On 3/6/2020 3:40 AM, Lawrence Crowell wrote:
Szangolies [ J. Szangolies, "Epistemic Horizons and the Foundations of
Quantum Mechanics," https://arxiv.org/abs/1805.10668 ] works a form
of the Cantor diagonalization for quantum measurements. As yet a full
up form of the CHSH or Bell inequality violation result is waiting.
There are exciting possibilities for connections between quantum
mechanics, in particular the subject of quantum decoherence and
measurement, and Gödel’s theorem.
If we think of all physics as a form of convex sets of states, then
there are dualisms of measures p and q that obey 1/p + 1/q = 1. For
quantum mechanics this is p = ½ as an L^2 measure theory. It then has
a corresponding q = ½
Which would give 1/p + 1/q = 4 ??
Brent
measure system that I think is spacetime physics. A straight
probability system has p = 1, sum of probabilities as unity, and the
corresponding q → ∞ has no measure or distribution system. This is any
deterministic system, think completely localized, that can be a Turing
machine, Conway's <i>Game of life</i> or classical mechanics. A
quantum measurement is a transition between p = ½ for QM and ∞ for
classicality or 1 for classical probability on a fundamental level.
What separates these different convex sets are these topological
obstructions, such as the indices given by the Kirwan polytope. The
distinction between entanglements is also given by these topological
indices or obstructions. How these determine a measurement outcome, or
the ontology of an element of a decoherent sets is not decidable. This
is where Gödel’s theorem enters in. A quantum measurement is a way
that quantum information or qubits encode other qubits as Gödel numbers.
The prospect spacetime, or the entropy of spacetime via event horizon
areas, is a condensate or large N-entanglement of quantum states then
implies there is a connection between quantum computation and
information accessible in spacetime configurations. These
configurations may either be the Bekenstein bound S = kA/4ℓ_p^2, or
quantum modified version S = kA/4ℓ_p^2 + quantum corrections. Then the
quantum processing or quantum Church-Turing thesis is I think
equivalent to the information processing of spacetime as black holes
and maybe entire cosmologies.
These are exciting developments.
LC
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