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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.

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Principle of Replication and the Particle Zoo

June 27, 2014

I am continuing to develop the new twist simulation, and hope to get first runs maybe in the next several weeks or months.  It’s been a good exercise because it has forced me to be very clear and explicit about how the model works.  To paraphrase Feynman very loosely, “the truth does not lie”–I can’t just make the theory work just because I want it to.  But the exercise has been good because it’s clarified some important concepts that are distributed all throughout this blog, and thus a casual reader is going to have a very difficult time figuring out what I am talking about and whether there’s any real substance to what I’m thinking.  While there is a *lot* of thinking behind this approach, here are the fundamental concepts that are driving how this simulation is being built:

The twist field concept starts with E=hv for all particles, and this is a statement of quantization.  For any given frequency, there is only one possible energy.  If we assume a continuous field, the simplest geometrical model of this is a full twist in a field of orientations.  E=hv implies no magnitude to the field, you can imagine a field of orientable dots within a background state direction–quantization results when only a complete rotation is permitted, thus implying the background default direction that all twists must return to.

The second concept is a duality–if there is a vast field of identical particles, say electrons, the dual of exact replication is a corresponding degree of simplicity.  While not a proof, the reason I call simplicity the dual of replication is because the number of rules required to achieve massive repeatability has to withstand preservation of particles in every possible physical environment from the nearly static state–say, a Milliken droplet electron all the way to electrons in a black hole jet.  The fewer the rules, the fewer environments that could break them.

The third concept is to realize causality doesn’t hold for wave phase in the twist model.  Dr. Bell proved that quantum entanglement means that basic Standard Model quantum particles cannot have internal structure if causality applies to every aspect of nature.  The twist model says that waves forming a particle are group waves–a change in phase in a wave component is instantaneous across the entire wave–but the rate of change of this phase is what allows the group wave particle to move, and this rate of change is what limits particle velocity to the speed of light.  This thus allows particles to interfere instantaneously, but the particle itself must move causally.  Only this way can a workable geometry for quantum entanglement, two-slit experiments, and so on be formed.

Within these constraints the twist model has emerged in my thinking.  A field twist can curve into stable  loops based on standard EM theory and the background state quantization principle.  A particle zoo will emerge because of a balance of two forces, one of which is electrostatic (1/r*2, or central force) and the other is electromagnetic (1/r*3).  When a twist curve approaches another twist curve, the magnetic (1/r*3) repulsion dominates, but when two parts of a curve (or separate curves) move away from each other, the electrostatic attractive force dominates.  Such a system has two easily identifiable stable states, the linear twist and the ring.  However there are many more, as can be easily seen when you realize that twist curves cannot intersect due to the 1/r*3 repulsion force dominating as curves approach.  Linked rings, knots, braids all become possible and stable, and a system of mapping to particle zoo members becomes available.

Why do I claim balancing 1/r*2 and 1/r*3 forces exist?  Because in a twist ring or other closed loop geometries, there are a minimum of two twists–the twist about the axis /center of the ring, and the twist about the path of the ring–imagine the linear twist folded into a circle.  Simple Lorentz force rules will derive the two (or more, for complex particle assemblies such as knots and linked rings) interacting forces.  Each point’s net force is computed as a sum of path forces multiplied by the phase of the wave on that path–you can see the resemblance to the Feynman path integrals of quantum mechanics.

Soon I’ll show some pictures of the sim results.

Hopefully that gives a clear summary of why I am taking this study in the directions I have proposed.

Agemoz

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Finally–A Particle Twist Solution Methodology

April 8, 2014

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

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

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

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

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

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

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

Agemoz

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

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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

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Twist Ring Acceleration Sim Results

July 7, 2013

The initial measurements are in, and still look promising.  To recap, one stable form of the twist in the Unitary Twist Field theory is in a ring where the twist curves on itself as a combination of the electrostatic 1/r^2 and magnetic field 1/r^3 strengths (this ratio is defined by the fine structure constant).  There are potentially many solutions, but only one possible planar solution other than the linear twist–the twist ring.  I posited that if this were true, placing a twist ring in an external electrostatic field would cause the curvature to vary depending on the distance from a source charged particle.  Computing this analytically is a challenge, yielding a 24 term LaGrange differential equation of motion, so I decided to do this iteratively.

