Posts Tagged ‘vector field’

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

Renormalization

June 25, 2017

I’m working on the math for the Unitary Twist Field Theory sim. The first sim to run is the easiest I know of, the electron/photon interaction, and if the theory doesn’t yield some reasonably good results, the theory is dead, there’s no point in going further. If that happens, hopefully there will be an indication of how to modify it to make it work, but this will be a defining moment for my work. Just recently, something quite astonishing came out of this work to find the equations of motion for the precursor field of this theory.

In the process of working out the force computations, I’ve been able to winnow down the range of possible equations that will rule the components of the interaction. Note first that the sim I am doing is discrete while the theory is continuous, simply to allow a practical implementation of a computer sim. I can add as many nodes as I want to improve accuracy, but the discrete implementation will be a limitation of the approach I am taking. In addition, forces can be local neighborhood only since according to the theory there is only one element to the precursor field, you can’t somehow influence elements through or outside the immediate neighborhood of an element. The field is also incompressible–you cant somehow squeeze more twist elements into a volume.

To express a twist with all of the required degrees of freedom in R3 + I, I use the e^i/2Pi(theta t – k x) factor. Forces on these twists must be normal to the direction of propagation–you can’t somehow speed it up or slow it down. Forces cannot add magnitude to the field–in order to enforce particle quantization (for example E=hv) the theory posits that each element is direction only, and has no magnitude. I use the car-seat cover analogy–these look like a plane of wooden balls, which can rotate (presumably to massage or relieve tension on your back while driving), but there is no magnitude component. The theory posits that all particles of the particle zoo emerge from conservative variations and changes in the direction of twist elements. To enforce rotation quantization, it is necessary that there be a background rotation state and a corresponding restoring force for each element.

In the process of working out the neighborhood force for each field element, I made an interesting, if not astonishing, discovery. At first, it seemed necessary that the neighborhood force would have a 1/r^n component. Since my sim is discrete, I will have to add a approximation factor to account for distances to the nearest neighbor element. Electrostatic fields, for example, apply force according to 1/r^2. This introduces a problem as the distance between elements approaches zero, the forces involved go to infinity. This is particularly an issue in QFT because the Standard Model assumes a point electron and QFT computations require assessing forces in the immediate neighborhood of the point. To make this work, to remove the infinities, renormalization is used to cancel out math terms that approach infinity. Feynman, for example, is documented to have stated that he didn’t like this device, but it generated correct verifiable results so he accepted it.

I realized that there can be no central (1/r^n) forces in the unitary twist field (this is the nail in the coffin for trying to use an EM field to form soliton particles. You can’t start with an EM field to generate gravitational effects–a common newbie thought partly due to the central force similarity, and you can’t use an EM field to form quantized particles either). Central force fields always result from any granular quantized system of particles issued from a point source into Rn, so assuming forces have a 1/r^n factor just can’t work. The granular components don’t dissipate, after all, where does the dissipated element go? In twist theory, you can’t topologically make a twist vanish. Thus the approximation factor in the sim must be unitary even if the field element distance varies.

Then a powerful insight hit me–if you can’t have a precursor field force dependent on 1/r^n, you should not need to renormalize. I now make the bold assertion that if you need to renormalize in a quantized system, something is wrong with your model. And, of course, then I stared at what that means for QFT, in particular the assumption that the electron is a point particle. There’s a host of problems with that anyway–in the last post I mentioned the paradox of an electron ever capturing a photon if it is a point with essentially zero radius. Here, the infinite energies near the point electron or any charged point particle have to be managed by renormalization–so I make the outrageous claim that the Standard Model got this part wrong. Remember though–this blog is not about trying to convince you (the mark of a crackpot) but just to document what I am doing and thinking. I don’t expect to convince anyone of this, especially given the magnitude of this discovery. I seriously questioned it myself and will continue to do so.

The Unitary Twist Field theory does not have this problem because it assumes the electron is a closed loop twist with no infinite energies anywhere.

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

Quantum State Superposition in the Precursor Field

January 1, 2017

I’ve been continuing to work on what a field would have to look like if it were the underlying mechanism for the particle zoo and force fields. One thing I haven’t discussed that will be noticed instantly by anyone who studies physics–this precursor field must allow quantum state superposition. I’ve so far posted a geometrical set of constraints, but I’ve always had an awareness that the model is incomplete–or won’t work at all–if I can’t provide some means for state superposition.

