Posts Tagged ‘twist’

Renormalization

June 25, 2017

I’m working on the math for the Unitary Twist Field Theory sim. The first sim to run is the easiest I know of, the electron/photon interaction, and if the theory doesn’t yield some reasonably good results, the theory is dead, there’s no point in going further. If that happens, hopefully there will be an indication of how to modify it to make it work, but this will be a defining moment for my work. Just recently, something quite astonishing came out of this work to find the equations of motion for the precursor field of this theory.

In the process of working out the force computations, I’ve been able to winnow down the range of possible equations that will rule the components of the interaction. Note first that the sim I am doing is discrete while the theory is continuous, simply to allow a practical implementation of a computer sim. I can add as many nodes as I want to improve accuracy, but the discrete implementation will be a limitation of the approach I am taking. In addition, forces can be local neighborhood only since according to the theory there is only one element to the precursor field, you can’t somehow influence elements through or outside the immediate neighborhood of an element. The field is also incompressible–you cant somehow squeeze more twist elements into a volume.

To express a twist with all of the required degrees of freedom in R3 + I, I use the e^i/2Pi(theta t – k x) factor. Forces on these twists must be normal to the direction of propagation–you can’t somehow speed it up or slow it down. Forces cannot add magnitude to the field–in order to enforce particle quantization (for example E=hv) the theory posits that each element is direction only, and has no magnitude. I use the car-seat cover analogy–these look like a plane of wooden balls, which can rotate (presumably to massage or relieve tension on your back while driving), but there is no magnitude component. The theory posits that all particles of the particle zoo emerge from conservative variations and changes in the direction of twist elements. To enforce rotation quantization, it is necessary that there be a background rotation state and a corresponding restoring force for each element.

In the process of working out the neighborhood force for each field element, I made an interesting, if not astonishing, discovery. At first, it seemed necessary that the neighborhood force would have a 1/r^n component. Since my sim is discrete, I will have to add a approximation factor to account for distances to the nearest neighbor element. Electrostatic fields, for example, apply force according to 1/r^2. This introduces a problem as the distance between elements approaches zero, the forces involved go to infinity. This is particularly an issue in QFT because the Standard Model assumes a point electron and QFT computations require assessing forces in the immediate neighborhood of the point. To make this work, to remove the infinities, renormalization is used to cancel out math terms that approach infinity. Feynman, for example, is documented to have stated that he didn’t like this device, but it generated correct verifiable results so he accepted it.

I realized that there can be no central (1/r^n) forces in the unitary twist field (this is the nail in the coffin for trying to use an EM field to form soliton particles. You can’t start with an EM field to generate gravitational effects–a common newbie thought partly due to the central force similarity, and you can’t use an EM field to form quantized particles either). Central force fields always result from any granular quantized system of particles issued from a point source into Rn, so assuming forces have a 1/r^n factor just can’t work. The granular components don’t dissipate, after all, where does the dissipated element go? In twist theory, you can’t topologically make a twist vanish. Thus the approximation factor in the sim must be unitary even if the field element distance varies.

Then a powerful insight hit me–if you can’t have a precursor field force dependent on 1/r^n, you should not need to renormalize. I now make the bold assertion that if you need to renormalize in a quantized system, something is wrong with your model. And, of course, then I stared at what that means for QFT, in particular the assumption that the electron is a point particle. There’s a host of problems with that anyway–in the last post I mentioned the paradox of an electron ever capturing a photon if it is a point with essentially zero radius. Here, the infinite energies near the point electron or any charged point particle have to be managed by renormalization–so I make the outrageous claim that the Standard Model got this part wrong. Remember though–this blog is not about trying to convince you (the mark of a crackpot) but just to document what I am doing and thinking. I don’t expect to convince anyone of this, especially given the magnitude of this discovery. I seriously questioned it myself and will continue to do so.

The Unitary Twist Field theory does not have this problem because it assumes the electron is a closed loop twist with no infinite energies anywhere.

