Posts Tagged ‘vector field’

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

Preparing First Collision Sim

June 22, 2017

I’ve been working fairly consistently on the simulation environment for the unitary twist field theory. I’m getting ready to set up a photon/electron collision, modeled by the interaction of a linear twist with a twist around a loop. The twist is represented by e^I(t theta – k x), yes, the same expression that is used for quantum wave functions (I’ve often wondered if we’ve misinterpreted that term as a wave when in fact the math for a twist has been in front of our noses all along).

This is a great first choice for a collision sim because in my mind there’s always been a mystery about photon/particle interactions. If the electron is really a point particle as the Standard Model posits, how can a photon that is many orders of magnitude larger always interact with one and only one electron, even if there are a gazillion electrons within one wavelength of the photon? The standard answer is that I’m asking the wrong or invalid question–a classical question to a quantum situation. To which I think, maybe, but quantum mechanics does not answer it, and I just get this sense that refusing to pursue questions like this denies progress in understanding how things work.

In twist theory there appears to be an elegant geometrical answer that I’m pretty sure the simulation will show–counting my chickens before they are in my hand, to be sure–the downfall of way too many bright-eyed physics enthusiasts. But as I’ve worked out before, the precursor twist field is an incompressible and non-overlapping twist field. If the electron is a closed loop of twists, and within the loop the twists revert back to the I direction (see previous posts for a little more detailed description), then any linear twist propagating through the loop will add a delta twist to some point in the interior of the loop. Since you cannot somehow overlap twists (there’s only one field here, you can’t somehow slide twists through each other. Each point has a specific twist value, unlike EM fields where you linearly combine distinct fields). As a result, the twist of the loop can unwind the linear twist going through it, causing the photon to disappear and the close loop will pick up the resulting linear twist momentum. This isn’t really a great explanation, so here’s a picture of what I think will happen. The key is the fact that the precursor field has one twist value for every point in R3. It’s an incompressible and unitary field–you cant have two twist values (or a linear combination–it’s unitary magnitude at every point!) at a given point, so the photon twists have to affect the twist infrastructure of the loop if it passes through the loop. It really will act a lot like a residue inside a surface, where doing a contour integral will exactly reflect the number of residues inside.

At least that’s what I think will happen–stay tuned. You can see why I chose this interaction as the first sim setup to try.

Agemoz

Quantum State Superposition in the Precursor Field

January 1, 2017

I’ve been continuing to work on what a field would have to look like if it were the underlying mechanism for the particle zoo and force fields. One thing I haven’t discussed that will be noticed instantly by anyone who studies physics–this precursor field must allow quantum state superposition. I’ve so far posted a geometrical set of constraints, but I’ve always had an awareness that the model is incomplete–or won’t work at all–if I can’t provide some means for state superposition.

The trouble with inventing a theory like this is that the job is truly humongous. The number of details that have to be verified as correct is really beyond the reach of one person or even a team of people, so I’ve had to trudge on knowing that this whole thing will be laughed off in seconds by experienced theoreticians who spot a missing or wrong claim. This is definitely one of them, if I don’t provide a believable mechanism for quantum state superposition, nobody will bother to look.

So–I’ve spent some time thinking on this. I actually have enough worked out that I want to try a sim of the model, but then I thought–no, make sure quantum states can work with the model. Otherwise the sim will be a waste of time and probably not really even interesting. Probably the easiest and simplest quantum state superposition to think about is electron spin, which I’m going to take the liberty of modelling with a twist ring. There are two spin parameters in a twist ring, one of which is degenerate by rotation(*). To isolate the true degrees of freedom in a gauge invariant system, I will set the ring rotation direction as clockwise, for example, and then see just one degree of freedom in the axial twist direction along the rotation direction–it can be either clockwise or counterclockwise. I will call this the spin of the particle, either up or down.

Now, to specify a quantum state superposition, the particle spin can be either up or down or a linear combination of spin-up and spin-down. Does the unitary twist field theory precursor field allow this? I believe it is easy to say yes. Treat the loop as a transmission line with a discontinuity sheath surrounding the twist. The twist itself is a Fourier construction of standing waves that can encapsulate such a linear composition of the up and down spin. If the particle encounters a spin detector, an operator acts on the linear composition to filter the wave composition and resolve the spin state.

