Posts Tagged ‘twists quantization’

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

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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

Nope: Precursor Field With a Background State Has to be Discontinuous

December 15, 2016

In the last post, I had come to the conclusion that the proposed R3 + I precursor field that would give rise to the particle zoo and EM and other fields could have twists and not have a discontinuity. This posed a problem, however, since quantization of a unitary twist field depends on the twist not being able to dissipate–that the discontinuity provides a “lock” that ensures particle stability over time. Further study has revealed that the extra I dimension does NOT topologically enable a continuous field that could contain twists.

The proof is simple. If the two ends of the twist are bound to the background state, but there is a field twist in between, it must be possible to create some other path connected to the endpoints that does not have a twist, since the background state must completely surround the twist path–see the diagram below. But this is impossible, because in a continuous system it must be topologically possible to move the paths close to each other such that an epsilon volume contains both paths yet has no discontinuities. Since this field is unitary and orientable (I like to use the car seat cover analogy, which is a plane of twistable balls for infinitesimal field elements), there is no “zero” magnitude possible. Somewhere in the epsilon volume there must be a region where the field orientations show a cut analogous to a contour integral cut.

It doesn’t matter how many dimensions the field has, if I’ve thought this through correctly, twists always require a discontinuity in a unitary orientable vector field.

This is a relief in most ways–otherwise this whole scheme falls apart if twists can dissipate. The only way a twist can unravel is in a collision with another twist of the opposite spin or some other similar geometrical construct.

Agemoz

twist_discontinuity_p1

Precursor Field Connection to Quantum Field Theory

November 8, 2016

I’ve done some pretty intense thinking about the precursor field that enables quantized particles to exist (see prior post for a summary of this thought process) via unitary field twists that tend to a background state direction. This field would have to have two types of connections that act like forces in conventional physics: a restoring force to the background direction, and a connecting force to neighborhood field elements. The first force is pretty simple to describe mathematically, although some questions remain about metastability and other issues that I’ll mention in a later post. The second force is the important one. My previous post described several properties for this connection, such as the requirement that the field connection can only affect immediate neighborhood field elements.

The subject that really got me thinking was specifically how one field element influences others. As I mentioned, the effect can’t pass through neighboring elements. It can’t be a physical connection, what I mean by that is you can’t model the connection with some sort of rubber band, otherwise twists could not be possible since twists require a field discontinuity along the twist axis. That means the connection has to act via a form of momentum transfer. An important basis for a field twist has to consist of an element rotation, since no magnitudes exist for field elements (this comes from E=hv quantization, see previous few posts). But just how would this rotation, or change in rotation speed, affect neighboring elements? Would it affect a region or neighborhood, or only one other element? And by how much–would the propagation axis get more of the rotation energy, if so, how much energy do other non-axial regions get, and if there are multiple twists, what is the combined effect? How do you ensure that twist energy is conserved? You can see that trying to describe the second force precisely opens up a huge can of worms

To conserve twist energy so the twist doesn’t dissipate or somehow get amplified in R3, I thought the only obvious possibility is that an element rotation or change of rotation speed would only affect one field element in the direction of propagation. But I realized that if this field is going to underlie the particle/field interactions described by quantum mechanics and quantum field theory, the energy of the twist has to spread to many adjacent field elements in order to describe, for example, quantum interference. I really struggled after realizing that–how is twist conservation going to be enforced if there is a distributed element rotation impact.

Then I had what might be called (chutzpah trigger warning coming 🙂 a breakthrough. I don’t have to figure that out. It’s already described in quantum theory by path integrals–the summation of all possible paths, most of which will cancel out. Quantum Field theory describes how particles interact with an EM field, for example, via the summation of all possible virtual and real particle paths via exchange bosons, for instance, photons. Since quantum field theory describes every interaction as a sum of all possible exchange bosons, and does it while conserving various interaction properties, all this stuff I’m working on could perhaps be simply described as replacing both real and virtual particles of quantum theory with field twists, partial or complete, that tend to rotate to the I dimension direction in R3 + I space (the same space described with the quantum oscillator model) of my twist theory hypothesis.

