of
the two-slit experiment with quantum particles
Frankfurt Institute of Advanced
Studies
Germany
Using nonlinear dynamics and
stability analysis as well as some catastrophe theory classification of
singularities, we analyze the two-slit experiments of quantum physics. It is
shown that assuming micro-spacetime to be a Fuzzy Kähler-like manifold K (E (∞)) with an inbuilt wave-particle
duality, at least one of the two slits is always unstable. Consequently, the
faintest interference with the experiment is sufficient to break the symmetry
of transfinite hopping motion of the elementary particle and its quasi-ghost
particle and leads to what is perceived on the other side of the
quantum-classical interface as a wave collapse.
In the present
interpretation the paradox posed by the two-slit experiment is a consequence of
the topology and geometry of the micro spacetime required by Gödel's
theorem.
An elementary stability analysis of the K
(E (∞)) model of the
two-slit experiment indicates that both slits are associated with instability
rather than stability. Consequently, we advance the hypothesis that a
hypersensitivity to perturbation is what is behind the so-called "wave
collapse" within our quantum space time topological-geometrical
interpretation. There are well-known classical experiments which display such
hypersensitivity. For instance the notorious discrepancy between the
theoretical and experimental buckling load of thin-walled elastic structures
caused by the most feeble imperfection or dynamical disturbance is due to
severe instability as explained in Koiter's theory.
The present elementary analysis is of course far
of being exhaustive. However we hope to have shown at least in principle that
there is a causal non-metaphysical and in principle down to earth explanation
to the so-called wave collapse mysterium.
In the present interpretation, wave collapse is
simply a consequence of the topology and geometry required by the undecidability
theorem of Gödel.
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