Agemoz

Precursor Field Continuing Work

October 28, 2016

I suspect that groundbreaking work in any field which involves the old saw of 5% inspiration, 95% sweat applies to what I’m doing with the precursor field. It may be a rather big chunk of chutzpah to call my work “groundbreaking”, but it’s definitely creative, and is definitely in the “tedious work out the details” phase. To summarize what I am describing here, I have invented an area of study which I’ve encapsulated with a concept name of the “precursor field”. As discussed in many previous posts, the one-line description of this area of study is “If a single field could bring forth the particle zoo, what would it look like”. For the last bunch of posts, I’ve been working out an acceptable list of assumptions and constraints for this field. Not very exciting, but I’m trying to be thorough and make reasonable conclusions as I work step by step on this. Ultimately I want to derive the math for this field and create a sim or analysis to verify that stable particles resembling the particle zoo will emerge.

Up to now, as discussed in many previous posts, I’ve been able to show that the precursor field cannot be derived from an EM field like DeBroglie and others have done, they failed to come up with a workable solution to enable emergence of stable quantized particles. Thus, there has to be a precursor field from which EM field behavior emerges. I’ve been able to determine that the dimensions of this precursor field has to encompass R3 + I as well as the time dimension. The field must be orientable without magnitude variation, so a thinking model of this field would be a volume of tiny weighted balls. Quantum mechanics theory, in particular, non-causal interference and entanglement, force the precursor field to Fourier decompose to waves that have infinite propagation speed, but particles other than massless bosons must form as group wave clusters. These will move causally because motion results from the rate of phase change of the group wave components, and this rate of phase change is limited (for as yet unknown reasons). The precursor field must allow emergence of quantization of energy by having two connections between field elements–a restoring force to I, and a neighborhood connection to R3. The restoring force causes quantized particles to emerge by only allowing full rotation twists of the precursor field. The neighborhood force would enable group wave confinement to a ring or other topological structures confined to a finite volume, thus causing inertial mass to emerge from a twist in the field.

I’ve left out other derived details, but that should give you a sense of the precursor field analysis I’ve been doing. Lately, I’ve come up with more conclusions. As I said at the beginning–this is kind of tedious at this point, but needs to be thought through as carefully as possible, otherwise the foundation of this attempt to find the precursor field structure could veer wildly off course. I’m reminded of doing a difficult Sudoku puzzle–one minor mistake or assumption early on in the derivation of a solution means that a lot of pointless work will follow that can only, near the end of the puzzle derivation, result in a visible trainwreck. I would really like for my efforts to actually point somewhere in the right direction, so you will see me try to be painstakingly thorough. Even then, I suspect I could be wildly wrong, but it won’t be because I rushed through and took conceptual shortcuts.

OK, let me now point out some new conclusions I’ve recently uncovered about the precursor field.

An essential question is whether the precursor field is continuous or is somehow composed of finite chunks. I realized that the field itself cannot exist in any quantized form–it must be continuous in R3 + I. Thus my previously stated model of a volume of balls is not really accurate unless you assume the balls are infinitely small. I make this conclusion because it appears clear that any field quantization would show up in some variation of a Michelson-Morley experiment, there would be evidence of an ether–and we have no such evidence. I thought maybe the field quantization could be chaotic, e.g, elements are random sized–but then I think the conservation of momentum and charge could not strictly hold throughout the universe. So, the precursor field is continuous, not quantum–thus making the argument that the universe is a computer simulation improbable.

The necessity for twists to allow quantized stable particle formation from a continuous field means that this field is not necessarily differentiable (that is, adjacent infinitesimals may have a finite, non infinitesimal difference in orientation). Quantization has to emerge from the restoring force, but cannot pre-exist in the precursor field.

