Posts Tagged ‘simulation’

Details of the Linear Twist Sim

January 9, 2018

(Updates 1 and 2 below)

It’s been an amazing week working on the unitary twist field sim.  Most of the kinks in the sim coding are fixed, and what I’m finding in the sim results I think are astonishing.  Here’s what I’m finding:

a. There is now little doubt in my mind that there is a class of precursor fields based on a rotation (unitary) vector field that produces stable linearly propagating twist particles.  I’ve attempted a geometric proof, and within the limits of the assumptions I am making, the particles appear to have to be able to exist in this type of field and are stable, and so far the sim results are confirming this.

b.  An unexpected result from the sim–the particles have to move as a single rotation at the limiting speed of the sim.  This is exciting because photons cannot exist unless they move at the speed of light, and this sim shows linear twists match this behavior.  As I concluded in my last post, I realized that special relativity has to have a part to play here and in the sim it shows up as only one possible speed for the linear twist.

c.  You cannot form a stable linear twist unless you do one full rotation as defined by the local background state.  Any other partial twist dissipates (or has to be absorbed by something, e.g, virtual particles).  There is an asymmetry in the leading and trailing edge angular momentum of any linear twist–the only way to resolve this is if both ends have the same change of momentum (leading edge incurs a momentum in the next cell, the trailing edge cancels out that momentum).  This property prohibits a twist from being stable unless it completes a rotation, in which case the same change in momentum happens on both the leading and trailing edge.

d.  It is looking probable (but not proven yet) that you can curve the twist path depending on the change of rotation vectors in the path of the linear twist.  As mentioned in one my prior posts, a closed loop will create a changing tilt of rotation vectors internal and external to the loop, thus (in theory) sustaining the closed loop.  This is a big difference between this precursor field and attempts to create stable particles out of an EM field.  You cannot change the path of a photon with some EM field.  However, for the unitary twist field, I’ve already shown that this should be possible geometrically (see back a few posts), but now I need to confirm it with a sim.

UPDATE 1:  here is a picture–probably the most unimpressive picture ever produced by a GPU graphics card!  Nevertheless, there’s a lot of computing that was done to generate it, and clearly shows both propagation and preservation of the emitted twist.  The junk to the upper left is left over from the initial conditions that emitted the twist, I’ll fix the startup code shortly, but I thought you’d like to see the early results that I thought were exciting…

UPDATE 2:  Better pictures coming.  Just like with real photons, I can make these particles any length, modeling the continuous range of frequencies available.  What is shown above is a fairly short “photon”, but I now have pictures of much lower frequency, hence longer, photon wave rotations.  I am still getting perfect reproduction of the photon model as it travels, thus solidifying the conclusion that this field yields stable solitons.  Next up–geometrically I can see that I should be able to get two parallel photons to lase–that is, phase lock.  I’ll start the sim with two out-of-phase photons near each other and see if they lock.  Stay tuned!

end of UPDATE 1 and 2

My biggest concern with thinking I have found something interesting as opposed to “not even wrong” or trivial is that I would have expected at least a few thousand real physicists would have already found this field behavior, perhaps fleshed this out a lot more than I have, and found it wanting as a theory underlying the formation of real-world particles.  This thing is simple enough that I just cannot believe that a lot of people haven’t already been here. I also still have a ton of unanswered questions (for example, issues with the background state concept, whether the +/-I state is necessary, and so on).

So–other than having a lot of fun exploring this, I don’t see anything yet that means I should write a paper or something.  I’ll keep plowing away.  As an uncredentialed amateur, I know it’s more likely I’ll win the lottery than being taken seriously by a professional researcher, and I’m fine with that.

One thing that’s going to be really fun is setting up a sim of a major collision of some sort–I hope I don’t induce a cybernetic singularity and wipe out the universe…. 🙂

Agemoz

Sim Works for Linear Twists

January 1, 2018

Happy New Year with hope for peace and prosperity for all!

