Hi Robin,
I usually use projections to 3D space to compare the radius. But in
calculations you have to be aware of the diverse factors given by the
torus metric and SO(4) metric.
So the correct question is: Which radius must be used for what
calculation. Comparing is just a curiosity!
Some basic topology knowledge is a prerequisite for understanding the
new model. It's not much what you must know but it will completely
change the way you think about physics and symmetry.
If you look at a fudged higher order QED Hamiltonian for an
energy-density then you must know much more that said above.
SO(4) physics is "simple.." but you must master the short gap.
J.W.
On 18.09.2020 00:55, Robin wrote:
In reply to Jürg Wyttenbach's message of Thu, 17 Sep 2020 23:22:05 +0200:
Hi Jürg,
If you are talking about a torus, then it would help if you make a distinction
between major and minor radius.
Things are tricky:
A torus diameter is 4R ! But the torus radius is only R! So its a matter
of perspective.
No, it's a matter of stating exactly what you mean, and leaving nothing to the
imagination. ;) (Because one person will
often imagine something completely different to someone else, given the same
"shorthand" description.)
I assume you are assuming a torus with a central hole that is zero in size. In
which case the major radius is twice the
minor radius.
If you look at the same distance circle radius "torus 2 radii" then the
4D radius - seen in 3D - is longer!
Does this mean "the 4D radius is longer than the 3D radius", or the "3D radius is longer
than the 4D radius", or "the
circumference of ... is longer than that of ...." or "some distance is longer than
some other distance"?
As you can see, I don't like ambiguity. ;)
[snip]
--
Jürg Wyttenbach
Bifangstr. 22
8910 Affoltern am Albis
+41 44 760 14 18
+41 79 246 36 06