There’s my hand-wavy analysis, no proof by any stretch of the imagination. That is a chore that will have to wait. It looks viable to me, but I have so many other alligators in this swamp that this will have to do for now.

Agemoz

*Note that it’s only degenerate in R3 for purposes of this example. In reality, the R3 + I background state will be different for the two loop rotations, thus providing the required degrees of freedom for both spin and the particle/antiparticle duality.

Precursor Field Forces

December 18, 2016

It looks clear now (see previous posts) that the precursor field (my underlying field proposal that is hypothesized to give rise to the particle zoo and EM and other fields) has to have a discontinuity to enable twists. This is great for quantization as mentioned in the previous post, but is really ugly for the math describing the field. Could nature really work this way? I’m dubious, but all of my analysis seems to show this is the only way, I’ve only gotten here because I have seen no other paths that appear to work.

For example, it’s obvious to everyone that an EM field can’t be the basis for quantization or solitons–lots of historical efforts that many have looked at and ruled out. Twists in a background state is a geometrical definition of quantization. Lattice and computer sim schemes are ruled out (in my mind, anyway) because I think there should be observable ether-like consequences. Adding an I direction to the R3 of our existence is necessary since twists in R3 could not provide the symmetries required for guage invariance and exchange particle combinations. The I dimension, which is merely an element pointing direction that does not lie in a physical real axis of R3, enables twist quantization, and unlike photon ring theories such as DeBroglie’s, can enable twist trajectory curvature–a necessity to allow closed loop solutions that confine particles to a finite volume. There are many more necessary constraints on this precursor field, but the most problematic is the need for field discontinuities. Any twist in a unitary orientable vector field has to be surrounded by a sheath where the twist disconnects from the background state pointing in the I direction.

Requiring discontinuities needed for enabling field twists is an ugly complication. We know already that any quantizing field theory underlying particle creation/annihilation cannot be linear since dissipation destroys particle stability–solitons cannot be formed. Almost by definition this means that the field has to have discontinuities, but mathematically describing such a field becomes very problematic. Obviously, such a field will not be differentiable since differentiability, at least finite differentiability, implies linearity.

As I’ve mentioned in previous posts, the precursor field has two connections that act like forces. From these connections arise linear and curving twists, exchange bosons of fields, and so on. The first force acts only on a field element, and provides a restoring force to the background state. The second, neighboring affect force, provides an influence on immediately adjacent neighboring elements of the precursor field. The first force should not be conceptually complex–it just means that, barring any other effect, a field element vector will return to the background state.

The second force is more complex. I see at least two options how this force might work. It should be obvious this force cannot be proportionate to the dimensional rate of change of rotation because discontinuities would make this force infinite. In fact, to keep a particle from dissociating, there must be an adhesion to nearby elements–but NOT across a discontinuity. Otherwise, the force due to the discontinuity would be far greater than the force holding the elements of the twists, where each end is bound to the background state (or to the 0 and 2Pi phase rotation connection of the closed loop twist). If that happens the forces across the discontinuity would be far greater that the force tying down the twist ends to the background state and our particle, whether linear or closed loop, would immediately be shredded into nothing.

The other possibility for the second force is to make it only proportionate to the timewise rate of change of adjacent elements (sort of like induction in magnetic fields), but again, the discontinuity sheath would bring in potential infinities.  Right now this approach does not show promise at all for a bunch of reasons.

I think the only viable description of the neighborhood force would be an adhesion to nearby states who’s orientation is the same or very slightly different. That is, the angular delta from nearby elements causes a force to make that delta 0, but if there is a rip or tear then no force occurs). An important side question is whether the neighborhood connection is stronger than the restoring to I force. It’s not clear to me right now if it matters–I think field quantization works regardless of which is stronger.

