Hi Joy:
Your reply was very helpful, thank you. Do you have anything at all to help
visualize the 7-sphere? Your 7-sphere paper is one which I have not even tried
to read as the geometry seems so daunting.
Hi Fred:
On Thursday, 31 October 2013 06:00:03 UTC, FrediFizzx wrote:
> A left handed electron can be either spin up or down. Same with a RH
> positron.
Oops. Yes, agreed. I should not have written "spin +". I was thinking of
"chirality" but wrote "spin". Either chiral structure can have either spin at a
detector. The chirality is a hidden variable. Joy writes about helicity very
clearly in his reply. Sorry.
Ben wrote:
> > kind of large-scale twist and wondering how the twist in the universe
> > could get
> > something back to its starting point so quickly! But I see the double
> > cover version now.
Fred wrote:
> I am not sure what you mean by "something back to its starting point so
> quickly".
Three years ago, I was wrongly thinking of a large scale twist in a 3D
universe. A universe-sized radius of curvature gets you back (maybe!) to a
starting point after an aeon. That was obviously no use. Travelling around a
very small radius of curvature, however, gets something back to its starting
point quickly enough but that is the territory of strings or maybe microscopic
BHs and that did not seem to be the correct territory for CA either.
I think that I follow the Dirac belt analogy. It involved a 3D body rotating
around a 3D body and getting back to its starting point after a 720 degree
rotation. It does not involve using extra dimensions beyond 3D, but if there
were a small compactified extra dimension, with a very small radius of
curvature, then a rotation of a body around that curvature would need 720
degrees for a full rotation. And as in Joy's similar point, in his reply, this
would be a global effect as the curled up extra dimension would be accessible
everywhere in our 3D.
<snip my earlier writing>
Fred replied:
> What you wrote above seems to be speculation. I believe that Joy's model
> works best with considering the void to be permeated with a Dirac field in
> addition to a Higgs field. Remember, since the Higgs boson is massive, it
> has to be very short ranged. And believed to be zero spin and no charge.
> However, the difference between the parallelized 3-sphere topology and
> charged fermions is that in the topology, you will have a sign flip after
> 180 degrees and with the fermion you get a sign flip in 360 degrees. I
> haven't quite reconciled that yet.
Yes, I admit to using speculation. Sorry for not being clearer. I often do
write that I am not a physicist, but forgot here. The trouble is that I can
visualize (maybe speculatively and wrongly) multiple dimensions using
particle/fields easier than I can using geometry. In my model, the electron
has colour charges but they are neutral overall. But just because the mean
colour charge is zero does not mean that colour is irrelevant to the electron.
In some ways I think Joy is fortunate that the 7-sphere is not needed to cater
for the electron behaviour. Well, Joy would be OK because he could re-write a
model using the 7-spere. But I would not be able to follow it yet.
In my speculation, the full dimensions of space would need to cater for four
short range particle properties (red colour charge, green colour charge, blue
colour charge, weak isospin) and two long range ones (electric charge, spin). I
see all those as containing opposing chiral properties eg red is chirally
opposite to antired. The world could subdivide into different chiral parts for
any of those six variables. AFAIK that is all there is. I do not know how
many dimensions that makes in total. A world or vacuum field could subdivide so
long as it has both chiralities within it. IMO the Higgs could do this. If the
Dirac field provides for the creation of e-/e+ pairs then the Dirac field can do
this too.
What is a 3-sphere? Joy notes that at each point on a 3-sphere one can have
two chirally opposite small 3D tangential spaces. So that is in total a 3-
sphere plus 6D? Yet the whole space is supposed to be 5D? Presumably the two
3D spaces can be thought of as one 3D space because each 3D space is somehow
exclusive of the other space, and that must be why a particle stays within its
starting chiral space. [And that is why the maths for one curvature should not
be mixed with the maths for the other curvature at the same time.] So we have
the 3-sphere plus 3D. And the 3-sphere is just the surface of a sphere and so
is just 2D. Hence 2D+3D=5D is the total dimensions?
I suppose that the radius of curvature of the 3-sphere is indeterminate? But
could it be a compactified string dimension?
Best wishes to you both.
Ben