# Fields and Particles

Here we show that fields can be used to create the illusion of particles. An eddy in a field is a countable quantity. Fields are just vectors (multidimensional numbers) attached to each point in space and time.

It is interesting to look at history.

• First it was thought that matter was a continuous quantity
• Then it was realised that matter was quantised into building blocks; atoms and molecules
• It was discovered that you can count the charge only in discrete quantities, so it was assumed that the charge carrier, the electron, is a particle
• Light was supposed to be a wave in the ether, since it exhibits wave-like properties, like diffraction
• Then light was discovered to have countable behaviour and was taken to be made up of particles (photons)

In quantum physics today both photons and electrons are taken to be both particles and waves at the same time. Two mutually contradictory concepts.

Here we take time and space not to be continuous quantities, but also to be quantised. All particles are rotating eddies in a discrete field. The countable particle-like character stems from the fact that eddies are countable by nature.

There are two ways to model a structure, by objects or by position.

As an example consider a chess board. If we wanted to organise the information contained in a set-up we could organise it in two ways. We can list the pieces and their position or we can list all the 64 squares and show which piece, if any, is located there.

If most of the spaces on the board are empty, then the first method is more efficient. The second method always requires the same number of entries, namely 64, regardless of how many pieces are on the board.

The first method is analogous to the concept of particles which have information attached to them about their position in space. Noting the state of the board by position however has a ‘Pauli principle’ built in. Each square can only be occupied by at most 1 piece. In the first method this would require some external rule checking that no 2 pieces are listed as occupying the same square.

Applying this to physics would mean that each point in space holds information about the strength and direction of the various fields and that the illusion of particles are in fact just patterns in the fields which are stable in the time direction. In effect, this explains particles by fields rather than the other way around.

Space and time are still considered to be continuous quantities in accepted physics, but now let’s take space and time also to be quantised in discrete steps. Each point in space-time is defined by the states of its predecessors. This means that there is a smallest distance and a smallest time unit too.

This idea is objectionable to traditional minded physicists because it means that space is organised as a three dimensional lattice and that there are absolute x, y, and z directions. A very unrelativistic point of view.

Let’s us summarise the situation. We have a multidimensional cubic ‘lattice’, each point of which contains a vector, which we may view as the field at that point. Some of the dimensions have a complexity gradient. We call these the time dimensions; other dimensions don’t have a complexity gradient; we call these the space dimensions. The state of each point is determined by the state of its predecessors. On the diagram below we see a grey cube and its 6 neighbour cubes in three dimensions.

The lattice is discrete in both space and time dimensions, this means that the coordinates of each point are a vector, and each point contains a vector. Each point is indistinguishable from all other points, but if we define an arbitrary origin and directions, we could have absolute coordinates for each point in space and time.

Cellular automata often have some patterns that are stable or replicate. One of the best known is the “glider”, the smallest stable pattern  in Conway’s Game of Life:

When a glider collides with something, new patterns emerge. This is very reminiscent of particles in accelerators colliding and making new particles.

In the Game of Life there are a large variety of stable patterns. To explore them we need to simulate them, Consider a “glider gun” in the Game of Life:

The pattern at the top is stable and continuously generates gliders. Formally proving that the glider gun produces gliders is equivalent to simulating it. There is no shortcut that avoids using the generating function that lies at the core of the cellular automaton.

You could consider a glider and the glider gun as types of particles. An analogue in physics would be a quark continuously generating gluons. You can study either gliders or gluons at the particle level, but you will never find the deeper and simpler underlying truth if you don’t consider the CA rules.

However, in employing simulation in our search we produce a mass of multi-dimensional vector data. We need to be able to recognise what we are looking for.

We can speculate how a stable pattern would look in our multidimensional sets and a good candidate is the corkscrew and its higher dimensional analogues. We will investigate how they would appear in multiple time dimensions when we consider worlds sideways in time.