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There are a number of parallels
that I see between the fractal-like Euclidean model of the universe, as
described on this page with its fundamental forces and particles on one hand and stringtheoretical
concepts on the other hand. A couple of examples:
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M-Theory with corresponding dimensional
viewpoints X1 - X5 |
- The fractal-universe can be "observed" from different dimensional
viewpoints(*) which would each give a different mathematical model as well, each
being associated with a unique number of dimensions. For the "closest"
dimensional viewpoints, i.e., the one from our own X4,
together with X1, X2, X3 and
X5, this would result in
rather concrete theories (5 in total), while the more "distant" viewpoints would be less
obvious, but nevertheless mathematically possible. I see here some links with
the theoretical possibility of many more stringtheories (in particular in
Euclidean space-times) while there must exist a dimension-independent
overall description (obviously M-theory) of the basic principles of each of them.
- Dualities in stringtheories could be associated with the dualities that I
have described between fermions and bosons. Each fermion in Xn
corresponds to a boson in Xn+1, i.e., they are
physically the same entity but described from a different dimensional
viewpoint. This may perhaps also be a basis for supersymmetry. In principle,
each particle should have a mathematically describable and associated
counter-particle from its neighboring dimensional viewpoint. It would however
be the same particle in fact, observed from another (higher or lower
dimensional) side.
- P-branes may be directly linked to particles in n dimensions
as listed in the table of section 5 and shown in the animations of section 6.
- "Curled up" dimensions in Calabi-Yau space is consistent with the way the
proper time dimension shows itself as fully contracted in the spatial environment of
an observer in Xn (see description in middle of
section 4). Each point in space contains all coordinates of the proper time
dimension. The Euclidean model assumes such dimensions to be closed and thus
circular.
The added value of Euclidean relativity lies in the fact that the Euclidean
space-time, extrapolated to the fractal-like model of the universe, is far better
equipped to support this "visually", allowing natural
interpretations of various elements of stringtheory, the lack of which seems to
have been hampering stringtheories from the beginning. The inherently confusing
Minkowski geometry is not really helpful in visualizations.
Perhaps the most interesting contribution of the fractal-universe model based
on Euclidean relativity is that quantum gravity results from it naturally. The full quantum description of electromagnetism based on a 4D
Euclidean space-time can in principle be ported one-to-one to gravity based on a
five dimensional Euclidean space-time with mass particles acting as its bosons.
(*)
The following conditions
(see
Section 2 in [2] ) define the
dimensional viewpoint in Xn :
- Observers in Xn have the skill to observe
dimensions 1 to n-1 as spatial dimensions.
- The dimension n is the equivalent for 'proper time' for
observers in Xn .
This definition means that we are observers in X4
where x4 is our proper time dimension but that for
instance in 3D Euclidean space X3, observers are
'Flatlanders', i.e., they live in a 2D space. They experience the third
dimension x3 as their equivalence of proper time,
while their basis for speed measurements is x4 .
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