XVIth International Workshop on
Quantum Systems in
Chemistry and Physics
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Examining the Limits of Physical Theory:
Analytical Principles and Logical Implications
Erkki J. Brändas
Department of Physical and Analytical Chemistry
Quantum Chemistr
Uppsala University
SE-751 20 Uppsala, Sweden
Our aim is to examine the characteristics and the rationale for developing an analytic foundation for rigorous extensions of quantum mechanics beyond its long-established domain in physics, chemistry and biology. Paradoxical and inconsistent issues related to the various attempts to apply microscopic organization to derive scientific laws in the macro-world are considered. The theoretical framework is augmented with quantum logical principles via a reformulation of Gödel’s theorems. We arrange the assemblage of the mathematical ideas as follows. First we give a detailed examination of the second order differential equation with respect to specific boundary conditions and associated spectral expansions, followed by a description in terms of general complex symmetric representations exemplified and derived from dilation analytic transformations. Associated dynamical time scales are represented and investigated via the corresponding Dunford formula. Relevant applications are reviewed and compared with conventional scattering theory analysing the directive performance and stability of the method. The manifestation and generation of triangular Jordan block entities are derived and further investigated in thermally excited scattering environments of open dissipative systems. Illustrative applications to condensed- and soft condensed matter are provided, and a surprising treatment is given to the Einstein laws of relativity. As a conclusion we emphasize the computational and model building advantages of a conceptual extension of quantum mechanics to rigorously incorporate universal complex resonance structures, their life times and associated localization properties. We also prove the appearance of non-conventional time evolution including the emergence of Jordan blocks in the propagator, which leads to the origin of so-called coherent dissipative structures derived via uniquely defined spatio-temporal neumatic units. This organization yields specific information bearing transformations, cf. the Gödel encoding system, which might connect developmental and building matters with functional issues within a biological framework at the same time providing back-ground dependent features of both special and general relativity theory.


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