I now have to continue to process and think about this revelation–can all this thinking I’ve been doing be reduced to nothing more than a different way to think about the particles of quantum field theory? Do I add any value to quantum field theory by looking at it this way? Is there even remotely a possibility of coming up with an experiment to verify this idea?

Agemoz

Precursor Field Constraints

August 31, 2016

I’m continuing to work through details on the Precursor Field, so called because it is the foundation for emergent concepts such as quantized particles and the EM field/Strong force. I mentioned previously that this field has a number of constraints that will help define what it is. Here is what I had from previous work: the precursor field must be unitary to satisfy the quantization implied by E=hv (no magnitude degree of freedom possible). It must be orientable to R3 + I, that is, SO(4) to allow field twists, which are necessary for particle formation under this theory. It must have a preferred background orientation state in the I direction to enable particle quantization. Rotations must complete a twist to the background state, no intermediate stopping point in rotation–this quantizes the twist and hence the resulting particle. This field must not necessarily be differentiable (to enable twists required for particle formation). There must be two types of field connections which I am calling forces in this field–field elements must have a lowest energy direction in the imaginary axis, such that there is a force that will rotate the field element in that direction. Secondly, it must have a neighborhood force whenever the field element changes its own rotation. I’ll call the first force the restoring force, and the second force the neighborhood force.

These constraints all result from a basic set of axioms resulting from the Twist Theory’s assumption that a precursor field is needed to form quantized stable particles (solitons).

Since then, I’ve uncovered more necessary constraints having to do with the two precursor field forces. Conservation of energy means that there cannot be any damping effect, which has the consequence that the twist cannot spread out. The only way this can occur is if the quantized twist propagates at the speed of light. This introduces a whole new set of constraints on the geometry of twists. I’m postulating that photons are linear twists which will reside on the light cone of Minkowski space, and that all other particles are closed loops. A closed loop on Minkowski space must also lie on a light cone for each delta on its twist path, which means that the closed loop as a whole cannot reach the speed of light. This can easily be seen because closed loops must have a spacelike component as well as a timelike component such that the sum of squares lies on the twist path elements light cone. This limits the timelike component to less than the speed of light (the delta path element has to end up inside the light cone, not on it).

One interesting side consequence is that a particle like the electron cannot be pointlike. The current collider experiments appear to show it is pointlike, but this should be impossible both because the Heisenberg uncertainty relation would imply an infinite energy to a pointlike particle but also because if an electron cannot be accelerated to exactly the speed of light, this forces its internal composition to have a spacelike component and thus cannot be pointlike. Ignoring my scientific responsibility to be skeptical (for example, another explanation would be massive particles are forced to interact within an EM field via exchange particles, thus slowing it down for reasons independent of the particle’s size–but if this were true, why doesn’t this also apply to photons), I have a strong instinct that says this confirms my hypothesis that particles other than the photon are closed loops with a physical size. This also makes sense since mass would then be associated with physical size since closed loops confine particle twist momentum to a finite volume, whereas a photon distributes its momentum over an infinite distance and thus has zero mass. Since collision scattering angles implies a point size, the standard interpretation is to assume that the electron is pointlike–but I think there may be another explanation that collider acceleration distorts the actual closed loop of the electron to approach a line (pointlike cross section).

Anyway, to get back on topic, my big focus is on how to precisely define the two forces required by the precursor field. I realized that the restoring force is the much harder force to describe–the neighborhood force merely has to translate the field elements change of rotation to a neighborhoods change of rotation such that the sum of all neighborhood force changes equals the elements neighborhood force. This gives a natural rise to a central force distribution and is easy to calculate.

