twist ring diameter

May 12, 2009

Wow, this twist ring is becoming a thing of beauty. Yes, it is mostly a semiclassical treatment and thus probably won’t be taken seriously by any working physicist now, yet I look at this and wished I had been there when these approaches were debated about 100 years ago.

I had thought about how to get momentum from a ring, and was considering computing how the ring would cause the radial motion without resorting to assuming a momentum from the ring’s charge distribution (I’m always looking for a cool Mathematica project, but each time so far, a bit of followup thinking has quickly determined analytic solutions not requiring computation). I had always assumed a dipole, but this has problems, and I got to a point where I realized that it just wouldn’t work. Yes, it would explain the radial motion, and the forces involved would be proportionate to the dipole momentum–but it would never create net forces in an electric field (or magnetic field). As mentioned previously, though, twists do work, and give the four unique particles: spin up electron, spin down electron, spin up positron, and spin down positron. So then I tried to see what kind of radius would be enforced by two twists of the same type. Is there a fixed radius resulting from the interference pattern of the twists? And to my astonishment, yes, there is a beautiful solution. If the twist rate is exactly the same as the speed of light around the ring, only then will the two twist fields cancel each other out, resulting in a net zero far field, and a stable “geosynchronous” dipole position!

In this system, the twists are continuously turning at the same rate as the propagation around the ring, thus creating standing waves that resemble a dipole. This explains why there are the previously mentioned working solutions using a dipole. There is only one possible radius for this system of twists, although other Schroedinger two body solutions will also give stable twist patterns presumably representing other particles (assuming, of course, that this ring model represents reality at all…). For example, we have good evidence that muons are a propagating braid of three strings of twists, each braid momentarily appearing in real space as one of three muon types–the slight twist displacement yielding the tiny mass associated with muons. Speculative, of course–but intriguing to me with possibilities.

I still don’t have proof of anything, though–and the twist ring does not yet provide an answer as to why *this particular mass*. In this model, electrons form from two twists with a very particular momentum, the God constant of posts I made a few years ago. In a scale less system, one of two things has to happen to explain what we see (constant mass for all electrons): either there is an intrinsic property of 3D scale-less systems with a fixed speed of all twists, or all rings are stimulated by a constant oscillating source (see previous posts, now thought to be unlikely), or there is only the illusion of constant mass, when in fact any radius ring will exhibit all our observed measurements of mass (I think this is unlikely, some aspect of the “real” radius would show up in different particles).

Right now I think the first case is the valid case–I just haven’t found the property of our system that enforces a particular ring radius. Note that the Standard Model uses the Higgs particle to enforce a quantized mass for particles, but what gave it its particular mass? This is a recursive question not unlike the What Created the Creator question. That argument doesn’t necessarily disqualify the validity of the Higgs solution, but I’m guessing that if the Higgs particle is found, no physicist will even then argue the elegant simplicity of the Standard Model. Obviously I don’t bother refuting the Standard Model, that is the domain of crackpots stupider than I, but the model’s inability to create a representation of the electron family that works as well as the twist ring makes me want to pursue the twist ring still further.

Is there something about the twist ring that would create a unique radius? The stable “geosynchronous” result enforces a particular radius given a particular twist rate, but the linear twist rate is not quantized. Why is the ring twist rate quantized? What is it that allows only one twist rate to form a local stable state (in other words, why are there no electrons with 1.1 electron masses).

We already know that twist propagation in this model goes at the speed c, and that the twist frequency determines the energy and momentum of the twist. We know that the twist is spin quantized, that is, can only do a twist angle that is a multiple of 2 Pi (hypothetically enforced by the start and finish complex field alignment requirement). We know that the particle phase component is non-causal, which implies that the twist angle state impact is noncausal as well. Whatever it is, if this twist ring has any connection to reality, there has to be something about the ring that constrains the rate of twisting. I’ll break for now to focus my thinking on possibilities here.

Agemoz

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twist ring

May 4, 2009

I spent some time thinking about the twist ring in the context of getting inertial mass from it. This is really important because this might point to an experiment that will for once and for all prove or disprove the ring idea for an electron–if a non-moving electron has a measurable ring size rather than the Standard Model point, relativistic collisions done in accelerators will distort the ring and make it look like a point. But if a non-linear field (for example) could show a motion explained by the ring components at different field points, a case could then be made for the ring model.