I realized that the emergence of twists within a volume (necessary to form stable solitons) puts a number of constraints on the connecting force (one of the two connections necessary for the precursor field). First, the connection cannot be physical, otherwise twists cannot exist in this field–twists require a discontinuity region along the axis of the twist. Thus, the connection force must work by momentum transfer rather than direct connection. Another way to put it is there cannot be “rubber bands” between each infinitesimal element. Momentum transfer doesn’t prohibit discontinuities in field orientation, but a physical direct connection would.

Secondly, the neighborhood connection can only work on adjacent infinitesimals. This is different than an EM field, where a single point charge affects both neighborhood and distant regions. EM forces pass through adjacent elements to affect distant elements, but the precursor neighborhood force can’t do that without presupposing another independent field. This discovery was a very nice one because it means the field math is going to be a whole lot easier to work with.

Third, the precursor field must be able to break up a momentum transfer resulting from a neighborhood force. It must be possible that if the action of one infinitesimal induces a neighborhood connection, it must be possible to induce this connection force to more than one neighboring infinitesimal, otherwise the only possible group wave construction would be linear twists (photons). A receiving infinitesimal could get partial twist momenta from more than one adjacent infinitesimal, thus the propagation path of a twist could be influenced by multiple neighbors in such a way to induce a non-linear path such as a ring.

Lastly (for now, anyway!) the restoring force means that sums of momentum transfers must be quantized when applied to another field infinitesimal. I realized it’s possible that a given infinitesimal could get a momentum transfer sum greater than that induced by a single twist. In order for particle energy conservation to work, among many other things, there must be a mechanism for chopping off excess momentum transfer and the restoring connection force provides this. The excess momentum transfer disappears if the sum is not enough to induce a second rotation. I can see from simple geometry that the result will always be a single path, it’s not possible for two twists to suddenly emerge from one. I think if you study this, you will realize this is true, but I can’t do that subject justice here right now. I’ll think about a clear way to describe this in a following post, especially since this work will set the groundwork for the field math.

I’ve come up with more, but this is a good point to stop here for now. You can go back to more interesting silly cat videos now ūüôā

Agemoz

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

Basis Field For Particles

July 16, 2016

I think every physicist, whether real or amateur or crackpot, goes through the exercise of trying to work out a geometry for the field that particles reside in.¬† This is the heart of many issues, such as why is there a particle zoo and how to reconcile quantum theory with relativity, either special or general.¬† There are many ways to approach this question–experimental observation, mathematical derivation/generalization, geometrical inference, random guessing–all followed by some attempt to verify any resulting hypothesis. I’ve attempted to do some geometrical inference to work out some ideas as to what this field would have to be.

Ideas are a dime-a-dozen, so throwing something out there and expecting the world to take notice isn’t going to accomplish anything.¬† It’s primarily the verification phase that should advance the block of knowledge we call science.¬† This verification phase can be experimental observation such as from a collider, mathematical derivation or proof, or possibly a thorough computer simulation.¬† This system of growing our knowledge has a drawback–absolute refusal to accept speculative ideas which are difficult or impossible to verify (for example, in journals) can lock out progress and inhibit innovation.¬† Science investigation can get hide-bound, that is stuck in a loop where an idea has to have ultimate proof, but ultimate proof has become impossible, so no progress is made.

This is where the courageous amateur has some value to science, I think–they can investigate speculative possibilities–innovate–and disseminate the investigation via something like a blog that nobody reads.¬† The hope is that pursuing speculative ideas will eventually reach a conclusion or path for experimental observation that verifies the original hypothesis.¬† Unlike professional scientists, there are no constraints on how stupid or uninformed the amateur scientist is and no documentation or credentials that says that science can trust him.¬† The signal-to-noise is going to be so high that it’s not worth the effort to understand or verify the amateur.¬† The net result is that no progress in our knowledge base occurs–professional scientists are stuck as publishable ideas and proof/verification become more and more difficult to achieve, but no one wants to bother with the guesses of an amateur.¬† I think the only way out is for an amateur to use his freedom to explore and publish as conscientiously as he can, and for professionals to occasionally scan amateur efforts for possible diamonds in the rough.

