Posts Tagged ‘renormalization’

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 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