The restoring force is harder. As I mentioned, conservation of energy requires that it cannot just dissipate into the field, and a quantum particle must consist of exactly one twist (otherwise the geometrical quantization would permit two or more particles). I’m thinking this means that a change in rotation due to the restoring force must be confined to a delta function and that the rotation twist must propagate at the speed of light, whether linearly (photons) or in a closed loop (massive particles). I suspect we can’t think of the restoring force as an actual force, but then how to describe it as a field property? I’ll have to do more thinking on this…

Agemoz

Quantizing Fields–Twist Field vs. Semiclassical and Canonical Field Quantization

August 28, 2016

I’ve done all this work/discussion here about this unitary twist field scheme and how it uses quantized rotations to a background imaginary axis. While my primary intent is for my benefit (keep track of where I am and to organize my thinking) I’ve tried to make it readable and clear for any readers that happen to be following my efforts. I try to be lucid (and not too crack-potteryish) so others could follow this if they wanted to. To be sure, my work/discussion on the unitary twist field is very speculative, a guess on why we have the particle zoo. However one big thought has been running through my head–if any of you are following this, you would be forgiven for wondering why I’m doing this field quantization work given that there is already plenty of well established work on first and second quantization of fields such as the EM field.

This is going to be a very tough but valid question to elaborate on. Let me start with a synopsis: my work on this precursor field, and quantum mechanics/field theory work are operating on very different subjects with the unfortunate common concept name of quantization. Quantum theory uses quantization to derive the wavelike behavior of particles interacting with other particles and fields. Unitary Twist Field theory uses a different form of quantization to help define an underlying basis field from which stable/semistable particles and fields (such as the EM field) can form.

Let me see if I get the overall picture right, and describe it in a hopefully not too stupidly wrong way.

Both quantum theory and my Unitary Twist Field work reference quantization as a means to derive a discrete subset of solutions concerning fields and particles from an infinite set of possible system solutions. Quantum theory (mechanics, field theory) derive how particles interact, and quantization plays a big part in constraining the set of valid interaction solutions. Unitary Twist Field theory (my work) involves finding a field and its properties that could form the particles and field behavior we see–an underlying field that forms a common basis for the particles and the interactions we see in real life. Quantum theory and the Standard Model currently provide no clear way to derive why particles have the masses and properties that they do, Unitary Twist Theory attempts to do that by defining a precursor basis field that creates solitons for both the stable/semistable particles and force exchange particles required by the Standard Model and quantum theory.

Standard Model particle/field interactions in quantum mechanics (first quantization) is a semiclassical treatment that adds quantization to particles acting in a classical field. Quantization here means extending the classical equations of motion to include particle wavelike behavior such as interference. Second quantization (either canonical or via path integrals, referred to generally as quantum field theory) extends quantization to fields by allowing the fields to spontaneously create and annihilate particles, virtual particles, exchange particles, fields, etc–it’s a system where every force is mediated by particles interacting with other particles. This system of deriving solutions gets generalization extension via gauge invariance constraints, this work gave rise to antiparticles and the Higgs Boson. Quantization here means that particle/field interactions interfere like waves, and thus there is generally a discrete set of solutions with a basis that could be called modes or eigenstates (for example quantized standing waves in electron orbitals about an atom).

The quantization I am using as part of the defining of the Unitary Twist Field is a completely different issue. I’ve done enough study to realize that the EM field cannot be a basis for forming particles, even by clever modification. Many smart minds (DeBroglie, Compton, Bohr, etc) have tried to do that but it cannot be done as far as anyone has been able to determine. I think you have to start with an underlying field from which both particles and the EM field could emerge, and it has to be substantially different than the EM field in a number of ways. I’ve elaborated on this in extensive detail in previous posts, but in a nutshell, quantization here means a orientable, unitary, 3D + I (same as the quantum oscillaor) field that has a preferred lowest energy direction to the positive imaginary axis. This field should produce a constrained set of stable or semistable solitons. If all goes well and this is a good model for reality, these soliton solutions should then match the particle zoo set and exhibit behavior that matches the EM field interactions with particles described in quantum theory and the Standard Model.

I am attempting to keep in mind that a twist field theory also has to be gauge invariant at the particle level, and has to be able to absorb quantum theory and the Standard Model. That’s to be done after I first determine the viability of the unitary twist field in producing a set of particles matching the known particle zoo. This is a truly enormous endeavor for one not terribly smart fellow, so just one step at a time…

Don’t know if that makes things clearer for readers, it does help narrow down and add clarity in my own mind of what I’m trying to do.

