My life's aim is a complete non-reducible description of everything we humans experience everyday.
Starting point are Albert Einstein's theories of relativity: S(pecial)R(elativity) and G(eneral)R(elativity). GR describes curvature of space-time as a result of mass(-speed)distribution in our universe. On so-called local-scale, i.e. infinitesimal level, curvature is negligible and a SR description can be used.
In 1920 Einstein wrote his C(omprehensive)A(ction)P(rinciple). This principle shows that all actions, given by their Lagrangians, always depend on the gravitational action.
In all used Euler-Lagrange descriptions, the equations of motion with all their characteristics, follow from the Lagrangian density. David Hilbert extended this description to GR with curved spacetime (1915).

In curved spacetime, all equations only remain invariant when all used matrices are tensors and all used spacetime-derivatives are so-called covariant derivatives.
Using covariant derivates, the order of derivation matters! All characteristics of covariant derivatives are given with the so-called curvature(Riemann-Christoffel)-tensor. This tensor has 20 degrees of freedom. Using standard GR-theory, the degrees of freedom of the curvature tensor reduces from 256 to 20 due to the Bianchi symmetry relations, but the actual reason is the non-commutativity of the covariant derivatives! So, CAP enforces all descriptions to use tensors and covariant derivatives, also in SR flat space. The Euler-Lagrange and Einstein-Hilbert descriptions actually are point-descriptions. All described objects are specified using a point in 4D spacetime. As a result all equations of motion follow from the Ricci tensor, i.e. the non-zero contracted curvature tensor, with the degrees of freedom halved (20 10). Mathematically the only way to solve this problem is doubling the degrees of freedom in the only possible non-reducible description of all symmetries of our 4D universe. Any exact description is a point-description! This is why all Q(uantum)M(echanics) descriptions assume elementary particles to be point-particles with so-called intrinsic characteristics, like spin. In April 1998 I concluded that all elementary particles should be described as extended particles using a point description in the 2D-plane orthogonal to the observed direction of motion given by the SR worldline.
At infinitesimal level and whenever curvature can be neglected, the solution can be described SR. The extendedness is very small, i.e. always non-observable. As a result a SR description suffices in all cases. The used inertial frame is chosen with origin at the average position of the harmonic oscillating point in the 2D-plane giving the center of energy of the extended particle. This origin specifies the position used as QM point-particle on the SR worldline.

The solution shows constants of motion following from symmetries. The time-like total energy H=E(p)+U(r) = hf = hω, with p the particle's momentum observed from the inertial frame, r the polar distance from the origin, f the frequency of oscillation in the 2D-plane, h Planck's constant, ω the angular-frequency and h Dirac's constant. The potential energy must result in harmonic oscillation: U(r) = ˝kr2, with k a force-constant to be determined. The space-like constant just is the angular momentum, i.e. spin S = hs in the direction of motion given by the wordline in the direction of motion of the particle (and inertial frame). Again h  is Dirac's constant and s must be any positive (half-)integer to describe any possible (fermion)boson. I.e. the used intrinsic angular momentum of QM comes to life when demanding QM to comply to Einstein's CAP.

The complete symmetry group of SR is the Poincaré-group. Any transformation of the CAP extended Poincaré-group can be represented with the sum of a symmetric transformation tensor and an anti-symmetrical transformation tensor. All fundamental elementary particles must follow from the most general symmetry group, i.e. the CAP extended Poincaré-group.
Elementary particles can be split into two different kinds: 1. Fermions, which are the sources of all force fields and have half-integer spin. 2. Bosons, which represent the force fields and have integer spin.
All members of the Poincaré-group are represented in a non-reducible way as: spin2xspin˝ + spin1xspin˝
The spin2 particle is the mass- and charge-less graviton with source the multiplied spin˝ mass.
The spin1 particle is the mass- and charge-less photon with source the multiplied spin˝ charge.
The average extendedness is proportional to the spin, so CAP enforces s > 0. Dimensional analysis now allows: s
є{2, , 1, ˝}
Both the Euler-Lagrange and the Einstein-Hilbert action mechanisms remain valid as long as the particles are specified with the average position on the SR worldline.
The EM-field isn't given completely with the Maxwell equations, which are given SR with the anti-symmetric EM-field tensor Fμν. Only after imposing a gauge-symmetry the EM-field is specified completely. All gauge-symmetry is related to the anti-symmetrical fields, because symmetric fields never yield any so-called gauge-symmetry! As a result the total gauge-symmetry of our 3D-universe just is: U(1)xSU(2)xSU(3).
The U(1)xSU(2) gauge bosons describe the mixed (given by the Weinberg angle) photon and chargeless and massive Z-boson and the massive and charged W± bosons.
The SU(3) gauge symmetry group describes all charged massive spin3/2 quarks, which must combine into hadrons, of which stable spin baryons and interacting bosons called gluons and mesons appear in real life.
In standard QCD all quarks are assumed to be spin˝ with assumed so-called isospin to end up with 4 degrees of freedom. However, the fact that quarks are never observed on their own is not explained in the standard model. To me, quarks must be intrinsic unstable, i.e. have spin3/2. The so-called isospin is nonsense!

When solving the equations of motion of extendedness in the 2D-plane orthogonal to the direction of motion (worldline), one requires B(oundary)C(onditions) to solve the D(ifferential)E(quations). Open BC have one degree of freedom extra. It's the positive  integer giving the amount of rotations in the 2D-plane before the motion repeats itself again. This degree of freedom must be the quantum number of the particles family.  The higher this number, the more interaction with the gravitational field, i.e. the higher the rest-mass. All fermions must have open BC, i.e. must have non-zero rest-mass! Closed BC describe bosons that only interact with other particles in the direction of motion, specified by the wordline. All elementary bosons have only one species. Only compound bosons have more so-called families.
I observe our universe as created from a singularity with a fixed total energy which resulted in our well-known Big Bang. This constant total energy scattered in all directions. Just after the Big Bang the energy density was the highest and decreased as scattering took place. During this scattering the entropy increased, as it still does. Experiences show we only have 3 particle families of fermions. All particle families came to life just after the start of the Big Bang when the energy density was the highest. This is why I assume that 3 particle families of fermions are a fixed fact of our universe.

In 2004 Grisha Perelman showed that knots are only possible in 3D-space, i.e. 4D-spacetime. Fermions always have mass, because they are described using open BC. As a result of this fact it's always possible to create a knot in the path of a fermion. I'm not saying that it'll ever happen, but it's possible! Fermions are the sources of all bosons, i.e. no fermions implies nothing at all. Based on this discovery of Perelman I concluded that the only possible universes have 3D-space, i.e. 4D-spacetime.


Last change: 08-08-2015 18:53:51