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Operational Patterns
in Quantum States

Operational Patterns in Quantum States


Full document GeniAlgebra.pdf can be found right hand

Abstract. A major issue for modern physics is how reality in terms of general relativity may emerge from quantum mechanics.

Two observations motivate this paper:

1) General relativity (GR) with Einstein's Field equation is highly recursive in how it is formulated. The energy distribution determines spacetime geometry and vice versa spacetime geometry determines local trajectories and the evolution of the mass-energy distribution. Such a feature is absent in quantum mechanics (QM). Here the systems state and observables are different things. A state cannot operate on itself. To introduce recursion into the core of QM requires an extended concept of what the state of a system is.

2) Many papers on collapse or decoherence deal with how observed classical reality is determined by QM. Common understanding is that the Universe evolves according to the Schroedinger equation - i.e. within a unitary U-process. I don't know of any work that considers the Universe - as we observe it - evolving according to a badly understood state reduction process (R-process).

This paper proposes an extension of the QM standard model to address both concerns. It enables two realities linked by their respective symmetries. Its final purpose is to enable state reduction dynamics to be defined as a simple random walk near process .

Introduction

The proposal in this paper has initially been motivated when looking for proceedings in artificial intelligence during the past decades. Though recent models and implementations perform quite successful on complex tasks the gaps are obvious. The understanding of intelligent reasoning and problem solving has not fundamentally improved over the past 20 years. A similar situation can be found in biology and psychology. They also fail to explain what really goes on. Still insufficient but yet most rigorous are attempts to explain intelligent behavior (and finally how consciousness may evolve) by quantum models.

After investigating a bit in a top-down model for decision taking this is a first attempt to translate some ideas into mathematics and apply some of the findings to physics.

When investigating in a reasonable modeling approach it appears that base quantum models together with wave reduction make sense in modeling conscious - or intelligent - decision taking. This works basically by translating quantum concepts of state, decoherence/collapse, operator, eigenvalues, eigenvectors to terms that make more sense to psychologists.

Of course there is an obvious issue in applying quantum models in this arena: Here one deals with interactions of two or more basically equivalent entities. The interaction may also work vice versa. This is not true for the standard model of decoherence that deals with operators and their intrinsic symmetries on the one hand and clearly separated states on the other with very different degrees of freedom. Therefore we probably need to consider an extended concept of what a state is.

On the other hand this all seems to deal with the question of reality. How do classical reality - dominated by gravity and general relativity - and quantum reality - characterized by the Schrödinger equation and the collapse process - correlate? Some authors support the idea that gravity in QM cannot be understood without a deeper insight into the wave reduction process. This point of view leads to two observations:

  1. General Relativity with Einstein's Field equation is highly recursive in how it is formulated. The energy distribution determines spacetime geometry and vice versa spacetime geometry (operator) determines local trajectories and the evolution of the mass-energy distribution (state). This feature is absent in quantum mechanics. Identifying states with operators fails alone because of different degrees of freedom. To introduce recursion in QM requires an extended concept of states.

  2. Many papers on collapse or decoherence deal with how observed classical reality is determined by QM. Common understanding is that the Universe evolves according to the Schroedinger equation – i.e. within a unitary U-process. I don't know of any work that considers the Universe - as we observe it - evolving according to a badly understood R(eduction)-process.

But what could be a hidden structure within the state of a quantum particle? There is nothing in the standard model that could answer such a question. Each attempt to artificially extend a state will certainly look ridiculous.

On the other hand it is obvious that you can embed operational information in quantum states. In quantum computing engineers are going to code operations and data in state superpositions of spin- ½ particles. They then need an artificial device - the computer - to get detected and finally executed. The approach in this paper is different in so far that it is looking for intrinsic information that may not need any artificial device to get executed. It deals with self referentiality of formal structures.

The final section describing a symmetric model for decoherence will show a door that is not there in the standard model. Further investigations may improve present understanding of the roles of QM, GR and intelligent decision taking within reality.

The approach obviously needs to redefine what a state is.

  • From a very basic point of view the definition should be discrete - i.e. integer based.

  • As quantum observables in the standard model always are hermitian operators and hence deal with real eigenvalues the definition should probably be based on real integers.

  • The internal structure of such a state should evolve out of symmetry arguments and

  • finally the standard model should emerge by simple principles.

So this is exactly the starting point here. Let's clear memories and start to forget almost everything about modeling in quantum physics. Leading to a revised modeling approach for states and operators on spin-½ particles the model should explain the role of integer, real or complex numbers and the Pauli spin matrices and not taking them as given or introduce any of them by reference to classical physics.

So this is what you should expect in the following.

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