In short my theoretical derived source of G(eneral)R(elativistic)
universe is the S(pecial)R(elativistic)
Poincaré-group extended to
comply to Einstein's
CAP. All
transformations of this group can be given with a
4x4 transformation tensor.
This tensor is specified completely with the sum of a symmetrical tensor S_{μν}
and an anti-symmetrical tensor A_{μν}. |

The
4D-spacetime universe is the
SU(3) gauge-symmetry. This gauge-symmetry
represents non-reducible all spin3/2
quarks as intrinsic unstable particles, quarks
only appear combined as so-called
hadrons.
The compound spin˝
fermions are called
baryons and the compound
bosons are called
gluons (keeping quarks of
a
baryon together) and
mesons. Only the
anti-symmetrical actions, related
to electrical charge, have
gauge-symmetry, because the symmetrical actions, related
to mass, don't allow so-called gauge-symmetry. In the symmetrical case all contributions cancel.
Therefore the
gravitational field can't be described as a gauge-field! All other force fields
are all related to charge and must be described using gauge-symmetry.So, the complete symmetry-group of our universe is given by the
CAP extendedPoincaré-group,
i.e. S_{μν}
en A_{μν},
and the U(1)x(SU(2)xSU(3) gauge-symmetry
related to the anti-symmetrical (charge related) actions.As shown experimentally,
gravitation
4D-spacetime.
This curvature can only be analyzed mathematically in linear
space-time.
This requires doubling of degrees of freedom (4 →
8), as Einstein solved using
Riemann's work. This is the fundamental reason
for the fact that the
curvature tensor, or
Riemann-Christoffel
tensor, has 20 degrees of
freedom, while the metric and the also 2-indices symmetrical
Ricci tensor only have 10
degrees of freedom. In 4D
curved space-time this is proven with the Bianchi
symmetry relations of the curvature tensor. According to
Einstein’s
C(omprehensive)A(ction)P(rinciple)
curvature must be taken into account in any description of physics.
So, also in any SR description
and also in every
QM
description!The only way to double the amount of degrees of freedom in a linear description is describing all non-reducible representations of the complete symmetry-group, i.e. all elementary particles, as harmonic oscillating point-particles in the 2D-plane
orthogonal to the observed direction of motion given by the
SR worldline. Characteristics
observed in QM also lead to this conclusion.The position of an extended elementary particle is given with its average position, i.e. the position on the
SR worldline. This is
also the position used in an
Euler-Lagrange description to obtain the
equations of motion. The particle itself, described exactly with a point-description
never is on its average
worldline, but oscillates harmonically in the
2D-plane orthogonal to this
worldline. The SR solutions
require B(oundary)C(onditions).
Bosons interact in the direction of motion only,
i.e. must be described with closed BC.
Fermions
are able to interact in all directions and as a result of that fact
can't be on the same space-time position together. So,
fermions
require open BC. Open
BC have one positive integer
degree of freedom extra. This is the
quantum number giving the particles family. The higher this
number, the higher the mass, because more interaction with the
gravitational field.The only massless particles are the spin1
photon and the
spin2
graviton. All other particles always have speeds
v < c(lightspeed).This is why paths of fermions allow
knots under transformations. I'm
not saying it'll actually happen (only maybe in a black hole),
but mathematical it is possible! Without fermions no resulting force-fields of
bosons, so all possible universes
require space that allows knots.In 2004 Grisha Perelman showed that only in
3D-space, i.e.
4D-spacetime
knots are possible.
This description appears completely correct, so every possible
universe must have 4D-spacetime!.Our universe is the result of a Last change: 05-10-2009 19:54:16 |