Is nature quantum non-local, complex holistic, or what?, I: Theory & analysis

Is Quantum Mechanics a general theory that applies to everything from subatomic particles to galaxies; is Nature governed by entanglements of linear superposition in Hilbert space or is it an expression of the nonlinear holism of emergence, self-organization, and complexity? This paper explores these issues in the context of extensions of the recently formulated approach to Chaos-Nonlinearity-compleXity [A. Sengupta, Chaos, nonlinearity, complexity: A unified perspective, in: A. Sengupta (Ed.), Chaos, Nonlinearity, and Complexity: The Dynamical Paradigm of Nature, in: StudFuzz, vol. 206, Springer-Verlag, Berlin, 2006, pp. 270–352] and proposes that Nature manifests itself only through a bi-directional, contextually objective adaptation of the Second Law of Thermodynamics. The mathematics developed is that of convergence in topological spaces, multifunctions, exclusion topology, and discontinuities, jumps, and multiplicities induced by difference equations rather than the smoothness and continuity of the Newtonian world of differential equations.In the second Part of this paper [A. Sengupta, Is Nature Quantum Non-local, Complex Holistic, or What? II—Applications, Nonlinear Analysis: RWA (2009), in press (doi:10.1016/j.nonrwa.2008.09.002)] to be referenced “II-”, we examine the bi-directionality of a self-organized, emergent, engine-pump system with specific reference of the role of gravity as the compressive agent responsible for generation and sustenance of the delicate homeostatic balance in life, structures, and patterns appearing in this Participatory Universe. Holism of “systems and processes that interact with themselves and produce themselves from themselves” calls for radically different techniques and philosophy from that adapted in the mainstream reductionist Newtonian paradigm that we are accustomed to.