OK, back to the title concept.¬† I’ve been doing a lot of thinking on the field of our existence.¬† I posted previously that a non-compressible field yields a Maxwell’s equation environment which must have three spatial dimensions, and that time is a property, not a field dimension as implied by special relativity.¬† I’ve done a lot more thinking to try to pin down more details.¬† My constraints are driven primarily by the assumption that this field arose from nothing (no guiding intelligence), which is another way of saying that there cannot be a pre-existing rule or geometry.¬† In other words, to use a famous aphorism, it cannot be turtles all the way down–the first turtle must have arisen from nothing.

I see some intermediate turtles–an incompressible field would form twist relations that Maxwell’s equations describe, and would also force the emergence of three spatial dimensions.¬† But this thinking runs into the parity problem–why does the twist obey the right hand rule and not the left hand rule?¬† There’s a symmetry breaking happening here that would require the field to have a symmetric partner that we don’t observe.¬† I dont really want to complexify the field, for example to give it two layers to explain this symmetry breaking because that violates, or at least, goes in the wrong direction, of assuming a something emerged from nothing.

So, to help get a handle on what this field would have to be, I’ve done some digging in to the constraints this field would have.¬† I realized that to form particles, it would have to be a directional field without magnitude.¬† I use the example of the car seat cover that is made of orientable balls.¬† There’s no magnitude (assuming the balls are infinitely small in the field) but are orientable.¬† This is the basic structure of the Twist Field theory I’ve posted a lot about–this system gives us an analogous Schroedinger Equation basis for forming subatomic particles from twists in the field.

For a long time I thought this field had to be continuous and differentiable, but this contradicts Twist Theory which requires a discontinuity along the axis of the twist.¬† Now I’ve realize our basis field does not need to be differentiable and can have discontinuities–obviously not magnitude discontinuities but discontinuities in element orientation.¬† Think of the balls in the car seat mat–there is no connection between adjacent ball orientations.¬† It only looks continuous because forces that change element orientation act diffusely, typically with a 1/r^2 distribution.¬† Once I arrived at this conclusion that the field is not constrained by differentiability, I realized that one of the big objections to Twist Field theory was gone–and, more importantly, the connection of this field to emergence from nothing was stronger.¬† Why?¬† Because I eliminated a required connection between elements (“balls”), which was causing me a lot of indigestion.¬† I couldn’t see how that connection could exist without adding an arbitrary (did not arise from nothing) rule.

So, removing differentiability brings us that much closer to the bottom turtle.¬† Other constraints that have to exist are non-causality–quantum entanglement forces this.¬† The emergence of the speed of light comes from the fact that wave phase propagates infinitely fast in this field, but particles are group wave constructions.¬† Interference effects between waves are instantaneous (non-causal) but moving a particle requires *changing* the phase of waves in the group wave, and there is a limit to how fast this can be done.¬† Why?¬† I don’t have an idea how to answer this yet, but this is a good geometrical explanation for quantum entanglement that preserves relativistic causality for particles.

In order to quantize this field, it is sufficient to create the default orientation (this is required by Twist Field theory to enable emergence of the particle zoo).¬† I have determined that this field has orientation possible in three spatial dimensions and one imaginary direction.¬† This imaginary direction has to have a lower energy state than twists in the spatial dimension, thus quantizing local twisting to either no twists or one full rotation.¬† A partial twist will fall back to the default twist orientation unless there’s enough energy to complete the rotation.¬† This has the corollary that partial twists can be computed as virtual particles of quantum field theory that vanish when integrating over time.

The danger to avoid in quantizing the field this way is the same problem that a differentiable constraint would require.¬† I have to be careful not to create a new rule regarding the connectivity of adjacent elements.¬† It does appear to work here, note that the quantization is only for a particular element and requires no connection to adjacent elements.¬† The appearance of a connection as elements proceed through the twist is indirect, driven by forces other than some adjacent rubber-band between elements.¬† These are forces acting continuously on all elements in the region of the twist, and each twist element is acting independently only to the quantization force.¬†¬† The twist discontinuity doesn’t ruin things because there is no connection to adjacent elements.

