Hey fediverse physicists and curious minds!

Some of you might recall a post from a while back where I shared early simulation results from a classical 1D "Pure Ether Theory" model, showing some promising soliton-like behavior and interactions ([[https://lemmy.world/post/30579344|Observation of Soliton-like Interactions...]]). That exploratory work, based on a simplified, classical framework, was a crucial step.

Since then, we've been working to formalize the theory into a fully relativistic framework, now calling it Unified Aether Dynamics (UAD). The core idea remains the same: reality emerges from a single, deterministic, continuous substance – the Aether. The goal is to show that fundamental physics, including [[Quantum Mechanics|quantum mechanics]] and [[General Relativity|gravity]], arises from the Aether's dynamics.
This rigorous relativistic formulation is built upon a foundation of five core axioms. These aren't just philosophical statements; they are principles that dictate the specific mathematical form of the Aether's [[Stress-Energy Tensor (Tuv)|Stress-Energy Tensor]], whose conservation law serves as the fundamental equation of motion.

We're currently developing a new, robust 1D simulator based directly on these relativistic axioms (the [[Relativistic 1D Foundational Simulator - Computational Core|Relativistic 1D Simulator]], where the GUI is now under development!), and I wanted to share the foundational principles it's built upon.
Here are the 5 core axioms of Unified Aether Dynamics:

1. The Aether as the Sole Fundamental Continuum
   Concept: Forget particles and empty space. Reality is one continuous, omnipresent substance: the Aether. Everything – fields, forces, particles, and even [[Spacetime|spacetime]] itself – are just different ways this single substance is behaving.

Mathematical Implication: Reality is described by continuous fields, primarily the Aether's rest-frame density ((\rho(x^\mu))) and its [[Four-Velocity|Four-Velocity]] field (
u
μ
(
x
μ
)
u
μ
(x
μ
)
), defined throughout [[Spacetime|spacetime]].

1. The Principle of Non-Zero Density
   Concept: The Aether can never reach zero density ((\rho > 0)). There's no true void. This isn't just a property; it's a fundamental resistance to being pulled infinitely thin.

Mathematical Implication: This principle is mathematically enforced through a unique component in the Aether's [[Equation of State (Relativistic)|pressure]] (
p
UAD
(
ρ
)
p
UAD
​
(ρ)
). Specifically, a [[Principle of Non-Zero Density|constraint pressure]] term (
p
constraint
p
constraint
​

) includes factors (like
(
ρ
/
ρ
0
)
−
ε
(ρ/ρ
0
​
)
−ε

) that cause the pressure to become infinitely repulsive as density approaches zero, preventing voids. Parameters μ, ε, and the [[Fundamental Densification Scale (ρ₀)|Fundamental Densification Scale]] ((\rho_0)) shape this force.

1. Scale-Dependent & Emergent Dynamics
   Concept: The Aether's behavior and the forces within it depend on its local density and how quickly that density is changing (gradients). This also means properties like the observed dimensions or [[Spacetime|spacetime]] geometry aren't fixed but emerge from the Aether's state and change depending on the scale you look at.

Mathematical Implication: The dependence on density and its gradients introduces non-linear dynamics. The constraint force derived from the [[Equation of State (Relativistic)|constraint pressure]] involves nonlinear terms that make its influence dominant at low densities relative to (\rho_0), driving scale-dependent behavior.

1. Conservation Principles as Foundational Constraints
   Concept: The total amount of Aether substance (mass-energy) and total momentum within any closed system are always conserved. These aren't just outcomes; they are fundamental laws that strictly constrain the form of the Aether's equations of motion.

Mathematical Implication: The Aether's dynamics must be governed by the [[Relativistic Conservation Law (∇µTµν = 0)|conservation of its Stress-Energy Tensor]], (\nabla_{\mu}T^{\mu\nu} = 0). This single tensor equation encapsulates the local conservation of energy and momentum and is the primary equation solved by the simulator.

1. Response to Compression (Equation of State)
   Concept: When the Aether is compressed (density increases), it pushes back. This resistance is pressure, and there's a defined relationship between density and this pressure.
   Mathematical Implication: This relationship is the [[Equation of State (Relativistic)|UAD Equation of State]],
   p
   UAD
   (
   ρ
   )
   p
   UAD
   ​
   (ρ)
   , which quantifies the total pressure as a function of density. This function combines a standard fluid pressure term (like
   k
   ρ
   γ
   kρ
   γ

) with the unique [[Principle of Non-Zero Density|constraint pressure]] term, defining how the Aether pushes back across all density scales. Parameters k, γ, μ, ε, and (\rho_0) determine this relationship.

These axioms provide the theoretical foundation for UAD. They define a deterministic, relativistic continuous substance whose dynamics, we hypothesize, give rise to everything we observe.

Our current work with the new relativistic 1D simulator is precisely focused on exploring the numerical consequences of these axioms. Can an overdensity profile, like the [[Initial Conditions (Relativistic)|Gaussian bump]] we use as an initial condition, evolve into a stable, localized structure that persists and interacts in non-trivial ways, as suggested by the previous classical model? The relativistic framework is essential to see if this behavior holds up under the full demands of relativity and if it could potentially align with the behavior needed to explain emergent [[Quantum Mechanics|quantum phenomena]] (like those described by the [[Schrodinger Equation|Schrodinger Equation]]).

What do you think of these foundational principles? Do they spark any questions or ideas?
Happy to discuss the axioms or the simulation approach!