Agemoz

Basis Field–NYAEMFT (Not Yet Another EM Field Theory)

July 19, 2016

If you’ve been following along in my effort to work out details of the Unitary Twist field, you will have seen the evolution of the concept from an original EM field theory to something that might be described as a precursor field that enables quantized sub-atomic particles, Maxwell’s field equations, relativity, and other things to emerge .  I’ve worked out quite a few contraints and corollaries describing this field–but I need to make it really clear what this field is not.  It cannot be an EM field.

My sidebar on this site calls it an EM field but now is the time to change that, because to achieve the goal of enabling the various properties/particles I list above, this field has to be clearly specified as different from an EM field.  Throughout physics history there have been efforts to extend the EM field description to enable quantization, General Relativity, and the formation of the particle zoo.  For a long time I had thought to attempt to modify the Maxwell’s field equations to achieve these, but the more I worked on the details, the more I realized I was going at it the wrong way.

The precursor field (which I still call the unitary twist field)  does allow EM field relations to emerge, but it is definitely not an EM field.  EM fields cannot sustain a quantized particle, among other things.  While the required precursor field has many similarities to an EM field that tempt investigators to find a connection, over time many smart people have attempted to modify it without success.

I now know that I must start with what I know the precursor field has to be, and at some point then show how Maxwell’s field equations can arise from that.

First, it can readily be shown that quantization in the form of E=hv forces the precursor field to have no magnitude component.  Removing the magnitude component allows a field structure to be solely dependent on frequency to obtain the structure’s energy.   This right here is why EM fields already are a poor candidate to start from.   It took some thinking but eventually I realized that the precursor field could be achieved with a composition of a sea of orientable infintesimal “balls” in a plane (actually a 3D volume, but visualizing as a 2D plane may be helpful).

The field has to have 3 spatial dimensions and 1 imaginary dimension that doesn’t point in a spatial direction (not counting time).  You’ll recognize this space as already established in quantum particle mechanics–propagators have an intrinsic e^i theta (wt – kx) for computing the complex evolution of composite states in this 3D space with an imaginary component, so I’m not inventing anything new here.  Or look at the photon as it oscillates between the real and imaginary (magnetic) field values.

Quantization can readily be mapped to a vector field that permits only an integer number of field rotations, easy to assign to this precursor field–give the field a preferred (lower energy) orientation in the imaginary direction called a default or background state.  Now individual twists must do complete cycles–they must must turn all the way around to the default orientation and no more.  Partial twists can occur but must fall back to the default orientation , thus allowing integration of quantum evolution over time to ultimately cause these pseudo-particles to vanish and contribute no net energy to the system.  This shows up in the computation of virtual particles in quantum field theory and the emergence of the background zero-point energy field.

Because of this quantized twist requirement, it is now possible to form stable particles, which unlike linear photons, are closed loop twists–rings and knots and interlocked rings.  This confines the momentum of the twist into a finite area and is what gives the particle inertia and mass.  What the connection is to the Higg’s field, I candidly admit I don’t know.  I’m just taking the path of what I see the precursor field must be, and certainly have not begun to work out derivations to all parts of the Standard Model.

The particle zoo then results from the tree of possible stable or semi-stable twist topologies.   Straight line twists are postulated to be photons, rings are electrons/positrons differentiated by the axial and radial spins, quark combinations are interlocked rings where I speculate that the strong force results from attempting to pull out an interlocked ring from another.  In that case, the quarks can pull apart easily until the rings start to try to cross, then substantial repulsion marks the emergence of the asymptotic strong force.

Quantum entanglement, speed of light, and interference behavior results from the particle’s group wave characteristics–wave phase is constant and instantly set across all distance, but particles are group wave constructions that can only move by changing relative phase of a Fourier composition of waves.  This geometry easily demonstrates behavior such as the two-slit experiment or Aharonov’s electron.  The rate of change of phase is limited, causing the speed of light limit to emerge.  What limits this rate of change?  I don’t know at this point.

