Timothy Winey
Tuesday, May 21, 2024
Two samples of Red wine were added to 2 jars with one jar (left) exposed to a Portable Static Torsion Field Generator for 10 minutes. Sodium alginate was then poured over both samples.
Samples were then mixed by swirling,
and extra alginate was added to both with the experimental jar (left) placed in a torsion field for an additional 20 minutes.
As the Alginate begins partially separating from the wine in both jars note the unusual swirling boundary layer dynamics of the gel in the experimental jar contrasted with the uniform separation of the gel in the control jar off to one side. The swirls of the gel in the experimental jar are reminiscent of so-called ‘strange attractors.’
A Lorentz system is a set of three differential equations originally developed by Edward Lorenz in 1963 as a simplified mathematical model for atmospheric convection. The system is defined by the following equations:
Strange Attractor
A strange attractor is a complex structure in the phase space of a dynamical system towards which trajectories tend to evolve over time. It has the following key characteristics:
Fractal Structure: Strange attractors have a fractal dimension, meaning they exhibit self-similar patterns at different scales.
Sensitive Dependence on Initial Conditions: Small differences in initial conditions can lead to vastly different trajectories, a hallmark of chaotic systems.
Non-Periodic: Unlike regular attractors which may be fixed points or limit cycles, strange attractors do not settle into a repeating pattern.
Lorenz Attractor
The Lorenz system is particularly famous for exhibiting a strange attractor, known as the Lorenz attractor. The Lorenz attractor appears as a butterfly or figure-eight shape in the phase space and is defined by the trajectories of the system under the given parameters. This attractor illustrates the chaotic nature of the Lorenz system: despite the deterministic nature of the equations, the long-term behavior is unpredictable and highly sensitive to initial conditions.
Significance
The Lorenz system and its strange attractor were among the first examples of deterministic chaos, illustrating that simple nonlinear systems can produce highly complex and unpredictable behavior. This discovery had profound implications for various fields, including meteorology, physics, engineering, and even finance, as it highlighted the inherent limits of predictability in complex systems.
Visualization
To visualize the Lorenz attractor, one typically plots the trajectories in three-dimensional space, with
𝑥
x,
𝑦
y, and
𝑧
z as the coordinates. The resulting plot shows the intricate, looping paths that never intersect yet fill a bounded region of space.
Conclusion
The Lorenz system and its strange attractor serve as a fundamental example in the study of chaos theory and nonlinear dynamics. They demonstrate how deterministic systems can behave in complex and unpredictable ways, fundamentally altering our understanding of dynamic systems and their long-term behavior.
Torsion Fields and Dynamical Systems
While torsion fields themselves are a theoretical concept primarily described in the context of geometric properties of spacetime or as fields in high-energy physics, one could theoretically consider the dynamics of systems influenced by torsion fields. If such a system exhibits chaotic behavior, it might also exhibit strange attractors. Here’s how this could be conceptualized:
Cosmology and Astrophysics: If torsion fields exist and have significant effects on cosmic scales, the dynamics of galaxies, black holes, or the early universe might exhibit chaotic behavior influenced by torsion. Modeling such a system could reveal strange attractors in the phase space of the system’s evolution.
Particle Dynamics: In the context of particle physics, if particles interact via torsion fields, their trajectories in phase space might show chaotic behavior under certain conditions. This could theoretically be studied to identify strange attractors.
Gravitational Systems: In the Einstein-Cartan theory, if torsion influences the motion of celestial bodies or the dynamics of spacetime itself, it could lead to complex, possibly chaotic behavior. Numerical simulations of such systems might reveal strange attractors.
While strange attractors are a well-established concept in the study of chaotic systems, their observation in torsion fields is a theoretical possibility rather than an empirical fact. If torsion fields do play a significant role in the dynamics of certain physical systems, it is conceivable that those systems could exhibit chaotic behavior and strange attractors. However, this remains a speculative area of research requiring further theoretical development and experimental verification.
References:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6837912/
No wonder weather predictions (esp regarding snow in the NC piedmont) rarely pan out. Is there an equivalent inverse force to torsion fields (a yang + for the yin - so-to-speak)