This finally gives me enough description that I can mathematically encode it into a simulation. I realize that just about all of you will not accept a theory with this sort of discontinuity built into every single particle. Like you, I really am quite skeptical this is how things work. I hope you can see the logic of how I got here, the step-by-step thinking I’ve done, along with going back and seeing if I overlooked a different approach (eg, more dimensions, string theory, etc) that would be more palatable. But that hasn’t happened, I haven’t seen any other schemes that could work as well as what I have so far.

Agemoz

Precursor Field Does Not Have to be Discontinuous

December 3, 2016

In trying to ferret out the properties of a precursor field that would give rise to the particle zoo and EM fields and so on, I had been working out just what this field would look like if it could form a loop. I have so far determined that it would have to reside in a orientable, unitary R3 + I vector field, the same dimensionality as the quantum oscillator field, and that to achieve E=hv quantization, quanta would take the form of twists in a background state pointing in the I direction. I figured out that a twist would curve in R3 if it formed a loop around a central background state region, because regardless of the loop topology in R3, it would always pass through a field orientation tilt toward the central I background region.

Up to now, the concept seemed to be workable, but I always have struggled with the field twist concept. I knew that in R3, you cannot have a field twist without a field discontinuity along the twist axis, which really caused me to doubt the veracity of the unitary twist theory. I know of no instance in the real universe where there’s a true discontinuity–even in black holes. To have our existence form from particles made of twists and field discontinuities has always seemed unlikely to the extreme–I have several times nearly abandoned this work because non-analytic fields seemed non-intuitive, non-differentiable, and non-geometrical.

However, when I tried to detail the specific mathematical possibilities for describing a curved twist in the R3 + I field, I discovered something quite surprising. Every mathematician probably knew this already–but when vector fields are described in four dimensions (R3 + I), axial twists can form in three of the four dimensions and not cause a discontinuity. The I orientation gives the field surrounding the twist an extra degree of freedom that removes the necessity for a discontinuity.

However, this does cause a different problem with the unitary twist theory. We all know that trying to form a soliton out of photons (an EM closed loop solution) is impossible because nothing can curve a photon into a ring. A big problem with trying to describe quantized photons out of EM waves is the dissipation problem, why doesn’t a quantized photon just radiate into nothing, thus losing the apparent quantization and conservation of energy? Currently, Standard Model physics doesn’t really provide an answer to that, but in unitary twist field theory work, I had determined that the discontinuities in a precursor field had acted as a lock that prevents unraveling of the particle, and thus may be necessary for particle stability. You can’t unravel a quantized twist in R3 (causing a particle loop or linear twist to disappear) because you would have to somehow resolve the discontinuity to the background state–and that definitely can’t be done in R3. But in R3 + I, there is no discontinuity required, and thus I think any twist configuration could disappear, thus potentially destroying the energy present in the particle.

So–which is it? We need R3 plus I to achieve quantization and closed loop twists–but R3 + I means we don’t have to have discontinuities–a far more realistic and likely representation of our universe via a unitary vector field, but with the disadvantage that what now enforces quantization? Are there solutions in R3 + I that still depend on a discontinuity for stability and conservation of energy?

Looks like more study and thinking is needed.

I’ll bet there’s a few scientists out there wondering if I could achieve something a lot more significant if I’d put all this time and energy into something worthwhile!

Agemoz

A Promising Precursor Field Geometry

November 29, 2016

I’ve been trying to find a geometrical description of how a unitary field twist could curve. If my hypothesis for the particle zoo arising from a precursor field is correct, the precursor field has to have a number of constraints. I’ve described what I know so far in depth in previous posts–here’s a summary of some of the basic requirements:
a: The precursor field cannot be an EM field with some sort of quantization added to it. The precursor field has to give rise to EM fields (and particles) but it has to be a continuous vector field with no magnitude (orientable only).
b: This field resides in R3 + I (same as the quantum oscillator spacetime) where quantization is achieved via twists that return to a background state pointing in the I direction.
c: There must be two connections built into the precursor field–a restoring force to I, and some kind of angular momentum transfer to neighboring field elements. This transfer force cannot be physical, otherwise field twists would not be possible since twists require a field discontinuity.
d: Field twists can be linear (eg photons) or confined to a finite space in the form of loops or knots or linked combinations of both.
e: There must be some means for a twist propagation to curve (otherwise the loop twists are not possible. I have investigated in detail various mechanisms within the R3 + I space, and believe I see a possibility enabled by the restoring force to the I dimension orientation.

