Dual
Reality
Full document DualReality.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. Based on my
previous proposal for an extension of the QM standard model this
paper investigates in a emergent Riemannian space. It shows that
this extended model enables a stochastic state reduction process
that simply follows geodesic curves in a 4dimensional spacetime.
Two observations motivate these papers
and those that probably will follow:
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 determines local trajectories and the evolution
of the massenergy distribution. This feature is absent in quantum
mechanics. Here the systems state and observables are different
things. A state cannot operate on itself. To introduce recursion in
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 focuses on the second item.
It proposes a toy model involving a single spin½ particle.
The Rprocess shows exactly the standard behavior under
observations, whereas the internal behavior can be modeled into a 4
dimensional Riemannian space.
Introduction
This paper and an earlier one had initially been
motivated by 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 behind intelligence, conscious behavior and
consciousness.
Still insufficient but yet most rigorous are attempts to explain
intelligent behavior (and finally how consciousness may evolve) by
quantum models.
The major objective here is to show that the approach presented
here looks promising enough to continue on that path. Its promise is
to finally establish one common model that lets QM and GR emerge. And
as a side effect we may find very new perspectives into artificial
intelligence and conscious behavior.
The proposed extension originally is a discrete integer based
model. Extended to reals it is equivalent to a complex model fully
isomorphic to QM standard model. The base concept is a triple (A,
B, v) of two complex operators A,B and a complex vector v.
The operator A is the classical observable, the operator B
represents the system, v is a perspective vector so that Bv
represents the classical state vector.
On a first sight the model simply adds complexity that seems to be
good for nothing. But indeed it provides some additional internal
structure. For simple spin½ particles its state B is a
complex vector of 8 real dimensions. This structure supports a simple
random walk like stochastic process. It is controlled by the external
operator A. This process externally behaves exactly as expected from
wave reduction: It leaves the state in one of two eigenstates of the
observable with the exact probabilities given by the QM standard
model. This process experiences external excitations and attractors
imprinted by the observable. It works like a grain of sand moving
randomly on a sound board and ultimately approaching a wave node.
This empirically developed process is quite amazing as it indeed
requires 8 real dimensions to work as a simple random walk.
Considering classical states with only 4 real dimensions will not
produce the correct probabilities. What externally looks like a
simple wave reduction caused by measurement now internally leads to
concepts of position, movement, acceleration, forces, attractors,
time. The entire process can easily be projected to 3 real
dimensions. The projected movements within this toy model follow
geodesic lines in a curved 4dimensional spacetime. To achieve the
expected results its crucial to leverage both the special GenI
specific mapping to the 2dimensional Hilbert space as well as its
discrete structure.
The first part deals with specifying this stochastic state
reduction process and discussing its features to some detail. The
second part will focus on a spacetime structure that “absorbs”
the process parameters and may be viewed as being imprinted by an
external operator. The third part gives some outlook to further
investigations in recursion and many particle systems.
