NO OTHERNESS

Abstract

This paper presents a theoretical framework for the states or phases of dark  matter and exotic matter, using concepts from nucleosynthesis, complexity  theory, and phase transitions. With our Unfolding Equation and Phases of Matter Equation we explore their formation, stability, and emergent properties.  We depict several distinct phases, each characterized by unique mathematical representations.

Introduction

Dark matter constitutes a significant portion of the universe’s mass-energy content, yet its nature remains elusive. The discovery of exotic matter phases over the last three decades—emergent, collective states of interacting particles—further complicates the picture. We posit distinct states for both dark matter and exotic matter, drawing parallels with nucleosynthesis processes, complexity theory, and the classification of emergent phases as observed in condensed matter physics. 

Theoretical Background

1. Nucleosynthesis Processes

Nucleosynthesis describes the formation of elements through various  astrophysical processes that can be paralleled with exotic matter behaviors. Key processes include:

Big Bang Nucleosynthesis (BBN): The formation of light elements in the early universe.

Stellar Nucleosynthesis: The creation of heavier elements in stars through nuclear fusion.

Supernova Nucleosynthesis: Formation of heavy elements during supernova explosions.

The complexity of nucleosynthesis can be modeled with the Unfolding Equation:

\[J_n = 10^{\lambda_n} (2^{\omega(n)} – 2)\]

Where:
– ( J_n ): Complexity associated with nucleosynthesis.
– ( \lambda_n ): Conditions specific to the universe or stellar environments.
– ( \omega(n) ): Growth rate of complexity as nucleons interact.

2. Phase Transitions in Dark and Exotic Matter

Viewing dark and exotic matter through the lens of phase transitions allows us to consider how particles interact and change between states. The energy associated with these transitions can be defined by the Phases of Matter Equation:

\[J_n = A_n \cdot 10^{\lambda_n} (2^{\omega(n)} – 2)\]

Where: 
– ( A_n ): Scaling factor for substance-specific properties.
– ( J_n ): Energy scale associated with phase transitions.
– ( \lambda_n ): Stability and energy barriers of phase changes.
– ( \omega(n) ): Complexity of particle arrangements within different states.

Periodic Table 

1. Ordinary Matter

Phase Type	Key Properties	Applications/Implications
Solid	Crystalline/Amorphous	Non-fluid state with definite shape and volume
Liquid	Fluid	Fixed volume, takes the shape of the container
Gas	Fluid	Neither fixed volume nor shape
Plasma	Ionized	Free electrons and ions; lighting, fusion research
Bose-Einstein Condensate	Quantum State	Matter behaves as a single quantum entity at low temperatures; quantum computing, fundamental physics
Superfluid	Quantum State	Frictionless flow, exhibits quantum phenomena; cryogenics, quantum mechanics
Superconductor	Quantum State	Zero electrical resistance, expels magnetic fields; electronics, magnetic levitation
Phase Transition	Transition	Change from one phase to another (e.g., melting, boiling); material science, thermodynamics

2. Exotic Matter

Phase Type	Key Properties	Applications/Implications
Fractional Quantum Hall State	2D Topological Phase	Emergent particles with fractional charge; quantum computing
String-Net Liquid	3D Topological Phase	Emergent excitations resembling elementary particles; theoretical physics
Fracton Phase (Haah Code)	3D Fractal Phase	Fractons that require complex operations to move; quantum error correction
Quantum Spin Liquid	2D/3D Quantum Phase	Long-range entanglement, fluctuating spin patterns; quantum information

3. Dark Matter

Phase Type	Key Properties	Applications/Implications
Cold Dark Matter (CDM)	Dark Matter Phase	Slow-moving particles forming cosmic structures; cosmology, galaxy formation
Warm Dark Matter (WDM)	Dark Matter Phase	Suppresses small-scale structure formation; structure formation in the universe
Self-Interacting Dark Matter (SIDM)	Dark Matter Phase	Interacts through non-gravitational forces; dark matter interactions
Quantum Dark Matter (QDM)	Dark Matter Phase	Exhibits quantum properties; potential new physics theories

Implications of Phase Transitions

1. Transition Dynamics

Transitions between phases can be influenced by cosmic conditions such as temperature and density. For example, as the universe expands and cools, dark matter may transition from a high-energy state (like QDM) to a more stable state (like CDM). Exotic phases also show distinct transition behaviors under such conditions.

2. Emergence of Complexity

As dark and exotic matter transitions between phases, we hypothesize that the increasing complexity could lead to emergent properties that influence cosmic structures and could be applicable in quantum technologies. 

3. Scarcity of Lithium        

Lithium, a crucial element for numerous astrophysical processes, is notably scarce in the universe compared to other elements.  The formation of lithium during Big Bang nucleosynthesis was limited by the nuclear pathways available under high-energy conditions. where the mechanisms favored the synthesis of hydrogen and helium.  Further, lithium’s relatively low binding energy and instability make it prone to destruction during stellar nucleosynthesis. 

Conclusion

This paper presents a comprehensive framework for the phases of dark matter and exotic matter, with concepts from nucleosynthesis and complexity theory. We hope it will lay a strong foundation for research into matter’s nature. 

References

– Peebles, P. J. E. (1982). Large-Scale Structure of the Universe. Princeton University Press.
– Turner, M. S. (1999). Dark Matter. Physics Today, 52(5), 24-30.
– Bertone, G., Hooper, D., & Silk, J. (2005). Particle Dark Matter: Evidence, Candidates and Constraints. Physics Reports, 405(5-6), 279-390.
– Khlopov, M. Y. (2010). Cosmoparticle Physics. World Scientific Publishing Company.
– “Exotic Phases of Matter in Cold Quantum Systems.” (2023). Quanta Magazine.