The huge overwhelming problem with this hypothesis is that we appear to have zero evidence for such a precursor field or a background state or the two force connections I’ve described, the restoring force and the neighborhood connection force. I trudged forward with this anyway, knowing no-one out there would give this concept a second’s thought. I searched for possibilities in R3 + I where a loop twist could form and be stable, and for quite a while couldn’t find anything that made any sense.

I’ll tell you, I almost threw in the towel thinking this is a stupid quest. No evidence for a precursor field, no self-sustaining loop geometries that I could see, and experimental physics says any loop solution has to be too small to measure–a basic monkey-wrench in the whole unitary twist idea. I thought a lot, I’m just a dumb crackpot that doesn’t even have it wrong.

Yet something in the back of my mind says to me–when you look at the big picture, the particle zoo has to have a reductionist solution. For this existence to arise from nothing, there has to be some kind of field that gives rise to stable clumps we know as particles. For reasons I’ve discussed in previous posts, this can’t be some sort of computer simulation, nor can there be a creating entity. This all has to arise from nothing, I think–and from a deductive perspective, to me that means a single field must underlie particle formation. I’ve been able to come up with a number of constraints that this field has to have. I keep coming back to not seeing evidence for it, so I feel like I’m wandering around in a sea of ideas with no ability to confirm or deny any intermediate details of how things work. I see no realistic possibility that I could convince somebody this would work, I can’t even convince myself of that. Yet–there has got to be something. I have faith that Humanity can’t have reached the limit of understanding already!!

Not knowing what else to do other than abandon ship, I looked at R3 + I twist solutions, just about all of which couldn’t possibly work. Most fail because of symmetry issues or fail to provide an environment where twists could curve or be self-sustaining, regardless of how I describe the precursor field forces. Just yesterday, however, I happened upon a solution that has some promise. As discussed in previous posts, the restoring force to I is an enabler for quantization, but I realized it’s also an enabler for altering the path of a twist. I used the example in a previous post of how a field twist in R3 will curve if a regional part of the field is tilted in another dimension (imagine propagating a falling dominoe sequence through a sea of dominoes that is already partway orthogonally tilted). I am still checking this out, but it looks like there is one way to form the twist where this happens–if the twist loop resides in two of the dimensions of R3, and the axial twist in that loop resides in the remaining R3 dimension, but the restoring force is to the I dimension direction, the center of the loop will hold an element pointing in the I direction, thus causing all of the surrounding elements including the twist loop itself to feel a swirly (ref the Calvin and Hobbes cartoon!) that causes the twist propagation to pass through the field that is curved toward the center of the R3 loop.

This concept is ridiculously difficult to visualize, but essentially the I restoring force causes the field to always twist toward the center, regardless of loop orientation within R3. This is what the unitary twist field has to have–any other dimensional geometry simply does not provide the necessary twist curve. Believe me, I tried all other combinations–this is the only one that seems to consistently work no matter what kind of a topological loop configuration is used. Here is a pathetic attempt to draw out what I am thinking…

Agemoz

twist_in_restoring_i

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 🙂

Agemoz

Precursor Field and Renormalization

September 25, 2016

As I work out the details of the Precursor Field, I need to explain how this proposal deals with renormalization issues. The Precursor Field attempts to explain why we have a particle zoo, quantization, and quantum entanglement–and has to allow the emergence of force exchange particles for at least the EM and Strong forces. Previous efforts by physics theorists attempted to extend the EM field properties so that quantization could be derived, but these efforts have all failed. It’s my belief that there has to be an underlying “precursor” field that allows stable quantized particles and force exchange particles to form. I’ve been working out what properties this field must have, and one thing has been strikingly apparent–starting with an EM field and extending it cannot possibly work for a whole host of reasons.

