Posts Tagged ‘electron’

Summary of Findings So Far

February 5, 2018

I took the time to update the sidebar describing a summary of the unitary twist field theory I’ve been working on.  I also paid to have those horrid ads removed from my site–seems like they have multiplied at an obnoxious rate on WordPress lately.

One problem with blogs describing research is the linear sequence of posts makes it really hard to unravel the whole picture of what I am doing, so I created this summary (scroll down the right-hand entries past the “About Me” to the Unitary Twist Field Theory) .  Obviously it leaves out a huge amount, but should give you a big picture view of this thing and my justification for pursuing it in one easy-to-get place.

The latest:  I discovered that the effort to work out the quark interactions in the theory yielded a pretty exact correlation to the observed masses of the electron, up quark and down quark.  In this theory, quarks and the strong force mediated by gluons is modeled by twist loops that have one or more linked twist loops going through the center.  This twist loop link could be called a pole, and while the twist rotation path is orthogonal to the plane of the twist loop, the twist rotation is parallel and thus will affect the crossproduct momentum that defines the loop curvature.  Electrons are a single loop with no poles, and thus cannot link with up or down quarks.  Up quarks are posited to have one pole, and down quarks have two.  A proton, for example, links two one-pole up quarks to a single two-pole down quark.

The twist loop for an up quark has one pole, a twist loop path going through the center of it.  This pole acts with the effect of a central force relation similar (but definitely is not identical to an electromagnetic force) to a charged particle rotating around a fixed charge source–think an atom nucleus with one electron orbiting around it.  The resulting normal acceleration results from effectively half the radius of the electron loop model, and thus has four times the rotation frequency and thus 4 times the mass of an electron.  The down quark, with two poles, doubles the acceleration yet again, thus giving 8 times the mass of an electron.

It will be no surprise to any of you that this correlates to the known rest masses of the electron, up quark, and down quark:  .511MeV, 2.3MeV, and 4.8MeV.

I can hear you screaming to the rafters–enough with the crackpot numerology!  All right, I hear you–but I liked seeing this correlation anyway, no matter what you all think!

Agemoz

Simulating the Universe

November 6, 2017

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

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

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

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

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

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

Agemoz

The Mystery of Particle Quark Combinations

July 27, 2017

Whenever I lose my car keys, I look in a set of established likely places. If that doesn’t work, I have two choices–look again thinking I didn’t look closely enough, or decide the keys are not where I would expect and start looking in unusual places.

There is a huge amount of data about quarks and the particle zoo, more specifically the collection of quark combinations forming the hadron family of particles. We have extensive experimental data as to what quarks combine to form protons, neutrons, mesons and pions and other oddities, many clues and data about the forces and interactions they create–but no underlying understanding about what makes quarks different or why they combine to form the particles they do–or why there are no known free quarks.

I could travel down the path of analyzing the quark combinations for insights, but I can absolutely guarantee that has already been tried by every one of the half million or so (guess on my part) physicists out there, all of whom have probably about twice my IQ. This is an extremely important investigative clue–I assume everything I’ve done has already been tried. Like the car keys, I could try where so many have already been, or I could work hard to do something unique, especially in the case of an unsolved mystery like quark combinations.

In my work simulating the unitary twist field theory, I have a very unusual outcome that perhaps fits this category–an unexpected (and unlikely to have been duplicated) conclusion. Unitary twist theory posits that there is an underlying precursor single valued field in R3 + I (analogous to the quantum oscillator space) that is directional only, no magnitude. This field permits twists, and restores to the background state I. Out of such a field can emerge linear twists that propagate (photons) the EM field (from collections of photons) and particles (closed loop twists). Obviously, photons cannot curve (ignoring large scale gravitational effects), so unitary twist theory posits that twists experiences a force normal to the twist radius. The transverse twists of photons experience that force in the direction of propagation, but the tangental twist must curve, yielding stable closed loop solutions.

Now let’s examine quarks in the light of unitary twist theory. In this theory, electrons are single loops with a center that restores to I (necessary for curvature and geometric quantization to work. The last few posts describe this in more detail). Quarks are linked loops. The up quark has the usual I restoring point, and an additional twist point that passes through it which I will call poles. This point is the twist from another closed loop. It’s not possible for this closed loop to be an electron, which has no poles other than I, but it could be any other quark. The down quark is a closed loop with two such poles.

The strong force is hypothesized to result from the asymptotic force that results when trying to pull linked quarks apart–no force at all until the twists approach each other, then a rapidly escalating region of twist crossing forces.

So far, so good–it’s easy to construct a proton with this scheme. But a neutron is a major problem–there’s no geometric way to combine two down quarks and an up quark in this model.

Here is where I have a potentially unique answer to the whole quark combinations mystery. Up to this far I can guarantee that every physicist out there has gotten this far (some sort of linked loop solution for quarks–the properties of the strong force scream for this type of solution). But it occurred to me that the reason a free neutron is unstable (about 15 seconds or so) is because the down quark in the unitary twist version of a neutron is unstable. It does have a pole left over, with nothing to fill it, no twist available. The field element at this pole is pointing at Rx, but there’s nothing to keep it there. It eventually breaks apart–and look at how beautifully the unitary twist field shows how and why it breaks up into the experimentally observed proton plus electron. Notice that the proton-neutron combination that forms deuterium *is* stable–somehow the nearby proton does kind of a Van Der Waals type resolution for the unconnected down quark pole. No hypothesis yet on the missing neutrino for the neutron decay, but still, I’m hoping you see some elegance in how unitary twist field theory approaches the neutron problem.

A final note–while I’m extremely reluctant to perform numerology in physics, note the interesting correlation of mass to the square of the number of poles. It might be supportive of this theory, or maybe just a numerical coincidence.

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

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

Geometry of the Twist Sim Math

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

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

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

 

Agemoz

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