I now have the sim working for one class of particles, the linear twist.  I fixed various problems in the code and now am getting reasonable pictures for both the ring and the linear twist.  Something is still not right on the ring, but the linear twist is definitely stable with one class of test parameters.  This is an important finding because my previous work seemed to be unable to create a model of a photon (linear twist), so I had focused on the ring case.  However, last night (New Year’s Eve, what a great way to start the New Year!) I realized the problem was my assumptions on how to set up the linear twist initial conditions.

Discrete photons are always depicted as a spiral rotation of orthogonal field vectors in a quantized lump.  I could not make my sim do this, both ends of the lump would not dissipate correctly no matter how I set up the initial conditions and test parameters–the clump always eventually disappeared.  I suddenly realized this picture of a photon is not correct–you have to go to the frame of reference of the photon motion to see what’s really going on.  The correct picture in the photon’s frame of reference is not a clump nor a spiral, but simply a column of vectors all in phase from start to finish (emission and absorption).  It’s the moving frame of reference at light speed that makes the photon ends appear to start and stop in transit.  The sim easily simulates the column case indefinitely.  It also should correctly simulate the ring case for the same reason–and in this case since the frame of reference goes around the ring, the spiral nature of the twist becomes apparent in the sim.  It should also create an effective momentum (wants to move in a straight line) to counteract the natural tendency to shrink into non-existence, but I don’t have the correct test parameters that that is happening yet.

One thing that should please some of you–all of you?  🙂   The background state so far is not necessary to produce these results!  That concept was necessary to produce a quantized lump for the linear photon, but as I noted, that’s not how photons work in their frame of reference.  That simplifies the theory–and the sim computation.  And, most importantly as I suggested in the previous post, seems to validate the concept of assuming that a precursor rotation (twist) vector field can form particles.

Agemoz

First Unitary Twist Field Sim Output–It’s a Three Ring Circus! (Update)

December 24, 2017

UPDATE:  errors in the sim calculations are distorting the expected output–it’s too early to make any conclusions yet.  Corrected results coming soon–the CUDA calculations work in 3D blocks over the image, including overlap borders.  As you might expect, the 4D computation gets complex when accounting for the overlap elements.  I had the blocks overlapping incorrectly, which left holes in the computation that caused the soliton image to be substantially distorted.  I still see strong indications that there will be stable solitons in the results, but need to correct a variety of issues in the sim before drawing any conclusions.  Stay tuned…

The first results from the Unitary Twist Field Theory are in, and they are showing a three ring circus! Here are the sim output pictures. The exciting news is that the field does produce a stable particle configuration that is very independent of the initial boundary conditions and strength of the background state and the neighborhood connection force–the same particle emerges from a wide variety of startup configurations. Convergence appears visible after about 20 iterations, and remains stable and unchanging after 200000 steps. So–no question that this non-linear field produces stable solitons, thus validating my hypothesis that there ought to be some field that can produce the particle zoo. Will this particular field survive investigation into relativistic behavior, quantum mechanics and produce the diversity of particles we see in the real world? I created this theory based on the E=hv constraint that implies a magnitude-free field and a background state, a rotation vector field that includes the +/-I direction, and many other things discussed in previous posts, so I think this field is a really good guess. However, it wouldn’t surprise me at all that I don’t have this right and that changes to the hypothetical field will be necessary.  As usual, as in any new line of research work, it’s quite possible I’m doing something stupid or this is the result of some artifact of how I am doing the simulation–it doesn’t look like it to me, but that’s always something to watch out for.  However, here I am seeing good evidence I have validated this line of inquiry–looking for a non-linear precursor field that produces the particles and force-exchange particles of the Standard Model.

It’s very hard to visualize even with the 4D to 2D projected slices I show here. I color coded the +I (background state) dimension as red, -I direction as black, and combined all three real dimensions to blue-green. Note there is no magnitude in a unitary twist field (mathematicians probably would prefer I call this a R3+I rotation unitary vector field), so intensity here simply indicates the angular proximity to the basis vector (Rx, Ry, Rz, or +/-I). For now, you’ll have to imagine these images all stacked on top of each other, but I’ll see if I can get clever with Mathematica to process the output in a 3D plot.