This was a lot easier, and has yielded promising results that suggest I might be on the right track.  The initial sims showed correct qualitative behavior with repulsion or attraction depending on the external field polarity, and I could visually see the correct acceleration behavior.

Next, I added quite a bit of numerical analysis code to the sim of the twist ring path, and was able to verify that a linearly varying field will cause the path of motion to accelerate at a constant rate–and that this acceleration is proportionate to the strength of the field within some level of accuracy.  Much more needs to be done to confirm these measurements, but the initial results show that this type of model (twist ring) will give electrostatic behavior.  Here’s a pic where you can see the displacement with time (the parabolic curve).  Following that, you’ll see my initial data set along with the Mathematica solution for the first three crossing points of the parabola–more computations will be done to establish that this really is a parabola.

From here, I will see if the correct mass results from the ratio of the strength of the 1/r^2 component to the 1/r^3 component in an electron.  There should also be other twist loop solutions possible in 3D, I’ve limited myself to the easiest (planar) solution to start.

Agemoz

twist_ring_measured_repel

Here’s the initial sim time crossing points, along with the Mathematica solve solutions:

Running the Unitary Field Twist simulation to numerically derive the change in x as
a field is asserted on a 1/r^2 - 1/r^3 twist ring.  The field affects the curvature
(magnetic component).  The result generates the qualitative expected movement as if
there was a central force effect (q^2/r^2).  These results are an attempt to measure
the acceleration factor as a function of relative field strength (magnetic to
electrostatic).

Since the equations of motion due to the 1/r^2 - 1/r^3 equation in a linear field
were 24 parameter LaGrange equations of motion, I attempted to get an analytic
solution by examining the iterative numerical results.

Here is the result for 1:1 (1/r^2 to 1/r^3) field strength at distance 10 with
radius 1.5 and ring velocity 0.10545 and source field strength factor .0005.
The sim showed a cycle time of about 90.

field strength 0.00025
22:  11.457            (doesnt start at zero because cycle max x is not at zero)
14545: 15
25213: 20
34448: 25
43234: 30

using the first 3 terms in quadratic solution, I get
x = 8.92 10^9 * t^2 + .000114 * t + 11.455

field strength 0.0005
22:  11.457            (doesnt start at zero because cycle max x is not at zero)
10421: 15
17772: 20
24406: 25
30503: 30

using the first 3 terms in quadratic solution, I get
x = 1.912 10^8 * t^2 + .000141 * t + 11.454

field strength 0.0010
22:  11.457            (doesnt start at zero because cycle max x is not at zero)
7372: 15
12572: 20
17233: 25
21626: 30

using the first 3 terms in quadratic solution, I get
x = 3.82 10^8 * t^2 + .000200 * t + 11.453

More terms need to be computed, but there is a clear linear proportionality to the 
acceleration component of the curve, consistent with the expected electrostatic
relation of field strength proportionate to the acceleration of the destination
particle.

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Quantized Fields

July 11, 2012

No, I’m not going to talk about the Higgs boson.  Well, except to make one reference to it as far as my work is concerned:  it’s a new (but long predicted, and not yet shown to actually be the Higgs) particle and field to add to the particle zoo.  A step backwards, in a way–I think our understanding will advance when we find underlying connections between particles and fields, but adding more to the pile isn’t helpful to a deeper understanding.  Oh, and that the Higgs approach adds an inertial property to mass particles, a mechanism caused by a drag effect relative to the field.  That matters to my work because it appears to be a different mechanism than how I propose mass gets attached to particles.  Yes, it calls into question the validity of my work, but so do a whole bunch of other things.  I’m proceeding anyway.

I got some interesting results from some simulation efforts–a second stable state with three components.  It is particularly interesting because it appears to settle into a three way braid–and more importantly, seems to progress to faster and faster speeds–limited to the speed of light.  Not sure why it does that, more investigative work to determine if this is a model problem or real behavior of the three twist solution.  Does make me think of a neutrino, but that’s pure speculation.  Here’s some curious pics.  These sim has all three twists with equal momentum.  I’m going to set one or two twists to double momentum and see what happens.  I also need to fix the attraction/repulsion in these cases, currently these cannot represent reality because of three charge values instead of two in real life (+,-)–but you can see what a fertile ground the twist model shows.

