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 massenergy 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 Uprocess. I
don't know of any work that considers the Universe  as we observe
it  evolving according to a badly understood state reduction
process (Rprocess).
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 topdown 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:
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 massenergy 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.
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 Uprocess. 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 spin½ 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.