As mentioned extensively in previous posts, the fundamental geometry of this precursor field is an orientable 3D+I dimensional vector field. It cannot have magnitude (otherwise E-hv quantization would not be constrained), must allow vector twists (and thus is not finite differentiable ie, not continuous) and must have a preferred orientation in the I direction to force an integral number of twists. Previous posts on this site eke out more properties this field must have, but lately I’ve been focusing on the renormalization problem. There are two connections at play in the proposed precursor field–the twist quantization force, which provides a low-energy state in the I direction, and a twist propagation force. The latter is an element neighborhood force, that is, is the means by which an element interacts with its neighbors.

The problem with any neighborhood force is that any linear interaction will dissipate in strength in a 3D space according to the central force model, and thus mathematically is proportionate to 1/r^2. Any such force will run into infinities that make finding realistic solutions impossible. Traditional quantum field theory works around this successfully by invoking cancelling infinities, renormalizing the computation into a finite range of solutions. This works, but the precursor field has to address infinities more directly. Or perhaps I should say it should. The cool thing is that I discovered it does. Not only that, but the precursor field provides a clean path from the quantized unitary twist model to the emergence of magnetic and electrostatic forces in quantum field theory. This discovery came from the fact that closed loop twists have two sources of twists.

The historical efforts to extend and quantize the EM field is exemplified by the DeBroglie EM wave around a closed loop. The problem here, of course, is that photons (the EM wave component) don’t bend like this, nor does this approach provide a quantization of particle mass. Such a model, if it could produce a particle with a confined momentum of an EM wave, would have no constraint on making a slightly smaller particle with a slightly higher EM wave frequency. Worse, the force that bends the wave would have the renormalization problem–the electrostatic balancing force is a central force proportionate function, and thus has a pole (infinity) at zero radius. This is the final nail in the coffin of trying to use an EM field to form a basis for quantizing particles.
The unitary twist field doesn’t have this problem, because the forces that bend the twist are not central force proportionate. The best way to describe the twist neighborhood connection is as a magnetic flux model. In addition, there are *two* twists in a unitary twist field particle (closed loop of various topologies). There is the quantized vector twist from I to R3 and back again to I, that is, a twist about the propagation axis. And, there is also the twist that results from propagating around the closed loop. Similar to magnetic fields, the curving (normal) force on a twist element is proportionate to the cross-product of the flux change with the twist element propagation direction. My basic calculations show there is a class of closed loop topologies where the two forces cancel each other along a LaGrangian minimum energy path, thus providing a quantized set of solutions (particles). It should be obvious that neither connection force is central force dependent and thus the  renormalization problem disappears.  There should be a large or infinite number of solutions, and the current quest is to see if these solutions match or resemble the particle zoo.

In summary, this latest work shows that the behavior of the precursor field has to be such that central force connections cannot be allowed (and thus forever eliminates the possibility that an EM field can be extended to enable quantization). It also shows how true quantization of particle mass can be achieved, and finally shows how an electrostatic field must emerge given that central force interactions cannot exist at the precursor field level. EM fields must emerge as the result of force exchange particles because it cannot emerge from any central force field, thus validating quantum field theory from a geometrical basis!

I thought that was pretty cool… But I must confess to a certain angst.

Is anybody going to care about these ideas? I know the answer is no. I imagine Feynman (or worse, Bohr) looking over my shoulder and (perhaps kindly or not) saying what the heck are you wasting your time for. Go study real physics that produces real results. This speculative crap isn’t worth the time of day. Why do I bother! I know that extraordinary claims require extraordinary proof–extraordinary in either experimental verification or deductive proof. Neither option, as far as I have been able to think, is within my reach. But until I can produce something, these ideas amount to absolutely nothing.

I suppose one positive outcome is personal–I’ve learned a lot and entertained myself plus perhaps a few readers on the possibility of how things might work. I’ve passed time contemplating the universe, which I think is unarguably a better way to spend a human life than watching the latest garbage on youtube or TV. Maybe I’ve spurred one person out there to think about our existence in a different way.

