User: If mass and G are not fundamental what causing the gravity end rest energy etc… ?

Assistant: In the WILL Relational Geometry (RG) framework, traditional concepts like “mass” and the gravitational constant “$G$” are not considered fundamental physical entities or independent axioms. Instead, they emerge from a more foundational principle: SPACETIME $\equiv$ ENERGY (doc. Part I - Principle: Ontological Principle: Removing the Hidden Assumption). This principle asserts that the structure of spacetime and the dynamics of energy are two aspects of a single unified relational entity, called WILL (doc. Part I - Definition: WILL).

Here’s how WILL RG addresses your question:

What is the cause of gravity?

Gravity, in WILL RG, is not a force caused by mass, nor does it arise from a pre-existing spacetime fabric. Instead, it is understood as an emergent relational energy structure (doc. Part I - Principle: Ontological Principle: Removing the Hidden Assumption).

1. Dissolution of False Separation: The framework posits that physics has historically operated under a “false ontological split” where “fixed manifold + metric” (structure) was separated from “fields + constants” (dynamics) (doc. Part I - Section: The contemporary split: an unpaid ontological bill). Removing this hidden assumption directly leads to the identity SPACETIME $\equiv$ ENERGY (doc. Part I - Principle: Ontological Principle: Removing the Hidden Assumption).
2. Emergent Geometry: Spacetime is not a container; it is an emergent property of relational energy transformations (doc. Part I - Abstract, doc. Part I - Summary: Foundational Principles). Gravity is specifically associated with the omnidirectional relational transformation carried by the $S^2$ geometric carrier, quantified by the potential projection $\kappa$ (doc. Part I - Theorem: Minimal Relational Carriers of the Conserved Energy Resource, doc. Part I - Section: Potential Energy Projection on $S^2$).
3. Unified Field Equation: The relationship between geometry and energy is expressed by the Unified Geometric Field Equation: \(\boxed{\kappa^2 = \frac{R_s}{r} = \frac{\rho_{\text{field}}}{\rho_{\text{max}}}}\) This equation shows that the geometric scale ($\kappa^2$, related to $R_s/r$) is intrinsically linked to the energy density ratio ($\rho/\rho_{\max}$), demonstrating that geometry is energy, and energy is geometry (doc. Part I - Section: Unified Geometric Field Equation, doc. Part I - Theoretical Ouroboros).

What is the cause of rest energy and mass?

Mass and rest energy are fundamentally the same concept in WILL RG, representing an invariant internal aspect of a system.

1. Rest Energy as Invariant Projection: Rest energy ($E_0$) is defined as the invariant projection of total energy (denoted $E$) onto the internal (Phase) component ($\beta_Y$) of the $S^1$ kinematic carrier (doc. Part I - Theorem: Invariant Projection of Rest Energy). This means: \(E \beta_Y = E_0\) Where $\beta_Y = \sqrt{1-\beta^2}$ is the Phase projection (internal existence), and $\beta$ is the Amplitude projection (external interaction) (doc. Part I - Definition: The Phase Projection (Internal Evolution)). This $E_0$ is the energy measured in the system’s own rest frame ($\beta=0, \beta_Y=1$).
2. Mass Equivalence: Within the framework (where $c=1$ for dimensional bookkeeping), mass ($m$) is simply identified with this invariant rest energy ($E_0$). Therefore, “mass is the invariant projection of total rest energy” (doc. Part I - Corollary: Rest Energy and Mass Equivalence, doc. Part I - Summary: Rest Energy and Mass Equivalence). It is not an intrinsic property of an object, but a “comparative structure” between states and observers (doc. Part I - Definition: Energy).

If $G$ is not fundamental, what is its role?

The gravitational constant $G$ is not a fundamental physical constant defining the strength of a force, but rather a unit conversion factor or “translation constant” (doc. Part I - The Role of G as Translation Constant).

1. Derived Calibration Tool: In WILL RG, fundamental physical calculations (like determining the Schwarzschild radius $R_s$) are performed using purely geometric and dimensionless parameters (e.g., $\kappa, \beta$). If one wishes to express these geometric scales in legacy units (e.g., kilograms for mass), then $G$ acts as the necessary converter (doc. Part I - Theorem: Constants as Converters). The standard definition $R_s = \frac{2Gm_0}{c^2}$ is not an input, but an inversion to express the derived geometric scale $R_s$ in terms of legacy mass $m_0$ and the conversion constant $G$.
2. Historical Artifact: The kilogram is a human convention. In WILL RG, “mass” ($m_0$) is a secondary bookkeeping device, while the fundamental quantity is the dimensionless ratio $\kappa^2 = R_s/r$, which encodes the energy density ratio $\rho/\rho_{\max}$ (doc. Part I - Remark: Historical Artifact).

In summary: gravity arises from the geometric manifestation of energy itself, mass is the invariant internal aspect of that energy, and $G$ is a human-invented tool for translating these geometric realities into a chosen system of units.