The Donut-Brane Particle
I’m presenting a teaser in today’s post. The teaser is a simplified (lie-to-children) version of a brane. I already know what the correct model should be and I know I can make it eventually in Blender, but because I anticipate the building of the proper model to be laborious, I’ll present the simple model first.
But before we dive deeper into the brane model, I’ll take you back over four and a half years to my realization that there is an elementary particle of energy and that can form as a fix to the multi-dimensional problem of string theory. According to Wikipedia:
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings move through space and interact with each other by vibrations.
The idea for the multiple dimensions has been that there is no space in the three space dimensions and the one time dimension for the vibrations of the strings, so we need additional dimensions. However, if the string is reduced to a spherical elementary particle of energy, moving at the speed of light, there is no need for these extra dimensions. The vibrations take place between physical particles of energy.
However, the pure idea of elementary particles of energy isn’t enough. One needs a clear connection of the particles with the current theory, and most of all, one needs a proper model how these particles make a particle with mass.
The somehow frustrating realization I have is that my new model isn’t exactly new for me at all. It’s just taking the model I’ve used in posts, such as “Good Vibrations”, or ”Why Does an Electron Twist?”, both three years ago, and adding both rotation and vibration to the model. At this simple level, I’m not changing the basic model at all: I’m just using Blender better. Instead of static models built quite laboriously, I’m taking advantage of geometry nodes. With these I can make individual spheres move in exactly the way I imagined them moving already three-four years ago. But before I didn’t know how to use these tools. But as I realized that I needed to learn them, I just asked ChatGPT to help me build the model. I don’t know about the newer more advanced versions of ChatGPT, but it took many tries to get the model working as I wanted. It definitely wasn’t effortless.
Before I show you the model, this is what the geometry nodes for just one string of spheres looks like:
And to make the twelve strings in today’s model, I had to make 12 copies of the nodes, and change three variables: the major one being the z rotation in the second transform geometry node. The first minor variable is the sign of the multiply node after the upper scene time node. By giving neighboring string opposite signs, this allows the strings to vibrate 180 degrees out of sync, or allow the spheres of neighboring strings to collide between two of its neighbors. The second minor variable is the color in the set material node, that allows me to use two colors for the model, which helps in the visualization.
And finally, this is the animated brane particle:
Each of the strings moved mostly in a straight path, but with rotations along two axes. But besides just rotating, the strings also collide with neighboring strings, generating vibrations.
So, why is this a brane particle? According to the Wikipedia article on branes:
In string theory and related theories (such as supergravity), a brane is a physical object that generalizes the notion of a zero-dimensional point particle, a one-dimensional string, or a two-dimensional membrane to higher-dimensional objects.
Well, this is very much a two-dimensional representation of zero-dimensional point particles. Of course, my theory suggests that zero-dimensional is a bit of a stretch (pardon the pun). Rather, the particles are so small that they can be simplified to zero-dimensional points, while actually having volume. And unlike in the Wikipedia article, my branes aren’t higher-dimensional, at least in the conventional sense of string theory.
So, is this a true representation of a brane? No, it isn’t. For the vibrations not to make the strings unravel, there needs to be an interaction that forces the donut-shaped array of strings to be confined into relatively narrow tube. The simplest such interaction is for there to be two entangled donuts, very much like in my last post. Except there needs to be two levels of twisting: the counterclockwise twist of the primary donut, and the clockwise twist of the two donuts around each other.
It might be that I’ll be able to create this model very quickly, or I might get stuck with some limitation of Blender. The model already has almost 40 nodes for each string. I wouldn’t be surprised if I encountered some serious hurdles still. Then again, once I have the final Blender model of the entangled donuts ready, I should be able to convert the model into equations. The first non-multidimensional brane equations.
But even as an incomplete lie-to-children model, I’m very happy with this.
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