Posts Tagged ‘quantization’

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One Rule To Rule Them All: The One Question Every Human Being Must Ask

August 18, 2016

I’ve been doing a great deal of thinking and analysis on what the precursor field would have to be.  I’ve had some discussions and conclusions about the precursor field that I’ll get into shortly here–but I wanted to digress a little because one of the discussions homed in on why I’m doing this work.  The discussion was extensive but revealed a crucial point about humanity’s search for meaning.  Let’s see if I can summarize the extensiveness of this conversation down to the bare essentials in a clear way:

The main driver for the approach I am taking is that this universe emerged from nothing.  To put it another way by using a popular physics aphorism, it’s not turtles all the way down, the first turtle emerged from nothing.  As I detailed in several previous posts, I see how this could happen–essentially a massive generalization of the principle that infinity times zero can give a finite number.  This drives many of the requirements of the precursor field that I am developing which causes emergence of quantized particles and emergence of particle motion and the EM field, the strong force, and related properties.

This question–did the universe emerge from nothing–is *the* most fundamental question a human being can ask, and is beautiful and elegant in its own right.  It encompasses many issues, especially the question “Is there a God”.  It’s rare that a question can be formed with such simplicity in our language.  The whole study of philosophy of all forms spends a lot of time clarifying what is a “real” question versus what is semantics, i.e, an artifact of the language we choose to work in.

For example, the common philosophical study of “I seek the Truth” raises semantic questions like “what do you mean by truth?”  “What does the concept of seeking mean?”  Or, the question “What is the meaning/purpose of life?”  Well, what does “meaning” mean to you?  How do you define life?  Does it involve consciousness?  Memory?  A tree is alive, and on a very long timescale likely has the same stimulus/response capability as faster moving animals or humans.  It’s really tough to extract the various philosophical issues out of the semantics of most questions.

But the question “did the universe emerge from nothing”, while not immune from semantics, cuts to the core issue easily and elegantly.  It asks whether the observed rules of our existence are intrinsic or not.  If there is even just one rule that has to be there in addition to nothing (and yes, there are semantic issues with “nothing”, so we do have to tread carefully even here)–then the universe didn’t emerge from absolutely nothing.  Then you are forced to ask what caused that rule to emerge, and with a lot of thought I think you have to declare that there is a God–an intellect, a being, or other organized structure that formed the universe.  Then you have to ask what formed those.  It is a recursion of thought that leads some to say “it’s turtles all the way down”, that there is no beginning.  But if you do that, you still are saying there is a God, I think.  This question is so elegant because the dividing line is so precise.  Either the universe emerged from nothing, or else there is no point in continuing because a God or Being or Computer or *something* takes a turtle, puts it there, and voila, we as humans emerge.

The assumption of a God is so problematic in my mind–you simply cannot answer the question of how did this universe get created, you also *cannot ask the question why are we here*!!!  By defining a God, we have taken that question out of our hands and put it in the hands of an unknowable entity.  By saying it’s turtles all the way down (similar to saying there is no beginning, the universe has always existed), we throw up our hands and say these questions cannot be answered.

On the other hand, if we study the approach that we came from nothing, there is a path that can truly be followed, and that is exactly what I am trying to do.  I assume this precursor field had to emerge from nothing and that constrains the characteristics of the field in many ways.  For example, the particle zoo has to emerge from it, so a geometrical basis should exist.  Or, getting on the subject I’ve been focusing on, the precursor field has to emerge from nothing, so it cannot have extra degrees of freedom, which implies rules preceded the field–a no-no in forming the field description.  If there are rules, there has to be a God of some form.

The astonishing thing to me is how clear the path for humanity has to be.  There really is only one study worth doing–how could we emerge from nothing.  Any other explanation for our existence appears to have no fundamental value in investigating!