The old idea was that the process of applying an electrostatic force to a ring causes a change in path of the wave that might be found to be dependent on the frequency of the wave, and thus would be a connection to the ring’s momentum. When I did this analysis years ago, I ran into some issues. I did find a force proportionate to the field, but it was “close” rather than exact–and it depended on the field having a sinusoidal component at the frequency of the ring. There’s a number of problems here–the orientation and phase of the ring relative to the field, the quantum entanglement requirement that phase doesn’t behave causally, and worst of all–it doesn’t work in a multiparticle environment (the field will not be single sinusoidal anymore).

So, some more thinking lately, because I wanted to revisit the inertial mass idea. I thought that the inertial component might show up as the difference in field values or perhaps by computing the second order effect of a 1/r^2 non-linear field. However, this really doesn’t work, because since the ring has both a and – component, there cannot be a net effect. It is possible that there is a step effect depending on the ring phase–if the positive charge is closer to the field source, a step will go in that direction, then when the negative charge is there, there is a step in the opposite direction, and so on. In time, it is conceivable that there would be a net result, but I don’t think so–as soon as the step is taken, there will then be a *stronger* repulsion, hence a bigger step in the reverse direction, taking us back (literally) to square one. Even if there were a delta, why does an antiparticle move in the opposite direction–it also is a spinning particle with a positive and negative step.

Then it hit me–all these problems can be solved with a *twisted* ring! Now the scheme works in a uniform field–because the opposite side of the twist has the opposite twist–an unraveling that is necessary for the quantized ring energy (the wave vectors of each dipole element has to line up to connect). Now, the twist on the opposite side has the opposite spin and opposite direction, thus canceling each other out–resulting in both sides having the force applied in the same direction and working together to move the particle one way or the other. Electron rings then would spin one way or the other, whereas positrons would *twist* in the opposite direction. And this scheme has no dependency on a sinusoidal field or multiparticle field sources.

Let’s make sure that twist rings provide the right number of degrees of freedom:

a: spin up electron: ^ v, spinning clockwise (right hand rule twist in v dir)
b: spin down electron: v ^, spinning counterclockwise (right hand rule twist)
c: spin up positron: ^ v, spinning clockwise (left hand rule twist in v dir)
d: spin down positron: v ^, spinning counterclockwise (left hand rule twist)

This doesn’t work, because the spin up and spin down cases as shown are identical. Careful study will show that a clockwise spin from the top view looks like a counterclockwise spin from the bottom view, even the twists and spin moment will be the same. But if the twist pair is either a pair of identical twists or opposite twists (either a Pi/2 -Pi/2 twist or a Pi/2 Pi/2 twist) then the antiparticle spin-up and spin down will be geometrically different than the particle spin-up and spin down. The trouble with that is–only the twists that are opposite will have a net force in the same direction for both poles. But then there’s a problem with quantization–an unraveling does not have to be a multiple of Pi for a twist angle. Only the Pi twist followed by another Pi twist will enforce an integral momentum.

So–how do we get the required two degrees of freedom with a twist ring? By realizing that the twist has a complex phase component. There is a spin phase within the spin ring. When we look at *what* spins in the twist, we see a complex vector–so you could imagine, for example, that the twist has the real component first, then the imaginary component–or, vice versa. The necessary and sufficient two degrees of freedom are only provided by a ring–the direction of the twist relative to the ring spin direction, and the phase direction of the complex components of the twist. The standard model point electron cannot do anything with a point except say that we don’t know what distinguishes a spin up from a spin down electron or from a positron and an electron. Only the twist ring provides the exact model needed for the correct number of degrees of freedom.

Agemoz

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state of thinking

April 15, 2009

Well, I stepped back once again because my construction is getting a bit unwieldy and needs some organization. There are several questions about how to proceed because the amount of speculation has considerably exceeded the available data to support or suggest it. I need experimental data or analysis that will either strengthen or disprove these concepts–if I keep building, I get lots of interesting ideas, but get further and further from conclusions that either feed back on themselves to help prove the base concepts, or from conclusions that are actually usable to me in deciding what to do in my finite lifetime existence.

