[General] SU(2) equation set

[John Williamson]

Hello everyone,

Yes Al – I could not agree more. We can do better though, as I have said before. I always say to others that, if one truly understands anything, one should be able to explain it at any level. Mums are important!

It is good to get some of the other members of the Williamson tribe involved (Cheers David!). These creatures do not suffer much from a lack of self-belief (inherited from my father). David has just invoked our mother, who, as it happens, I was just explaining this (the new theory) to in the early hours of the morning about a week ago. You must all be a bit careful to stay polite now. My other brother Pete, without irony, suggested at one stage when confronted by a gang of twenty or so nutters throwing stuff at (our and any other) passing cars on a new years morning that he and I should get out and “sort them out” – believing that two Williamsons working together were up to any conceivable challenge. If you think that is a bit mad it can get worse, if our sister (Janet) were to get involved on the other side everyone else would be simply outnumbered, even if she was just by herself (just ask Martin!). The explanations here are going to be, by necessity, a bit analogic. For better ones read the papers (links given below).

Ok .. here goes .. the new theory -explained for everyones mother ….

The basic principle of how (small) things work is that such things may exist and may change  -but only if that change is balanced by an equal and opposite change – everywhere and everywhen.

The physical expression of this may be written as a change equation – a differential equation in space and time. The change equation for the fields alone may be written in english as : the sum total of change is zero.

For example, let the way things change in space and time (the 4-differential) be called “d” and the six components of the changing things, the field, be denoted “F”. Expressed mathematically the expression dF=0 then encompasses the allowed changes the field, by itself, might make.  The only questions to explain (to mum) are : what is appropriate for a definition of “d”, “F”, what does one mean by “0” and what is this “=” thing anyway?

Now there is an old principle in computer science SASD (structured analysis- structured design) where code to model process should be based on the underlying primitives of the process. If one expresses both the field and differential in term of the proper nature of space and time, then one may hope that the equations, expressed in this way, would parallel some element of the truth, some part of “reality” (whatever that is!).

Now Adam has expressed amazement that merely changing the mathematics of the expression of field and differential from the standard tensor form to the Williamson-van-der-Mark form should lead to essentially new results such as eq. 21 in the paper (for those of you who do not yet have it) at :

http://eprints.gla.ac.uk/110966/1/110966.pdf


One should not be surprised – the standard tensor form encompasses neither the (proper non-commutative) nature of spatial and space-time rotations, nor the full proper (non-division algebra) of the experimental nature of space relative to time. Normal tensor algebra is good, very good, but not quite good enough for the task in hand.  Doing this more correctly (as standard texts, such as Jackson do not, as they use a normal tensor algebra) leads to dF=0 giving all four (and not just two, as in Jackson) of the Maxwell equations governing the way electro-magnetism works at once, as in equation 6 to 9 in the paper above.

So just what do the Maxwell equations, dF=0 mean for (non-mathematical) mothers? They mean that changes in the parts of the electromagnetic field are allowed but must balance. Reaction and equal and opposite re-action. Just like Newton. Such an equation allows force-free oscillation (Albrecht) amongst its six components. What is waving is the field. What it is waving in is the field. Simple. This is a force-free motion. What do I mean by that. Not that there are no forces (one can always define forces), but that the forces also balance (locally everywhere, for all time and in all proper frames) , giving a net zero force however, whenever and wherever you look at it.

Proof (do not let mum read this bit – unless she asks to): write down the generalized Lorentz force. This is a product of field F and current J. The current  in the Maxwell equations is given by dF=J. That means one may generalise FJ=0 by replacing J by dF. Rewriting “J” as “dF” one has FdF = 0 as a force-free condition. Clearly, if dF=0, force-free motion is satisfied, as FdF is also zero if dF is zero. Hence the usual Maxwell equations dF=0 imply force-free motion of the elements of the electromagnetic field (and they always did). Also they imply momentum conservation. Just fill in the field momentum density (E cross B) in Eq 21 and try it for yourself. It is just a constant. Simple.

Ok so far so just normal. That is just electromagnetism as it stands – albeit in a more elegant form. So what is new in the Maxwell-Williamson equations 6-13?

What is new is adding in a dynamical pair of rest-mass terms in the new theory – p-vot and q-vot. As well as 4 new equations describing a 4-current (v-vot -not new) and an angular momentum (spin) density (t-vot -new). These are added, not as ad hoc additions as in Barrett (see SU(2) discussion with David), but as basic space-time forms, just as fundamental as are mass and field.