The trouble with inventing a theory like this is that the job is truly humongous. The number of details that have to be verified as correct is really beyond the reach of one person or even a team of people, so I’ve had to trudge on knowing that this whole thing will be laughed off in seconds by experienced theoreticians who spot a missing or wrong claim. This is definitely one of them, if I don’t provide a believable mechanism for quantum state superposition, nobody will bother to look.

So–I’ve spent some time thinking on this. I actually have enough worked out that I want to try a sim of the model, but then I thought–no, make sure quantum states can work with the model. Otherwise the sim will be a waste of time and probably not really even interesting. Probably the easiest and simplest quantum state superposition to think about is electron spin, which I’m going to take the liberty of modelling with a twist ring. There are two spin parameters in a twist ring, one of which is degenerate by rotation(*). To isolate the true degrees of freedom in a gauge invariant system, I will set the ring rotation direction as clockwise, for example, and then see just one degree of freedom in the axial twist direction along the rotation direction–it can be either clockwise or counterclockwise. I will call this the spin of the particle, either up or down.

Now, to specify a quantum state superposition, the particle spin can be either up or down or a linear combination of spin-up and spin-down. Does the unitary twist field theory precursor field allow this? I believe it is easy to say yes. Treat the loop as a transmission line with a discontinuity sheath surrounding the twist. The twist itself is a Fourier construction of standing waves that can encapsulate such a linear composition of the up and down spin. If the particle encounters a spin detector, an operator acts on the linear composition to filter the wave composition and resolve the spin state.

There’s my hand-wavy analysis, no proof by any stretch of the imagination. That is a chore that will have to wait. It looks viable to me, but I have so many other alligators in this swamp that this will have to do for now.

Agemoz

*Note that it’s only degenerate in R3 for purposes of this example. In reality, the R3 + I background state will be different for the two loop rotations, thus providing the required degrees of freedom for both spin and the particle/antiparticle duality.

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

Precursor Field Does Not Have to be Discontinuous

December 3, 2016

In trying to ferret out the properties of a precursor field that would give rise to the particle zoo and EM fields and so on, I had been working out just what this field would look like if it could form a loop. I have so far determined that it would have to reside in a orientable, unitary R3 + I vector field, the same dimensionality as the quantum oscillator field, and that to achieve E=hv quantization, quanta would take the form of twists in a background state pointing in the I direction. I figured out that a twist would curve in R3 if it formed a loop around a central background state region, because regardless of the loop topology in R3, it would always pass through a field orientation tilt toward the central I background region.

Up to now, the concept seemed to be workable, but I always have struggled with the field twist concept. I knew that in R3, you cannot have a field twist without a field discontinuity along the twist axis, which really caused me to doubt the veracity of the unitary twist theory. I know of no instance in the real universe where there’s a true discontinuity–even in black holes. To have our existence form from particles made of twists and field discontinuities has always seemed unlikely to the extreme–I have several times nearly abandoned this work because non-analytic fields seemed non-intuitive, non-differentiable, and non-geometrical.

However, when I tried to detail the specific mathematical possibilities for describing a curved twist in the R3 + I field, I discovered something quite surprising. Every mathematician probably knew this already–but when vector fields are described in four dimensions (R3 + I), axial twists can form in three of the four dimensions and not cause a discontinuity. The I orientation gives the field surrounding the twist an extra degree of freedom that removes the necessity for a discontinuity.

However, this does cause a different problem with the unitary twist theory. We all know that trying to form a soliton out of photons (an EM closed loop solution) is impossible because nothing can curve a photon into a ring. A big problem with trying to describe quantized photons out of EM waves is the dissipation problem, why doesn’t a quantized photon just radiate into nothing, thus losing the apparent quantization and conservation of energy? Currently, Standard Model physics doesn’t really provide an answer to that, but in unitary twist field theory work, I had determined that the discontinuities in a precursor field had acted as a lock that prevents unraveling of the particle, and thus may be necessary for particle stability. You can’t unravel a quantized twist in R3 (causing a particle loop or linear twist to disappear) because you would have to somehow resolve the discontinuity to the background state–and that definitely can’t be done in R3. But in R3 + I, there is no discontinuity required, and thus I think any twist configuration could disappear, thus potentially destroying the energy present in the particle.

So–which is it? We need R3 plus I to achieve quantization and closed loop twists–but R3 + I means we don’t have to have discontinuities–a far more realistic and likely representation of our universe via a unitary vector field, but with the disadvantage that what now enforces quantization? Are there solutions in R3 + I that still depend on a discontinuity for stability and conservation of energy?