I hope you find this digression fascinating and helpful why I am doing this study.   It has so far led to the following conclusions, some of which I’ve described in previous posts:

The precursor field cannot require continuity (differentiability) otherwise quantized twists are not possible, and such twists are required for the formation of stable particles in the particle zoo

The field has no vector magnitude, it is a unitary directional field with an R3 + I dimension plus time.  This means that the field elements are orientable (that is, there is a property of the field element that distinguishes from other field elements both by physical location and by direction)

The elements of the field do not move.  They can only rotate.  Movement is an emergent concept that results from the formation of rotation structures that can propagate through the field

Rotation of a field element induces rotation of neighborhood field elements.  This induction is infinity elastic otherwise the field would be forced to be continuous and differentiable, which is contradictory to enabling field twists

Field elements are quantized by creating a preferred orientation to the imaginary dimension direction.  This, combined with the ability to form field twists, is what allows the formation of stable particles

There are other properties I am uncovering, but this list is a good starting point for setting up a computer simulation and for analytic derivations.  My goal is to uncover the specific quantized states available and see if they match with what we see in the particle zoo.

Agemoz

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

July 19, 2016

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

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

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

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

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

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

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

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

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

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

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

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

Agemoz

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Mathematical Basis for Twist Theory

September 28, 2015

The field twist theory I’ve been working on is designed to provide a geometrical basis for the particle zoo as well as provide a non-bizarro explanation of quantum entanglement.  I’ve had a bit of a breakthrough thinking that provides a mathematical foundation for the theory.

The theory posits that particles arise from electromagnetic fields (there, I said it, I’ve lost 95% of you already!).  For that to be a tenable hypothesis, I have to modify Maxwell’s equations to provide quantization.  A preposterous proposition since that has already been done successfully and particles predicted with the renormalizable Yang-Mills gauge invariant extension/generalization of Maxwell’s equations and the Lorentz force equations.

The problem is that half of Maxwell’s equations, the particle terms, are empirical.  According to my studies, there is currently no known means, not even the Higg’s field, for explaining why the masses are what they are.  The twist field theory attempts to derive the particle zoo by positing a variation of Maxwell’s field equations that replaces the particle terms.  Geometrically, quantization can be mapped to a rotation of a field vector where there is a preferential background state, that is, there is a potential to go to a background ground state.  For this to be achievable using Maxwell’s equations and maintain gauge invariance, there is only one possible such state–the imaginary vector of the EM field.  A quantized packet of energy would require a specific energy to complete one and only one rotation–a twist–to this background state.  The remaining issue is field dissipation–there is only one way that a twist rotation would not dissipate.  It must move axially at the speed of light and must not have a diffuse axial radius.

Once these criteria are met, it is possible to construct a variety of rings and knots and links that should give rise to the particle zoo and the required masses.  The simplest non-linear case is a ring, which has counteracting magnetic field interactions to quantize the loop size (the twist provides one term, the loop itself provides the counteracting term).  As I mentioned, this can all be achieved by replacing the particle terms in Maxwell’s equations with a potential to the imaginary background state.  Such a modification could answer the question of “if this is a valid modification to Maxwell’s equations, why hasn’t it been experimentally observed” because there is no ability to create a sensor made of particles capable of directly observing this background state.  It is this background state potential that shows up when E=hv is measured.  The requirement that the twist axis diameter be non-diffuse would be the explanation for why elementary particles such as the electron are showing zero radius within observable limits.

Interesting investigation for me–I suppose science fiction for the vast majority of you!  But that’s fine–I never said I was doing any great, just some interesting thinking with the studies I’ve done.

Agemoz

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22 Years!

September 9, 2015

It’s been 22 years since I started as an amateur crackpot, and have nothing more to show for it except that I’m still an amateur crackpot.  However, I did reach the goal of a better understanding of the physics behind the particle zoo and the history of physics.  I still think that my basic premise could work to produce the array of particles and force mediators we know to exist.  The idea is analogous to the Schroedinger wave solutions for excited electrons and is based on the assumption that at quantum scales there is a way (other than gravity) to curve EM waves.  We already know that this outcome cannot result from Maxwell’s equations alone, so I have proposed that EM field twists can occur.  These could be considered strings and consist of an axially rotating field vector that propagates only at speed c.  If the axis is a straight line, we have a photon that cannot rest and has no rest mass.  However, a twist that forms in a closed loop must only exist in quantized structures (any point on the loop must have a continuous vector twist rotation, so only complete rotations are possible).  Loops can exist as a simple ring or more complex knots and linked knots and would provide the basis for a particle zoo.  The loop has two counteracting magnetic fields that curve and confine the loop path, thus enabling the soliton formation of a stable particle–the twist about the axis of the twist, and the rotation of the twist about the center of the loop. Mass results from the momentum of the twist loop being confined to a finite volume, inferring inertia, and electric charge, depending on the loop configuration, results from the distribution of  magnetic fields from the closed loop.  Linked loops posit the strong force assembly of quarks.

