Posts Tagged ‘simulation’

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

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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

Finally–A Particle Twist Solution Methodology

April 8, 2014

About six months ago, I was able to show qualitatively that the twist field had more than one stable solution, which implies that it could represent more than just the photon and electron variants.  I was easily able to show that any set of closed contours (twist paths) were topologically equivalent as long as no contour crosses, and the unitary field twist theory meets this constraint because twist paths are central force attractive (1/r^2 magnitude) but are repulsive by 1/r^3, so the sum is asymptotically repulsive as a twist path approaches another twist path.  This was a big breakthrough because now any interlinked loops or knots become unique and stable solutions, opening the door for representing the particle zoo.

I thought, great, now all I have to do is get some quantitative solutions and determine the relative mass to the twist field ring, and that would prove (or disprove, perhaps) the whole twist field concept.

Turns out, that is an extraordinarily difficult problem, and I’ve spent the last six months trying to figure out how to do it.  I finally figured out a crude iterative way to do it.

You would think this is a simple LaGrange mechanics problem, but my in-depth study seems to show this isn’t a workable approach.  The contour potential energy must be computed at every point, and is the integral of all other points of the entire contour set.  In fact, this problem has a stunning similarity to Feynman path integrals, with the complication that everything (all contour points) can move in 3D+T.  It cannot be assumed that the contours are symmetric, in fact if this indeed does model real particles, it’s easy to show that most solutions are not symmetric (contours are identical but displaced or rotated).  Worse, it’s likely many solutions are not stable in time, so methodologies invoking gauge invariance can’t be used here.

It was almost immediately obvious that trying to find a minimum path for the contour in the 1/r^2 – 1/r^3 field wouldn’t work (the field is an integral of all contours, but the contour path changes in each delta time), hence the LaGrange mechanics couldn’t be used in practice, the resulting differential equations would be phenomenally complex.  Simple iterative methods don’t work because there are constraints that are not really workable in an array  simulation–the energy of a loop must remain constant, so its length may not vary–but assuming constant spacing of simulation nodes doesn’t work for several reasons.  First, the solution loop length is not known, and fixing it defeats the goal of quantitatively finding that length.  Second, applying iterations to a chain of segments means that moving one segment means that a large set of adjacent segments also has to move instantaneously–not impossible, but each segment also has its own movement directives, which then would recursively affect the original movement directive.  I thought, well, let’s just make the segments stretchable, but adding that into the vector field complicates the computation significantly and appears to destroy the actual force balance between contour elements.  It’s a mess, believe me, I tried.

The approach I came up with is to just find any topologically equivalent set of contours and just start with that.  Compute the vector field neighborhood around each contour node and  then adjust each contour at each contour point until the vector field has minimal magnitude on each contour point.  Yes, there is considerable danger that doing this method of  iteration of contours will not be stable and converge, but I can see several outcomes that should yield valuable information anyway.  First, if nearly all vector field magnitudes point outwards (or all inwards), this means that the contour energies (and hence loop length) should be adjusted, so closure to a stable mass value should be possible regardless of the stability of the contour path shape iteration.  Second, there are many topologically unique solutions–that is already trivial to see.  If one contour set isn’t timewise stable or does not converge, either a different contour set could be tried or data from the iteration could be used to find a better starting point for the contour path.

I will put together a new sim (technically no longer a sim, but a generator) that does this contour vector field neighborhood and makes it easy to adjust the contour paths.  I have no doubt that over time I will come up with better and faster methods to arrive at solutions.

Agemoz

UPDATE:  Some additional thinking showed that taking a vector field derivative will yield the contour normal, and the direction will directly give the desired expansion directive.  It would be nice if the normal magnitude would also give the minima that would establish the optimized twist path, but it won’t–it will only give the minimum for that point given that the rest of the contour paths are unchanged.  As soon as any other portion of the paths change, this minimum will also change.  Perhaps there is a LaGrange multiplier scheme that will work to find the minima for all points on all paths.  I’m quickly sensing that there are a number of mathematical tools that can be brought to bear on this problem.

Confirmed–Twist Model Now Functioning

July 26, 2013

sim_sample_r1_r2

Picture shows a sample run of the twist ring with an external field.  Red curve is displacement, black curve is twist ring velocity, blue is the acceleration of the twist ring (it decreases over time as the twist ring moves away from the source (located off image to the left).  The initial acceleration rise is not real, but an artifact due to a moving average getting enough data to compute.

I modified the model from a dipole approximation to an integrated sum of components on the ring, and got very clean results   I did a large number of runs with varying field strength and displacements, and am getting very clear correlation with the expected analytic behavior.  Looks like it is now working as expected–yayy!  There’s still a lot more to be done including characterizing the exact analytic acceleration factor and working out other solutions in R3.  Since this solution class is planar, the sim can get a valid solution in 2D, but other solutions will require expansion of the sim to handle 3D cases.  In addition, I’d like to further refine the model to operate in an atom (Schroedinger wave equation) and to investigate a relativistic model variation.