The foundation for most of this thinking comes from one of two paths–broad philosophical thinking about life, in particular the realization that life forms from particular arrangements of already existing particles (and similarly, death actually is not the destruction of anything, but the disconnection of these arrangements), thus clearly showing that life and consciousness are *ideas* that can form from any prolific array of entities with an appropriate set of interactive rules. Thus, the meaning of the concept of existence is much more tenuous than our senses would lead us to believe. The second path of thinking is the reductionist attempt to get more data about the underlying structure at the particle level. This effort is predominantly centered on permutations of the twisted ring field model of photons, electrons, and positrons (other particles have not been studied yet). By gaining a geometrically better model than the current zoo specified by the Standard Model, I hope to be able to draw conclusions, or at least better direct, the first path that is vastly larger in its potential impact to how I live my life.

At this point, the philosophical path has me convinced that God does not exist in a way that is portrayed in any religion that I know of–a conscious being with intelligence that can and/or does interact with our existence. I do not see God as having an intellect like ours (possible, but I think that will turn out to be an anthropomorphic view of God) but instead a more generalized “presence” for lack of a better word. Tragedies like the Holocaust, 911, and other unnecessary losses of innocent life suggest that God does not intervene–indeed, I have at last concluded that Jesus’s death at the cross was genuinely profound, but not for the reasons described in Christianity. Jesus laid down a “fleece”, a call for God’s intervention, that is the extreme limit of what is humanly possible. Jesus’s cry “Why have you forsaken me?” at the point of death is the most profound expression that God does not intervene in a way that would show his existence or that would establish an absolute good. Yes, there is an argument that the activity that followed is a description of Jesus’s resurrection, but my attentive reading of the Bible seems fairly suggestive that these were all the result of wishful thinking and self-fulfilling prophesy by the attending witnesses. Obviously, I could be wildly wrong, and condemned for making these conclusions–but I seek truth as best as I can establish it, and that is what I have concluded at this point with what I have learned and observed.

So–with that stone in the foundation of the meaning of existence, where does that leave this thinking path? First, I think it strengthens the idea and importance of the deep level of freedom we enjoy in this existence. There is no absolute good or meaning to life, so we are free to find our own meaning to our existence. The drawback, of course, is that then there is no answer to “what is the meaning of life”, we are free to find our own meaning, there isn’t a default one. The problem with this is that an empty, unthinking lifestyle is still just as empty and thus can be cause for pointless action and despair. However, by resisting this despair and deeply understanding this freedom, I then gain a purpose to life! I understand that meaning to my life will come when I define for myself what meaning to life makes sense for me. For now, meaning definitely is formed when I try to comprehend the basic concepts of the formation of existence and seeking answers to the particular implementation of ideas we find ourselves in. Secondly, unfortunately, my hunch that life has a finite timespan is bolstered with this conclusion about God. It seems unlikely that there is any afterlife of any sort that means anything. When I die, I will experience something akin to sleep, and my waking up will be like a butterfly (or something) from a caterpillar–with nothing preserved along the way. All the atoms that made me will be shuffled around, mixed with others in the vicinity, and maybe another existence will form. This means a couple of things–I will have no perception of a time interval after death to a re-awakening–and, I will have no awareness of the idea of me in a previous existence. They will be the same atoms, but those atoms that stored my memories and experiences will be completely reshuffled in such a way that the memories are totally lost.

So–from the point of view of my existence, there is no afterlife or reincarnation. I must face the utter reality that I have a finite life. I only have so much time to draw conclusions or do whatever analysis before no more will be done. This does point out a bad and a good path to what we do with our life: If we live in such a way as to have what we (or religion) thinks is a better afterlife for our own selves (such as going to heaven or paradise), we are engaging in selfish, wishful, and wasteful activities. On the other hand, making this world a better place (however we choose to define that) is a valid and worthwhile outcome of our study for meaning and purpose–because our re-arranged atoms could easily form another life in this world, and when all, or even most, of the lives in the world recognize that, there is a cumulative improvement to what it means to live. Happiness comes in short term, long term, and sacrificial forms. Once an intelligent life understands that sacrificing some for future arrangements of his atoms, he has gained a purpose and meaning to life that has greater significance than any accomplishment he does in this life (I think).

