Posted: Thu May 26, 2011 7:13 am
I completely agree that we shouldn't just ignore the problem of 'gluing' electric field toward the center of e.g. electron:
- because of singularity, the interaction cannot be just pure electromagnetism - it has to deform (e.g. into weak/strong interaction),
- if field in vacuum would enforce that charge(/spin) inside a region can obtain only integer values (like for topological charge), particles could be just such stable field configurations themselves (solitons).
There are some models searching for field configurations of e.g. electron, like 'Penrose twistors', or just as solitons guarded by topological constrains like charge or spin.
One such approach is of prof. Faber (paper) - there is a field of directions: a point from 2D sphere in each point of spacetime, which is equator of 3D sphere, but going out costs energy (potential term).
So the simplest topologically nontrivial configuration is hedgehog (we cannot have fractional charges) - but to avoid topological conflict, it has to get out of the equator (2D sphere) in the center of electron, toward one of 2 poles of 3D sphere (choosing spin) - it gives electron rest energy, which through Lorentz invariance became also inertial mass. Vacuum dynamics of this field occurs to recreate electromagnetism on effective level.
This simple model doesn't leave place for e.g. internal clock of particles required for their wave nature and can only model single electron - the perfect situation would be having a single field, which family of topological solitons correspond with our particle menagerie and their dynamics - it seems it can be obtained by just adding auxiliary axes perpendicular to Faber's main axis and make deformations less abstract, getting quite promising ellipsoid field - here are pictures.
- because of singularity, the interaction cannot be just pure electromagnetism - it has to deform (e.g. into weak/strong interaction),
- if field in vacuum would enforce that charge(/spin) inside a region can obtain only integer values (like for topological charge), particles could be just such stable field configurations themselves (solitons).
There are some models searching for field configurations of e.g. electron, like 'Penrose twistors', or just as solitons guarded by topological constrains like charge or spin.
One such approach is of prof. Faber (paper) - there is a field of directions: a point from 2D sphere in each point of spacetime, which is equator of 3D sphere, but going out costs energy (potential term).
So the simplest topologically nontrivial configuration is hedgehog (we cannot have fractional charges) - but to avoid topological conflict, it has to get out of the equator (2D sphere) in the center of electron, toward one of 2 poles of 3D sphere (choosing spin) - it gives electron rest energy, which through Lorentz invariance became also inertial mass. Vacuum dynamics of this field occurs to recreate electromagnetism on effective level.
This simple model doesn't leave place for e.g. internal clock of particles required for their wave nature and can only model single electron - the perfect situation would be having a single field, which family of topological solitons correspond with our particle menagerie and their dynamics - it seems it can be obtained by just adding auxiliary axes perpendicular to Faber's main axis and make deformations less abstract, getting quite promising ellipsoid field - here are pictures.