Or, perhaps more pessimistically, I’m just a crackpot. The lesson of the Man of La Mancha is about truly understanding just who and what you are, and reaching for the impossible star can doing something important to your character. I like the image that perhaps I’m an explorer of human existence, even if perhaps not a very good one–and willing to share my adventures with any of you who choose to follow along.

Agemoz

Precursor Field Constraints

August 31, 2016

I’m continuing to work through details on the Precursor Field, so called because it is the foundation for emergent concepts such as quantized particles and the EM field/Strong force. I mentioned previously that this field has a number of constraints that will help define what it is. Here is what I had from previous work: the precursor field must be unitary to satisfy the quantization implied by E=hv (no magnitude degree of freedom possible). It must be orientable to R3 + I, that is, SO(4) to allow field twists, which are necessary for particle formation under this theory. It must have a preferred background orientation state in the I direction to enable particle quantization. Rotations must complete a twist to the background state, no intermediate stopping point in rotation–this quantizes the twist and hence the resulting particle. This field must not necessarily be differentiable (to enable twists required for particle formation). There must be two types of field connections which I am calling forces in this field–field elements must have a lowest energy direction in the imaginary axis, such that there is a force that will rotate the field element in that direction. Secondly, it must have a neighborhood force whenever the field element changes its own rotation. I’ll call the first force the restoring force, and the second force the neighborhood force.

These constraints all result from a basic set of axioms resulting from the Twist Theory’s assumption that a precursor field is needed to form quantized stable particles (solitons).

Since then, I’ve uncovered more necessary constraints having to do with the two precursor field forces. Conservation of energy means that there cannot be any damping effect, which has the consequence that the twist cannot spread out. The only way this can occur is if the quantized twist propagates at the speed of light. This introduces a whole new set of constraints on the geometry of twists. I’m postulating that photons are linear twists which will reside on the light cone of Minkowski space, and that all other particles are closed loops. A closed loop on Minkowski space must also lie on a light cone for each delta on its twist path, which means that the closed loop as a whole cannot reach the speed of light. This can easily be seen because closed loops must have a spacelike component as well as a timelike component such that the sum of squares lies on the twist path elements light cone. This limits the timelike component to less than the speed of light (the delta path element has to end up inside the light cone, not on it).

One interesting side consequence is that a particle like the electron cannot be pointlike. The current collider experiments appear to show it is pointlike, but this should be impossible both because the Heisenberg uncertainty relation would imply an infinite energy to a pointlike particle but also because if an electron cannot be accelerated to exactly the speed of light, this forces its internal composition to have a spacelike component and thus cannot be pointlike. Ignoring my scientific responsibility to be skeptical (for example, another explanation would be massive particles are forced to interact within an EM field via exchange particles, thus slowing it down for reasons independent of the particle’s size–but if this were true, why doesn’t this also apply to photons), I have a strong instinct that says this confirms my hypothesis that particles other than the photon are closed loops with a physical size. This also makes sense since mass would then be associated with physical size since closed loops confine particle twist momentum to a finite volume, whereas a photon distributes its momentum over an infinite distance and thus has zero mass. Since collision scattering angles implies a point size, the standard interpretation is to assume that the electron is pointlike–but I think there may be another explanation that collider acceleration distorts the actual closed loop of the electron to approach a line (pointlike cross section).

Anyway, to get back on topic, my big focus is on how to precisely define the two forces required by the precursor field. I realized that the restoring force is the much harder force to describe–the neighborhood force merely has to translate the field elements change of rotation to a neighborhoods change of rotation such that the sum of all neighborhood force changes equals the elements neighborhood force. This gives a natural rise to a central force distribution and is easy to calculate.