The biggest objection to such a twist model (aside from assuming an unobserved variation of Maxwell’s equations that enables such a twist field) is the resulting quantized size of particles.  Electrons have no observed dimensional size, but this model assumes they result from twist rings that are far larger than measurements indicate.  I have to make another assumption to get around this–that collisions or deflections are the result of hitting the infinitely small twist ring axis, not the area of the ring itself.  Indeed, this assumption helps understand why one and only one particle can capture a linear twist photon–if the electron were truly infinitely small, the probability of snagging a far larger (say, infrared) photon is vanishingly small, contrary to experiment (QFT posits that the electron is surrounded by particle/antiparticle pairs that does the snagging, but this doesn’t answer the question of why only one electron in a group will ever capture the photon).

In order for this twist theory to work, another assumption has to be made.  Something needs to quantize the frequency of axial twists, otherwise linear twists will not quantize like loops will.  In addition, without an additional constraint, there would be a continuous range of closed loop energies, which we know experimentally does not happen.  In order to quantize a photon energy to a particular twist energy, I posit that there is a background state direction for the twist vector orientation.  In this way, the twist can only start and finish from this background state, thus quantizing the rotation to multiples of 2 pi (a complete rotation).  This assumption leads to the conclusion that this background state vector must be imaginary, since a real background state would violate gauge invariance among many other things and probably would be detectable with some variation of a Michelson-Morley experiment (detecting presence of an ether, or in this case an ether direction).  We already describe quantum objects as wave equations with a 3D real part and an imaginary part, so this assumption is not wildly crack-potty.

So in summary, this twist field theory proposes modifying the EM field math to allow axial twists in a background state.  Once this is done, quantized particle formation becomes possible and a particle zoo results.  I’ve been working hard on a simulator to see what particle types would emerge from such an environment.

One remaining question is how does quantum entanglement and the non-causal decoherence process get explained?  I propose that particles are group waves whose phase instantly affects the entire wave path.  The concept of time and distance and maximum speed c all arise from a limit on how fast the wave phase components can change relative to each other, analogous to Fourier composition of delta functions.

You will notice I religiously avoid trying to add dimensions such as the rolled up dimensions of various string theories and multiple universes and other such theories.  I see no evidence to support additional dimensions–I think over time if there were other dimensions connected to our 3D + T, we would have seen observable evidence, such as viruses hiding in those dimensions or loss of conservation of some quantities of nature.  Obviously that’s no proof, but KISS to me means that extra dimensions are a contrivance.  My twist field approach seems a lot more plausable, but I may be biased… 🙂

Agemoz

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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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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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Atom Energy Quantization

July 30, 2013

I have taken a digression from my sim work to think about quantization of atomic energy levels.  These energy levels, to a first order in the simplest (hydrogen) atom, are defined by the Rydberg equation.  The rest energy of elementary particles such as the electron is defined by E=hv, and I have posited that field twists geometrically achieve this quantization.  I’ve then followed down a bunch of different paths testing this hypothesis.  However, it’s not just rest mass that is quantized.  The kinetic energy of electron orbitals in an atom are also quantized.  In the non-relativistic case we can look at the solutions of the Schrodinger equation, although refinement of the solutions for spin and other 2nd order and quantum effects has to be applied.  Ignoring the refinements, does this quantization also imply field twists?

I think so for the same reason as the E=hv rest mass case–to achieve a modulo energy value that quantizes, a geometric solution requires a twist in a background vector field state.  There has to be a lowest energy state called the background state.  You can imagine a plane of floating balls that each have a heavy side and a tenuous connection to adjacent balls.  Most balls will tend to the heavy side down state (obviously, this is a gravitational analogy, not a real solution I am proposing).  But if there is a twist in a string of balls, the local connection for this twist is stronger than the reverting tendency to the background state, and the twist becomes topologically stable.  Several geometrical configurations are possible, a linear twist could model a photon, while a twist ring could model an electron.  What could model the energy states of an electron around an atom?