These extra terms are not used in the photon paper above, but the mass terms are introduced in the electron paper at :

http://eprints.gla.ac.uk/110952/1/110952.pdf

The extended new equation, including all terms is dG=0 (in the papers in the links eqs 6-13 in the first and (slightly less general) Eq. 4 in the second). These are is, in my view, the Dirac equation as it should have been. It is not the Dirac equation, because Dirac made a mistake and added the mass as an odd not an even term – wrongly. Dirac is good – very very good (and very beautiful!). It contains a good part of the truth. It is good, but not quite just good enough. It mixes what should be field-like terms with what ought to be current-like terms. The new equation is, I think, better and (in my eyes) even more beautiful.

What the new equation says is that adding rest mass and spin, properly, leads to a set of equations of motion for field, current, angular momentum and rest mass, in which all changes in all elements are balanced by equal and opposite changes.  All changes in the sixteen elements of mass, current, field, angular momentum and q-vot.

The new equations have the advantage over the Maxwell equations in that they encompass Newton’s laws as a special case as well. They also describe, for the first time, the balance between current and angular momentum (the big “mystery” bit in modern physics).

Ok, I’m  going to attempt an explanation of the (not for the faint-hearted) morphing of one set of eight to the other set of eight, in words. To try to explain these a little more to mother (and here this may get challenging) think of the first eight as six planes and two “point-boxes” one is just a point as opposed to a line or a plane, the other (the quadrivector) is a unit 4D cube in space time: x times y times z times t–that is perhaps the hardest bit if your mum is not a mathematician or a physicist. Do your best! Now these morph smoothly back and forth to the other set of eight ( the four unit lines and the four unit volumes.) The point stretches to a line, the planes fold down into lines or out into boxes, the 4D box folds down into  3D box. At the same time the lines morph into the planes and project down onto the point. The boxes fold down to planes or stretch up into the 4D box. At each change, though everything changes, nothing changes. In a stable configuration, each point, line,plane, box or the hyperbox is filled from others as it itself fills them. This is the inner dance of the (light or material) particles. The full equation dG=0 just expresses this in a mathematical form.

There you go. The new equation encompasses how all these things (mass, current, field, spin and q-vot) may flow into one another and back again. How, then, the quantum wave waves. The equation may be wrong in detail (I even think it is, as it stands) as it is written in a right-handed basis and I think it should be in a left handed basis. Both work just fine at the level of Newton and Maxwell though – which version is correct will be found in detailed future experiment. No matter – it is good enough to be going on with!

That is what the new theory is about It is about saying new things, thinking new thoughts, and trying a new path in physics.

This adventure, ladies and gentlemen, should be fun!

Regards, John (W)

________________________________
From: General [general-bounces+john.williamson=glasgow.ac.uk at lists.natureoflightandparticles.org] on behalf of Stephen Leary [sleary at vavi.co.uk]
Sent: Saturday, November 14, 2015 12:57 AM
To: david williamson
Cc: general at lists.natureoflightandparticles.org; pete at leathergoth.com; Nicholas Bailey; Mark, Martin van der
Subject: Re: [General] SU(2) equation set

Gentlemen,

Sorry for no response so far. I'm travelling at the moment. I should be back in Glasgow on Monday.

Kind regards
Stephen

Sent from my iPhone

On 13 Nov 2015, at 09:57, david williamson <david.williamson at ed.ac.uk<mailto:david.williamson at ed.ac.uk>> wrote:


On 13 Nov 2015, at 14:40, af.kracklauer at web.de<mailto:af.kracklauer at web.de> wrote:

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”!

Hello,

Well yes, that is evident. It is up to you lot, to make sure you do something about this establishment, and the luminaries therein wearing those “emperor's new clothes” or standing on those wobbly pedestals. It is equally and fundamentally important to expose this as it is to seek the nature of matter ...



[…] An antidote for this syndrom is FIRST to produce a proposal or schimatic "for dummies."  One that "your mother could understand.”

… but I happen to think that the former is one which one could easily be understood by one’s mother. Let’s see some proper effort (and why not some publications too) focussed there.

DavidW.

The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.natureoflightandparticles.org/pipermail/general-natureoflightandparticles.org/attachments/20151115/3b2e31dd/attachment.htm>