This 3D simulation of a three twist interaction stabilizes into three way braid

This 3D projection of a three way twist array eventually stabilizes into a closely interacting stable entity

But the real work I’ve been doing lately is not these sims–instead, it’s my thinking about the continuous property of fields and quantization.  If the unitary twist field is continous, it is blocking–a twist bend cannot propagate through another twist bend if it is separated by a plane with background state orientation–another way of saying a continuous unitary field cannot be linear.  Real EM fields are linear.  Are they also continuous?  At first, I said no, they can’t be,  since real EM fields should be blocking as well.  But then I realized that unlike the unitary twist field, real EM fields are linear (effectively can pass through each other) because the field of one source can add on top of another field from another source.  In this case, the magnitude of the field at a given point is not constrained, so this is what makes the fields of QFT work, that is, be continuous and also linear.

Mathematically, that is possible–but now I believe that even the QFT model of fields such as the EM field cannot be continuous for a different reason, field quantization.  QFT says you cannot extract any energies from the field that don’t meet the quantization constraint.   Unitary twist fields will derive this quantization because only full twists from and to the background field direction are possible and topologically stable.  Any partial twist must return to the background state and will dissipate.  Here’s why I now think that any quantized field cannot be continuous.  Let’s talk unitary twist field first.  I had a groundbreaking discovery with unitary twist fields a month or so ago when I found that if this field is continuous, it is possible to create a situation where it blocks passage of field states.  If you put two oppositely charged particles separated by a distance r, symmetry requires that a plane separating the two particles must have zero twist, and thus one particle would see zero twist at distance r/2–the same thing it would see at an infinite distance.  The problem is, then there is a situation where there is no difference from the uncharged background state and the first particle cannot respond differently than if there were no nearby charged particles.  The bisecting plane with zero bend acts as a barrier preventing or blocking  the other particle from affecting the first.

OK, that was the unitary twist field case.  Now the QFT case doesn’t have this problem since the bisecting plane holds magnitudes, not the zero background state of the unitary twist field.  Therefore, the first particle can be subject to the effects of the second particle since the bisecting plane no longer blocks.

But, QFT fields have a different problem that still says it can’t be continuous.  A non-continuous field is the saving grace that might allow unitary twist fields to be a valid underlying solution–if the field is not continuous, but is granular.  If the QFT field has to be granular, then unitary twist field theory becomes a valid underlying architecture for QFT (of course, other constraints or problems might invalidate unitary twist theory, but right now granularity allows the unitary twist field to be non-blocking, otherwise there’s no way it could work).  In the granular case, a given epsilon neighborhood sees these passing components going from one particle to the other without blocking.  Thus, any quantized field such as QFT fields or unitary twist fields will be linear (and div and curl will be zero) if and only if the granular parts do not interact.

As I continued down this path of thinking, I began to realize that whether the QFT EM field or the unitary twist field are correct real world descriptions, neither of them can be continuous.   You could argue that the field itself is continuous but the particles that are extracted from the field are quantized, but this idea has serious fails if you create a field from a limited number of quanta.  Inductive reasoning is going to force either model of the field to be composed of granular components–it will not be possible to create a field from two quanta that is continuous because the information of the quanta is preserved.  Why do I say that?  Because a two quanta field that is continuous may only release a quantized particle from the energy of the field.  If the quanta information is preserved in the field, I cannot see any way that a definition of continuous could apply to this field.

Now, if the field is composed of quanta that do not interact, then linearity will result simply by the ability of packing more or less quanta into a set epsilon volume.  Linearity means that the quanta cannot interact (otherwise magnitudes at some points will not sum, a linearity requirement).  Therefore, the quantized field can be considered granular and infinitely sparse, that is, no constructive summation of fields can cause loss of total volume density of quanta.  In other less obtuse and verbose words, the quantized field must not be continuous and must consist of non-interacting quanta, regardless of whether we are talking unitary twist field or QFT EM fields.  If you buy this, then the twist field is not blocking and is still a potentially valid description of reality.  If this is true, then the geometrical basis for quantization comes from the twists returning to a background state, a conclusion that QFT currently does not provide, and thus  unitary twist field theory work is still a worthwhile effort.