OK, now just a bit on the second path: more data is needed. I’m starting to put together an idea for a Mathematica project that will form an analytical solution (Schroedinger solution) of the Twist Ring. Here’s what’s currently in progress here, the goal is to find a way, experimentally or analytically, to prove or disprove the ring model of the electron. There are many aspects to consider:

a: the unitary wave model provides a clear-cut method for describing quantum entanglement.
b: the twist model provides a clear-cut geometrical way to describe quantized energy states for photons and electron/positrons, and geometrically explains the anti-particle existence of electrons versus no antiparticle existence of photons.
c: the ring model explains why electrons seem to have no diameter (loop distortion at relativistic speeds)
d: explanation of charge attraction/repulsion of single particle pairs. Attempts to determine the adjustments to the model necessary for analyzing multiple particle combinations.
e: no current model explains the specific mass of electrons (why there are no particles with mass slightly heavier or lighter–the quantized energy of rings does not derive from the quantization of energy states since this quantization permits any possible energy of a photon as long as frequency is an independent variable. In the ring theory, any mass/frequency combination can exist by varying the radius of the ring. Currently I am proposing that the twist model and the unitary wave model (with its noncausal phase property) may yield a quantized electron mass.
f: Possibly related to item e, the ring model should, but does not yet, derive the measured speed of light.

Agemoz

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why 3D+T?

January 15, 2009

I had a wonderful insight that takes the twist quantization to a marvelous level: It explains why there has to be three dimensions plus time. In my previous post I began trying to mathematically describe some of the thinking work I have done, especially in supporting the proposition of twists as a way to obtain quantization, and the unitary phase wave model to explain entanglement (entanglement and Bell’s theorem show that quantum theory cannot be local, and thus is not causal in every aspect. I proposed that if particles are a group wave Fourier composed of unitary but phase adjusted complex waves, the constraints satisfy quantum mechanics). By adding the requirement that a single quantum particle such as a photon is a twist such that the twisting material must return to the original orientation, the E=hv quantization is geometrically realizable.

I had a great insight–I was trying to think of modeling the ring approach for particles with these constraints in Mathematica. I have been working in 1D, and have been asking how an electron could absorb a sufficient energy photon such that it is destroyed into two high energy photons. In my view of how particles and photons work, there are two stable states, straight line quantized twists, and circular quantized twists (recognizing that other particle types are other geometric combinations of twists. Soo–I thought I’ll work in 2D to model particle ring behavior. But then I quickly realized, this cant work–the working view requires that rings intercept photons, which means that a third dimension has to exist. 1D allows photons, 2D allows rings, and 3D allows conversion between rings (mass) and energy (photons), with T being required for describing sequences of events. Hence in order to have energy exchanges and absorption/emission in the ring model, it is necessary to have the 3D+T. I visualized a photon capture by an electron as an arrow through the middle of a circle target, the ring.

A bit of an aside here… I read a bit of Hofstadter’s book “I am a Strange Loop”, and saw a description how physicists have abandoned the various permutations on Bohr’s atom, that is, the various forms of the semiclassical model of the atom and electron. I guess I have to be honest with you and say, yes, I’m more or less going down this rejected path, but with some important distinctions–first and foremost, I am building what looks like a semiclassical electron (a ring) but within a non-local scheme using twists to enforce quantization. Well, dear reader, if there are any of you out there–there it is–that description of my work is a truth here, and you’ll have to decide if I’m flogging a long dead horse or using the semiclassical model as a stepping stone to real truths about our existence.