All this has been extensively documented in the 168 previous posts on this blog.  As some point soon I plan to put this all in a better organized book to make it easier to see what I am proposing.

However, I felt the need to post here, the precursor field I call the Unitary Twist Field is *not* an EM field, and really isn’t a modified or quantized EM field.  All those efforts to make the EM field create particles, starting with de Broglie (waves around a ring), Compton, Bohm, pilot wave, etc etc just simply don’t work.  I’ve realized over the years that you can’t start with an EM field and try to quantize it.  The precursor field I’m taking the liberty of calling the Unitary Twist Field has to be the starting point if there is one.

Agemoz

Simulation Construction of Twist Theory

December 2, 2014

Back after dealing with some unrelated stuff.  I had started work on a new simulator that would test the Twist Theory idea, and in so doing ran into the realization that the mathematical premise could not be based on any sort of electrostatic field.  To back up a bit, the problem I’m trying to solve is a geometrical basis for quantization of an EM field.  Yeah, old problem, long since dealt with in QFT–but the nice advantage of being an amateur physicist is you can explore alternative ideas, as long as you don’t try to convince anyone else.  That’s where crackpots go bad, and I just want to try some fun ideas and see where they go, not win a Nobel.  I’ll let the university types do the serious work.

OK, back to the problem–can an EM field create a quantized particle?  No.  No messing with a linear system like Maxwell’s equations will yield stable solitons even when constrained by special relativity.  Some rule has to be added, and I looked at the old wave in a loop (de Broglie’s idea) and modified it to be a single EM twist of infinitesimal width in the loop.  This still isn’t enough, it is necessary that there be a background state for a twist where a partial twist is metastable, it either reverts to the background state, or in the case of a loop, continues the twist to the background state.  In this system–now only integer numbers of twists are possible in the EM field and stable particles can exist in this field.  In addition, special relativity allows the twist to be stable in Minkowski space, so linear twists propagating at the speed of light are also stable but cannot stop, a good candidate for photons.

If you have some experience with EM fields, you’ll spot a number of issues which I, as a good working crackpot, have chosen to gloss over.  First, a precise description of a twist involves a field discontinuity along the twist.  I’ve discussed this at length in previous posts, but this remains a major issue for this scheme.  Second, stable particles are going to have a physical dimension that is too big for most physicists to accept.  A single loop, a candidate for the electron/positron particle, has a Compton radius way out of range with current attempts to determine electron size.  I’ve chosen to put this problem aside by saying that the loop asymptotically approaches an oval, or even a line of infinitesimal width as it is accelerated.  Tests that measure the size of an electron generally accelerate it (or bounce-off angle impact particles) to close to light speed.  Note that an infinitely small electron of standard theory has a problem that suggests that a loop of Compton size might be a better answer–Heisenberg’s uncertainty theorem says that the minimum measurable size of the electron is constrained by its momentum, and doing the math gets you to the Compton radius and no smaller.  (Note that the Standard Model gets around this by talking about “naked electrons” surrounded by the constant formation of particle-antiparticle pairs.  The naked electron is tiny but cannot exist without a shell of virtual particles.  You could argue the twist model is the same thing except that only the shell exists, because in this model there is a way for the shell to be stable).

Anyway, if you put aside these objections, then the question becomes why would a continuous field with twists have a stable loop state?  If the loop elements have forces acting to keep the loop twist from dissipating, the loop will be stable.  Let’s zoom in on the twist loop (ignoring the linear twist of photons for now).  I think of the EM twist as a sea of freely rotating balls that have a white side and a black side, thus making them orientable in a background state.  There has to be an imaginary dimension (perhaps the bulk 5th dimension of some current theories).  Twist rotation is in a plane that must include this imaginary dimension.  A twist loop then will have two rotations, one about the loop circumference, and the twist itself, which will rotate about the axis that is tangent to the loop.  The latter can easily be shown to induce a B field that varies as 1/r^3 (formula for far field of a current ring, which in this case follows the width of the twist).  The former case can be computed as the integral of dl/r^2 where dl is a delta chunk of the loop path.  This path has an approximately constant r^2, so the integral will also vary as r^2.  The solution to the sum of 1/r^2 – 1/r^3 yields a soliton in R3, a stable state.  Doing the math yields a Compton radius.  Yes, you are right, another objection to this idea is that quantum theory has a factor of 2, once again I need to put that aside for now.