Studying these pictures shows a composite structure of two parallel R3 rings and an orthogonal interlocking -I ring, and something I can’t quite identify, kind of a bridge in the center between the two rings, from these images. These pictures are the 200000 step outputs.  You can ignore the image circles cursors in some of the screen capture shots, I should have removed those!

More investigation results to come, stay tuned!

Agemoz

Unitary Twist Field Sim Update

December 3, 2017

I have been developing and refining CUDA code that runs a simulation of the Unitary Twist Field theory. This theory essentially says that all particles and exchange particles have an underlying “precursor” field. Put another way, I’m positing that U(1) x SU(2) x SU(3) will emerge from a single unitary rotation field in R3 + I. The proposed field is non-linear because it also has a background state rotation vector potential. This quantizes twists in the field, and provides a mechanism for twist propagation to curve, thus enabling closed loop twists. The work on the simulation is designed to allow observation of the behavior of such a field in a variety of boundary condition situations.

This work is very much in its infancy, but has already yielded some very interesting insights. The crucial question I want to answer at this point is whether this field can yield stable closed loop twists. The background state potential is crucial for distinguishing this theory from any that are based on linear equations such as Maxwell’s field equations. The background state concept emerged from the need to quantize field behavior geometrically via unit twists in the field. Conceptualizing the behavior of a rotation space in two or even three dimensions appears to show that it should be possible to create stable solitons, but is this true in four dimensions over time–the R3 of our existence plus the +/- I dimension needed for the background state orientation.

I have been working hard to work out the rules for the R3 + I field, but four dimensions is very hard to visualize and work out a geometry of theorems. The simulation environment is designed to assist with this effort.

The sim work has already exposed some pretty critical understanding of what a twist ring would look like. I had originally envisioned a ring of twisting vectors surrounded by the background rotation state +I. However, it turns out things are a lot more complicated than that. If the twisting vectors are in R3 and not in I (the current hypothesis for the simplest closed loop particle), this cannot be stable unless the center of the ring is pointing to -I. The surprising result was that both the +I and -I are stable states when a +I potential is applied! By itself, the -I state would be metastable but any neighborhood connection would make both +I and -I stable–in 2 dimensions and possibly in 3 dimensions–still thinking through the latter case. But the theory requires 4 dimensions, is the ring stable in that case? My mind cannot swallow the 4 dimensional case, but the sim work showed some fascinating elaboration of the R3 + I case.

The -I center must be surrounded by a shell of real (R3) rotations (see illustration below). There must be a transition from +I to R3 to -I and back again, but in all dimensions of R3. There is only one possible way to create a surface of contiguous R3 vectors. I was able to rule out the normal vectors on the surface, because there appears to be no way to transition contiguously to +I or internally to -I without creating a discontinuity. But a surface of tangental vectors would work, provided that the tangental vectors at the equator of the sphere point in the same circumerential (eg, x-y) direction, gradually pointing up to the normal direction, which would be -I at the center, +/- Z at the poles of the surface, and +I outside of the surface. In essence, this work is showing there is only one possible way to form a ring and it actually is enclosing the -I center with a surface of real vectors. Essentially the ring looks like a complementary pair of vortexes with the ring being the common top of the vortexes. It should be possible to create more complex structures with multiple -I poles, but right now the important question is this: is this construct stable. I’m hoping that the sim will verify if this rotation vector model of the ring dissipates in some way. I can envision that the -I core cannot unwind, that it is locked and stable, but it is really hard to prove that in my mind in four dimensions. The sim should show it, I’ll keep you posted.

