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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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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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twists

October 26, 2008

Some pretty interesting thinking, but difficult to pin down. I thought a lot about the twist in the surface that I hypothesized explains the quantization of particles. I previously had proposed that a single twist would best explain quantization, but needed to really nail down this concept. On a second path, I did a lot of thinking about the idea of ideas.

First–about twists. The going premise is that this is a world which doesn’t require a guiding creator, otherwise the main point of all this thinking is answered–and as a corollary, no further thinking really is needed, because a guiding creator could alter the existence according to His whims, thus making logical analysis less useful. The much more interesting question is whether the universe as it is could come into being without such a creator. In this scenario, logical analysis is particularly useful because the formation of our existence is not guided or sustained, but must result purely from consequence–the purest target of logical analysis.

So, in proceeding down the path of scaleless system formation, the integration of quantization observations appears to suggest that our 3D world either consists of a twist of a two-state material within the 3D world, or that the 3D world is a surface of a 4D bubble, and the twist is about an axis rotating into the 4D world. The twist itself should not have a radial dimension but must vary in the length along the axis of the twist to generate the degree of freedom required by unconstrained photon energy. This approach makes a whole lot of sense when we think of the EM field properties of a propagating photon as well as the Plancks constant (E = hv) quantization of particles. But it raises a bunch of questions, too: if only full turns of the twist can exist due to quantization, it would seem that a field rip or cut is required about the twist axis–and it would appear to require that the field has two components so that the components line up before and after the twist, although this is consistent and implied by the E and M nature of photons as well. But–how can this cut exist without being a field discontinuity? One thing for sure–if particles are explained as rings of twist pairs, or more complex structures of twists, such cuts imply that they cannot dissipate. Topologically, a twist with cuts in 3D space cannot be equivalent to any continuous field, and thus is stable. Such a system, having no path to dissolution, will lead to conservation of matter/energy if one assumes that particles and photons are systems of twists. Particles become self contained sets of twists rotating, say, in a circle at the speed of light, while photons are linear sets of twists propagating in a straight line. One thus could interchange energy and mass, but it is not possible for the total energy represented by either form to be added to or removed.

Twists thus are an exciting possibility for representing the quantized state of the EM field, and strengthens the case for some variation of the charge loop hypothesis that I’ve proposed throughout this journal. But those questions remain. There is that need for a field discontinuity (implied anyway by conservation–any analytic field solution would dissipate). Why does the twist have to propagate? It appears that observation does not allow the twist to stay in one place. Another question–the twist is stable in time and space–whether in energy form (photons) or matter, so since interchange between mass and energy forms is possible, but one way or the other, the twist cannot vanish or spontaneously appear. Yet, quantum theory specifies that a pure vacuum is not the lowest energy state, that in such cases, photon pairs or electron-positron pairs (or other particle combinations) will spontaneously appear. Why? Does the twist model explain this in some way? The converse, where particles annihilate, and the situation where electrons absorb a photon, all beg for understanding using this twist theory. And what about the other forces, the Strong and Weak forces and gravity–what role do these play in this twist theory?

Uggh. That’s enough to swallow for one day…

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Group waves and twists

September 27, 2008

Let me go to another thread of thought that comes from the group wave thinking I have done. You may recall, this is the attempt to explain quantum behavior by stating that particles in our existence, both massive and massless, are formed by a Fourier composition of all possible unitary magnitude wave frequencies. The waves have no intrinsic causality such that a change in phase at a given frequency affects the whole wave instantaneously (providing the mechanism for various quantum paradoxes such as the two-slit experiment and quantum entanglement). If this collection of waves is completely random, there are no particles (do an inverse Fourier transform of a constant value, this will give nothing in physical space). But if the waves have phase such that (for example, in 1D space) the wave phase is equal to e^(Pi I freq), then a delta function, that is, a particle, will exist in physical space. The particle moves if the wave phases have a constant e^ (Pi I x0) applied to it over an interval of time. Using the same analysis you can also create or annihilate more particles on the same collection of unitary waves. You can re-state laws of conservation of energy, charge, and other properties in terms of allowable changes in the phase behavior of these waves.

With such a system you can create finite causality of a group wave construction such as a delta function and its movement (that is, a speed limit c) by limiting how quickly the phases can shift. I explained all of this previously, but now I have new thoughts on this. One of them came when trying to envision just what a photon is–in such a system the photon emerges as a Fourier decomposition along a straight line. But what is the mathematical structure of this photon, and how could such a construction emerge from a scaleless system? Well, one very important result of this model is that the construction must result from an infinite range of wave frequencies *all with the same magnitude*. This magnitude is important, it is an unconstrained parameter of the system but must be constant across all frequencies (otherwise the emergence of group causality is very problematic).