So, it turns out (see many previous posts on this) that there are many good reasons to use this as a basis for electrons and positrons, two of the best are how special relativity and the speed of light can be geometrically derived from this construct, and also that the various spin states are all there, they emerge from this twist model.  Another great result is how quantum entanglement and resolution of the causality paradox can come from this model–the group wave construction of particles assumes that wave phase and hence interference is instantaneous–non-causal–but moving a particle requires changing the phase of the wave group components, it is sufficient to limit the rate of change of phase to get both relativistic causality and quantum instantaneous interference or coherence without resorting to multiple dimensions or histories.  So lots of good reasons, in my mind, to put aside some of the objections to this approach and see what else can be derived.

What is especially nice about the 1/r^2 – 1/r^3 situation is that many loop combinations are not only quantized but topologically stable, because the 1/r^3 force causes twist sections to repel each other.  Thus links and knots are clearly possible and stable.  This has motivated me to attempt a simulation of the field forces and see if I can get quantitative measurements of loops other than the single ring.  There will be an infinite number of these, and I’m betting the resulting mass measurements will correlate to mass ratios in the particle zoo.  The simulation work is underway and I will post results hopefully soon.

Agemoz

PS: an update, I realized I hadn’t finished the train of thought I started this post with–the discovery that electrostatic forces cannot be used in this model.  The original attempts to construct particle models, back in the early 1900s, such as variations of the DeBroglie wave model of particles, needed forces to confine the particle material.  Attempts using electrostatic and magnetic fields were common back then, but even for photons the problem with electrostatic fields was the knowledge that you can’t bend or confine an EM wave with either electric or magnetic fields.  With the discovery and success of quantum mechanics and then QFT, geometrical solutions fell out of favor–“shut up and calculate”, but I always felt like that line of inquiry closed off too soon, hence my development of the twist theory.  It adds a couple of constraints to Maxwell’s equations (twist field discontinuities and orientability to a background state) to make stable solitons possible in an EM field.

Unfortunately, trying to model twist field particles in a sim has always been hampered by what I call the renormalization problem–at what point do you cut off the evaluation of the field 1/r^n strength to prevent infinities that make evaluation unworkable.  I’ve tried many variations of this sim in the past and always ran into this intractable problem–the definition of the renormalization limit point overpowered the computed behavior of the system.

My breakthrough was realizing that that problem occurs only with electrostatic fields and not magnetic fields, and finding the previously mentioned balancing magnetic forces in the twist loop.  The magnetic fields, like electrostatic fields,  also have an inverse r strength, causing infinities–but it applies force according to the cross-product of the direction of the loop.  This means that no renormalization cutoff point (an arbitrary point where you just decide not to apply the force to the system if it is too close to the source) is needed.  Instead, this force merely constrains the maximum curvature of the twist.  As long as it is less that the 1/r^n of the resulting force, infinities wont happen, and the curve simulation forces will work to enforce that.  At last, I can set up the sim without that hokey arbitrary force cutoff mechanism.

And–this should prove that conceptually there is no clean particle model system (without a renormalization hack) that can be built from an electrostatic field.  A corollary might be–not sure, still thinking about this–that magnetic fields are fundamental and electrostatic fields are a consequence of magnetic fields, not a fundamental entity in its own right.  The interchangability of B and E fields in special relativity frames of reference calls that idea into question, though, so I have to think more about that one!  But anyway, this was a big breakthrough in creating a sim that has some hope of actually representing twist field behavior in particles.

