Emergence of Force Fields

In the 1970s, Russian physicist Vitaly Efimov explored quantum mechanics equations to assess the behavior of triplets of particles, such as protons and neutrons. He found that three quantum entities could unify into a state akin to Borromean rings, where three circles are interconnected but no two are directly linked. In this configuration, the forces generated by the trio surpass the individual forces of each particle. Experimental evidence has confirmed the existence of such forces. The Efimov effect is a property that emerges collectively and cannot be attributed to any single particle.

Shapes that enter and exit AdS boundaries combine in unpredictable ways. Ultimately, a mix of various shapes confined within a boundary may result in an Efimov state, where the compression of one dimension facilitates the merging of shapes. Certain combinations can yield emergent properties, which might represent a rudimentary form of awareness.

Instances of primitive awareness can be observed in Professor John Conway's Game of Life. In this cellular automaton, cells are either black or white. The rules for determining the colors after each iteration in a two-dimensional cell space are as follows:

For a 'populated' space: - Each cell with fewer than two neighbors dies, representing solitude. - Each cell with four or more neighbors dies due to overpopulation. - Each cell with two or three neighbors survives.

For an 'empty' space: - Each cell with exactly three neighbors becomes populated.

In a four-dimensional AdS space, a potential rule could be: - When a shape (Platonic solid) matches at most one neighbor, it remains unchanged (i.e., does not transform into its dual); - When a shape matches two or more neighboring shapes, it transforms into its dual.

This proto-awareness or interaction between shapes can be expressed through a series of rules. Numerous combinations of shapes might exhibit proto-awareness. As they repeatedly traverse boundaries, increasingly complex rules arise due to cumulative Efimov effects. The development of these intricate rules in AdS space reflects the mathematical principles of symmetry.

Mathematicians assert that a physical law demonstrating invariance under certain transformations exhibits symmetry. A conserved current is associated with the symmetry present in the fundamental physics at play. In quantum mechanics, the probability current quantifies the flow of probability over time and area. Mathematician Emma Noether established that continuous symmetry implies the existence of conserved quantities over time. In the context of AdS space, the repeated traversal of identical shapes through boundaries leads to the emergence of consistent patterns, or conserved values, aligning with symmetry mathematics.

While rules similar to Conway's Game of Life are straightforward, more complex rules may involve reordering how content appears within a boundary. Over numerous cycles, shapes might develop rules that allow them to manifest as sine and cosine waves in a time-like dimension of AdS space. Through the Efimov effect, this space containing waves could be perceived as a force field; it serves as the basis for a mathematical representation of energy.

Proponents of Sacred Geometry regard the flower of life as a pattern formed from triangles and circles, believed to embody ancient religious significance that illustrates the fundamental structures of space and time.

In light of the theories discussed, the flower of life pattern might symbolize energy in the zero-point field. According to quantum field theory, the universe is not merely a collection of isolated particles but rather a continuum of fluctuating fields: matter fields and force fields. All these fields possess zero-point energy, which leads to a re-emergence of an aether in physics. However, this aether cannot be treated as a physical medium if it is to remain consistent with Einstein's special relativity. Currently, physics lacks a comprehensive theoretical framework for understanding zero-point energy.

Mathematically, the Fourier transform enables the decomposition of a function into its fundamental frequencies, such as expressing a musical chord through its constituent notes' volumes and frequencies. Conversely, mathematical expressions (information) can also encapsulate various forms of energy. Information may be instantiated within force fields, although not all shapes necessarily transform into force fields; some may simply accompany them.

Emergence of Matter

Physicists posit that the Higgs field is a pervasive energy field throughout the universe. This energy field could be influenced by an Efimov effect, potentially overlaying the zero-point field associated with temperature-independent energy.

The Higgs field is linked to the Higgs boson, a fundamental particle that interacts with other particles like electrons, imbuing them with mass. As particles traverse the Higgs field, they slow down, akin to moving through treacle.

Just as physicists describe the Higgs field's role in mass generation, mathematical interpretations of shapes engaging with (or accompanying) force fields in AdS space yield mathematical representations of mass. Matter exemplifies how information is instantiated within AdS space-time, representing compressed information rather than strictly physical entities. Matter resembles an idea, a conceptual framework for describing multiple bits of information.

These mathematical representations of AdS matter are not necessarily equivalent to quantum particles in our universe. However, the existence of AdS matter may alter the nature of boundaries within AdS space, transforming a boundary into a black hole that contains its content as a hologram—information represented in one less dimension.

A future article will propose that dimensional compression results in content being projected onto the boundary of AdS space as if a gravitational force is at play. Professor Leonard Susskind from Stanford University has developed mathematical scenarios that align with this observation. His Second Law of Computational Complexity includes two equations, one of which, Kolmogorov Complexity, seems to relate to defining gravitational force.

With the emergence of force fields, energy, and matter, the content within a boundary in AdS space begins to mirror our early universe. However, AdS space within an AdS black hole possesses two time-like dimensions, allowing for at least two distinct methods of content presentation; each boundary may represent content differently. For instance, one boundary might illustrate rules governing particle attraction. The force of gravity mathematically expresses the impact of time dimension compression on particle behavior.

Causation

Spencer Brown's Laws of Form, when combined with a topological space that folds back onto itself, such as a Klein bottle, creates a time-like phenomenon—a (0, 1) bit of information that encapsulates its own history. The contraction of this time-like dimension within an AdS space boundary could generate meta-rules that lead to heightened mathematical complexity. Some of these meta-rules could introduce types of causation, such as "if 'x' occurs, then 'y' follows," where the history of a (0, 1) bit of information integrates into the rule. Causation might not exist in the initial AdS space but is introduced (via Efimov effects) to facilitate the display of complex content within a boundary—in one less dimension.

The earliest rules emerging from Efimov effects might echo the concept that "whatever can occur, will occur." Numerous possibilities may exist for how content within an AdS black hole can be represented in its boundaries. A multitude of iterations could be necessary before rules paralleling "whatever can happen, does happen" materialize. However, chaos theory demonstrates how remarkably intricate shapes can arise from relatively simple fractal equations. In essence, complex outcomes may stem from Efimov effects, which apply straightforward rules.

Once rules (information) regarding causation are integrated into AdS space, new rules may emerge that link events/rules across boundaries. For instance, if the gravitational force is excessively weak or strong, content within a boundary may explode or implode; neither scenario would align with the comprehensive implications of a meta-rule stating "whatever can happen, does happen."

The regulation governing gravitational force could correspond to a principle mandating that every new rule should enhance mathematical complexity whenever feasible. For example, escalating mathematical complexity might be associated with uncovering pathways to greater awareness.

The preceding discussion serves as a glimpse into how the laws of physics may have developed. While numerous possible universes exist, rules that lead to increased mathematical or quantum complexity may represent some of the most fruitful concepts to explore in understanding the origins of the laws governing our universe.

Introducing the potential for feedback as a means of amplifying rule complexity raises questions about the emergence of living organizations and consciousness. These topics will be explored in subsequent articles.

The question posed in this article is: Could the exploration of mathematical complexity illuminate the creation of our universe?

For a comprehensive view of all articles to be published in this series, please visit https://readmedium.com/orbiting-stars-and-origin-of-our-universe-338906930f51

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