Posts Tagged ‘vector field’

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Noncausal Interactions, part II

December 11, 2012

I want to clarify the previous posting on how I resolve the noncausal paradox in unitary twist field theory–after all, this is the heart of the current struggle to create a quantum gravity theory.  Here, I’m continuing on from the previous post, where I laid out the unitary twist field theory approach for quantum interactions.  In there, I classified all particle interactions as either causal physical or noncausal quantum, and quantum interactions fall into many categories, two of which are interference and entanglement.  These two quantum interactions are non-causal, whereas physical interactions are causal–effects of physical interactions cannot go faster than the speed of light.

Many theories have attempted to explain the paradoxes that result from the noncausal quantum interactions, particularly because relativity theory specifies that no particle can exceed the speed of light.  The Copenhagen interpretation, multiple histories, string theories such as M theory, the Pilot wave theory, etc etc all attempt to resolve this issue–but in my research I have never found anyone describe what to me appears to be a simple solution–the group wave approach.

In my previous posting, I described this solution:  If every particle is formed as a Fourier composition of waves, the particle can exist as a group wave.  Individual wave components can propagate at infinite speed, but the group composition is limited to speed c.  This approach separates out particle interactions as having two contributors:  from the composite effect of changing the phase of all wave components (moving the center of the group wave) and the effect of changing the phase of a single fundamental wave component.  If the individual wave components changed, the effect is instantaneous throughout spacetime, but there is a limitation in how quickly the phase of any give wave component can be changed, resulting in a limitation of how quickly a group wave can move.

It’s crucial to understand the difference, because this is the core reason why the paradox resolves.  Another way to say it is that when a change to a wave component is made, the change is instantaneous throughout R3–but the rate of change for any component has a limit.  An analogy would go like this: you have two sheets of transparency paper with a pattern of parallel equally spaced lines printed on it.  If you place each sheet on top of each other at an angle, you will see a moire pattern.  Moving one sheet relative to the other will move the moire pattern at some speed limited by how quickly you moved the sheet.  But note that every printed line on that sheet moved instantaneously relative to every other line on that sheet–instantaneous wave component movement throughout R3.  Note that the interference pattern changes instantaneously, but the actual movement of the moire pattern is a function of how fast the sheets are moved relative to each other–exactly analogous to what we see in real life.  This is the approach that I think has to be used for any quantum gravity theory.

Agemoz

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Noncausal interactions in the Unitary Twist Field Theory

December 10, 2012

It’s been a little while since I’ve posted, partly because of my time spent on the completion of a big work project, and partly because of a great deal of thinking before posting again (what a concept!  Something new!).  This blog has traveled through a lot of permutations and implications of the unitary twist field theory.  It starts by assuming that the Standard Model is valid, but then tries to create an underlying geometry for quantization and special relativity.  This twist vector field geometry is based on E=hv, and has worked pretty well–but when we get to entangled particles and other noncausal aspects of quantum theory, I’ve needed to do some new thinking.  While the noncausal construct is easily built on group wave theory (phase information propagates at infinite speed, but group Fourier compositions of waves that make up particles are limited to speed c), there are significant consequences for the theory regarding its view of the dimensional characteristics of the 3D+T construct of our existence.

As I mentioned, the unitary twist field theory starts with E=hv, the statement that every particle is quantized to an intrinsic frequency.  There really is only one way to do this in a continuous system in R3+T:  a twist within a background state vector field.  Twists are topologically stable, starting from the background direction and twisting to the same background direction with an integral turn.  Quantization is achieved because partial turns cannot exist (although virtual particles exist physically as partial turns for a short time before reverting back to the background state).  With this, I have taken many paths–efforts to verify this pet theory could really work.  For example, I tested the assumption of a continuous system–could the field actually be a lattice at some scale.  It cannot for a lot of reasons (and experiments appear to confirm this), especially since quantization scales with frequency, tough to do with a lattice of specific spacing.  Another concern to address with twist field theory occurs because it’s not a given that the frequency in E=hv has any physical interpretation–but quantum theory makes it clear that there is.  Suppose there was no real meaning to the frequency in E=hv–that is, the hv product give units that just happen to match that of frequency.  This can’t be true, because experimentally, all particles quantum interfere at the hvfrequency, an experimental behavior that confirms the physical nature of the frequency component.