Agemoz

PPS:  Update–getting closer.  I’ve worked out the equations, hopefully correctly, and am in the process of setting them up in Mathematica.  If you want to make your own working sim, the two forces sum to a flux field which can be parametrically integrated around whatever twist paths you create.  Then the goal becomes to try to find equipotential curves for the flux field.  The two forces are first the result of the axial twist, which generates a plane angle theta offset value Bx = 3 k0 sin theta cos theta/r^3, and Bz = k0 ( 3 cos^2 theta -1)/r^3.  The second flux field results from the closed loop as k0 dl/r^2).  These will both get a phase factor, and must be rotated to normalize the plane angle theta (some complicated geometry here, hope I don’t screw it up and create some bogus conclusions).  The resulting sum must be integrated as a cross product of the resulting B vector and the direction of travel around the proposed twist path for every point.

Yang-Mills Mass Gap

January 12, 2014

My study of vector field twists has led to the discovery of stable continuous field entities as described in the previous post (Dec 29th A Particle Zoo!).  I’ve categorized the available types of closed and open solutions into three broad groups, linear, knots, and links.  There’s also the set of linked knots as a composite solution set.  I am now trying to write a specialized simulator that will attempt quantitative characterization of these solutions–a tough problem requiring integration over a curve for each point in the curve–even though the topology has to be stable (up to an energy trigger point where the particle is annhiliated), there’s a lot of degrees of freedom and the LaGrange methodology for these cases appears to be far too complex to offer analytic resolution.  While the underlying basis and geometry is significantly different, the problem of analysis should be identical to the various string theory proposals that have been around for a while.  The difference primarily comes from working in R3+T rather that the multiple new dimensions postulated in string theory.  In addition, string theory attempts to reconcile with gravity, whereas the field twist theory is just trying to create an underlying geometry for QFT.

One thing that I have come across in my reading recently is the inclusion of the mass gap problem in one of the seven millenial problems.  This experimentally verified issue, in my words, is the discovery of an energy gap in the strong force interaction in quark compositions.  There is no known basis for the non-linear separation energy behavior between bound quarks or between quark sets (protons and neutrons in a nucleus).  Dramatically unlike central quadratic fields such as electromagnetic and gravitational fields, this force is non-existent up to a limit point, and then asymptotically grows, enforcing the bound quark state.  As far as we know, this means free quarks cannot exist.  As I mentioned, the observation of this behavior in the strong force is labeled the Yang-Mills Mass Gap, since the energy delta shows up as a mass quantization.

As I categorized the available stable twist configurations in the twist field theory, it was an easy conclusion to think that the mass gap could readily be modelled by the group of solutions I call links.  For example, the simplest configuration in this group is two linked rings.  If each of these were models of a quark, I can readily imaging being able to apply translational or moment forces to one of the rings relative to the other with nearly no work done, no energy expended.  But as soon as the ring twist nears the other ring twist, the repulsion factor (see previous post) would escalate to the energy of the particle, and that state would acquire a potential energy to revert.  This potential energy would become a component of the measurable mass of the quark.

The other question that needs to be addressed is why are some particles timewise stable and others not, and what makes the difference.  The difference between the knot solutions and the link solutions is actually somewhat minor since topologically knots are the one-twist degenerate case of links.  However, the moment of the knot cases is fairly complex and I can imagine the energy of the configuration could approach the particle energy and thus self-destruct.  The linear cases (eg, photons, possibly neutrinos as a three way linear braid) have no path to self destruct to, nor does the various ring cases (electron/positrons, quark compositions).  All the remaining cases have entwining configurations that should have substantial moment energies that likely would exceed the twist energy (rate of twisting in time) and break apart after varying amounts of time.

The other interesting realization is the fact that some of these knot combinations could have symmetry violations and might provide a geometrical understanding of parity and chirality.

One thing is for sure–the current understanding I have of the twist field theory has opened up a vast vein of potentially interesting hypothetical particle models that may translate to a better understanding of real-world particle infrastructure.

Agemoz

A Particle Zoo!