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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Unitary Twist Field Dreams

April 12, 2012

I’m going to do something a little different in this post.  It’s every amateur’s dream to be taken seriously by the professionals, so I’m going to have a little fun today and pretend that a physics professor looked at this and decided to be nice (he just got a big grant approved for his research and was feeling unusually magnanimous) and go over it with me.  This is not for real–a real professor would almost certainly not give the time of day to an amateur’s ideas–it just is too much work to dig in and be precise about why any set of ideas wont work, nevermind those from someone who hasn’t spent a lifetime dedicated to this field of study.  But, amateurs all get their Walter Mitty dreams, and this is mine–and this is my blog, so I can do what I durn please here!  Actually I don’t care if I’m recognized for anything I come up with, but it’d be cool if some part of it turned out to be right.  Anyway, here goes.

Prof Jones:  Hello, what do you have for me?

Me:  I have this set of ideas about how particles form from a field.

Prof Jones:  You have a theory [suppresses noisy internal bout of indigestion]

Me:  Well, yes.  I think there is a geometrical basis for quantum and special relativistic behavior of particles.

Prof Jones:  We already have that in QFT.  Are you adding or revising existing knowledge?  I’m really not interested in someone telling me Einstein or anybody else was wrong…

Me:  I believe I am adding.  I have tried to take a overall high-level view of what is now known, especially the E=hv relation and the special relativity Lorentz transforms, and see some conclusions that make sense to me

Prof Jones:  Well, I’ve had a lot of ideas thrown at me, and they are a dime-a-dozen.  It’s not the idea that’s important but the logic or experiment that supports it.  A good theory explains something we don’t understand and allows us to successfully predict new things we otherwise would not find.  Is yours a good theory?  Do you have supporting evidence or experiment?  Can you predict something I don’t already know with QFT?  Does it contradict anything I already know?  If you can’t pass this complete criteria, the theory isn’t going anywhere but the round file.

Me:  I don’t have anything that proves it.  I don’t have anything it predicts right now but I see some possibilities.  I don’t think it contradicts anything, but there are some question marks.

Prof Jones:  Urrg…. Well, this is your lucky day.  I happen to be in the mood for shooting down the bright ideas of poor suckers that think Nobel prizes are given out like puppies from a puppy mill to people that haven’t paid their dues in this very, very tough field.  So, let’s start with this question:  What makes you think you are the one that has come up with something new in quantum theory?  After all, you can’t argue that the set of smart-enough people that actually can legitimately call themselves physicists, theoretical or related, have spent cumulative millions of lifetimes trying to break down the data and clues we have to solve the very well-known problem you are looking at.  Don’t you think someone, or many someones, with a much deeper background than you would have long since considered whatever you have and passed it by fairly quickly?

Me:  [meekly] yes.

Me:  But I have thought about this for a very long time, and refined it, and received feedback, and really tried hard to make sure it makes sense.

Prof Jones:  Unfortunately, so has every honest physics PhD, and I’m afraid they are going to have a lot more mental “hardware” than you, having both genuine talent and also having brutally difficult training in abstract mental comprehension and synthesis ability and current knowledge.

Me: OK.  I guess I could quit doing this–I just find it so interesting.

Prof Jones: [softens just slightly, realizing there’s a lot of snarky but not-classy power in putting down those who try, but are so limited in resources or study time].  Well, just so you understand.  You aren’t going anywhere with this.  But let’s see what you got.  Before I dig in, I want to know what you are adding to existing theory, as succinctly as you can communicate.

Me:  Alright.  I thought about the way quantization works on particles and fields, and in both cases the E=hv relation defines very explicitly what must happen.  I spent a lot of time trying to construct a model of a system that is continuous but obeys this relation at the smallest scale.  I came up with three constraints that describe such a system–in fact, it looks to me that the E=hv relation actually specifies a geometrically defined system.  These constraints are:

1: The quantization is enforced by a rotation in a vector field, that is, a twist.

2: To ensure that only single complete rotations can occur, the field must have a local background state that the rotation returns to.

3: To ensure that the energy of the rotation cannot dissipate, the vector field must be unitary.  Every field element must have constant magnitude but can rotate in 3D+T spacetime.

Prof Jones:  I see what you are getting at.  The E=hv relation only allows discrete energy states for a given frequency within an available continuous energy range.  A twist is a modulus operation that works in a continuous 3D field to provide such discrete states provided that there is a default idle state, which would be your background vector orientation.  However, you realize that EM fields do not have limitations on magnitude, nor is there any evidence of a background state.