So–many paths have been taken, many studies to test the validity of the unitary twist field theory, and within my limits of testing this hypothesis, it seems so far the only workable explanation for quantization.  I believe it doesn’t appear to contradict the Standard Model, and does seem to add a bit to it–an explanation for why we see quantization using a geometrical technique.  And, it has the big advantage of connecting special relativity to quantum mechanics–and I am seeing promising results for a path to get to general releativity.  A lot of work still going on there.

However, my mind has really taken a big chunk of effort toward a more difficult issue for the unitary twist field theory–the non-causality of entangled particles or quantum interference.  Once again, as discussed in previous posts here, the best explanation for this seems pretty straightforward–the particles in unitary twist field theory are twists that act as group waves.  The group wave cluster, a Fourier composition, is limited to light speed (see the wonderful discovery in a previous post that any confined twist system such as the unitarty twist field theory must geometrically exhibit a maximum speed, providing a geometrical reason for the speed of light limit).  However, the phase portion of the component waves is not limited to light speed and resolves the various non-causal dilemmas such as the two-slit experiment, entangled particles, etc, simply and logically without resorting to multiple histories or any of the other complicated attempts to mash noncausality into a causal R3+T construct.

But for me, there is a difficult devil in the details of making this really work.  Light-speed limited group waves with instantaneous phase propagation raises a very important issue.  Through a great deal of thinking, I believe I have shown myself that noncausal interactions which require instantaneous phase propagation, will specify that distance and time be what I call “emergent” concepts–they are not intrinsic to the construction of existence, but emerge–probably as part of the initial Big Bang expansion.  If so, the actual dimensions of space-time are also emergent–and must come from or are based on a system with neither–a zero dimensional dot of some sort of incredibly complex oscillation.  Why do I say this?  Because instantaneous phase propagation, such as entangled particle resolving, must have interactions in local neighborhoods that do not have either a space or time component.  Particles have two types of interactions–ones where two particles have similar values for R3+T (physical interactions), and those that have similar values only in phase space.  In either case, two particles will affect each other.  But how do you get interactions between two particles that aren’t in the same R3+T neighborhood?  Any clever scheme like the Standard Model or unitary twist field theory must answer this all important question.

Physicists are actively trying to get from the Standard Model to this issue (it’s a permutation of the effort to create a quantum gravity theory).  As you would expect, I am trying to get from the unitary twist field theory to this issue.  Standard Model efforts have typically either focused on adding dimensions (multiple histories/dimensions/string theories) or more exotic methods usually making some set of superluminal assumptions.  As mentioned in previous posts, unitary twist field theory has twists that turn about axes in both an R3 and a direction I that is orthogonal to R3 in time.  Note that this I direction does not have any dimensional length–it is simply a vector direction that does not lie in R3.  When I use the unitary twist field theory to show how particles will interact in R3+T, either physically or in entangled or interfering states, those particles would simply have group wave constructs with either a matching set of R3+T values (within some neighborhood epsilon value) or must have matching phase information in the I space.  In other words, normal “nearby”  interactions between two particles happen in a spacetime neighborhood, but quantum interference interactions happen in the I space, the land that Time and Space forgot.  There is no dimensional length here, but phase matches allow interaction as well.  This appears to be a fairly clean way to integrate noncausal behavior into the unitary twist field theory.

Obviously, there are still things to figure out here, but that is currently the most promising path I see for how unitary twist field theory will address the noncausal interaction construct issue.

