Trenton said:
Jarekd you are right. A 3D entity such as the hedgehog is required for charge. I googled hedgehog topology. I almost wished I hadn't but only almost. It is a far better model.
One of places they use this kind of topological singularities are liquid crystals, which can have thermodynamical tendency to form 2D sheets, 1D tubes or 0D hedgehog-like e.g. micelles.
In field theories it is a bit similar (but also different: wave-like instead of diffusion-like) - assume a field which has energetic tendency to locally break symmetry, like choosing a direction.
These directions can form e.g. hedgehog configuration, or generally any singularity of integer topological charge ... or maybe also more complicated topological structures - corresponding to further particles.
Does all this mean though, that all charged particles are indeed EM waves or photons which by means not altogether clear, have become hedgehogs and are radially rather than linearly oscillating - and that this obstructed action (in that the whole no longer propagates at c) is responsible for the charge?
From topological point of view, being charged particle means being hedgehog-like configuration.
Photon is a different story - it does not have charge, but it has angular momentum - it is kind of twist-like wave, like behind marine propeller.
I shall read up your other stuff on the strong/weak interactions and the Higgs but this might take me some time. It seems to me though, that both the strong and weak forces are really the laws of math and are not as fundamental as they are claimed. Hedgehogs appear to like the company of other hedgehogs even if they are the same sex as is proved by the high energy difference between atomc and mollecular hydrogen (covalent electrons). Siamese hedgehogs or particular multi-hedgehog configurations, perhaps forming a single albeit more complex soliton entity, have a lower energy level. In the nucleus where the energy levels are much higher a mix of the sexes is required to smothe the way but the principle is the same. Nobody has ever called covalence a fundamental force as far as I know so why attribute the quark configurations to one?
I don't like the idea of seeing particles as just abstract objects out of the field, while every charge is singularity of electric field - I believe we should search for concrete models for structure of fields near/inside particles.
There are probably different models possible, but we should always have in mind the successes of the Standard model - that while constructing Feynman diagrams for scenarios on these solitons, we should finally get constants in agreement with the current models.
As for Higgs, is it really true that this long lost boson is the reason why all other particles have mass or is that just the BBC correspondents talking twaddle again? Einstein's GR describes gravity very much better than the BBC and a soliton hedgehog wave would neatly explain inertia - moving the hedgehog would automatically deform space since otherwise part of the wave would go superluminal and the other part subluminal.
Soliton particle models also need Higgs-like potential: to handle the situation in the center of singularity, we have to get out of this potential - giving particle rest energy/mass.
But I don't know if it requires/implies a special corresponding "Higgs particle" - which in fact is just one of thousands metastable states.
