Ulla Mattfolk
Hi Ulla,
I think I found the general idea for all this puzzle and in trying to correlate all. The spherical geometric topological algebras and the spherisation with hidden dark parameters and the 3D spherical Bloch volumes for the 3 systems.So we need series for the 3 systems and so with the mathematical tool, we choose the series with the 3D volumes. The center being the biggest volumes and after we increase the number but decrease the volumes around. Now we consider extension of dimensions from these 3D spherical volumes for the n qubits and so then we consider the n dimensional Hilbert space, so the Bloch vectors are correlated, operators… we must be concrete for the multiqubit spaces. I have studied the work of Bob Coecke and so we the categories of our quantum mechanics can be ranked, we need diagrammatic reasonings, tensor categories, operators instead of the geometric pictures.And so the higher dimensional state spaces become important. The Pauli matrix becomes relevant also and the density matrix so.
The 3D Spherical Bloch volumes so is fundamental yes but is extended for multi-qubits and multidimensions. The spherical object so exists always mathematically but is extended. The 3 systems, photons, DM, DE so can be considered with specific series of volumes like basis but we choose a system because we don’t know the real universal series that the universe utilize, but we can create series to mimic.
SU(2n) is considered so and we go in a spherical deeper topological analysis. It is like we keep the basis of 3D spherical volume for the universe,the universal 3D sphere, cosmology and its cosmological 3D spheres and quantum mechanics with 3D quantum spherical volumes for the 3 systems merging,but we utilise the higher dimensions and maths for the mathematical puzzle of multi-states and the evolution and interactions at this quantum scale.So the spherical geometric topological algebras I invented are like the Lie group Geometry and Hopf fibrations like in the works of Jenny but with a kind of structure between the 2 main scales in 3D, cosmological and quantum. SU and SO groups so can be correlated for internal and external systems, and we respect the relativistic groups, we just add deeper hidden dark parameters in considering the informational DE and DM quantas of mass, so the Lorentz symmetries are extended.
I probably need help for the generalizations of the tool in higher dimensional manifolds for this general idea.
The relevance is that we link all, and so the mixed states are not just noise but have a concrete physical structure: the 3D spherical volumes. The density matrices with this DE encoding the 2 others give relevant road to compute. It is not easy for the n-qubit Bloch representations and with the Hilbert space and the matrices and Pauli works. The vectors, generators, operators, constraints… it is complex for the SU(2ⁿ) algebraic sense. The relevance is about the mixed quantum states and hidden cosmological fields and parameters. But there are ways for the Hamiltonians, Lagrangians, couplings…
I ask me how do for the Lorentz symmetry in fact in adding the deeper parameters without breaking the GR and QFT, like if we had a bridge, so we utilise subgroups and specific properties.
But the general mixed quantum state of an n-qubit system can be extrapolated with SU(2ⁿ) generators and Bloch components from these 3D spherical Bloch volumes of 3 systems merging with higher dimensional analysis respecting the spherical logic. The thing I am a little confused is about the Hamiltonian of hidden dark parameters. I don’t assert of course about the DE encoding the photons and DM. But that makes sense universally speaking and we have a structure for the informations. And an explanation for the Higgs portal mechanism with the DM and so a new mass energy information equivalence completing the works of Einstein. I repeat we don’t break the laws and this GR, we just complete it in going farther than our actual observable bridges.
I study actually the perturbation theory because it seems a possible road for all this puzzle and the hidden dark parameters. But the fact that this information is not from the photons oscillating and this GR is interesting because we have a physical structure and it can measurable and testable in logic if we succeed to find the experiments. Decoherences of quantum states can give answers maybe.
The formalization must be consistent and I need helps for the density matrix extensions with the higher dimensional analysis of 3D spherical quantum Bloch volumes of 3 systems merging. For the couplings to SU(2ⁿ), the Hamiltonian , the perturbations, the quantum states , decoherences,, the hidden parameters....also I need help I think, alone I cannot do all .It is not easy.I have always the impression it is never finished furthermore, that is why I have never published. The relativistic invariance imust be respected . SU(2ⁿ) × SO(3,1) ensures consistent multi-qubit Hilbert space evolution in spacetime with the extended higher dimensional 3D spherical quantum Bloch volumes and Hopf fibrations can be added like the works of Jenny. There are experiments also to do with decoherences, or at the LHC and others but Hopf fibrations and spherical topological geometric algebras formalize the 3D spherical volumes across scales.
This ensures that higher-dimensional Hilbert space analysis respects the emergent 3D spherical structure, giving both computational and physical meaning to mixed states.
In this framework, mixed quantum states are structured, physically meaningful, and linked to cosmological hidden fields, giving a concrete mathematical, physical, and testable proposal consistent with GR, QFT, and Hilbert space quantum mechanics.