Agemoz

 

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Experimental Confirmation of Lattice-Free Spacetime

September 1, 2012

In my previous post, I posited that spacetime cannot be a lattice at Planck scale distances, and by sheer coincidence, this completely different experimental report also confirms the likelihood that spacetime is smooth at this scale:

http://www.space.com/17399-gamma-ray-photons-quantum-spacetime.html

A smooth spacetime means that Planck scale lumpiness (a lattice of one of the types I describe in the previous post) will not explain quantization.  I suspected that anyway, because quantization is scale independent.  Low energy photons are quantized over distances that are enormously vast (hundreds of orders of magnitude) compared to Planck scale distances, so I did not see how a lattice could induce that quantization.

The field twist is also scale independent, so is another nice arrow in the quiver for unitary twist field theory.  But I’m grappling with a big problem as I develop the specular simulator for the unitary field twist theory.  The probability of electron motion is affected by its ability to self absorb a virtual photon, and this probability is directly proportionate to the fine structure constant.  I believe that this number is the square of the probability to emit and the probability to absorb, making each have about an 8 percent chance of occurring.  Physicists have absolutely no clue why this probability is what it is.  QFT gives no guidance but uses the experimentally determined value of interaction probability as a foundation for every quantum interaction of particles and fields.

As usual, I am trying to find a geometrical reason that the unitary field twist theory might give that probability–some ideas, but nothing obvious.  I have to figure something out before I can even start constructing the specular sim.

Agemoz

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Lattice fields and Specular Simulation (latest work)

August 25, 2012

The latest work on the twist model is proceeding.  This work makes the assumptions noted in previous posts–EM interactions are mediated by photons as a quantized linear field twists.  The current work assumes these photons comprise the macroscopic electrostatic and magnetic field,  are unitary, and that they are sparse (do not interact).  It assumes that the twist has a common imaginary axis and three real dimensions on R3, similar but not the same as the QFT EM field, which is a complex value on R3 (t is assumed in both cases).  Electron-photon interactions occur when a twist ring captures a linear twist and absorbs it.  I am assuming that a photon twist is magnetic when the real axis of the twist is normal to the real dimension direction of travel, and is electrostatic when the real axis of the twist is tangent to the direction of travel (note how relativistic motion will alter the apparent axis direction, causing the expected shift of photons from electrostatic to magnetic or vice versa).

This set of assumptions creates a model where the linear twist of the photon will affect a twist ring electron in different ways depending on the photon twist axis direction.  Yes, this is a rather classical approach that ignores the fact that quantum interactions are probability distributions, among other things.  My approach is to create a model simulation environment to test the hypothesis that quantization can accurately be represented by field twists, the foundation of the unitary twist field theory.  It does not currently include entanglement, which I represent as the assumption that field twist phase information is instantaneous but that particles (twists) are group wave assemblies that propagate no faster than the speed of light.

These assumptions require that I make changes to my current simulator, which is a lattice approximation of a continuous vector field twist.  I was able to show in that simulator that a continuous twist solution could not work due to the unitary field blocking effect.  From that (and from QFT), I concluded that the twist field must be sparse and specular, where interactions are mediated by linear twist photons that do not interact.  I cannot use my existing simulator for this model but must make a new version, which is underway.  It will take a while so my posts will become less frequent until I get this working.

However, since I am now going away from a lattice simulator to a sparse model simulator, it did make me think about lattices as a representation of existence, and I concluded that that cannot be.  I have often seen theories that our universe is a quantum scale lattice of Planck length.  This supposedly would explain quantization, but I don’t think it works–the devil is in the details.  If the lattice is periodic, such as an array of cube vertexes or tetrahedral vertices, then there should be angles that propagate photons differently than others.  If our existence is spinning on a periodic lattice, we should see harmonics of that spin as background noise.  Within the range of our ability to detect such “radiation” from space, neither are happening.