Me: I understand that.  I am proposing that because QFT shows how EM fields can be derived from quantum particles (photons), my theory would underlie EM fields.  I see a path where EM fields can be constructed from this Unitary Twist Field Theory from sets of quantized twists.  I agree that the background vector direction is a danger because it implies an asymmetry that could prevent gauge invariance–but I suspect that any detector built of particles that are formed from this twist mechanism cannot detect the background state.  The background state direction doesn’t have to be absolute, it can vary, and a unitary vector field has to point somewhere.  Continuity and energy conservation imply that local neighborhoods would point in the same direction.

Prof Jones:  Sets of quantized twists, hunh.  Well, you’ve got a very big problem with that idea, because you cannot construct a twist in a background unitary vector field without introducing discontinuities.  If you have discontinuities, you don’t have a unitary vector field.

Me: Yes, I agree.  However, if the twist moves at speed c, it turns out the discontinuities lie on the light cones of each point in the twist and are stable, each light cone path has a stable unchanging angle.  In a sense, travelling at the speed of light isolates the twist elements from what would be a discontinuity in a static representation.

Prof Jones:  I don’t think I agree with that, I would have to see proof.  But another question comes to mind.  In fact a million objections come to mind but let me ask you this.  You are constructing an EM field from this unitary vector field.  But just how does this single vector field construct the two degrees of freedom in an EM field, namely electrostatic fields and magnetic fields?  Just how are you proposing to construct charge attraction and repulsion and magnetic field velocity effects specified by Maxwell’s relations?  QFT is built on virtual particles, in the EM case, virtual photons.  How are you going to make that work with your theory?  You realize the magnitude, don’t you, of what you are taking on?

Me:  These are questions I have spent a great deal of time with over the last 20 years.  That doesn’t justify a bad theory, I know.  So I’ll just present what I have, and if this dies, it dies.  I’d just like to know if my thinking has any possible connection to the truth, the way things really are.  I realize that we have a perfectly workable theory in QFT that has done amazingly well.  But we also have a lot of particles and a lot of interactions that seem to me to have an underlying basis that QFT or relativity don’t explain, they just happen to work.  Renormalization works, but why?  These are some issues that tell me we can’t stop with QFT.

Prof Jones:  [sotto voce] The hubris is strong in this one.

Me: What

Prof Jones:  Nothing.  Go on.  What is your theory going to do with charge and magnetic behavior?

TO BE CONTINUED, SAME BAT-TIME, SAME BAT-CHANNEL

Agemoz

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Conservation of Twist Energy

April 2, 2012

 I worked for a while with the 1/r^2 – 1/r^3 solution set and quickly discovered that this is just a lucky subset of the twist field solutions–every solved solution is unstable.  I can’t even find the solution that works in the ring case that appears stable, although I quit working on this because I realized that the twist field would yield a lot of cases that dont go into the 1/r^2 – 1/r^3 subset of solutions.

So, I went back to the generalized twist field, and  realized I had set up my simulations wrong.  The twist, as explained in a much earlier post (“Turning Bicycle Wheel”), has to be in-line with the direction of travel in order for the circular polarization degree of freedom of a photon to exist.  But even so, simulations show that the width, and hence the energy of the photon, has to be conserved but is not if the twist is not moving at the speed of light.  Even when moving at the speed of light, it was not clear why the width would be constant–but it has to be, else conservation of energy wont happen.  How can I make a simulation which observes both the quantization and conservation of energy of the twists in the vector field?

I thought for a while about this, and attempted to draw a Minkowski diagram (3D + T) representation of the twist.

Picture of field twist in Minkowski spacetime

This got really interesting really fast.  After a few mis-draws (my mind isn’t very well wired to view things in 4D), I realized that in Minkowski space, there is no twisting of the photon along the light cone path–in fact, in the one case of a twist moving at speed c, there is no acceleration at all–no forces needed to explain the twist structure!  Each light cone path has a twist angle that does not change over time, thus showing how twist width is conserved and thus how a photon holds its energy quantum without dissipation.  It’s hard to see, but I attempted a diagram–note that along the red light-cone paths, there is no change of the field angle.  A narrowing of the twist width either timewise or space wise would require a merging or deviation of angle paths not possible without some force source.

This should provide a basis for how to simulate the twists in a way that conserves energy.

Agemoz

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