Looks like more study and thinking is needed.

I’ll bet there’s a few scientists out there wondering if I could achieve something a lot more significant if I’d put all this time and energy into something worthwhile!

Agemoz

A Promising Precursor Field Geometry

November 29, 2016

I’ve been trying to find a geometrical description of how a unitary field twist could curve. If my hypothesis for the particle zoo arising from a precursor field is correct, the precursor field has to have a number of constraints. I’ve described what I know so far in depth in previous posts–here’s a summary of some of the basic requirements:
a: The precursor field cannot be an EM field with some sort of quantization added to it. The precursor field has to give rise to EM fields (and particles) but it has to be a continuous vector field with no magnitude (orientable only).
b: This field resides in R3 + I (same as the quantum oscillator spacetime) where quantization is achieved via twists that return to a background state pointing in the I direction.
c: There must be two connections built into the precursor field–a restoring force to I, and some kind of angular momentum transfer to neighboring field elements. This transfer force cannot be physical, otherwise field twists would not be possible since twists require a field discontinuity.
d: Field twists can be linear (eg photons) or confined to a finite space in the form of loops or knots or linked combinations of both.
e: There must be some means for a twist propagation to curve (otherwise the loop twists are not possible. I have investigated in detail various mechanisms within the R3 + I space, and believe I see a possibility enabled by the restoring force to the I dimension orientation.

The huge overwhelming problem with this hypothesis is that we appear to have zero evidence for such a precursor field or a background state or the two force connections I’ve described, the restoring force and the neighborhood connection force. I trudged forward with this anyway, knowing no-one out there would give this concept a second’s thought. I searched for possibilities in R3 + I where a loop twist could form and be stable, and for quite a while couldn’t find anything that made any sense.

I’ll tell you, I almost threw in the towel thinking this is a stupid quest. No evidence for a precursor field, no self-sustaining loop geometries that I could see, and experimental physics says any loop solution has to be too small to measure–a basic monkey-wrench in the whole unitary twist idea. I thought a lot, I’m just a dumb crackpot that doesn’t even have it wrong.

Yet something in the back of my mind says to me–when you look at the big picture, the particle zoo has to have a reductionist solution. For this existence to arise from nothing, there has to be some kind of field that gives rise to stable clumps we know as particles. For reasons I’ve discussed in previous posts, this can’t be some sort of computer simulation, nor can there be a creating entity. This all has to arise from nothing, I think–and from a deductive perspective, to me that means a single field must underlie particle formation. I’ve been able to come up with a number of constraints that this field has to have. I keep coming back to not seeing evidence for it, so I feel like I’m wandering around in a sea of ideas with no ability to confirm or deny any intermediate details of how things work. I see no realistic possibility that I could convince somebody this would work, I can’t even convince myself of that. Yet–there has got to be something. I have faith that Humanity can’t have reached the limit of understanding already!!

Not knowing what else to do other than abandon ship, I looked at R3 + I twist solutions, just about all of which couldn’t possibly work. Most fail because of symmetry issues or fail to provide an environment where twists could curve or be self-sustaining, regardless of how I describe the precursor field forces. Just yesterday, however, I happened upon a solution that has some promise. As discussed in previous posts, the restoring force to I is an enabler for quantization, but I realized it’s also an enabler for altering the path of a twist. I used the example in a previous post of how a field twist in R3 will curve if a regional part of the field is tilted in another dimension (imagine propagating a falling dominoe sequence through a sea of dominoes that is already partway orthogonally tilted). I am still checking this out, but it looks like there is one way to form the twist where this happens–if the twist loop resides in two of the dimensions of R3, and the axial twist in that loop resides in the remaining R3 dimension, but the restoring force is to the I dimension direction, the center of the loop will hold an element pointing in the I direction, thus causing all of the surrounding elements including the twist loop itself to feel a swirly (ref the Calvin and Hobbes cartoon!) that causes the twist propagation to pass through the field that is curved toward the center of the R3 loop.

This concept is ridiculously difficult to visualize, but essentially the I restoring force causes the field to always twist toward the center, regardless of loop orientation within R3. This is what the unitary twist field has to have–any other dimensional geometry simply does not provide the necessary twist curve. Believe me, I tried all other combinations–this is the only one that seems to consistently work no matter what kind of a topological loop configuration is used. Here is a pathetic attempt to draw out what I am thinking…

Agemoz

twist_in_restoring_i