However, my thinking here is by no means complete–this default orientation to the imaginary direction, and the force that it implies, is a new field rule.¬† Where does this energy come from, what exactly is the connection between elements that enforces this default state?

 

Oh, this is long.¬† Congratulations on anyone who read this far–I like to think you are advancing science in considering my speculation!

Agemoz

Simulation Construction of Twist Theory

December 2, 2014

Back after dealing with some unrelated stuff.¬† I had started work on a new simulator that would test the Twist Theory idea, and in so doing ran into the realization that the mathematical premise could not be based on any sort of electrostatic field.¬† To back up a bit, the problem I’m trying to solve is a geometrical basis for quantization of an EM field.¬† Yeah, old problem, long since dealt with in QFT–but the nice advantage of being an amateur physicist is you can explore alternative ideas, as long as you don’t try to convince anyone else.¬† That’s where crackpots go bad, and I just want to try some fun ideas and see where they go, not win a Nobel.¬† I’ll let the university types do the serious work.

OK, back to the problem–can an EM field create a quantized particle?¬† No.¬† No messing with a linear system like Maxwell’s equations will yield stable solitons even when constrained by special relativity.¬† Some rule has to be added, and I looked at the old wave in a loop (de Broglie’s idea) and modified it to be a single EM twist of infinitesimal width in the loop.¬† This still isn’t enough, it is necessary that there be a background state for a twist where a partial twist is metastable, it either reverts to the background state, or in the case of a loop, continues the twist to the background state.¬† In this system–now only integer numbers of twists are possible in the EM field and stable particles can exist in this field.¬† In addition, special relativity allows the twist to be stable in Minkowski space, so linear twists propagating at the speed of light are also stable but cannot stop, a good candidate for photons.

If you have some experience with EM fields, you’ll spot a number of issues which I, as a good working crackpot, have chosen to gloss over.¬† First, a precise description of a twist involves a field discontinuity along the twist.¬† I’ve discussed this at length in previous posts, but this remains a major issue for this scheme.¬† Second, stable particles are going to have a physical dimension that is too big for most physicists to accept.¬† A single loop, a candidate for the electron/positron particle, has a Compton radius way out of range with current attempts to determine electron size.¬† I’ve chosen to put this problem aside by saying that the loop asymptotically approaches an oval, or even a line of infinitesimal width as it is accelerated.¬† Tests that measure the size of an electron generally accelerate it (or bounce-off angle impact particles) to close to light speed.¬† Note that an infinitely small electron of standard theory has a problem that suggests that a loop of Compton size might be a better answer–Heisenberg’s uncertainty theorem says that the minimum measurable size of the electron is constrained by its momentum, and doing the math gets you to the Compton radius and no smaller.¬† (Note that the Standard Model gets around this by talking about “naked electrons” surrounded by the constant formation of particle-antiparticle pairs.¬† The naked electron is tiny but cannot exist without a shell of virtual particles.¬† You could argue the twist model is the same thing except that only the shell exists, because in this model there is a way for the shell to be stable).

Anyway, if you put aside these objections, then the question becomes why would a continuous field with twists have a stable loop state?¬† If the loop elements have forces acting to keep the loop twist from dissipating, the loop will be stable.¬† Let’s zoom in on the twist loop (ignoring the linear twist of photons for now).¬† I think of the EM twist as a sea of freely rotating balls that have a white side and a black side, thus making them orientable in a background state.¬† There has to be an imaginary dimension (perhaps the bulk 5th dimension of some current theories).¬† Twist rotation is in a plane that must include this imaginary dimension.¬† A twist loop then will have two rotations, one about the loop circumference, and the twist itself, which will rotate about the axis that is tangent to the loop.¬† The latter can easily be shown to induce a B field that varies as 1/r^3 (formula for far field of a current ring, which in this case follows the width of the twist).¬† The former case can be computed as the integral of dl/r^2 where dl is a delta chunk of the loop path.¬† This path has an approximately constant r^2, so the integral will also vary as r^2.¬† The solution to the sum of 1/r^2 – 1/r^3 yields a soliton in R3, a stable state.¬† Doing the math yields a Compton radius.¬† Yes, you are right, another objection to this idea is that quantum theory has a factor of 2, once again I need to put that aside for now.