So, suppose the lattice is not periodic but is a random clustering of vertexes, which solves the problem of periodicity causing background frequencies.  In that case, I would expect that photon propagation would have velocity variation as it propagated through varying spacing of vertexes.  There would have to be an upper bound to the density of vertexes to ensure apparent constant speed, and I struggle to think what would enforce that bound.  This is probably the most workable of the lattice ideas, but due to the necessity of a vertex spacing constraint, there would have to be an upper limit to the allowable energy of a photon, something we have no evidence for.  At this point, I think there is no likelihood that existence can be described as a lattice.  That hypothesis is attractive because we can easily imagine a creator God could build a computer that could most easily create a model of existence using a lattice of some form.  But even though the Planck length lattice is far too small for us to detect directly, I don’t think the evidence points that way.  (Side note:  it’s so interesting to look at early literature to see the historical evolution of what people thought formed the underlying basis for our existence–early on, God creating and controlling a mechanical model, then universe models were complex automated assemblies of gears and pullies, then the steam-engine or steam-punk type of machine, then mechanical computing engines, and now computer program driven machines simulating a lattice…  What is next? !)

Back to the lack of evidence for an underlying lattice to our existence.  This is a more important  realization than it might appear, especially from a philosophical standpoint.  If there was evidence that the universe was built on a lattice, that would strongly imply creation by a being, because a lattice is an underlying structure and constraint.  Evidence that there is no lattice, which is what I think I am seeing, would imply that there is no higher being because it is hard for me to imagine constructing a world without a lattice.  Of course, it would only be a mild implication, because my ability to imagine how a universe could be constructed without a lattice is limited.  Nevertheless, it is a pointer in the direction of existence coming from nothing rather than being constructed by a God.

Pretty interesting stuff!  More to come as the new simulator work gets underway.
Agemoz

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Unitary Continuous Fields Cannot be Linear

June 11, 2012

Well, after considerable thought on that surprising revelation of the previous post, I realized that it is true only for unitary fields.  The QFT solution can be both continuous and linear, because the magnitude of an EM field is not constrained.  I thought of the case of a rogue wave on water, and realized that the median plane symmetry problem results from the  ability of the unitary field to block information from passing.  A unitary field that has a stable state over any surface will block information from passing through.  The median plane between two oppositely charged particles, by symmetry, has to consist of background state vectors, but the field that QFT resides in is non-blocking–think of the rogue wave on water analogy.  One wave can ride on top of another because the magnitude is not constrained, and thus is not blocking.  Information from one charged particle will make it through the median plane to the other particle–but NOT in my unitary twist field theory.

This is a show-stopper for unitary twist field theory.  Unitarity (of field magnitude) is necessary to geometrically create quantization.  I see two options:  either my original premise that the field is sparse, or something other than field magnitude is constraining twist magnitude.

Agemoz

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Continuous Fields Cannot be Linear

June 10, 2012

A shocking revelation for me, in all my years both as a professional electrical engineer and as an amateur physicist.  I realize I have zero credibility out there with anyone, but at least for myself, I have discovered something fundamental about fields that I did not know.  Perhaps if I were a mathematician I would have worked this out.  Nevertheless, it is quite provable in my mind, and has enormous impact on how I must model the two particle interaction, whether by QFT or unitary twist field theory.

The concept of linear central force fields means that multiple potential sources create the field by means of linear superposition.  If you have two sources of potential, the effect on the field at any point is the sum of the effect due to either one.  There are potential corner cases such as if the potential is infinite at the point source, but in every finite potential situation, the field is the sum of all sources at that point.  Electrostatic fields are supposedly both continuous and linear, but this cannot be at the quantum scale.

I have been discussing in previous posts the concept of a median plane between two charged sources, and particularly enlightening was the attraction case of a positive and negatively charged particle.  Between these two particles will be a median plane whose normal runs through both particles.  This median plane can have no absolute potential (relative to the electrostatic field potential at infinite distance).  This field cannot pass any information, even about the existence of, one charged particle through this median plane.  In fact, it is well known in electrostatics that if you put a metal plane between two particles and ground it, you will get the same charge field distribution as if the second particle wasn’t there–it cannot be determined if the second particle actually exists or not.