OK, with that said, let’s go back to that arrow penetrating a circle. When I create a Mathematica model, the circle has its size because the twists only exist if the start of the circle matches the twist orientation of the end of the circle. The same is true for the linear version–the start of a forward moving twist must match the end, and thus enforces a quantization since any partial twist is not allowed to exist. The critical question is–so far my model uses a linear sum of waves to build particles and photons. How can a circle be a stable state? I realized, because of the same reason–there is a system of a pair of twists such that if they didnt move in a circle, the twists would not exist on their own–they would have to be HALF twists!!! It’s sort of like an energy well problem–assuming impassable walls, there are no solutions that exist that have low energy particles escaping–the lowest energy state is to stay in the well. There is no solution to the ring that provides a full twist linear particle and yet conserves momentum. But shoot a sufficient energy particle through the center, and all of a sudden, there is energy and momentum so that two full twists (photons resulting from the annihilation of the electron) can form.

The key now is to find the mathematical description of twists such that the quantization of twists can be enforced within a Schroedinger wave equation.

agemoz

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Unitary Phase Wave Solution

January 7, 2009

Well, back from a good holiday vacation–and now I have a new (legitimate!) copy of Mathematica 7, my favorite playground, a gift courtesy of my son who works at Wolfram! I like it already!

The foundation of a lot of my thinking in the last 6 months has been due to the logical deduction that quantum mechanics, in particular quantum entanglement, logically implies that quantum particles have a noncausal wave phase that has an integer number of twists, the cause of the quantization of energy, momentum, and so on. Since the interference effects of various quantum experiments are non-causal, but all momentum derived characteristics are causal, the implication is that Fourier construction of particles is built on a continuum of waves where the phase information is noncausal but the group wave construction of a particle is causal (limited by the speed of light). Since Fourier compositions have two degrees of freedom, phase and amplitude, the amplitude component has to be unitary in order for twists to truly cause quantization, so the logical conclusion is that the universe can be analyzed as a 3D + T sum of unitary complex valued waves, such that a change in phase affects the entire wave instantly.

In this system, all existence at any point in time is defined solely by the phase values for each frequency. Adding the quantization constraint points to an additional requirement that the quantum particle must twist such that the entry and exit along the axis are in the real plane (thus forcing a fixed energy in the twist). I further postulate that electrons and other particles of mass result from geometrical constructions of these twists.

All this has been discussed at length, but now I want to mathematically detail the implications of the unitary noncausal phase wave model.

First, I will describe some implications that can be shown just by looking at the 1D model. Let’s localize a particle as a delta function, and Fourier compose into a set of frequency components: (and I will leave off the time component for now)

Coeff(k) = Integral(e^i 2Pi (k x) * delta(x0) dx) = e^(i 2Pi (k(x0)))

This shows that each wave coefficient is a unitary complex value (our system of unitary complex waves) and that to create a particle from nothing, all we have to do is set the phase of each wave frequency to k(x0–that is, each wave will get a coefficient that is linear to k*x0. Note that any random setting for phase will not yield any particles (f(random phase) = 0), since Integral(e^(i 2Pi (x + random_phase)dx over all x = 0. But a particle will emerge if the phases linearly follow the frequency.

Now with this, can we show how laws of conservation and the speed of light might emerge for such a particle construction? Well, conservation of the particle momentum and mass will result if the phase(k) has constraints on how it can change. If we move the particle, the x0(t) value gets a delta x added to it, which translates to a multiplier e^(i 2Pi (theta t – k(delta x))). This will have the effect of rotating all of the phase components about the real axis, but does not change the relative distribution of phases.

What does it mean to add a quantity to the phase that is linear to the coefficient frequency?

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twists and quantization

November 13, 2008

I wouldn’t fault you for asking so what? to twists, since I claim that the solution should be valid for standard model physics, in particular as solutions to the Schroedinger and Dirac equations. But twists bring some new things to the table. First, the one dimensional nature of the twist provides for two degrees of freedom in 3D (see prior two posts), thus permitting both satisfactory twist models for both circularly polarized photons and electron/positrons, assuming they are rings. Second, this one dimensional topological structure shows a geometrical means for a tiny particle to absorb a low energy (and hence very very large) photon in its entirety (to me, this is an important question that standard model physics doesn’t appear to raise at all, as far as I know). And third, and conceivably most importantly, the requirement that a twist must contain one or more complete turns provides a geometrical mechanism that explains Einstein’s discovery of quantized photons (the Standard Model does not provide a reason for why quantization exists).

