0 0;} _filtered #yiv8784497291 {panose-1:2 4 5 3 5 4 6 3 2 4;} _filtered #yiv8784497291 {font-family:Cambria;panose-1:2 4 5 3 5 4 6 3 2 4;}#yiv8784497291 #yiv8784497291 p.yiv8784497291MsoNormal, #yiv8784497291 li.yiv8784497291MsoNormal, #yiv8784497291 div.yiv8784497291MsoNormal {margin:0cm;margin-bottom:.0001pt;font-size:12.0pt;font-family:Cambria;}#yiv8784497291 .yiv8784497291MsoChpDefault {font-family:Cambria;} _filtered #yiv8784497291 {margin:72.0pt 90.0pt 72.0pt 90.0pt;}#yiv8784497291 div.yiv8784497291WordSection1 {}#yiv8784497291 Hi Chip,
Replies in blue as usual ...

Hi John W. Yes, I agree that field is not the most fundamental, not the best we can do given the available data.  I have had some time to work through a bit of the math in you papers, and find it to be extremely similar to what I am thinking the full set of field equations actually are (for what that is worth).  I am very encouraged, but it takes me some time to digest the detail, so bear with me. I have a habit of trying to go step by step and prove everything.  Sometimes a good habit, but time consuming.
Working through the maths precisely is SO important. I tend to come from the other end – seeing all at once but having real trouble getting the detail precisely correct. Martin is my usual foil for this - but is good to have backup!

There are one or two choices, not more, to be made in that process. One important one is left-handed or right-handed. This has consequences for a set of signs (for example for the magnetic field). This is why, you will find a minus sign at one point in the paper – to fix the sign to be that adopted conventionally (in Jackson, for example). I think we (humanity, collectively) may well have made a mistake in the past in certain choices – sign of the electron charge, right instead of left handed – that sort of thing. Actually – I think, in retrospect, we got the charge right – it should be negative, but I think we may have got the handedness wrong. I do not know this – it is merely a (quite strong) feeling at the moment. It is easy enough to get the Maxwell equations right with any set of right or left, electron positive or negative. The proof, one way or the other, will come from detailed agreement (or not) with experiments on charge and spin. On top of this there is always the possibility that I have simply made a mistake somewhere in the derivation of the equations. As I have said before – I can get the sign wrong in signing my name.
Yes, the perfect balancing of the forces we know must exist from the empirical evidence. Yet in agreement with what we have been able to establish, like Maxwell’s equations.
Maxwell’s as they stand balance the forces only in the free-field case where there are no charges present. If this was all, charge should then simply explode under its own internal forces. This is the enduring mystery (over a century) of the (till last year) unknown “Poincare stresses” which are presumed to hold the electron charge together (see Feynmann, or Poincare). The motto of my home county of Clackmannanshire is “look around you” (in Scots “look aboot ye”). The Maxwell-Williamson equations, by introducing a rest-mass term, do not have this problem. Motion in a double loop is also, then, force free. “Experiment” is often thought of as being some big Silver machine in a far country. Not always so. Look aboot ye – electrons do not explode! Thank you.
I have to thank you too – and all of the (lots!) of you who responded to my call for “help” last week. I needed only one extra referee in the industry area – and I used you Chip. Unfortunately, an administrator in my University has decided to block my application for funding on the grounds that it is “research negative”. We are now required, in any grant application, to get funding to cover a replacement to support our base research effort – pay for administrators, research technicians – lighting, heating etc. This means an application to free up teaching time for research gets classed as “research negative”. Unfortunately, the Leverhulme trust (to whom I applied) will not provide funding for anything other than the replacement costs for teaching – and will also not consider a grant not supported by the home institution. So my application has already been rejected – not by the funder, but by my own institution.. Thank you anyway. Looks as though I will be tied up again next year with a lot of teaching! Oh well. The management seems a bit puzzled as to why many of their star researchers have already left. I wonder if this kind of thing has anything to do with it?I should apologise to some of you others as well. The whole thing has made me a little shorter tempered than usual and this may have come across.I love teaching though – and would not like to give it up – but if anyone knows of a body out there who would like to fund some full-time research at a critical moment in its development, please let me know. Chip
Regards, –John. 
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