This is profoundly important because of Einstein’s discovery that photon reception in a photomultiplier tube is quantized. What does it mean to be quantized? It means that at a given frequency, there is a minimum amount of energy possible in a photon, and it means that the amount of energy that any set quantity of photons can have is an integer multiple of this minimum. This means that there is something about the nature of a photon that has only so much energy and no more or less. In my model, the amplitude is constant (and could be considered a cosmological constant) for all waves composing the photon, so the only possible variable is the number of cycles of a single photon. If there is more than one cycle to a photon, it seems that the photon would be divisible, and that higher energy collections of photons would yield fractional photons, so I conclude that the photon must compose of exactly one cycle.

In the Fourier decomposition of unitary waves, the delta function that emerges would be due to one or more *twists* of the field in 3D space. This twist is topologically stable and accounts for the enduring stability of the photon as it travels through the universe–only the interception of the photon by a ring of twists (a massive particle) can deconstruct the twists.

Why is the twist such an important answer? Because it provides a solid and believable mechanism for the most important question in quantum theory–Why is there quantization? Why does a discretization appear in a continuous scale-less system? Photons can have an infinite range of frequencies, but only discrete energies: Twists provide an answer–it is not possible to have a partial twist in a 3D spatial system, the twist must return the field to its starting state. Thus there is either no twist, or a complete 360 degree twist, thus causing the observed quantization.

There is no possible field construction other than a twist that can topologically reside in 3D space without having a dimension normal to the direction of travel. But–is it one twist or two? If it is one twist, it is difficult to assign a frequency (energy) to the photon because the model assumes a unitary set of waves of varying frequency. If it is two twists, then a new degree of freedom is added based on the separation in time and distance of the twists. The longer the separation, the lower the energy of the photon. But how can the photon not vary in energy by changing the separation distance? I don’t know, but now I think that two twists is not workable–instead, there is another way to add the necessary degree of freedom if one assumes a momentum of twisting. The faster the twist, the greater the energy.

What’s interesting about twists is considering the zoo of massive particles and how to explain the proliferation of particle types (in a constant effort to bring physics down to the One Rule). It’s conceivable that the various particles are various geometrical permutations of sets of twists. The ring of two twists, my hypothesis for the electron and positron) is one of the simplest. The direction of the twist about the ring spin determines whether the particle is matter or antimatter. I can imagine that protons composed of three quarks might actually be a stable three way configuration of twists of the spacetime field. Muons might be some other geometrical combination of twists.

An unanswered question that is getting some of my thinking is why does a ring of two twists only have one possible stable state? For a given frequency, the field wave magnitude defines the quantized energy, but there are a continuous infinite number of frequencies available–why does the electron have just one of those?

More thinking on this idea to come..

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entangled particle consequences

July 8, 2008

Another important revelation on entangled particles–particles either are un-entangled (resolve only to one particular state) or are entangled (share orthogonal states with one or more other particles). If, say, two particles are entangled, they share a pair of states, such that when one particle resolves to one of the two states, the other particle must resolve to the other. It’s extremely handy to represent this situation with a complex variable where the states are represented by a vector basis (not necessarily the real and imaginary axes). Resolving a particle state (e.g, an electron with spin up or spin down states) means projecting the current superposed pair of states to one or the other basis vector, and if the particle is entangled with another, then the other particle must resolve to the opposite (orthogonal) basis vector.

You can think of this by representing the superposed state of each vector by a sum of waves, each representing one of the basis vectors, that are constantly shifting phase. When one particle resolves in a detector, that wave (basis vector) is removed from the sum, leaving the other particle with only the remaining wave basis vector to resolve to.

But look at this–in the previous post, I said there was evidence that the wave phase information is not affected by distance since entanglement remains in effect regardless of the separation between the entangled particles. Here’s even better evidence, and a new insight, for me, at least: entanglement still happens regardless of what is put in between the particles after they fly apart. You could conceivably put a planet or a star or even a black hole in between the two particles and entanglement resolution would still happen. You could attempt to block every possible Feynman type path between the particles and theory says the particles must resolve to different states. Whoa! The resolving of the entanglement condition is not using the physical space between the separating particles to communicate–the phase information is either coupled via another non-causal dimension–or, my previous hypothesis, there is no distance between the particles as far as wave phase is concerned!! Really, if you think about it, those two ideas can be considered equivalent, since a non-causal dimension really means there is no distance within it, and thus it truly is not a dimension by definition.

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