One thing is pretty clear–the energy of the lowest state (S orbital) is about 8 orders of magnitude smaller than the rest mass energy of the electron, so there’s no way a single field twist would give that quantization.  The electron twist cannot span the atom orbital–the energy level is too far off.  The fact that the energy levels are defined by the Rydberg equation as 1/r^2 increments suggests either that each energy level adds a single twist that is distributed over the orbital surface (causing the effect of 1/r^2 over a unit area), or that the energy level is the result of n^2 new twists.  Since I cannot imagine a situation which would enforce exactly n^2 new twists for each quantized orbital energy level, I think the former is the right answer.  There is a constant energy twist being applied each time an orbital reaches another excitation level, distributed over a surface.

But what quantizes that first energy level (corresponding to the 1.2 10^-5 cm wavelength)?  This cannot be related to the electron wavelength (2.8 10^-13 cm) because the S orbital is a spherical cloud that is far larger than an EM field twist solution would give.  An EM twist about a charged stationary object would have about 4 times the classical radius of the electron–but the actual cloud is around 7 orders of magnitude larger.  The thing that causes the atom orbital size to be so large is the strong force, which prevents the electron and the positively charged nucleus from collapsing.  Trouble is, this is a complication that I don’t have any thoughts about how the Twist Field theory would work here, other than recognizing that any type of quantization requires a return to a starting state–implying a twist.  DeBroglie proposed that the probability function wave has to line up, but we don’t really have a physical interpretation of a probability distribution in quantum mechanics, so what does it mean physically for that wave to line up?  No such problem in Twist Field theory, and twists are so closely related to the sine waves involved (they are a reverse projection) that I don’t think it’s preposterous to propose field twists as an underlying cause.

But there’s a lot of gaping holes in that explanation that would require a lifetime of investigation.

Agemoz

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Not So Fast, Model Might Work After All

July 19, 2013

I had decided (in the last post) that the model I was using couldn’t be right for several reasons in spite of some promising sim results. But upon thinking about it, I realized I was a little too hasty–I discovered a way that a potential (scalar) function could work in accelerating a twist ring in spite of the orientation problem and the curvature problem.    This is an important question because it gets at the heart of why a particle would move due to EM fields.  Conventional theory just asserts the Lorentz force laws, and this works under all relativistic situations.  Conventional theory also says that the electron is an immeasurably small particle.  I have worked out that the twist field particle, which would not be immeasurably small, shows that as it is accelerated relativistically, it stretches to approach the behavior of a linear twist–asymptotically approaching radius size zero.  My hypothesis is that scattering experiments make the electron appear to be infinitely small because of this stretching.  I do have to admit that this experimental result is the chief reason why other physicists discount any electron theories that require non-point like models.

Anyway, back to the sim conclusions–I’ve been trying to create a hypothesis as to why it moves as it does with the twist field theory, and created my simulation environment to test the hypothesis.  I needed to know how a particle knows which way to move when there is one or more nearby sources, and I need it to work right regardless of relativistic behavior.

A big question is whether the particle as a twist ring would sense a variation of field magnitude, or whether the field has to be a vector and the particle senses which way to move based on this vector (which would be a vector sum if there was more than one source).  The scalar field is preferable because then motion can result from the potential function, but I had thought that the orientation problem as well as the curvature problem of negative fields (see previous post) meant that the twist field ring would have to respond to a vector field, that the particle would have to accelerate independent of the orientation.  I also think the stretching of the ring in a relativistic situation might not hold up to correct behavior, but the scalar field is more likely to work than the vector field (simpler–fewer complications in different scenarios).

However, I realized that all of these reasons for thinking the twist sim model are wrong are not all-encompassing. There’s a way around them, which means I have to check those out.  First, the negative field situation, which uses curvature analysis to show a paradox (stronger curvature for a field component that is on the far side of the ring).  I had done the math and things worked correctly, but had reasoned that the math couldn’t be right because it implied a force that didn’t decay with distance.  Now I realize the math is right, because there are three components that add to create the normal acceleration that determines the local curvature of the ring.  The end result of this sum is that while a weaker far-side field cannot induce more curvature, a cancelling out of part of the sum of the near-side acceleration caused by the negated field would result in *less* acceleration there and would achieve the same acceleration (as the far-field stronger field)  for source particles that attract.  The sim was correct, I just wasn’t drawing the right conclusion.