The only way a field can pass information across this median plane is if the field is not continuous.  If the field  is created by a spaced array of quantized particles, such that they never, or almost never, interact, then the effect of the field can be made linear.  Indeed, shooting real photons at each other could collide, but that is exceeding rare, and modeling the field by photons, virtual or real, in either QFT or unitary twist field theory,  would produce a linear superposition of fields.  But there is no question now in my mind that if I simulate this, I cannot assume a continuous electrostatic field, such a thing cannot exist.  This field has to be almost entirely empty, with only very sporadic quantized particles, then I can see how linearity would be possible.  Every quantized particle that interacts with a quantized particle from the other source will distort the appearance of linearity, so the fact that deviations from linearity are experimentally unmeasurable strongly points to a extremely sparse field component density.

I had thought that QFT virtual particles could construct a continuous field in a Taylor or Fourier series type of composition, but it is clear that it cannot.  The QFT virtual particles must be exceedingly sparse, just like the twists in unitary twist field theory.  It also suggests that QFT virtual particles would have to clump in some way in order for localized neighborhoods in the field to obey conservation.

Now I see a workable model for twists.  The median plane problem cannot exist if the field is not continous.

Agemoz

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What Electrostatics Tells Us

June 7, 2012

I am attempting to work out a viable unitary twist field approach for the attraction and repulsion of charged particles.  I’ve discovered symmetry requires that the vector field would have to have a median plane where there is only a background state, which leads to problems describing how one particle would communicate via the field to another particle (so that the particles, if identically charged, would experience a force of repulsion.   It appears that this problem would also be experienced by QFT since it mediates by virtual photons, which are best described as partial field components that mathematically sum to get the desired result, but individually do not obey various properties such as conservation of energy or momentum.

It will be instructive and potentially guiding to look at the two particle system from an electrostatics point of view.  Here are two figures, one for the two-electron case of repulsion, and one for the electron-positron case of attraction.  Note that the receiving particle experiences a force in the direction that is closest to the ground state potential in both cases.  If the field adjacent to a particle is radially unequal, the particle tries to move so that the field is closer to the ground state on every side of the particle.  It is interesting that in one case (the two electron repulsion state) the median plane is *not* at the ground potential, but in the attraction state, it is.  I see that from an electrostatics point of view, the median plane state, whether background or not, does not affect particle communication, whether by virtual photons in QFT or by bend of the imaginary vector in unitary twist field theory.  It is the field neighborhood, particularly the unequal, or unbalanced, aspect of the field near a particle that has to be responsible for forces on the particle.  It is not clear if the force is due to trying to minimize the overall field neighborhood to be close to the ground state, or if the force is merely trying to equalize the neighborhood (in fact, it is likely that both explanations mean the same thing given the relative nature of electrostatic potential).

The field near an electron when near another electron. Note how the force on a particle moves it toward a more equal field neighborhood.

 

Electrostatic field for the electon-positron attraction case. Once again, the particle moves to a field neighborhood closer to the ground state.

I will think on this, this means something for both QFT and unitary twist field theory–but exactly what is not clear in my mind yet.

Agemoz

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Symmetry Constraint on Charged Particle Geometry

June 5, 2012

In working out the details of how the complex unitary twist field would work on a system of two charged particles, I came across a very important discovery.  This holds true even if you don’t believe in the unitary twist field theory tooth fairy, even if you only think in terms of QFT virtual particles.

If you have two identical charged particles such as electrons separated by a distance r, symmetry geometry requires that the interaction cannot be static.  Any continuous static field in this system must have a plane perpendicular to the path between the particles that is the same as if there were no particles–that is, identical to the background field.  For standard QFT, this plane cannot have an electrostatic potential relative to the field out at infinity.  For the Complex Unitary Twist Field theory, this plane must be at the background field state in the imaginary dimension.