You could imagine an atom orbital electron starting to emit a twist in the EM field that would propagate as a photon, but suppose it doesn’t quite have enough free energy in an orbital level drop to produce a complete twist (rotation of the EM field that makes up a photon). Unable to propagate due to the requirement that the start and end points of a propagating photon must have the same normal vector direction, the orbiting electron retains the energy. Only those orbital drops that produce sufficient energy for the twist will emit.

This leads to the question, why wouldn’t a partial twist propagate, or exist at all? I have some ideas–it may be as simple as a topologically stable twist must point in the same direction as the background EM field (remember my proposal that produces particles simply by altering the phase of unitary waves–this is the only workable explanation for entangled particles, the two slit experiment, etc). This feels uncomfortable, though, since you could argue that there are local areas in a field where waves cancel, thus having no available direction to enforce quantization.

I’ll have to do some more thinking on that–but there’s no question in my mind that twists just about have to be the only available geometrical model that will give photon and particle quantization. I want to see if this sets the path for a good explanation for why rest state free electrons have a specific mass and no other.

Agemoz

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twists and Schroedinger

November 10, 2008

OK, with this twist stuff I’ve gone far enough that I need to reconnect with standard model physics. All this stuff with photons and electrons is well described by the Schroedinger and Dirac equation solutions. Does the twist concept fall in line with this well established work, and if so, does it add anything? I think the answer is yes, and yes. The Schroedinger wave equations should be consistent with the twist concept–it is essentially a Fourier summation of complex wave coefficients that should permit any analytic composition of waves that meets the E=hv requirement, Dirac working relativistically. What does seem to be a problematic issue is the sheath concept, but I’m not at the point where I’m convinced that it is necessary. More thought needs to happen on that.

What about the ring concept for electrons, is that going to pass muster with Schroedinger? Actually, probably the more relevant concern is why experimental physics has not detected internal structure with the electron. High energy scattering produces two types of scattering angle distributions depending on whether there is internal structure to a particle or if it is infinitesimal point-like. If the particle is pointlike, there are essentially equal quantities of reflected particles at every angle–the majority of particles colliding with a point source will not hit, but when it does, there will be a much higher probability of sharply angled rebounds. if there is internal structure, interaction is going to be acting on a diffuse volume, and the majority of successful interactions will see low deflection. Quarks were found because scattering experiments showed internal structure to the proton–but even the highest energy scattering off of electrons shows no internal structure.

Since the twist has no radial dimension, a scattering off of the ring should be at any given instant the same as a point particle. What about a scattering difference based on whether a particle goes through the ring rather than outside (using a particle “smaller” than an electron)? There’s no question, the experimentally observed scattering distribution for an electron is radically different than for a proton. For now, my assumption is that such a particle collision with the ring will not interact unless it hits the twist directly–a knife edge collision that should behave the same as hitting a point particle.

You may be asking (is there really a “you” out there reading any of this? Inquiring minds want to know!!) if electrons are rings, how does that make a knife edge collision? Pretty clearly, the accelerated electron cannot be very sizable if the use of a relativistic electron produces the sharp bounce back when it has hit another particle. My thinking here is that when the ring is accelerated, it becomes a spiral–and the twist within the spiral must hold to c. In order for this to be true, there is no choice but the radius of the spiral must decrease (in fact, this is fascinating in its own right, because when you unroll this spiral, you get a delta distance right triangle that shows that the radial component must decrease by the special relativity beta factor, thus geometrically revealing the Lorentz equations of special relativity).

This radial decrease, when divided by the delta in distance caused by the accelerated particle’s velocity, is exactly Planck’s constant, yielding the uncertainty principle for the electron delta = dx * dp. In the relativistic limit, the ring becomes closer and closer to a straight line, such that it approaches the exact same state as a straight-line twist–that is, a photon of the same energy, at least according to my twist theory. An accelerated electron or positron (for that matter, this analysis would hold true regardless of the geometrical structure of one dimensional twists–any accelerated particle is going to have to asymptotically approach the point particle cross section unless there are multiple components like the proton or neutron).

