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!
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
Things are tricky:
A torus diameter is 4R ! But the torus radius is only R! So its a matter
of perspective.
If you look at the same distance circle radius "torus 2 radii" then the
4D radius - seen in 3D - is longer!
J.W.
On 17.09.2020 23:15, Robin wrote:
In reply to Jürg Wyttenbach's
In reply to Jürg Wyttenbach's message of Thu, 17 Sep 2020 22:04:39 +0200:
Hi,
>You can look up SO(4) in Wikipedia
>
>The group measure is 2^1/2. This is the length of the unit radius of the
>Clifford torus (formed by the tangent space). To get the standard norm
>(=1) you have to divide by
You can look up SO(4) in Wikipedia
The group measure is 2^1/2. This is the length of the unit radius of the
Clifford torus (formed by the tangent space). To get the standard norm
(=1) you have to divide by 2^1/2!
Or more simple. The radius for the standard circle is 1, but the
Clifford
In reply to Jürg Wyttenbach's message of Thu, 17 Sep 2020 11:54:01 +0200:
Hi Jürg,
Your theory is already difficult enough for us uncomplicated folk to
understand. It would perhaps help if you didn't use
shorthand. IOW please be very clear and precise, and don't leave any steps out.
I realize
Quite correct: 1/2 is missing.
The SO(4) radius is 1/2 of the measured one but gets enlarged by the metric.
So for the proton R_4D = 1/2 R_p *(2^1/2 ). This is the real radius from
the center of action/rotation!
J.W.
On 16.09.2020 22:35, Robin wrote:
In reply to Jürg Wyttenbach's message
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