What are the origins of force fields and mass? (# 10)

The origin of our universe may be discovered by combining several building blocks. One of these blocks is an explanation for the existence of fields and mass. The origin of these phenomena is the Efimov effect although much iteration may be required before such phenomena emerge. The Efimov effect is a result of combining quantum particles. This article follows on from Article #9 ‘What are the origins of space, time and quanta’ where Anti-de Sitter (AdS) space and boundaries are discussed.

Emergence of Force Fields

In 1970, a Russian physicist, Vitaly Efimov, was manipulating the equations of quantum mechanics to calculate the behaviour of sets of three particles, such as the protons and neutrons. He discovered that three quantum components can be combined to form a state similar to Borromean rings where three circles are interconnected but no two are directly linked. In such a state, the forces arising from the combination of the three particles are greater than the sum of the forces associated with individual particles. Physicists have demonstrated the existence of such forces in actual experiments. An Efimov effect is an emergent property that does not exist in any particle on its own.

When shapes enter and exit AdS boundaries, these shapes combine randomly. Inevitably, a collection of various shapes inside a boundary will result in the equivalent of an Efimov state where the compression of one dimension causes shapes to be combined. Some combinations of shapes create emergent properties which could be new rules equivalent to a primitive form of awareness.

Examples of primitive awareness are the rules in Professor John Conway’s Game of Life. In Conway’s game, cellular automatons are either black or white. In a two dimensional space consisting of cells, the rules for determining the colours of individual cells after an iteration are:

For a space that is ‘populated’:

• Each cell with one or no neighbours dies, as if by solitude.
• Each cell with four or more neighbours dies, as if by overpopulation.
• Each cell with two or three neighbours survives.

For a space that is ‘empty’ or ‘unpopulated’

• Each cell with three neighbours becomes populated.

In the context of an AdS space which has four dimensions, an example of a rule could be:

• When a shape (Platonic solid) is identical to a maximum of one neighbour, the shape remains unchanged i.e. does not change into its dual; and
• When a shape is identical to the shapes of two or more of its neighbours, the shape becomes its dual.

This proto-awareness or communication between shapes can be formalised as a set of rules. Many combinations of shapes could become proto-aware. After repeatedly going through boundaries, more complex rules emerge as a result of incremental Efimov effects. The emergence of increasingly complex rules associated with the shapes in AdS space is a consequence of the mathematics of symmetry.

According to mathematicians, when a law of physics does not change upon some transformation, that law is said to exhibit a symmetry. There is a conserved current corresponding to a symmetry in the underlying physics. In quantum mechanics, the probability current is a mathematical quantity describing the flow of probability in terms of probability per unit time per unit area. In brief, the mathematician Emma Noether proved that when a system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time. In the context of AdS space, when the same shapes repeatedly go through boundaries, regular patterns i.e. conserved values, emerge consistent with the mathematics of symmetry.

Rules like Conway’s Game of Life are relatively simple. More complex rules include re-ordering the way content is presented in a boundary. For example; after a large number of cycles, shapes may incorporate rules that make them appear as sine and cosine waves in a time-like dimension in AdS space. Through an Efimov effect, the space containing these waves may be interpreted as a force field; an Efimov effect is the source of a mathematical description of energy.

According to believers in Sacred Geometry, the flower of life is a pattern created out triangles and circles. This pattern is considered to contain ancient religious values depicting the fundamental forms of space and time.

In terms of the theory developed in these articles, the flower of life pattern could symbolise the energy in the zero point field. According to Wikipedia:

… According to quantum field theory, the universe can be thought of not as isolated particles but continuous fluctuating fields: matter fields … and force fields … All these fields have zero-point energy. These fluctuating zero-point fields lead to a kind of reintroduction of an aether in physics, since some systems can detect the existence of this energy; however, this aether cannot be thought of as a physical medium if it is to be Lorentz invariant such that there is no contradiction with Einstein’s theory of special relativity. … Physics currently lacks a full theoretical model for understanding zero-point energy.

In mathematics, a Fourier transform can be used to decompose a function into its constituent frequencies e.g. the expression of a musical chord in terms of the volumes and frequencies of its constituent notes. The reverse is also true, mathematical expressions (information) describe various forms of energy. Information can be instantiated in force fields. Not all shapes, however, necessarily become force fields. A shape could ‘accompany’ a force field.