So, it turns out (see many previous posts on this) that there are many good reasons to use this as a basis for electrons and positrons, two of the best are how special relativity and the speed of light can be geometrically derived from this construct, and also that the various spin states are all there, they emerge from this twist model.¬† Another great result is how quantum entanglement and resolution of the causality paradox can come from this model–the group wave construction of particles assumes that wave phase and hence interference is instantaneous–non-causal–but moving a particle requires changing the phase of the wave group components, it is sufficient to limit the rate of change of phase to get both relativistic causality and quantum instantaneous interference or coherence without resorting to multiple dimensions or histories.¬† So lots of good reasons, in my mind, to put aside some of the objections to this approach and see what else can be derived.

What is especially nice about the 1/r^2 – 1/r^3 situation is that many loop combinations are not only quantized but topologically stable, because the 1/r^3 force causes twist sections to repel each other.¬† Thus links and knots are clearly possible and stable.¬† This has motivated me to attempt a simulation of the field forces and see if I can get quantitative measurements of loops other than the single ring.¬† There will be an infinite number of these, and I’m betting the resulting mass measurements will correlate to mass ratios in the particle zoo.¬† The simulation work is underway and I will post results hopefully soon.

Agemoz

PS: an update, I realized I hadn’t finished the train of thought I started this post with–the discovery that electrostatic forces cannot be used in this model.¬† The original attempts to construct particle models, back in the early 1900s, such as variations of the DeBroglie wave model of particles, needed forces to confine the particle material.¬† Attempts using electrostatic and magnetic fields were common back then, but even for photons the problem with electrostatic fields was the knowledge that you can’t bend or confine an EM wave with either electric or magnetic fields.¬† With the discovery and success of quantum mechanics and then QFT, geometrical solutions fell out of favor–“shut up and calculate”, but I always felt like that line of inquiry closed off too soon, hence my development of the twist theory.¬† It adds a couple of constraints to Maxwell’s equations (twist field discontinuities and orientability to a background state) to make stable solitons possible in an EM field.

Unfortunately, trying to model twist field particles in a sim has always been hampered by what I call the renormalization problem–at what point do you cut off the evaluation of the field 1/r^n strength to prevent infinities that make evaluation unworkable.¬† I’ve tried many variations of this sim in the past and always ran into this intractable problem–the definition of the renormalization limit point overpowered the computed behavior of the system.

My breakthrough was realizing that that problem occurs only with electrostatic fields and not magnetic fields, and finding the previously mentioned balancing magnetic forces in the twist loop.¬† The magnetic fields, like electrostatic fields,¬† also have an inverse r strength, causing infinities–but it applies force according to the cross-product of the direction of the loop.¬† This means that no renormalization cutoff point (an arbitrary point where you just decide not to apply the force to the system if it is too close to the source) is needed.¬† Instead, this force merely constrains the maximum curvature of the twist.¬† As long as it is less that the 1/r^n of the resulting force, infinities wont happen, and the curve simulation forces will work to enforce that.¬† At last, I can set up the sim without that hokey arbitrary force cutoff mechanism.

And–this should prove that conceptually there is no clean particle model system (without a renormalization hack) that can be built from an electrostatic field.¬† A corollary might be–not sure, still thinking about this–that magnetic fields are fundamental and electrostatic fields are a consequence of magnetic fields, not a fundamental entity in its own right.¬† The interchangability of B and E fields in special relativity frames of reference calls that idea into question, though, so I have to think more about that one!¬† But anyway, this was a big breakthrough in creating a sim that has some hope of actually representing twist field behavior in particles.