Agemoz

Simulating the Universe

November 6, 2017

That title is a bit of a tease, although it is what I’m trying to do, at least on some level. I went through a major redo of my physics simulation software because it was based on the Unity environment, which, while easy to get working and makes use of physics intrinsics built into the Unity graphics environment, turned out not to be suitable for my sim runs. Even with a fairly highpowered PC and some level of optimization work, it was too slow and could not realistically process a large enough field array memory. I could have eventually learned enough about Unity to overcome my initial findings, but I am several orders of magnitude off from the performance I needed, so I did a massive learning curve effort and switched to CUDA programming. This turned out to be pretty close to ideal for what I needed, because in the end the physics provided in Unity wouldn’t work anyway–I would have had to write my own physics, never mind the performance and memory limitations. CUDA is turning into a fantastic environment for what I want to do.

This did get me thinking about the big-picture view of what I am doing. I can imagine the overarching intelligent being or beings (either God or real physicists) overlooking what I am doing–“Oh look, a little doofus putzing around on a computer thinking he will find new physics, God and the meaning of existence!” Yup, that’s exactly what I’m doing, although there’s been a huge amount of guided thinking before initiating the sim process.

There has to have been hundreds of thousands of real physicists who have created field sims with various ideas for algorithm kernels and nobody has found something that’s even close to a match for observed science. What makes me think I can do what so many have already tried? Here’s what I think: it’s partly because of what we know of EM field central force behavior. I’m betting that a large percentage of people think the underlying field that gives rise to EM fields, gravity and particles must have central force behavior, and set up field kernels that dissipate over distance. As I’ve noted in a previous post, this cannot work for a bunch of reasons, one of the strongest being that QFT interactions never work this way (all forces are mediated by quantized exchange particles that do not dissipate). So why do EM fields and gravity have central force behavior? It’s not because the underlying field is central force. I discovered several years ago something that’s probably obvious to any physicist–any point source granular emission system will look like a central force system if the far-field perspective is taken. This means that the underlying precursor field has to be far different than the obvious guesses based on experiment.

Some realistic means for providing field quantization must be built into the field kernel for QFT to work. I thought for a long time and realized the only geometric means to get quantization specified by E=hv is to provide a modulus function on the precursor field with a preferred state. What I mean by that is that field elements cannot have magnitude, they can only rotate, and in addition have a preferred “lowest energy” rotation state. This rotation can propagate in either a line or in some system of closed loops, but must have an integer number of turns (or twists, thus forming the name of the theory: Unitary Twist Field). Now, for a particle such as an electron or photon or proton to be stable in our existence (R3), the lowest energy direction must point in another direction dimension than in R3, otherwise our universe would have sampling noise detectable by radio telescopes, the Michelson Morley ether detector, or similar sensors. I arbitrarily point this dimension in the I direction. When I set up this list of constraints on a precursor field, I can analytically show that there are two “wells” of field states that should form stable states and hence solitons in the field. Once I lad locked down the constraints necessary for an underlying field, I was able to develop a field kernel that should give rise to a particle zoo, and then I was ready to set up a sim or see if more analytic work could be done.

I’m guessing that most physicists have access to simulation tools like mine (actually likely far better), but I would be pretty surprised if someone has taken the path I have taken. I am very fond of using the “million physicist tool”–that is, it’s been around 100 years and no smart physicist has come up with an underlying field kernel, so any scheme I come up with *must* be “out-of-the-box” thinking. That is, a good rule for investigations that aren’t worth doing is an investigation that has likely been done by 1 or more of a million physicists. As I said, I suspect a lot of people have gone down various central force paths because of EM and gravitational field behavior–but I discovered years ago that a precursor field cannot be central force, and cannot be linear, along with a bunch of other painfully worked out constraints I just mentioned.

In other words, I don’t think anybody else has been in this room I’m standing looking around in. I see promise here (the two energy wells provided by this field kernel) and am hopeful that a CUDA sim will shine light on it.