December 29, 2013

After that last discovery, described in the previous post, I got to a point where I wondered what I wanted to do next.  It ended the need in my mind to pursue the scientific focus described in this blog–I had thought I could somehow get closer to God by better understanding how this existence worked.  But then came the real discovery that as far as I could see, it’s turtles all the way down, and my thinking wasn’t going to get me where I wanted to go.

So I stopped my simulation work, sat back and wondered what’s next for me.  It’s been maybe 6 months now, and while I still think I was right, I miss the fun of thinking about questions like why is there a particle zoo and whether a continuous field could form such a zoo.  While I don’t sense the urgency of the study anymore, I do think about the problem, and in the recent past have made two discoveries.

One was finding a qualitative description of the math required to produce the field vector twist I needed for my Unitary Field Twist theory, and the second was a way to find the available solutions.  The second discovery was major–it allowed me to conceptualize geometrically how to set up simulations for verification.  The problem with working with continuous vector fields required by the twist theory is that solutions are described by differential equations that are probably impossible to solve analytically.  Sometimes new insights are found by creating new tools to handle difficult-to-solve problems, and to that end I created several simulation environments to attempt numerical computations of the twist field.  Up to now, though, this didn’t help finding the available solutions.

What did help was realizing that the base form of the solutions produce stable solutions when observing the 1/r(t)^3 = 1/r(t)^2 relation–the relation that develops from the vector field’s twist-to-transformation ratio.  Maxwell’s field equations observe this, but as we all know, this is not sufficient to produce stable particles out of a continuous field, and thus cannot produce quantization.  The E=hv relation for all particles led me to the idea that if particles were represented by field twists to some background state direction, either linear (eg, photons) or closed loops, vector field behavior would become quantized.  I added a background state to this field that assigns a lowest energy state depending on the deviation from this background state.  The greater the twist, the lower the tendency to flip back to the background state.  Now a full twist will be stable, and linear twists will have any possible frequency, whereas closed loops will have restricted (quantized) possibilities based on the geometry of the loop.

For a long time I was stuck here because I could see no way to derive any solutions other than the linear solution and the ring twist, which I assigned to photons and electrons.  I did a lot of work here to show correct relativistic behavior of both, and found a correct mass and number of spin states for the electron/positron, found at least one way that charge attraction and repulsion could be geometrically explained, found valid Heisenberg uncertainty, was able to show how the loop would constrain to a maximum velocity for both photons and electrons (speed of light), and so on–many other discoveries that seemed to point to the validity of the twist field approach.

But one thing has always been a problem as I’ve worked on all this–an underlying geometrical model that adds quantization to a continuous field must explain the particle zoo.  I’ve been unable to analytically or iteratively find any other stable solutions.  I needed a guide–some methodology that would point to other solutions, other particles.  The second discovery has achieved this–the realization that this twist field theory does not permit “crossing the streams”.  The twists of any particle cannot cross because the 1/r(t)^3 repulsion factor will grow exponentially faster than any available attraction force as twists approach each other.  I very suddenly realized this will constrain available solutions geometrically.  This means that any loop system, connected or not, will be a valid solution as long as they are topologically unique in R3.  Immediately I realized that this means that links and knots and linked knots are all valid solutions, and that there are an infinite number of these.  And I immediately saw that this solution set has no morphology paths–unlike electrons about an atom, you cannot pump in energy and change the state.  We know experimentally that shooting high energy photons at a free electron will not alter the electron, and correspondingly, shooting photons at a ring or link or knot will not transform the particle–the twists cannot be crossed before destroying the particle.  In addition, this discovery suggests a geometrical solution to the experimentally observed strong force behavior.  Linked loops modelling quarks will permit some internal stretching but never breaking of the loop, thus could represent the strong force behavior when trying to separate quarks.  And, once enough energy were available to break apart quarks, the resulting particles could not form free quarks because these now become topologically equivalent to electrons.

My next step is to categorize the valid particle solutions and to quantify the twist field solutions, probably by iterative methods, and hopefully eventually by analytic methods.

There’s no question in my mind, though–I’ve found a particle zoo in the twist field theory.  The big question now is does it have any connection to reality…

Agemoz