In short my theoretical derived source of dark matter and energy. Dark matter, i.e. matter independent of the EM-field, must be elementary particles. All compound particles exist out of charged quarks and as a result have an area with non-zero charge density.
First my analysis of all possible elementary particles in our universe.
Our universe is given completely using a non-reducible symmetry analysis. This analysis must be relativistic. The complete symmetry group of our 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 Sμν and an anti-symmetrical tensor Aμν.

The CAP extended Poincaré-group has 2x10 + 1x6 = 26 degrees of freedom instead of the 10 degrees of freedom of the continuous complete SR Poincaré-group.
Any description of what we experience always has causes and consequences. This is why the complete SR symmetry-group, described with Sμν and Aμν, will be given using fermions (massive half integer spins) as sources of bosons as force-fields.
The 10 degrees of freedom of the symmetrical tensor Sμν are given by the spin˝ masses as sources and the resulting spin2 gravitational field.
The 6 degrees of freedom of the anti-symmetrical tensor Aμν are given by the spin˝ charges as sources and the resulting spin1 EM-field.
The Maxwell equations of the EM-field don't specify this field completely. Only after using so-called gauge-symmetry the EM-field is given completely. The EM-field has U(1)-gauge-symmetry, given SR with the Lorentz gauge-symmetry. The electroweak theory, a mixed gauge-theory, is given by the U(1)xSU(2) gauge-symmetry, in which the photon (the non-reducible description of the spin1 EM-field) appears mixed (given by the so-called Weinberg-angle) with the massive Z and W± gauge-bosons. The only additional gauge-symmetry possible in our 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 extended Poincaré-group, i.e. Sμν en Aμν, and the U(1)x(SU(2)xSU(3) gauge-symmetry related to the anti-symmetrical (charge related) actions.

As shown experimentally, gravitation curves 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 black hole in another universe turning into a singularity. This singularity was characterized with a first phase of the Big Bang in which 3 elementary particle families of fermions came to life. After the Big Bang all matter scattered from the singularity in all 3D-spacelike directions, with a constant total energy and total angular-momentum of our universe. The energy density only decreases so the 3 particles families of fermions are a given fact of our universe. The singularity of the black hole in the other universe terminates by vapourization into our universe.

Dark matter is nothing but neutrinos. Back to Toms weblog

Last change: 05-10-2009 19:54:16