Agemoz

Discovery: Precursor Field has Two Stable Potential Wells

October 14, 2017

potential_wellMy work described on this blog can be summarized as trying to find and validate a field that could sustain a particle zoo. Previous posts on this blog detail the required characteristics and constraints on one such field, which I call a precursor field. When I began building the mathematical infrastructure needed to analyze this field, I made an absolutely critical discovery that strongly validates the whole field-to-particles approach.

I give it the “precursor” name because there are many fields in known physics, and this precursor field has to form a foundation for all of them. I’ve pursued many paths in my investigation, described in many of my previous posts, and in summary have determined the following:

The precursor field must be single valued, unitary (directional only, no magnitude), continuous, but not necessarily analytic. It must form from a basis of three real (physical) dimensions but the field element can also point in an imaginary dimension. Because the field value is unitary with no magnitude component, it can be modeled as a rotation field.      The field must have a background state pointing in the imaginary direction. I also discovered that the precursor field and its operators cannot be one of the existing fields in physics such as the EM field. It’s a new field that creates the basis for something like the quantized photon mediated EM field or the strong and weak force interactions in quarks.

If you question any of these requirements, I’d recommend looking back in previous posts where I justify my thinking–this simple paragraph just summarizes much of the work I have done in the past. I don’t want to revisit that right now, but to give you new news of a big discovery I have made about this field in the last few weeks.

I have been preparing both an analytic infrastructure and a computer sim that will hopefully provide some level of validation or refutation of the precursor field concept. The analytic work sets up the algebra that the sim will follow.
There are many issues with assuming that a continuous field will produce a particle zoo, but the biggest is what might be called the soliton problem. You can easily prove that Maxwell’s field equations cannot produce a stable particle, so historically, many efforts to quantize or otherwise modify these equations have been done without success. Compton and DeBroglie are famous for attempting this using an EM field (waves around a ring, sphere of charge, etc.) but no one has succeeded in a theory that successfully confines the EM field potentials into a stable soliton. I’ve long been convinced that you cannot use an EM field as a particle basis, and the QFT model of exchange particles (quantized photons in the case of EM field interactions) supports this way of thinking.

I discovered that the aforementioned precursor field can form either of two types of stable potential wells. The fact that the precursor field is directional only, thus field values cannot go to zero, combined with the omnipresent tendency to go to the default background state, leads both to quantization (only full integer twists out of and then back into the background state are stable) and to the formation of stable potential wells around either the background state or its opposite. I found that the background state tendency can be described as a force that is strongest when an element’s direction is normal to the background state, but is zero at either the background state or its opposite! It turns out it is nearly linear and thus forms a potential well near both zeroes. Thus a stable particle can form around a negative background state pole. You could also form a stable positive pole in a negative background state region (think antiparticles), and could even link together or overlap multiple particles in a chain or set of rings and have the result be stable. I can even visualize spontaneous formation of particle/antiparticle pairs so crucial to QFT, but that’s jumping the gun a bit right now.

It’s such an incredibly important step forward to find a field with a set of operators that could form stable particles, and I believe I’ve done that. The key is having the scalar field be unitary and having a preferential orientation–this set of field characteristics appears to succeed at producing solitons where all others have failed.

UPDATE: While this was an important finding, further work has shown that the background force has to be accompanied by a neighborhood connection, otherwise a discontinuity or possibly other cases may destabilize the particle.  To truly prove that this field can produce stable particles, all issues and details need to be fully flushed out. I suspect that the idea is on the right path but I have more work to do.

Agemoz

Preparing First Collision Sim

June 22, 2017

I’ve been working fairly consistently on the simulation environment for the unitary twist field theory. I’m getting ready to set up a photon/electron collision, modeled by the interaction of a linear twist with a twist around a loop. The twist is represented by e^I(t theta – k x), yes, the same expression that is used for quantum wave functions (I’ve often wondered if we’ve misinterpreted that term as a wave when in fact the math for a twist has been in front of our noses all along).