Secondly, I realized that the orientation problem may cancel itself out.  I’ve reasoned that since some orientations cause every point on the twist ring to see exactly the same field, so a solution that depends on the particle sensing the delta field cannot work in that case, and thus invalidates that solution as a general one.  But it is possible that the potential is sensed whether or not the delta field is sensed.  There has to be different behavior between a constant potential field and a sloping potential.  If the orientation problem is real, then there would be no difference in what the particle sensed from source particles and what it would sense if there were no source particles.  The field component would be the same in the local neighborhood  in either case and there would be no information available that would indicate where the particle would move to.   But a solution that has acceleration also due to potential alone, regardless of a change in potential, would work–kind of a switching between normal and tangental effects.  I will pursue this more–this idea isn’t flushed out yet.

If the delta potential *is* sensed, then this means that particles like the electron must have non-zero size, otherwise the delta field that the particle sees would still be flat.  Then the only information where the sources were would come from a directional component resulting from the vector sum of source fields at that point (where the ring is located).  Current experiment appears to show that the base electron has no size, which means it cannot sense potential across the twist ring.  In addition, the notion that an electron is imeasurably small has a real problem with Heisenberg’s uncertainty relation.  It is fundamental to the twist ring theory that the electron does have physical size, the Lorentz transforms arise from that, and the E=hv quantization of the ring depends on that.  One way or the other, a determination has to be made whether we have a scalar or vector field inducing motion.  The sim model I have now depends on a scalar field (potential) and is qualitatively correct.

So, in summary–the question of whether motion results from travel through a potential is still possible–and unresolved.   More work ahead.

Agemoz

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Sim Results Show Wrong Acceleration Factor

July 18, 2013

Well, it looked promising–qualitatively, it all added up, and everything behaved as expected.  But it’s a “close, but no cigar”.   The acceleration at each point should be proportional to 1/r^2, but after a large number of runs, it’s pretty clearly some other proportionality factor.  I’ve got some more checking to do, but looks like I don’t have the right animal here.  One thing is clear though–this model, which attracts and repels, is the first one that shows qualitatively correct behavior.  If twist rings have mass due to the twist distortion, this is the first model that shows it, even if the mass can’t be right.

So, I stepped back and ran through the list of assumptions, and see some flaws that might guide me to a better solution.  Many theories die in the real world because of the glossy effect, as in, I glossed over that and will deal with it later, it’s not a major problem.  I unintentially glossed over some problems with the model, and in retrospect I should have addressed them from the get-go.

First, twist rings (as modelled in my simulation) have a real planar component, but twist through an imaginary axis.  The twist acts as an E field in the real space and as a magnetic field in the imaginary space.  The current hypothesis is that the loop experiences different field magnitudes from the source particle, and this causes a curvature change that varies around the loop.  The part of the loop that is further away will experience less curvature, the closer part more curvature (curvature is a function of the strength of the magnetic field from the source particle).  This simulation shows that if that is the model, you do indeed get an acceleration of the ring proportionate to the distance from the source particle–and the acceleration is toward the source particle–attraction!  If you switch the field to the negative, you get the same acceleration away–repulsion.  So far, so good, and the sim results made me think–I’m on the right track!  I still think I might be on the right track, but the destination is further away than I thought.

First, as I mentioned, the sim results seem to show pretty clearly that the acceleration is not the right proportionality (1/r^2).  That might just be a computational problem or just indicate the model needs some adjustments.  But there are some things being glossed over here.  First, while the model works regardless of how many particles act as a source, there is always one orientation where every point on the ring is equadistant from the source particle–in this case, there is no variation in curvature.  The particle would have to act differently depending on orientation.  It could be argued that the particle ring will always have its moment line up with the source field, and so this orientation will never happen–fine, but what happens when you have two source particles at different locations?  The line-up becomes impossible.  OK, let’s suppose some sort of quantum dual-state for the ring–and I say, I suppose that is possible, some kind of sum of all twist rings, or maybe a coherence emerges depending on where the source particles are, but then we no longer have a twist ring.  In addition, the theory fixes and patches are building up on patches, and I’d rather try some simpler solutions before coming back to this one.  The orientation problem is a familiar one–it shoots down a lot of geometrical solutions, including the old charge-loop idea.