Agemoz

PPS:¬† Update–getting closer.¬† I’ve worked out the equations, hopefully correctly, and am in the process of setting them up in Mathematica.¬† If you want to make your own working sim, the two forces sum to a flux field which can be parametrically integrated around whatever twist paths you create.¬† Then the goal becomes to try to find equipotential curves for the flux field.¬† The two forces are first the result of the axial twist, which generates a plane angle theta offset value Bx = 3 k0 sin theta cos theta/r^3, and Bz = k0 ( 3 cos^2 theta -1)/r^3.¬† The second flux field results from the closed loop as k0 dl/r^2).¬† These will both get a phase factor, and must be rotated to normalize the plane angle theta (some complicated geometry here, hope I don’t screw it up and create some bogus conclusions).¬† The resulting sum must be integrated as a cross product of the resulting B vector and the direction of travel around the proposed twist path for every point.

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

New Papers on Speed of Light Variation Theories

April 28, 2013

A couple of papers to a European physics journal (http://science.nbcnews.com/_news/2013/04/28/17958218-speed-of-light-may-not-be-constant-physicists-say?lite –probably not the best place to get accurate reviews, but interesting anyway) attempt to show how the speed of light is dependent on a universe composed of virtual particles.¬† The question here is why isn’t c infinite, and of course I’ve been interested in any current thinking in this area because my unitary twist field theory posits that quantum interference results from infinite speed wave phase propagation, but that particles are a Fourier composition that moves as a group wave that forms a twist.¬† Group waves form a solition whose motion is constrained by the *change* in the relative phases of the group wave components.

Both theories were interesting to me, not because they posited that the speed of light would vary depending on the composition of virtual particles, but because they posit that the speed of light is dependent on the existence of virtual particles.  This is a match with my idea since virtual particles in the unitary twist field theory are partial twists that revert back to a background vector state.  Particles become real when there is sufficient energy to make a full twist back to the background state, thus preserving the twist ends (this assumes that a vector field state has a lowest energy when lining up with a background vector state).  But virtual particles, unlike real particles, are unstable and have zero net energy because the energy gained when partially twisting is lost when the twist reverts back to the background state.

These papers are suggesting that light propagates as a result of a constant sequence of particle pair creation and annhiliation.¬†¬† The first glance view might be that particle pair creation is just a pulling away of a positron and an electron like a dumb-bell object, but because charged particles, virtual or real, will have a magnetic moment, it’s far more likely that the creation event will be spiralling out–a twist.¬† Yes, you are right to roll-your-eyes, this is making the facts fit the theory and that does not prove anything.¬† Nevertheless, I am seeing emerging consensus that theories of physical behavior need to come from, or at least fully account for, interactions in a sea of virtual particles.¬† To keep the particle zoo proliferation explanation simple, this sea of virtual particles has to be some variation of motions of a single vector field–and in 3D, there’s only two simple options–linear field variation, and twists.¬†¬† Photons would be linear twists and unconstrained in energy–but particles with rest mass would be closed loops with only certain allowed energies, similar to the Schrodinger electron around an atom.¬† Twists in a background vector field also have the advantage that the energy of the twist has to be quantized–matching the experimental E=hv result.

Agemoz

Lattice fields and Specular Simulation (latest work)

August 25, 2012

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

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

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

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

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

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

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

Quantized Fields

July 11, 2012

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

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

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

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

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

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

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

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

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

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

Agemoz

The Quandary of Attraction, part II

April 23, 2012

I mentioned previously that the attraction between two opposite charged particles appears to present a conservation of momentum problem if electrostatic forces are mediated by photon exchanges.  Related to this issue is the question of what makes a photon a carrier of a magnetic field versus an electrostatic field. QFT specifies that this happens because the field (sea of electron-positron pairs/virtual particle terms) absorbs the conservation loss, but as far as I can find, does not try to answer the second question.