So–can you see why I think the twist theory, and also the ring theory for the electron (or other particles, which will have some other geometrical combinations of twists) isn’t as far off from established science as perhaps you might have first thought when reading this? Nevertheless, this all assumes the scattering results of hitting a ring of twists would be indistinguishable from hitting a point particle. More thinking, and perhaps some analysis, is needed to see if that’s really true.

Agemoz

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twist field

November 2, 2008

This will be a short post, but not because I haven’t been doing a lot of thinking about the latest ideas about twists. Quantum mechanics epitomized by E=hv says that there is a minimum energy in a photon of a specific frequency, and that any emission of light is an integer multiple of this energy. I came to the conclusion that one workable solution that gives quantized states to a scaleless system is to permit the system to have a substance that normally is homogeneous but can have twists embedded within the substance system. These twists have the nice property of having the right number of degrees of freedom to form photons of circular polarization, and if my ring theory is used, electrons/positrons have the right number of degrees of freedom (spin up/down, matter/antimatter). It explains why electrons have antiparticles but photons do not. This line of thought seems like the strongest possibility because a system of twists is the only possible system that can produce waves that have a fixed amplitude (all our known macroscopic wave systems other than EM radiation has waves that have non-quantized amplitude).

It also explains the stability of quantum particles, since a system with a twist in it is not topologically equivalent to a system without twists. There is no morphism from one to the other, so twists have stability over space and time, even when traveling the length of the universe.

A system of twists has some important assumptions, though, and I spent some time trying to figure them out. At first, I was perturbed by the cut requirement–a twist in 3D requires a discontinuity surrounding the length of the twist. As I realized that the discontinuity must be some topological version of a cylinder where the field is only joined to the twisting material at the end of the cylinder, it began to plague me how a homogeneous material could have a discontinuity. Since the twist has no radial dimension (otherwise electrons could not absorb a photon that is many orders of magnitude bigger), and since the quantized nature of twist energy requires that twists must complete one entire turn of 360 degrees, this sheath cannot consist of empty space and still be a valid solution.

I realized the twist substance must not be homogeneous–it must be composed of at least two distinct materials or states. Eeew, how can a scaleless system evolve to produce this condition? Well, that’s where a lot of my thinking is going. Even the solution using an empty space cylinder cut is a solution of two states, material or no material. This solution doesn’t enforce the integer twist state requirement of quantization, so I have come to the point that our universe has to have two possible states or forms of existence. This actually makes sense when considering the macroscopic EM field as having two orthogonal states. Note that special relativity says that E fields become M fields and vice versa depending on the relative frame of reference–the implication being that there is one material here but it can exist in one of two states or some linear combination of both. Special relativity also severely constrains what kinds of systems we can consider–the photon still has to be a photon no matter how our frame of reference moves.

So–how can a scaleless system produce a two state material–and more importantly, for a system that allows twists, this material must be a surface with one state on one side, and the other state on the other side. Only then can a quantized twist occur, because at each end of the cylinder, the material must connect with the same polarity. Can you visualize this scheme? It’s easier if imagining the 2D analog, where the twist has a cut on either side and there is a mobius-like twist between the cuts. You can see that if the material has both ends with the correct polarity of connections, there has to be a full 360 degree turn–nothing else will work. It’s a wonderful way to visualize why our universe has quantization, but how would a scaleless system produce a two-sided surface like this?

I think the answer is actually pretty obvious–it is probably homogeneous, but is a directional material. When the material is pointing within the 3D surface, it is one state, when it is pointing orthogonal to the 3D surface (in a 4th dimension direction) it is another state–and the states have to be common at the ends of the cylinder, but can twist within it. Ahh, ok–that feels pretty good–except there is (in this scaleless model) no 4D direction, so how can something “point” that way? What does it mean to point, anyway??!
More to come.

Agemoz

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more on twists

October 27, 2008

Well. That thinking on the idea of ideas left me in a funk. It’s becoming somewhat clear to me that there’s not much more to go on that for now–I got to a point where I realized if there is no guiding creator, that we are just some fungus covering a blob of rock–it doesnt really really matter whether we are a self ideating idea or not. Makes me non too optimistic that we will find a purpose/meaning to life.