 

But if this is true, then that becomes a point where the behavior of one particle cannot affect the other–there is no field potential.  I won’t go into the QFT case, but the analogy is similar when I try to work a geometric solution in the twist field case.  I had found a way that the bend of the twist field imaginary background vector would specify the effect of charge on the second particle.  But this bend has to be symmetric in this system, with a plane in the middle where the bend is the same as the overall background field with no charges.  Oops–the problem shows up where there is no way to communicate the bend effect to the second particle without creating a paradox–an impossible field situation.

 

Any static field between two identical charged particles must have a plane between them that cannot pass the charge effect. The charge effect must pass dynamically across this plane

I said, uh-oh–the unitary twist field can’t work this way with bends.  Then I realized this has to be true for QFT too!  The symmetry of the system says that there is no way that the charged particle force can be conveyed within a static field.  There has to be something dynamic passing through the plane–virtual photons for QFT, and probably some type of background vector motion for the unitary twist field.  These two theories have to converge, and symmetry is going to severely constrain what has to be happening across the plane.  Even if you ignore unitary twist field theory, and just make the statement that QFT claims that virtual photons are not real (and unitary twist field theory specifies virtual photons as partial field twists that don’t complete but revert back to the background vector state), this symmetry problem forces the virtual photons to have both a physical field property and a property of motion.

Agemoz

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Vector Field Neighbors

May 28, 2012

I have been thinking a lot about the latest work on twist fields.  It has a lot of good things about it, it appears to successfully add quantization and special relativity to a vector field.  It opens up a possible geometry for the particle zoo.

But if this is really going to be workable or provable, I’m going to have to create a simulation, and that has to start with a mathematical basis.  And that wont come until I understand how the vector field operates on neighbors.  Yes, the unitary twist field has the right configuration to make things work, but the actual quantitative behavior is completely dependent on how the field propagates in space and time.  Up to now, the model looks like a sea of rotating balls, each with a black point spot that normally points in an imaginary direction, but can temporarily point in a real space formed by three real basis vectors orthogonal to the imaginary direction.  (Note that this discrete representation simplifies visualization, but there is no reason that the correct solution can’t be continuous, in fact I suspect it is).  If there is a connection between adjacent ball directions, the necessary quantization, stable particle formation, and special relativity behaviors will result.  However, a quantitative specification of these behaviors is entirely and completely specified by the nature of this neighborhood connection.

How does one ball affect its immediate neighbors?  Can a ball affect nearby balls that are not immediate neighbors?  Can a ball move in 3D or is everything that happens solely a function of ball rotation in place?  I see only two possible connections, one I call gear drive (a twist motion induces an adjacent ball in the twist plane to twist in the same (or opposite) direction) and the other I call vortex drive (a ball twist causes an adjacent ball on the twist axis to turn in the same or opposite direction).  Both of these forces could also induce normal twists, for four possible neighbor connections.  Which, or what set, of these neighbor interactions are valid descriptions of how balls move?  And what mathematically is the exact amount of dispersion of twist to neighbors?  Is the field continuous or can discontinuities occur?

Certainly the requirement for continuity is a powerful constraint, allowing discontinuities from the imaginary to any of the real axes, but prohibiting discontinuities between the real axes or in the imaginary direction.

These are the questions I have been pondering a lot.  I have come up with a nice framework but now I have to work out just how the vector field neighbor connection must happen before I make any further progress.

Agemoz

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Fine Structure Constant Hunting

May 1, 2012

Built into current QED (quantum electrodynamics) is the QFT process of pertubative accumulation of virtual photons.  Each possible virtual photon term is assigned a unitless  probability (actually,  probability amplitude capable of interfering with other terms)  of occurrence called the fine structure constant.   Searching for the reason for the value of this constant is a legendary pursuit for physicists, Feynman made the famous comment about it:

It’s one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man.