This may all be science fiction, but it is the only working geometrical model I know of that shows correct underlying attraction and repulsion in an external field.  QFT does mathematically derive attraction, but momentum conservation is an issue.  In electrostatic attraction, photons emitted by the source particle have to pull the destination particle toward it–an apparent violation of conservation of momentum.  I believe the QFT solution has the field absorbing the difference in momentum, but where does that momentum go once absorbed?  The Twist Field solution clearly successfully solves that issue, and this successful result also points out some other important question resolutions.

Previously, I have posted that I felt that a point size particle for the bare electron was not possible because then its active neighborhood could not detect a direction for field potential.  It would require a field vector and act on direction, which we know can’t be true–the electron is attracted to a charged source regardless of orientation.  The electron has to be able to sense a localized change in potential, and the Twist Ring model clearly shows how that would work.  There are still questions in my mind that the solution is clearly independent of either source or destination orientation, and there’s some real questions in my mind whether this works in relativistic environments, but one thing is for sure–this is the first time I’ve seen a working model that has the correct quantitative behavior.

Agemoz

Not So Fast, Model Might Work After All

July 19, 2013

I had decided (in the last post) that the model I was using couldn’t be right for several reasons in spite of some promising sim results. But upon thinking about it, I realized I was a little too hasty–I discovered a way that a potential (scalar) function could work in accelerating a twist ring in spite of the orientation problem and the curvature problem.    This is an important question because it gets at the heart of why a particle would move due to EM fields.  Conventional theory just asserts the Lorentz force laws, and this works under all relativistic situations.  Conventional theory also says that the electron is an immeasurably small particle.  I have worked out that the twist field particle, which would not be immeasurably small, shows that as it is accelerated relativistically, it stretches to approach the behavior of a linear twist–asymptotically approaching radius size zero.  My hypothesis is that scattering experiments make the electron appear to be infinitely small because of this stretching.  I do have to admit that this experimental result is the chief reason why other physicists discount any electron theories that require non-point like models.

Anyway, back to the sim conclusions–I’ve been trying to create a hypothesis as to why it moves as it does with the twist field theory, and created my simulation environment to test the hypothesis.  I needed to know how a particle knows which way to move when there is one or more nearby sources, and I need it to work right regardless of relativistic behavior.

A big question is whether the particle as a twist ring would sense a variation of field magnitude, or whether the field has to be a vector and the particle senses which way to move based on this vector (which would be a vector sum if there was more than one source).  The scalar field is preferable because then motion can result from the potential function, but I had thought that the orientation problem as well as the curvature problem of negative fields (see previous post) meant that the twist field ring would have to respond to a vector field, that the particle would have to accelerate independent of the orientation.  I also think the stretching of the ring in a relativistic situation might not hold up to correct behavior, but the scalar field is more likely to work than the vector field (simpler–fewer complications in different scenarios).

However, I realized that all of these reasons for thinking the twist sim model are wrong are not all-encompassing. There’s a way around them, which means I have to check those out.  First, the negative field situation, which uses curvature analysis to show a paradox (stronger curvature for a field component that is on the far side of the ring).  I had done the math and things worked correctly, but had reasoned that the math couldn’t be right because it implied a force that didn’t decay with distance.  Now I realize the math is right, because there are three components that add to create the normal acceleration that determines the local curvature of the ring.  The end result of this sum is that while a weaker far-side field cannot induce more curvature, a cancelling out of part of the sum of the near-side acceleration caused by the negated field would result in *less* acceleration there and would achieve the same acceleration (as the far-field stronger field)  for source particles that attract.  The sim was correct, I just wasn’t drawing the right conclusion.

Secondly, I realized that the orientation problem may cancel itself out.  I’ve reasoned that since some orientations cause every point on the twist ring to see exactly the same field, so a solution that depends on the particle sensing the delta field cannot work in that case, and thus invalidates that solution as a general one.  But it is possible that the potential is sensed whether or not the delta field is sensed.  There has to be different behavior between a constant potential field and a sloping potential.  If the orientation problem is real, then there would be no difference in what the particle sensed from source particles and what it would sense if there were no source particles.  The field component would be the same in the local neighborhood  in either case and there would be no information available that would indicate where the particle would move to.   But a solution that has acceleration also due to potential alone, regardless of a change in potential, would work–kind of a switching between normal and tangental effects.  I will pursue this more–this idea isn’t flushed out yet.

If the delta potential *is* sensed, then this means that particles like the electron must have non-zero size, otherwise the delta field that the particle sees would still be flat.  Then the only information where the sources were would come from a directional component resulting from the vector sum of source fields at that point (where the ring is located).  Current experiment appears to show that the base electron has no size, which means it cannot sense potential across the twist ring.  In addition, the notion that an electron is imeasurably small has a real problem with Heisenberg’s uncertainty relation.  It is fundamental to the twist ring theory that the electron does have physical size, the Lorentz transforms arise from that, and the E=hv quantization of the ring depends on that.  One way or the other, a determination has to be made whether we have a scalar or vector field inducing motion.  The sim model I have now depends on a scalar field (potential) and is qualitatively correct.

So, in summary–the question of whether motion results from travel through a potential is still possible–and unresolved.   More work ahead.

