InterJournal Complex Systems, 149
Status: Submitted
Manuscript Number: [149]
Submission Date: 971212
Revised On: 991117
The Use of Complexity to Solve Dilemmas in Physics: A New World Model with Classical, Quantum, Cosmological, and Sociolegal Applications
Author(s): Harold Ruhl

Subject(s): CX.43, CX.28, CX.19, CX.09, CX.02

Category: Article

Abstract:

The work of Kurt Godel, Allen Turing, Georg Cantor, and Gregory Chaitin relevant to Formal Axiomatic Systems (FAS) is first applied to system trajectories in a fully quantified state space [one with discrete,isolated points] and after establishing an applicable uniqueness theorem a new formulation of entropy is developed. This entropy formulation is in terms of a quantity called the computational complexity length of the particular (FAS) and the individual computational complexity lengths of its various theorems. This FAS currently totally describes the system's trajectory through its state space including: 1) the system's current and ultimate computational complexity, 2) the system's current structural complexity, and 3) the system's current deterministic behavioral complexity. It is argued based on the above referenced mathematical results most especially Godel's incompleteness theorem that the system's current computational complexity length (a program length in bits) monotonically increases as the top level system moves along its trajectory. The current and available final values of this measure are identified as the current and equilibrium entropies of the system. The mathematical form and thus the algebra of entropy are preserved. Probability considerations are not used. Thus a universally applicable strong form of the entropy portion of The Second Law of Thermodynamics is derived without recourse to Statistical Mechanics. The concepts of order and disorder are revisited and made compatible with the mathematical model. From this new perspective it is argued that entropy is increasing order [the increasing but finite body of what is computable even if complex]rather than increasing disorder [the always present uncountable infinity of the uncomputable]. It is further argued that the attempt to retrace the system trajectory by means of time reversal is a logical error. It would require a type of closed loop in the system trajectory which is not allowed under the model. This resolves the question of why time has an arrow by providing the necessary logical asymmetry to the system trajectory. Quantum perturbations which break determinism in this model by creating a new current system FAS, are then identified as inherent in the model and rationalized as the result of Godel's incompleteness theorem. The model is initially based on two assumptions, however, this is reduced to just one via a discussion of why there is something rather than nothing. The initiation of something coincides with the breaking of two symmetries. Entropy now increases monotonically and the laws of physics as represented by at least the alphabet of the system FAS are not constant with time. This allows for two forces that can be the foundation of particle physics. An apparent consequence of the model is that physical systems are born at the edge of chaos and do not evolve to this condition. The model is able to predict many aspects of far from equilibrium systems now under major investigation including the frequently observed power law number/size relations for physical events. The value of the idea of "self organized criticality" to the understanding of complex systems is reevaluated under the model. The model's inherent global perturbations [global because the system FAS is what is perturbed], which are shown to be naturally bilaterally correlated to the system's trajectory, and their ability to resolve some of the dilemmas of Cosmology [origin and expansion rate of the universe for example], particle physics [why three families etc.] Quantum Mechanics [the Aspect experiment and the violation of Bell's inequality], the origin of life, and several social and economic consequents, are discussed in light of the model. All in all the model is quite simple. There are no mathematical equations in the core model. This is actually reasonable since when the universe is just starting its FAS may be too small to include arithmetic.

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