Part of the difficulty here is that attempting to apply classical thinking to a QFT problem doesn’t work very often.¬† Virtual photons in QFT do not meet the same momentum conservation rules we get in classical physics, either in direction or quantity.

But, since I hypothesize an underlying vector field structure, it is interesting to pursue how the Unitary Twist Field theory would deal with these issues.

I ruled out any scheme involving local bending of the background field vector.¬† This would be an appealing solution, easy to compute, and easy to see how different frames of reference might alter the electrostatic or magnetic nature.¬† But this doesn’t work because you must assume any possible orientation of the electron ring, and it is easy to show that a local bend would be different for two receiving particles at equal distance but different angles from a source particle.¬† I worked with this for a while and found there is no way that the attraction due to a delta bend would be consistently the same for all particle orientations.

The only alternative is to assume that the field consists of twists, either full or partial returning back to the background state (photons and virtual photons respectively).¬† Why does an unmoving electron not move in a magnetic field but is attracted/repelled in an electrostatic field?¬† QFT answers this simply by assuming that the electrostatic and magnetic components of the field are quantized and meet gauge invariance.¬†¬† My understanding of QFT is that asking if a single photon is magnetic or electrostatic is not a valid question–the field is quantized in both magnetic and electrostatic components, composed of virtual photon terms that don’t have a classical physical analog.

I suppose the unitary twist field theory is yet another classical attempt.¬† Nevertheless, it’s an interesting pursuit for me, mostly because of the geometrical E=hv quantization and special relativity built in to the theory.¬† It seems to me that QFT doesn’t have that connection, and thus is not going to help derive what makes the particle zoo.

This underlying vector field does not have two field components real and imaginary, just one real.¬† Even if this unitary twist field thing is bogus, it points to an interesting thought.¬† If¬† our desired theory (QFT or unitary twist field) wants to distinguish between a magnetic field or an electrostatic field using photons, we only have one degree of freedom available to do the distinction–circular polarization.¬† What if polarization of photons was what made the field electrostatic or magnetic?

An objection immediately comes to mind that a light polarizer would then be able to create electrostatic or magnetic fields, which we know doesn’t happen.¬† But I think that’s because fields are made of much lower energy photons.¬† Fourier decomposition of a field would show the vast majority of frequency components would be far lower even when the field energy is very high–in the radio frequency range.¬† Polarizing sheets consist of photon absorbing/retransmitting atoms and would be constrained to available band jumps–I’m fairly certain that there is no practical way to construct a polarizer at the very low frequencies required–even the highest orbitals of heavy atoms are still going to be way too fast.

If polarization is the distinguishing factor, then it poses some interesting constructions for the unitary twist field approach.¬† If it is not, then the magnetic versus electrostatic can only be an aggregate photon array behavior, which seems would have to be wrong–a thought experiment can be constructed that should disprove that idea.¬† Quantization of a very distant charged particle effect, where the quantized field particle probability rate is slow enough to be measurable, could not show the distinction in any given time interval.

Supposing polarization is the intrinsic distinction in single photons.  Unitary twist fields have two types of linear twist vectors, those lying in the plane common to the background vector and normal to the direction of travel, and those lying in the plane common to the background vector and parallel to the direction of travel.  (There is a degenerate case where the direction of travel is the same as the direction of the background state, but this case still has circular polarization because there are now two twist vectors in the planes with a common background vector and a pair of orthogonal normal vectors).

Since static particles are affected by one twist type (inline or normal) and not the other, and moving particles are affected by the other twist type, one proposal would be that the particle experiences only the effect of one of the twist types relative to the path of motion and the background vector.  For example, if the particle is not moving, only twists normal to the direction of travel will alter the internal field of the receiving particle such that it moves closer or further away (attraction or repulsion).  A problem with this approach is the degenerate case, which must have both and eletrostatic and magnetic response, but both twist vectors will be inline twists, there is no twist normal to the background state that will include the background state vector.

More thinking to come…

Agemoz