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Chaos theory (or chaology [1]) is an interdisciplinary area of scientific study and branch of mathematics. It focuses on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions. These were once thought to have completely random states of disorder and irregularities. [2]
The theoretical study of time travel generally follows the laws of general relativity. Quantum mechanics requires physicists to solve equations describing how probabilities behave along closed timelike curves (CTCs), which are theoretical loops in spacetime that might make it possible to travel through time. [1] [2] [3] [4]
Over time, the differences in the dynamics grow from almost unnoticeable to drastic. In chaos theory , the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.
“Chaos is a fact of life … and a part of dynamical systems theory,” Lin explains to Popular Mechanics in an email. “Some systems are inherently chaotic, while others are not.
In new research published in the American Physical Society's peer-reviewed journal Physical Review A, scientists from Italy (led by Alessandro Coppo) try to translate one theory of time into real ...
Chaos theory is sometimes pointed out as a contradiction to Laplace's demon: it describes how a deterministic system can nonetheless exhibit behavior that is impossible to predict: as in the butterfly effect, minor variations between the starting conditions of two systems can result in major differences. [9]
This results in a complicated and unpredictable wandering over longer periods of time. [1] Control of chaos is the stabilization, by means of small system perturbations, of one of these unstable periodic orbits. The result is to render an otherwise chaotic motion more stable and predictable, which is often an advantage.
Quantum chaos is the field of physics attempting to bridge the theories of quantum mechanics and classical mechanics. The figure shows the main ideas running in each direction. Quantum chaos is a branch of physics focused on how chaotic classical dynamical systems can be described in terms of quantum theory.