So many quantizations (memorandum)

NOTICE

• DO NOT TRUST THE FOLLOWING
• glücklichneujahr!!!

QUANTIZATION

• mathematical form which represent infinite dimensional space
• must be separable (and summable) under certain restriction

INFINITELY MANY WAYS OF QUANTIZATION

• wave functions
• linear operators (hamiltonian, probability density, observations, ..)
• paths (in path integral)
• homotopies (might be used in generalization of path integral)
• wavelets
• triangulations of relativistic universe (simplicial decomposition)
• chain complexes (in homology algebra, as generalization of triangulation and observation, and these might be used in future categorical formulations)
• quantum sets (a la Takeuti and Ozawa, as parametrized boolean algebra and generalization of von Neumann's quantum logic)
• formulae valid in various systems of non-standard analysis allowing infinitely many infinitesimals
• (anything that forms topology and can be completed when bounded, given adequate interpretation)

What would be the "22nd century maths"?

• it looks just a matter of encoding (only after when throughly carried out, it should likely be realized that also old maths can be fully employed to formulate and solve)
• similarly in definition of Borel sets, it might include somewhat disguised (and likely finitized in properties of prime numbers) form of transfinite ordinals (order types) to order topologies
• it means: we might need meta-topology, which is just a topology itself, over topologies

Why?

• Since it must be a first-order approximation of "framework subsuming any possible mathematically-definable compatible and incompatible views as reflecting the only reality"
• "views" might be considered as topological spaces
• And it must eliminate infinities (poles) with finitization and interpretation

Completeness of probability measure and abstract 3-body problem (memorandum)

NOTICE

• DO NOT TRUST THE FOLLOWING

multi-body system and probability

• what is probabilistic system?
• deriving virtual one-body approximation of multi-body system with probability
• or collapsing into one wave function
• complete measure turns many-body into one-body "falling" into incomparably large "ground"
• Lagrangian of the system make definite description for virtual one-body

future and incomplete probability measure

• sum of contributions from possible Feynman diagrams (no a priori completeness assured)
• estimating contributions from indistinguishable states as zero
• ignoring experimentally unobserved states
• completeness of cases might change over history and environment
• (added) e.g. solar neutrino density and probabilities of beta-decay or other phenomena involving weak forth
• expectation or Knightian uncertainty (tail risk that should be hedged only with longer-than-the-longest bond)
• abstract 3-body problem or game with indefinite sum

gravity or entropic force

• uncertain quantum entropy, indefinite radius of the universe
• Baysian gravity?
• is gravitational constant really constant?

TODO

• understand path integral, S-matrix and Wheeler-DeWitt theory
• relate them with gravity model of trade and transportation