Owing to the remarkable agreement between precise quantum chemical predictions and the most accurate experiments including sophisticated advanced instrumentation, it is usually concluded that the many-body Schrodinger equation in particular and also quantum mechanics in general describe reality to an unsurpassed exactitude. However, the correlation between the micro- and the macroscopic (classical) levels leads to well-known paradoxes in our fundamental scientific understanding. Hence, 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. In this discourse, we will see the fundamental importance of the notion of so-called unstable states, their definition, determination, and characterization. Within this vein, paradoxical and inconsistent issues related to the various attempts to apply microscopic organization to derive scientific laws in the macroworld are considered. The theoretical framework is augmented with quantum logical principles via a reformulation of Goders 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 general formulation via precise complex symmetric representations exemplified and derived from dilation analytic transformations. Associated dynamical timescales are represented and investigated via the corresponding Dunford formula. Relevant applications, where the above-mentioned unstable or metastable states emerge, are reviewed and compared with conventional bound-state and scattering theories with an analysis of their directive performance and stability. The manifestation and generation of triangular Jordan block entities as extended versions of nonstationary states are derived and further investigated and generalized to 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 continuation of quantum mechanics to rigorously incorporate universal complex resonance structures, their life times, and associated localization properties. We also prove the appearance of nonconventional time evolution including the emergence of Jordan blocks in the propagator, which leads to the origin of so-called coherent dissipative structures (CDSs) derived via uniquely defined spatiotemporal neumatic (from the Greek pneuma) units. This self-referential organization yields specific information bearing transformations, cf. the Godel encoding system, which might connect developmental and building matters with functional and mental issues within a biological framework at the same time providing background-dependent features of both special and general relativity theory. With these theoretical ideas as background, we advocate a new clarification of the dilemma facing micro macro correlates including an original characterization of unus mundus, i.e., the underlying holistic reality. Examining the Limits of Physical Theory: Analytical Principles and Logical Implications
Elsevier, 2012. 33-117 p.