All kinds of research, study, and guesses have gone into trying to figure out why this number is what it is, and I can guarantee you this is a fruitless pursuit.  Think about it, there have been maybe millions of physicists over the last 100 years, the vast majority with IQs well north of 150, all putting varying amounts of effort into trying to figure out where this number comes from.  If none of them have come up with the answer yet, which they haven’t, the odds of you or I stumbling across it is certifiably close to zero.  That is an effort that I consider a waste of time. For one thing, this is a no-numerology physics blog.

One bad trait of many amateur physicists is to theorize answers by mixing up various constants such as pi, e, square roots, etc, etc and miraculously come up with numbers that explain everything.  Note, no knowledge required of the underlying science–just mix up numbers until something miraculous happens, you get a match to an actual observed physical constant (well, so close, anyway, and future work will explain the discrepancy.  Yeah… riiiight).  Then you go out and proselytize your Nobel prize winning theory, to the annoyance of everyone that sees what you did.  This is also called Easter egg hunting, and really is a waste of time.  Don’t do that.  Hopefully you will never ever see me do that.

Nevertheless, physicists are desperate for reasons why the fine structure constant is what it is, and all kinds of thought, analysis, and yes, numerology, have already gone into trying to find where it comes from.  Why do I insert a post about it in the midst of my step by step procedure of working out the role of unitary twist field theory in the electron-photon interaction?  Because, as I mentioned, the fine structure constant is fundamental to mathematically iterating terms in the QFT solution to this particular QED problem.  It stands to reason that an underlying theory would have a lot to say about why the fine structure constant is what it is.

Unfortunately, it’s clear to me that it’s not going to be that simple.  Pertubative QFT is exactly analogous to the term factors in a Taylor series.  You can create amazing functions from a polynomial with the right coefficients–I remember when I was much younger being totally amazed that you could create trigonometric functions from a simple sum of factors.  Just looking at the coefficients really tells you very little about what function is going to result, and that is exactly true in pertubative QFT.  The fine structure constant is your coefficient multiplier, but what we don’t have is the actual analytic function.  The fine structure constant has a large number of ways to appear in interaction computation, but the direct connection to real physics is really somewhat abstract.  For example, suppose I could geometrically explain the ratio of the charge potential energy between two electrons separated by distance d with the energy of a photon who’s energy is defined by that same distance d, which is defined as the fine structure constant value.  But I can’t.  The fact that it takes 137 of these photons (or equivalantly a photon with 1/137 the distance) to hold together two electrons to the same distance is not physically or geometrically interesting, it is a numerology thing.  Pursuing geometric reasons for the 137 is a lost cause, because the fine structure constant is a coefficient multiplier, an artifact of pertubative construction.

Nevertheless, I do see a way that the fine structure constant might be derived from the unitary twist field theory.  Don’t hold your breath–obviously a low IQ type like me isn’t likely to come up with any real discovery here.  Even so, I should follow through.  Here’s the deal.  Take that picture in the previous post, the second “Figure 2” that shows the effect of bending the imaginary vector.  I need to go back and edit that diagram, the circle ring is the twist ring electron, and fix that to be fig 3.  Anyway, the force on that electron ring is going to be determined by one of two things–the amount of the bend or the difference delta of the bend on one side of the ring versus the other.  The bend will gradually straighten out the further you get from a remote charge.   This computation will give the motion and hence the inertia of any self-contained twist (only the linear twist, the photon, will experience no net force from an imaginary bend).  This will be a difficult computation to do directly–but remember we must have gauge invariance, which leads to my discovery that a ring with an imaginary bend must have a frame of reference with no bend.  Find this frame of reference, and you’ve found the motion of the electron ring in the first frame of reference–a much easier computation to do.  This is real analysis and logical thinking, I think–not Easter egg hunting.

Agemoz

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