Agemoz

Sim Results Show Wrong Acceleration Factor

July 18, 2013

Well, it looked promising–qualitatively, it all added up, and everything behaved as expected.  But it’s a “close, but no cigar”.   The acceleration at each point should be proportional to 1/r^2, but after a large number of runs, it’s pretty clearly some other proportionality factor.  I’ve got some more checking to do, but looks like I don’t have the right animal here.  One thing is clear though–this model, which attracts and repels, is the first one that shows qualitatively correct behavior.  If twist rings have mass due to the twist distortion, this is the first model that shows it, even if the mass can’t be right.

So, I stepped back and ran through the list of assumptions, and see some flaws that might guide me to a better solution.  Many theories die in the real world because of the glossy effect, as in, I glossed over that and will deal with it later, it’s not a major problem.  I unintentially glossed over some problems with the model, and in retrospect I should have addressed them from the get-go.

First, twist rings (as modelled in my simulation) have a real planar component, but twist through an imaginary axis.  The twist acts as an E field in the real space and as a magnetic field in the imaginary space.  The current hypothesis is that the loop experiences different field magnitudes from the source particle, and this causes a curvature change that varies around the loop.  The part of the loop that is further away will experience less curvature, the closer part more curvature (curvature is a function of the strength of the magnetic field from the source particle).  This simulation shows that if that is the model, you do indeed get an acceleration of the ring proportionate to the distance from the source particle–and the acceleration is toward the source particle–attraction!  If you switch the field to the negative, you get the same acceleration away–repulsion.  So far, so good, and the sim results made me think–I’m on the right track!  I still think I might be on the right track, but the destination is further away than I thought.

First, as I mentioned, the sim results seem to show pretty clearly that the acceleration is not the right proportionality (1/r^2).  That might just be a computational problem or just indicate the model needs some adjustments.  But there are some things being glossed over here.  First, while the model works regardless of how many particles act as a source, there is always one orientation where every point on the ring is equadistant from the source particle–in this case, there is no variation in curvature.  The particle would have to act differently depending on orientation.  It could be argued that the particle ring will always have its moment line up with the source field, and so this orientation will never happen–fine, but what happens when you have two source particles at different locations?  The line-up becomes impossible.  OK, let’s suppose some sort of quantum dual-state for the ring–and I say, I suppose that is possible, some kind of sum of all twist rings, or maybe a coherence emerges depending on where the source particles are, but then we no longer have a twist ring.  In addition, the theory fixes and patches are building up on patches, and I’d rather try some simpler solutions before coming back to this one.  The orientation problem is a familiar one–it shoots down a lot of geometrical solutions, including the old charge-loop idea.

Here’s another issue:  I make the assumption that there is a “near side” and a “far side”, which has the orientation problem I just mentioned–a corollary to that is that it also could get us in trouble as soon as relativity comes in play since near and far are not absolute properties in a relativistic situation).  I then get an attraction by assuming the field is weaker on the far side and thus there is less curvature.  The sim shows clearly the repulsion acceleration away from the source when this is done.  Then I cavalierly negated the field and Lo! I got attraction, just like I expected.  But I thought about this, and realized this doesn’t make physical sense–a case of applying a mathematical variation without thinking.  This would mean that the field caused *greater* curvature when the twist point is further away (the far side).  Uhh, that does not compute…

While not completely conclusive, this analysis points out first, that a solution cannot depend on source field magnitude variation alone within the path of the ring.  The equidistant ring orientation requires (more correctly, “just about” requires, notwithstanding some of the alternatives I just mentioned) that the solution work even if all neighborhood points on the ring have exactly the same source field magnitude.  In addition, there’s another more subtle implication.  The direction a particle is going to move has to come from a field vector–this motion cannot result from a potential function (a scalar)  because within the neighborhood of the ring, the correct acceleration must occur even if the potential function appears constant over the range of the twist ring.

This is actually a pretty severe constraint.  In order for a twist ring to move according to multiple source particles, a vector sum has to be available in the neighborhood of the twist ring and has to be constant in that neighborhood.  The twist ring must move either toward or away from this vector sum direction, and the acceleration must be proportionate to the magnitude of the vector sum.  Our only saving grace is the fact that this vector sum is not necessarily required to lie in R3, possible I3–but a common scalar imaginary field of the current version of the twist theory is unlikely to hold up.

Is the twist field theory in danger of going extinct even in my mind?  Well, yes, there’s always that possibility.  For one thing, I am assuming there will be a geometrical solution, and ignoring some evidence that the twist ring and other particles have to have a more ghostly (coherent linear sum of probabilities type of solution we see in quantum mechanics).  For another, my old arguments about field discontinuities pop up whenever you have a twist field, there’s still an unresolved issue there.

But, the driving force behind the twist field theory is E=hv.  A full twist in a background state is the only geometrical way to get this quantization in R3 without adding more dimensions–dimensions that we have zero evidence for.   Partial twists, reverting back to the background state, are a nice mechanism for virtual particle summations.  We do get the Lorentz transform equations for any closed loop solution such as the twist theory  if the time to traverse the loop is a clock for the particle.  And–the sim did show qualitative behavior.  Fine tuning may still get me where I want to go.

Agemoz