The initial measurements are in, and still look promising. To recap, one stable form of the twist in the Unitary Twist Field theory is in a ring where the twist curves on itself as a combination of the electrostatic 1/r^2 and magnetic field 1/r^3 strengths (this ratio is defined by the fine structure constant). There are potentially many solutions, but only one possible planar solution other than the linear twist–the twist ring. I posited that if this were true, placing a twist ring in an external electrostatic field would cause the curvature to vary depending on the distance from a source charged particle. Computing this analytically is a challenge, yielding a 24 term LaGrange differential equation of motion, so I decided to do this iteratively.
This was a lot easier, and has yielded promising results that suggest I might be on the right track. The initial sims showed correct qualitative behavior with repulsion or attraction depending on the external field polarity, and I could visually see the correct acceleration behavior.
Next, I added quite a bit of numerical analysis code to the sim of the twist ring path, and was able to verify that a linearly varying field will cause the path of motion to accelerate at a constant rate–and that this acceleration is proportionate to the strength of the field within some level of accuracy. Much more needs to be done to confirm these measurements, but the initial results show that this type of model (twist ring) will give electrostatic behavior. Here’s a pic where you can see the displacement with time (the parabolic curve). Following that, you’ll see my initial data set along with the Mathematica solution for the first three crossing points of the parabola–more computations will be done to establish that this really is a parabola.
From here, I will see if the correct mass results from the ratio of the strength of the 1/r^2 component to the 1/r^3 component in an electron. There should also be other twist loop solutions possible in 3D, I’ve limited myself to the easiest (planar) solution to start.
Agemoz
Here’s the initial sim time crossing points, along with the Mathematica solve solutions:
Running the Unitary Field Twist simulation to numerically derive the change in x as a field is asserted on a 1/r^2 - 1/r^3 twist ring. The field affects the curvature (magnetic component). The result generates the qualitative expected movement as if there was a central force effect (q^2/r^2). These results are an attempt to measure the acceleration factor as a function of relative field strength (magnetic to electrostatic). Since the equations of motion due to the 1/r^2 - 1/r^3 equation in a linear field were 24 parameter LaGrange equations of motion, I attempted to get an analytic solution by examining the iterative numerical results. Here is the result for 1:1 (1/r^2 to 1/r^3) field strength at distance 10 with radius 1.5 and ring velocity 0.10545 and source field strength factor .0005. The sim showed a cycle time of about 90. field strength 0.00025 22: 11.457 (doesnt start at zero because cycle max x is not at zero) 14545: 15 25213: 20 34448: 25 43234: 30 using the first 3 terms in quadratic solution, I get x = 8.92 10^9 * t^2 + .000114 * t + 11.455 field strength 0.0005 22: 11.457 (doesnt start at zero because cycle max x is not at zero) 10421: 15 17772: 20 24406: 25 30503: 30 using the first 3 terms in quadratic solution, I get x = 1.912 10^8 * t^2 + .000141 * t + 11.454 field strength 0.0010 22: 11.457 (doesnt start at zero because cycle max x is not at zero) 7372: 15 12572: 20 17233: 25 21626: 30 using the first 3 terms in quadratic solution, I get x = 3.82 10^8 * t^2 + .000200 * t + 11.453 More terms need to be computed, but there is a clear linear proportionality to the acceleration component of the curve, consistent with the expected electrostatic relation of field strength proportionate to the acceleration of the destination particle.
Agemoz's Physics Blog 