Emergence of Matter

Physicists believe the Higgs field is a field of energy that exists in every region of the universe. Such a field of energy could have a temperature created though an Efimov effect. This field of energy could lie on top of the zero point field which is associated with energy that does not have a temperature.

The Higgs field is accompanied by a fundamental particle known as the Higgs boson that the field causes to interact with other particles, such as the electron. Particles interacting with the field are ‘given’ mass and, like objects passing through treacle, become slower as they pass through the field.

Analogous to physicists’ understanding of how the Higgs field gives rise to mass, mathematical descriptions of shapes interacting with (or accompanying) force fields in AdS space give rise to mathematical expressions of mass. Matter is an example of how information is instantiated in AdS space-time. Matter is analogous to compressed information. Matter is not necessarily physical. Matter is more like an idea, a way of describing multiple bits of information.

These mathematical descriptions of AdS matter are not necessarily the same as quantum particles in our universe. The creation of AdS matter, however, potentially changes the nature of boundaries in AdS space. A boundary inside AdS space becomes a black hole and contains the content of that black hole as a hologram i.e. content in one less dimension.

A subsequent article suggests dimensional compression causes content to be displayed in the boundary of AdS space as if there is a force of gravity. Professor Leonard Susskind of Stanford University has developed mathematical scenarios consistent with this observation. Susskind’s Second Law of Computational Complexity includes two equations, one of which, Kolmogorov Complexity, appears to be associated with defining the force of gravity.

With the creation of force fields, energy and matter, content inside a boundary in AdS space starts to resemble our early universe. AdS space inside an AdS black hole, however, has two time-like dimensions and thus there are at least two possible ways of displaying content i.e. there are two boundaries which could display content differently. For example, content in one boundary may appear as rules describing how particles are ‘attracted’ to each other. The force of gravity is a mathematical way of expressing how the compression of a time dimension affects the behaviour of particles.

Causation

Spencer Brown’s Laws of Form in association with a topological form of space that folds back and absorbs itself e.g. a Klein bottle, creates a time-like phenomenon i.e. a (0, 1) bit of information that instantiates its own history. Contraction of this time-like dimension in a boundary of AdS space could create meta-rules that lead to increasing mathematical complexity. Some of these meta-rules could be the equivalent of introducing types of causation e.g. when ‘x’ happens then ‘y’ will happen where the history of a (0, 1) bit of information becomes part of the rule. Causation may not exist in the original AdS space but is introduced (via Efimov effects) as a way of displaying complex content in a boundary i.e. in one less dimension.

Some of the first rules emerging from Efimov effects could be the equivalent of ‘What can happen, does happen’. There may be many ways that content inside an AdS black hole can be displayed in the boundaries of that space. A bazillion iterations may be required before rules equivalent to ‘What can happen, does happen’ emerge. Chaos theory, however, shows how surprisingly complex shapes can emerge from relatively simple fractal equations. In other words, complex consequences could be the outcomes of Efimov effects i.e. application of relatively simple rules.

Once rules (information) about causation are incorporated into AdS space, new rules may emerge linking rules/events in one boundary with rules/events in the other boundary. For example, when the gravitational force is too weak or too strong, the content in a boundary explodes or implodes; neither outcome would be consistent with exploring all the implications of a meta-rule of ‘What can happen, does happen’.

The rule for setting the gravitational force could be consistent with a rule that requires every new rule to lead to increasing mathematical complexity wherever possible. For example, increasing mathematical complexity could be associated with discovering pathways for increasing awareness.

The foregoing discussion is an example of how the laws of physics may have emerged. While there may be many possible universes, rules resulting in increasing mathematical or quantum complexity may be some of the more productive ideas to examine in order to determine whether the origin of the laws in our universe can be explained.

When the possibility of feedback is introduced as a means of increasing the complexity of rules, ideas about the origin of living organisations and consciousness arise. These ideas are discussed in subsequent articles.

The question for this article is:

Could the idea of exploring mathematical complexity explain the creation of our universe?

To view the headings of all the articles to be published in this series please click on https://readmedium.com/orbiting-stars-and-origin-of-our-universe-338906930f51

To obtain a copy of the book ‘Orbiting Stars’ which contains the first drafts of all these articles, please visit https://www.amazon.com