Here’s another issue:  I make the assumption that there is a “near side” and a “far side”, which has the orientation problem I just mentioned–a corollary to that is that it also could get us in trouble as soon as relativity comes in play since near and far are not absolute properties in a relativistic situation).  I then get an attraction by assuming the field is weaker on the far side and thus there is less curvature.  The sim shows clearly the repulsion acceleration away from the source when this is done.  Then I cavalierly negated the field and Lo! I got attraction, just like I expected.  But I thought about this, and realized this doesn’t make physical sense–a case of applying a mathematical variation without thinking.  This would mean that the field caused *greater* curvature when the twist point is further away (the far side).  Uhh, that does not compute…

While not completely conclusive, this analysis points out first, that a solution cannot depend on source field magnitude variation alone within the path of the ring.  The equidistant ring orientation requires (more correctly, “just about” requires, notwithstanding some of the alternatives I just mentioned) that the solution work even if all neighborhood points on the ring have exactly the same source field magnitude.  In addition, there’s another more subtle implication.  The direction a particle is going to move has to come from a field vector–this motion cannot result from a potential function (a scalar)  because within the neighborhood of the ring, the correct acceleration must occur even if the potential function appears constant over the range of the twist ring.

This is actually a pretty severe constraint.  In order for a twist ring to move according to multiple source particles, a vector sum has to be available in the neighborhood of the twist ring and has to be constant in that neighborhood.  The twist ring must move either toward or away from this vector sum direction, and the acceleration must be proportionate to the magnitude of the vector sum.  Our only saving grace is the fact that this vector sum is not necessarily required to lie in R3, possible I3–but a common scalar imaginary field of the current version of the twist theory is unlikely to hold up.

Is the twist field theory in danger of going extinct even in my mind?  Well, yes, there’s always that possibility.  For one thing, I am assuming there will be a geometrical solution, and ignoring some evidence that the twist ring and other particles have to have a more ghostly (coherent linear sum of probabilities type of solution we see in quantum mechanics).  For another, my old arguments about field discontinuities pop up whenever you have a twist field, there’s still an unresolved issue there.

But, the driving force behind the twist field theory is E=hv.  A full twist in a background state is the only geometrical way to get this quantization in R3 without adding more dimensions–dimensions that we have zero evidence for.   Partial twists, reverting back to the background state, are a nice mechanism for virtual particle summations.  We do get the Lorentz transform equations for any closed loop solution such as the twist theory  if the time to traverse the loop is a clock for the particle.  And–the sim did show qualitative behavior.  Fine tuning may still get me where I want to go.

Agemoz

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Gaussian Wave Packets

February 20, 2013

It’s been a little while since I’ve posted, mostly because I have an unrelated big project going on, so I’ve been focusing on trying to get that out the door.  And, I’m working on getting the twist ring inertial math to work, a laborious project since the Lagrangian equation of motion has too many variables for solving.  I’m trying to find ways to simplify.  In addition, I also have an iterative sim of the inertial response ready to go but haven’t had time to set it up and run it.  Hopefully with the other project almost done I’ll get to it this weekend.

One thought I’ve had in the meantime–many  quantum mechanics exercises involve modeling a photon with a wave packet that is described as having the Gaussian integral form.  The most basic variation of this form (Integral[Exp[-x^2]]) is a bell shaped curve with amplitude 1 at zero and asymptotically goes to zero at +/- infinity.  I’ve had lots of lectures where an oscillating squiggle is used to represent the magnitude of the quantized photon wave packet.

A very interesting thought occurred to me is that this integral is a great representation of the unitary twist version of a photon packet.  A one dimensional magnitude projection of a twist from the Unitary Twist Field Theory would be represented exactly by a Gaussian curve, and if we use a complex value r to completely represent the twist function, then the Gaussian integral becomes Integral[Exp[-r^2]] and then this can be interpreted as a working model of twists–and thus support the notion that the twist theory has a well proven basis in the math of quantum mechanics.  Do I buy that, or should my skepticism meter be dinging my thinking process?  Right now, the idea looks pretty workable–it seems pretty clear that the r form clearly would represent a twist as well as a Gaussian envelope packet over a frequency of oscillation of E and B fields–making the twist theory a viable alternative to the magnitude constrained wave packet interpretation.  For the twist theory to be acceptable, there has to be a path to the math of quantum mechanics, and I think I see how this could happen.

Agemoz

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