Consider the behavior and properties of subnuclear particles such as electrons and protons. These include

• Such particles maintain their existence and properties over time and spatial translation.
• Such particles have antiparticles.
• Like particles repel each other and unlike particles are attracted to each other.
• When a particle and its antiparticle come together they annihilate each other and create radiation.

Now consider an elastic strip whose two ends are fixed vertically. First take the case in which there is a single twist of 180° in the strip. That twist can be moved back and forth along the strip and it maintains its existence. Over time it also maintains its existence. These are the first properties of subnuclear particles cited above. Thus a twist is in the nature of a particle. (The strip is the universe in which it exists.)

Physically the twist is distributed evenly along the strip. It only appears to be concentrated at the point where the strip surface is parallel to the line of sight of the viewer. This is rather amazing, but not relevant for the purpose of the model.

A twist is topological; i.e., this means that no amount of stretching or compression of the strip will make the twist disappear.

The antiparticle of a twist is just a twist in the opposite direction. Note that there can only be two types of twists.

Now consider two separate twists in the same direction put into the strip. These twists cannot be forced together. In other words, they repel each other. They appear to be located at the quarter points of the strip, but they are each distributed over a half length of the strip.

If one twists is put into the strip at one end and another twist in the opposite direction is put in at the other end these twists will come together and annihilate each other. The energy that was stored in the twists goes into the vibration of the elastic strip after the annihilation.

In the case of multiple twists in different directions the end result after any annihilations preserves the net number of twists. This is like a conservation law.

There is nothing special about having the ends of the strip vertical. This specification was made to make visualization easier. The ends just needed to be parallel and they can just as well be brought together to make the strip a band. Then the band is a closed universe with particles as shown below.

This simple model illustrates how particleness and its characteristics can arise from topological considerations. It does not capture all of the physics of subnuclear particles but it provides some delightful insights for the topic.

Imagine a long narrow strip with billions upon billions of twists with a small portion being antitwists. Occasionally an antitwist annihilates with a twist and creates vibrations in the strip. This would be a quasi-one dimensional universe. Ours is a quasi-three dimensional universe involving twists in space we cannot imagine.

Reference:

Roger Dodd, J. C. Eilbeck, John D. Gibbon and Hedley C. Morris, Solitons and Nonlinear Wave Equations, Academic Press, London, 1982.