The restoring force is harder. As I mentioned, conservation of energy requires that it cannot just dissipate into the field, and a quantum particle must consist of exactly one twist (otherwise the geometrical quantization would permit two or more particles). I’m thinking this means that a change in rotation due to the restoring force must be confined to a delta function and that the rotation twist must propagate at the speed of light, whether linearly (photons) or in a closed loop (massive particles). I suspect we can’t think of the restoring force as an actual force, but then how to describe it as a field property? I’ll have to do more thinking on this…

Agemoz

Quantizing Fields–Twist Field vs. Semiclassical and Canonical Field Quantization

August 28, 2016

I’ve done all this work/discussion here about this unitary twist field scheme and how it uses quantized rotations to a background imaginary axis. While my primary intent is for my benefit (keep track of where I am and to organize my thinking) I’ve tried to make it readable and clear for any readers that happen to be following my efforts. I try to be lucid (and not too crack-potteryish) so others could follow this if they wanted to. To be sure, my work/discussion on the unitary twist field is very speculative, a guess on why we have the particle zoo. However one big thought has been running through my head–if any of you are following this, you would be forgiven for wondering why I’m doing this field quantization work given that there is already plenty of well established work on first and second quantization of fields such as the EM field.

This is going to be a very tough but valid question to elaborate on. Let me start with a synopsis: my work on this precursor field, and quantum mechanics/field theory work are operating on very different subjects with the unfortunate common concept name of quantization. Quantum theory uses quantization to derive the wavelike behavior of particles interacting with other particles and fields. Unitary Twist Field theory uses a different form of quantization to help define an underlying basis field from which stable/semistable particles and fields (such as the EM field) can form.

Let me see if I get the overall picture right, and describe it in a hopefully not too stupidly wrong way.

Both quantum theory and my Unitary Twist Field work reference quantization as a means to derive a discrete subset of solutions concerning fields and particles from an infinite set of possible system solutions. Quantum theory (mechanics, field theory) derive how particles interact, and quantization plays a big part in constraining the set of valid interaction solutions. Unitary Twist Field theory (my work) involves finding a field and its properties that could form the particles and field behavior we see–an underlying field that forms a common basis for the particles and the interactions we see in real life. Quantum theory and the Standard Model currently provide no clear way to derive why particles have the masses and properties that they do, Unitary Twist Theory attempts to do that by defining a precursor basis field that creates solitons for both the stable/semistable particles and force exchange particles required by the Standard Model and quantum theory.

Standard Model particle/field interactions in quantum mechanics (first quantization) is a semiclassical treatment that adds quantization to particles acting in a classical field. Quantization here means extending the classical equations of motion to include particle wavelike behavior such as interference. Second quantization (either canonical or via path integrals, referred to generally as quantum field theory) extends quantization to fields by allowing the fields to spontaneously create and annihilate particles, virtual particles, exchange particles, fields, etc–it’s a system where every force is mediated by particles interacting with other particles. This system of deriving solutions gets generalization extension via gauge invariance constraints, this work gave rise to antiparticles and the Higgs Boson. Quantization here means that particle/field interactions interfere like waves, and thus there is generally a discrete set of solutions with a basis that could be called modes or eigenstates (for example quantized standing waves in electron orbitals about an atom).

The quantization I am using as part of the defining of the Unitary Twist Field is a completely different issue. I’ve done enough study to realize that the EM field cannot be a basis for forming particles, even by clever modification. Many smart minds (DeBroglie, Compton, Bohr, etc) have tried to do that but it cannot be done as far as anyone has been able to determine. I think you have to start with an underlying field from which both particles and the EM field could emerge, and it has to be substantially different than the EM field in a number of ways. I’ve elaborated on this in extensive detail in previous posts, but in a nutshell, quantization here means a orientable, unitary, 3D + I (same as the quantum oscillaor) field that has a preferred lowest energy direction to the positive imaginary axis. This field should produce a constrained set of stable or semistable solitons. If all goes well and this is a good model for reality, these soliton solutions should then match the particle zoo set and exhibit behavior that matches the EM field interactions with particles described in quantum theory and the Standard Model.

I am attempting to keep in mind that a twist field theory also has to be gauge invariant at the particle level, and has to be able to absorb quantum theory and the Standard Model. That’s to be done after I first determine the viability of the unitary twist field in producing a set of particles matching the known particle zoo. This is a truly enormous endeavor for one not terribly smart fellow, so just one step at a time…

Don’t know if that makes things clearer for readers, it does help narrow down and add clarity in my own mind of what I’m trying to do.

Agemoz