My recent paper at scribd and vixra are as close as anything on earth to
properly specifying "the next" new unification of physics, and what we really know.
Of the three key steps, rewriting the book on time and letting bosons be bosons (not real particles if fundamental) are objectively clear, and more a matter of empirical
follow-up by others than of things needed from me. Even the new strong nuclear part in section 3 calls out for experiments and appreciation of experiments now,
I now see how the electron part requires further theoretical work, beyond what is described in the paper. Also, my new paper corrects one minor labeling problem in the earlier paper on "stability" but a few more or needed. This blog will outline what needs to be added or changed.
The 'tHooft-Polyakov model, extended by an eta term, is a major step TOWARDS a decent first model of the electron, but has some flaws which need to be corrected.
On the positive side... it shows how CHARGE can lead to a kind of zero-radius limiting solution, where the non-charge part of the mass-energy is positive definite and goes to zero, close to provong stability. That replicates some very essential properties of the electron, ala De Broglie, and should not be lost... in a more refined model,
building n what we learn from this "simple" example. Also, it includes three bosonic fields, the A-super-a for a=1, 2, 3, which is the multiplicity we see in electroweak theory. Obviously, I do not agree with every last details of today's quantum electroweak model, but for a next model of the electron it is reasonable to preserve features which have been verified by experiment;
existence of three bosonic fields in the very model of the electron itself is appropriate.
But there are features which disqualify it as well. First, there is a total lack of mechanisms to choose a particular charge in the entire R3 space of possible charges. There is no explanation of why we see just one point in that space, at least in the case of he electron... and we do not see a lot of near-electrons out there. That in turn implies that the stability is just a kind of metastability. Second, there is no explanation for why our A (electromagnetism) is so different from W and Z.
There is then an obvious way to fix the problem.
EWT being a parity-violating model, we use the e-mu-nu=lambda-rho tensor for ordinary covariant vectors (pseudovectors), not spinors.
I also obtained Hobart (1965) yesterday, which shows how very easy it is to get stable "solitons" with second order derivatives in the Lagrangian (though the electron is not a star). It provides encouragement.
We basically need to use teh Lagrangian of electroweak theory as the main starting point, but replace the spinor "Q" fields with vector fields using the e-mu...
tensor to hold it together, using something like the ordinary Higgs term in place of the 'tHooft-Polyakov one (initially), and otherwise replicating as closely as possible the kind of mechanism in my paper on 'tHooft-Polyakov. That's the key next step.
One caveat, of course, is that details of that Higgs term can be changed, and that may be the most important step after that, to meet Macgregor's empirical challenge. Here it should not be so hard, since we do not need to worry about renormalizability.
Some important details....
CERNS says they "saw" W and Z in the sense that they saw a kind of four-c hannel interaction which outputs what they predict Z and W decay into. But we also see four channel processes for the "photon." It seems reasonable to believe all three are fundamental fields, not particles or solitons as such. But why not HIggs likewise? It seems we need to re-evaluate more than just the "particlehood" of Higgs. Macgregor's challenge already suggests as much, and suggests a more harmonious posisbility...
recaling that we do nt need HIggs term for mass (that's in charge) but for singularity/stabilization. Maybe simple fourth order aspects can take care of that without a HIggs term at all. But still, the role of A versus Z and W must be in teh second-stage model. (The first stage EWT-like version would srill fit all we know,
which is a big step up... on the path.)
Also... I have a green notebook with the rather elaborate PDE details of the analysis I mention in the paper on "stability". Someday I do need to write those down, though most physics texts these days are annoying in not including such tedious details. Time for a higher standard. But at 5AM, maybe that time is still not instant for me.
A key result in my "stability" paper is that the current 'tHooft ansatz for that model,
even interpreted as the limit as eta goes to zero, is WRONG. We get a decent singular soliton solution, as eta goes to zero, but it isn't the one of Higgs mass they now
assume/get. That one is not the miniumum energy solution, or the limit of the minimum energy solutions. Wrong limit; failure to analyze limits. That kind of problem often screws up people fundamentally naive about mathematics. Fortunately, the correction gets us closer to what we need to explain in empirical reality. But is there a new ansatz... or do we start to need computers? It would be nice to know... but
the Stage One plausible model (starting from EWT) might be a better base anyway.
And there we need invoke only one charge, which may help the analysis.
A strategy for proving stability (which Bogolmony has certainly NOT done, a great myth of the GUT people, almost like a crago cult)...
woould try to START from the "Q stability" which the stability paper cites...
though the energy expression minus the charge term is clearly nonnegative, and indefinite modes must be treated properly. (we have SOME indefinite modes which exist even in a strictlt stable chaoiton, like translation and gauge transformation, but we need to be sure there are none which violate chaoiron status.) To "complete" the stability proof... a bnecessary first step is to consider exactly one new perturbation, (delta C Q, delta C A), where CQ is the derivartive of the scalar C (total charge) with respect to the Q field values...
That's necessary, and ignored by Bogolmonyi etc.
But in the delta squared H "matrix", there are also cross-terms which should be conisdered for a complete proof of stability. That's worth doing for all three models I have discussed here (tHooft-Polyakov plus etz; stage one EWT; moditied EWT).
But Stage one EWT is the most important for now, and proof of the necessary condition involving charge perturbations is the most immediate check needed.
Now: the real problem is how to reconcile this with all my other time opressures,
not just job but "saving the world" stuff. All unique personal responsibilities, it seems, in a world of people having real troubles tying their shoelaces.
I do hope someone else can take over... eventually take over all of it, as I do seem to be a typical aging mortal of 64.
Will anyone on earth EVER understand what an electron is? Even better, while we still have ways to use such knowledge?
Let me emphasize that this post is HIGHLY short-term and tentative, like what I put in my green notebooks, sometimes worked out, but in general groping....
My immediate followup was to reread Taylor's book on Gauge Theories and Weak Interactions, a very nice review of EWT. Perhaps just W and B are enough for the first stage model, with electron as emerging as a soliton of them. No need for the e four tensor at this stage; the simple wedgies in the W basics may be all we need, remembering how we do have electron and positron as well. But extra terms of course..
and care to make sure that charge and handedness of the soliton properties have a link. It does not sound radially symmetric exactly, b ut is even the tHooft Polyakov ansatz so?
Hey... if you can do it, please do so. My only reason for feeling that I should be the one to take this on is that no one else really has. But OK, I also think it's good for my general education.