The twist exploration is a lot more interesting. The neat thing about rings of twists is that it has the right number of degrees of freedom for electron/positrons and probably extends to all particle/antiparticles pairs–and best of all explains why photons do not have an antiparticle. The direction of the twist relative to the spin around the ring creates either the particle (right hand twist, assuming clockwise spin) or antiparticle (left hand twist). And particle absorption of photons has always been a mystery to me–how can a tiny electron truly absorb a photon that can be many orders of magnitude bigger–kind of like a gnat that sometimes swallows a whale, only much larger. But a twist has no radial dimension, so as long as the aim is good, a photon going through the center of an electron ring will always change the momentum of the ring no matter how big the photon is. And, explaining why photons do not have an antiparticle is simple when a photon is represented as a linear twist: a photon antiparticle is just the same photon with opposite circular polarization–a twist going in the opposite direction.

Now, how about the quantum characteristic of same frequency photons in similar paths taking up the same phase (the principle of a laser)? And how about spin-up vs spin down electrons? Seems like there is a need for one more degree of freedom, where is it? The experimentally observed photon polarization vector is two dimensional and probably provides a clue–the twist itself has another degree of freedom in 3D space. In 2D space, there is only one way to twist about an axis embedded in the 2D plane, causing a rotation within 3-space–but in 3D, there are *two* available axes to twist about, one orthogonal within 3D space, and another orthogonal within 4D space. Note that there is no actual displacement in the n+1 space since the twist has no radial dimension, but the twist has a rotation such that a radial component would move into that space.

What’s fascinating about this is that the existence of 2D twists could, via the scaleless system principle, define the emergence of a third dimension… oooh…

I’ll take up the laser in a future post..

Agemoz

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The Idea of Ideas

October 27, 2008

The second train of thought I have had is the idea of ideas. In a previous post, I realized that an existence can emerge with ideas. As always, I’m assuming no guiding creator–if there is one, than my attempts to think about things is moot, because the creator can have any reason He desires for the decisions we see. Only if this creation is unguided does logical thought have a purpose. This is the reasoning behind The One Rule post a while back. If there are multiple independent rules guiding the creation, then that requires something that created the distinguishing factors. Only if there is one rule (for example, the rule could be that nothing created this existence, it came into being from nothing–the train of thought behind the scaleless system of previous posts).

What does it mean for a system to emerge with ideas? This system shows observable quantum entanglement. If the noncausual nature of entanglement is taken as it appears, this says that there is an emergent quality of time and distance that is not fundamental. If these are not fundamental, then the property of distinction is emergent also, thus implying that countability and measurability are emergent properties. If these are emergent then it logically follows that logical analysis itself is an emergent property, it is *not* intrinsic to existence. It is possible in our existence because the One Rule as applied in our existence appeared to eventually have produced countability.

This means that the very idea of ideas is an emergent property of our existence.

This is a very weird thought. But remember that there is a whole bunch of stuff associated with the concept of an idea. An idea can be thought of as a synthesis of prior assumptions and ideas. Ideas have three forms: the pre-emergent form which is a conclusion which could be drawn if the right assumptions and prior ideas are present, the emergent or abstraction form where an entity has thought of the conclusion based on logical thinking, and the realized form, where the idea is implemented in a system which has the necessary assumptions and prior realized ideas.

Let’s talk about idea realization. We are nothing more than an idea. When we die, no twists disappear (assuming no mystical soul or other elements that would violate the One Rule). All the particles in our body still will exist, all the energy will still be there, just in a significantly less ordered state–and increasing in disorder as we decompose. But the ability to perform logical analysis is lost permanently, and memories stored in the biological components of our brain and spine are no longer retrievable (since no ordered system exists which can receive and process those memories). If no twists are lost (and if our dying doesn’t really impact quantum formation or annihilation of twists), that shows that our living state is merely a realization of an idea–the formation of, among other things, a set of twists that in some internally formed way is able to perceive an abstraction of itself and of the concept of ideas.

Hmmm. Time to chew on this some more–this is strange territory for me…

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