This is a great first choice for a collision sim because in my mind there’s always been a mystery about photon/particle interactions. If the electron is really a point particle as the Standard Model posits, how can a photon that is many orders of magnitude larger always interact with one and only one electron, even if there are a gazillion electrons within one wavelength of the photon? The standard answer is that I’m asking the wrong or invalid question–a classical question to a quantum situation. To which I think, maybe, but quantum mechanics does not answer it, and I just get this sense that refusing to pursue questions like this denies progress in understanding how things work.

In twist theory there appears to be an elegant geometrical answer that I’m pretty sure the simulation will show–counting my chickens before they are in my hand, to be sure–the downfall of way too many bright-eyed physics enthusiasts. But as I’ve worked out before, the precursor twist field is an incompressible and non-overlapping twist field. If the electron is a closed loop of twists, and within the loop the twists revert back to the I direction (see previous posts for a little more detailed description), then any linear twist propagating through the loop will add a delta twist to some point in the interior of the loop. Since you cannot somehow overlap twists (there’s only one field here, you can’t somehow slide twists through each other. Each point has a specific twist value, unlike EM fields where you linearly combine distinct fields). As a result, the twist of the loop can unwind the linear twist going through it, causing the photon to disappear and the close loop will pick up the resulting linear twist momentum. This isn’t really a great explanation, so here’s a picture of what I think will happen. The key is the fact that the precursor field has one twist value for every point in R3. It’s an incompressible and unitary field–you cant have two twist values (or a linear combination–it’s unitary magnitude at every point!) at a given point, so the photon twists have to affect the twist infrastructure of the loop if it passes through the loop. It really will act a lot like a residue inside a surface, where doing a contour integral will exactly reflect the number of residues inside.

At least that’s what I think will happen–stay tuned. You can see why I chose this interaction as the first sim setup to try.

Agemoz

Sim Infrastructure in Place

June 2, 2017

An exciting day! I found a better working environment for sims, and very quickly was able to get some elementary particle sims up and running. I like to think I finally actually did something noteworthy by creating an easy to use infrastructure that allows me to investigate and test mathematical concepts such as the unitary twist field theory that are far too difficult to solve analytically, even with simplifying assumptions. If I had chosen physics as a career path, one major area for contribution is setting up new environments or mathematical tools that allow others to build and test theories.
I have been writing a C program but it was taking forever and I was bogging down on the UI and result display. So I took a look at the Unity gaming SDK and realized this might be a perfect way to get past that and quickly into theory implementation. It more than met my expectations!
CERN has nothing on me! Next up are Petavolt collisions! Well, not really, first I have a lot of model generation to do to truly represent the precursor field theory I’ve detailed in previous posts. In addition, the display is very coarse and needs to be refined–the cubes are nodes in discretized points on the twist.  I want to get fancier but for now it’s pretty amazing to watch as the loop twists and turns.  The funny and amazing thing is, though, I really could do a collision sim in a few hours. This infrastructure makes it very easy to set up interaction math and boundary conditions. Maybe my theory is hogwash, but this infrastructure isn’t–could I have finally made a usable contribution to science? If any of you are interested in this, send me a comment or email and maybe I’ll detail what I’m doing here.

Precursor Field Forces

December 18, 2016

It looks clear now (see previous posts) that the precursor field (my underlying field proposal that is hypothesized to give rise to the particle zoo and EM and other fields) has to have a discontinuity to enable twists. This is great for quantization as mentioned in the previous post, but is really ugly for the math describing the field. Could nature really work this way? I’m dubious, but all of my analysis seems to show this is the only way, I’ve only gotten here because I have seen no other paths that appear to work.

