Chaotic solitons and the foundations of physics: a potential revolution

• Published in: Applied mathematics and computation Vol. 56; no. 2; pp. 289 - 339
• Main Author: Werbos, Paul J.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 01.07.1993; Elsevier
• Subjects: Classical and quantum physics: mechanics and fields; Exact sciences and technology; Field theory; General theory of fields and particles; Mathematical methods in physics; Nonlinear and nonlocal theories and models; Nonlinear dynamics and nonlinear dynamical systems; Nonlinear or nonlocal theories and models; Other topics in mathematical methods in physics; Physics; Statistical physics, thermodynamics, and nonlinear dynamical systems; The physics of elementary particles and fields; Theory of quantized fields; Chaos; Mathematical method; Partial differential equations; Quantum field theory; Mathematical physics; Solitons
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/0096-3003(93)90126-Y

This paper will present a skeleton outline of new mathematical tools, based on concepts from quantum field theory (QFT), which could open up a new approach to understanding chaotic solitons and other chaotic modes for classical PDE in four dimensions. It will argue that a further development of these tools could lead to a radical reformulation of physics, with large potential implications both for technology and for biology. The central ideas include: the use of statistical moments as a way of mapping a complicated attractor to a point in Fock space; the use of reification or dressing operators to transform the statistical dynamics into a linear Schrodinger-like equation with a Hermitian “Hamiltonian”; the use of localized eigenvectors in Fock space to characterize chaotic solitons; in applications to QFT, the assumption of time- symmetry (rather than forwards time) in microscopic causality, which makes it possible to derive the measurement formalism of QFT; the use of field operators to calculate expectation values, and a truly four-dimensional approach that is equivalent but simpler than the usual approach of QFT. The potential implications, while speculative, could be extremely large; however, they cannot be realized or defined more precisely without additional mathematical research. There are many new research opportunities here in many different directions, all of them with large potential impact.