Chaotic solitons and the foundations of physics: a potential revolution

摘要

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.