For example, it’s obvious to everyone that an EM field can’t be the basis for quantization or solitons–lots of historical efforts that many have looked at and ruled out. Twists in a background state is a geometrical definition of quantization. Lattice and computer sim schemes are ruled out (in my mind, anyway) because I think there should be observable ether-like consequences. Adding an I direction to the R3 of our existence is necessary since twists in R3 could not provide the symmetries required for guage invariance and exchange particle combinations. The I dimension, which is merely an element pointing direction that does not lie in a physical real axis of R3, enables twist quantization, and unlike photon ring theories such as DeBroglie’s, can enable twist trajectory curvature–a necessity to allow closed loop solutions that confine particles to a finite volume. There are many more necessary constraints on this precursor field, but the most problematic is the need for field discontinuities. Any twist in a unitary orientable vector field has to be surrounded by a sheath where the twist disconnects from the background state pointing in the I direction.

Requiring discontinuities needed for enabling field twists is an ugly complication. We know already that any quantizing field theory underlying particle creation/annihilation cannot be linear since dissipation destroys particle stability–solitons cannot be formed. Almost by definition this means that the field has to have discontinuities, but mathematically describing such a field becomes very problematic. Obviously, such a field will not be differentiable since differentiability, at least finite differentiability, implies linearity.

As I’ve mentioned in previous posts, the precursor field has two connections that act like forces. From these connections arise linear and curving twists, exchange bosons of fields, and so on. The first force acts only on a field element, and provides a restoring force to the background state. The second, neighboring affect force, provides an influence on immediately adjacent neighboring elements of the precursor field. The first force should not be conceptually complex–it just means that, barring any other effect, a field element vector will return to the background state.

The second force is more complex. I see at least two options how this force might work. It should be obvious this force cannot be proportionate to the dimensional rate of change of rotation because discontinuities would make this force infinite. In fact, to keep a particle from dissociating, there must be an adhesion to nearby elements–but NOT across a discontinuity. Otherwise, the force due to the discontinuity would be far greater than the force holding the elements of the twists, where each end is bound to the background state (or to the 0 and 2Pi phase rotation connection of the closed loop twist). If that happens the forces across the discontinuity would be far greater that the force tying down the twist ends to the background state and our particle, whether linear or closed loop, would immediately be shredded into nothing.

The other possibility for the second force is to make it only proportionate to the timewise rate of change of adjacent elements (sort of like induction in magnetic fields), but again, the discontinuity sheath would bring in potential infinities.  Right now this approach does not show promise at all for a bunch of reasons.

I think the only viable description of the neighborhood force would be an adhesion to nearby states who’s orientation is the same or very slightly different. That is, the angular delta from nearby elements causes a force to make that delta 0, but if there is a rip or tear then no force occurs). An important side question is whether the neighborhood connection is stronger than the restoring to I force. It’s not clear to me right now if it matters–I think field quantization works regardless of which is stronger.

This finally gives me enough description that I can mathematically encode it into a simulation. I realize that just about all of you will not accept a theory with this sort of discontinuity built into every single particle. Like you, I really am quite skeptical this is how things work. I hope you can see the logic of how I got here, the step-by-step thinking I’ve done, along with going back and seeing if I overlooked a different approach (eg, more dimensions, string theory, etc) that would be more palatable. But that hasn’t happened, I haven’t seen any other schemes that could work as well as what I have so far.

Agemoz

Geometry of the Twist Sim Math

January 5, 2015
Here is a drawing of the forces on the twist path that the simulator attempts to model.

Here is a drawing of the forces on the twist path that the simulator attempts to model.

I created a picture that hopefully shows the geometry of the simulation math described in the previous post (see in particular the PPS update).  This picture attempts to show a generator twist path about point A in red, with the two force sources F(loop) and F(twist), which are delta 1/r^2 and 1/r^3 flux field generators respectively.  The destination point D path is shown in blue.  The parametric integral must be computed for every source point on each destination point–this will give a potential field.  When the entire set of curves lies on an equipotential path, one of many possible stable solutions has been found (it’s already easy to establish that any topologically unique closed loop solution will not degenerate because the 1/r^3 force will repel twist paths from crossing each other).  There probably is a good LaGrange method for finding stable solutions, but for now I will work iteratively and see if convergence for various linked or knotted loops can be achieved.

 

Agemoz