EmeWave: Emergent Waves, applied to EM

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This page describes my attempt to build an autonomous computational model of fundamental physics, based generally on the cellular automaton framework, but using analog state values instead of the usual binary or discrete ones. The theory has now converged on a complete description of electrodynamics in terms of the coupled Maxwell and Dirac equations, implemented in an analog cellular automaton. In effect, this is the cellular automaton version of the existing Neoclassical Electrodynamics approach, as outlined in more detail in the papers below. Gravitation has also been incorporated into the framework, where it can produce stable Planck-scale black holes.

There are four papers on this work:

Here is the abstract for the electrodynamics journal paper, to give a sense of the approach:

The coupled Maxwell-Dirac electrodynamic system is implemented in an analog (continuous-valued) cellular-automaton operating within a three dimensional regular face-centered cubic lattice. This system consists of a second-order Dirac wave equation for the electron (i.e., the minimally-coupled Klein-Gordon equation with spin, operating on two complex state variables), coupled with electromagnetic potential field versions of Maxwell's equations in the Lorenz gauge. Both Dirac and Maxwell's equations are standard second-order wave equations with some additional terms. An analog cellular automaton produces such wave equations as one of the simplest possible models that exhibits any physically interesting behavior. Furthermore, it avoids standard objections by achieving rotationally symmetric propagation at cellular-scales through the use of a 26 neighbor update equation for the laplacian. To achieve numerical stability, parity must be broken, which may provide an explanation for properties of the weak force. The behavior of an electron trapped by a fixed positive charge is simulated, providing a model of the hydrogen atom system. Overall, this framework may provide an appealing mechanistic model of electrodynamics.

And here is the abstract for the long, informal paper:

A good way to really understand something is to try to build it yourself from scratch. This paper takes this approach to understanding the physical universe. We seek to build an autonomous model that produces known physics in a completely self-contained manner, as a way of understanding how nature works, automatically and without any human or other form of intervention, to produce the known universe. This approach leads naturally to a continuous-valued cellular automaton model, with the standard wave equation as one of the simplest possible forms of interaction that does anything interesting. A small modification of this equation produces the Klein-Gordon (KG) equation, which provides a good description of the propagation of a particle as a wave packet of charge, which is strictly conserved by this equation. Somewhat amazingly, this simple KG equation captures most of the major features of our physical universe, including special relativity, quantum and classical Newtonian mechanics. We further refine our equations to produce coupled dynamics between Maxwell's equations (in potential form) for the electromagnetic force (which obey a basic wave equation), and the second-order Dirac equation for the electron/positron, which is a variant of the KG equation. Gravitation is also included, as a wave-propagating field that alters the coupling constants for the other wave fields, to produce the space and time warping of general relativity. Although still incomplete, we show how this model provides an extremely simple account of much of known physics, including several emergent phenomena that come along ``for free.'' from more basic assumptions. Standard objections to such an approach (e.g., lack of rotational symmetry) are addressed through the use of all 26 neighbor interactions in the second-order wave function. We conclude that there are no major objections to thinking that this model provides an accurate description of reality.

Simulation Software

The simulation software for these models is available through this svn command:
```svn checkout --username anonymous --password emergent http://grey.colorado.edu/svn/emergent/emewave/trunk ~/emewave
```
it is built on top of Emergent -- you must install the emergent package for your platform prior to compiling the above code. The CMakeLists.txt file contains information about how to compile (requires cmake -- see www.cmake.org) -- basically just:
```cd ~/emewave
mkdir build
cd build
cmake ../
make
(sudo) make install
```

Electrodynamics Movies

Here are some movies from the electrodynamics version of the model, showing a stable electron wave rotating and oscillating around a central postive nucleus charge distribution. Display is as follows: the top-left panel shows the 1a component of the dirac charge wave field, the top-right is the 2a component, bottom-left is the charge density rho (as generated by the dirac waves only), and bottom-right is the scalar electromagnetic potential A_0. For each, one slice through a 200^3 sized universe (with edges wrapping around) is plotted, with values coded by height and color (red = positive, blue = negative, zero = transparent grey). The dirac field variables rotate (1a & b) and oscillate (2a & b) around the central positive charge distribution. The resulting charge rho is centrally distributed. This pattern remains stable indefinitely, although some of the dirac wave value leaks out over time (but average net charge remains stable, while oscillating over shorter time periods).
• Small-scale hydrogen atom model:

Black Hole Movies

Here are some movies from the gravitational version of the model, showing stable black hole dynamics. Display shows wave field on left, gravitational field on the right, with typically 29 x 29 x 5 or 9 (horiz, depth, vert) cells shown. The state value is represented both by the height of the plane at each point, and by color & transparency (solid yellow = highly positive, transparent grey = zero, solid light blue = highly negative).
• Basic stable black hole (30x30x30 univ, 1 frame per update, 60 frames):
• Collapse of an energetic wave into a black hole (30x30x30 univ, 1 frame per update, 704 frames):
• Gravitational attraction and merging of two black holes, initially separated by 10 cells, into one (58x50x50 univ, one frame every 10 updates, 712 frames):
• "Repulsive" motion of two black holes, initially separated by 20 cells (58x50x50 univ, one frame every 100 updates, 310 frames):
• Black Hole moving down an imposed gravitational gradient (.004 * X coordinate gravitational field injected at the edges, 58x50x50 univ, one frame every 100 updates, 1141 frames):
• "Random" motion of one black hole (58x50x50 univ, one frame every 100 updates, 307 frames):
• Gravitational attraction and merging of two black holes, initially separated by 10 cells, into one (30x30x30 univ, one frame every 10 updates, 883 frames):