Next Steps from Derivation 5: GSC Research Priorities

Strategic research directions for advancing the Ground State Configuration model from theoretical foundations to observational validation.

Immediate Theoretical Priorities

These tasks are essential for placing the theory on a fully rigorous mathematical footing.

Prove the Conservation of the Effective Stress-Energy Tensor

The document assumes that $\nabla^\mu T_{\mu\nu}^{eff} = 0$. The next step is to prove this from the GSC's first principles. This would involve showing that the dynamics of the underlying quantum information state naturally lead to a conserved quantity that can be identified with energy and momentum. This is a crucial consistency check.

Explicitly Define the Path Integral Components

The path integral for the metric, $g_{\mu\nu}(x) = \frac{1}{Z} \int \mathcal{D}C \, e^{iS[C]/\hbar} \, h_{\mu\nu}(x, C)$, contains two conceptual objects that must be defined:

The Measure $\mathcal{D}C$:

Define a precise mathematical measure over the space of all possible Causal Sets.

The Metric Operator $h_{\mu\nu}(x, C)$:

Propose a specific, well-motivated operator that extracts a continuous metric value from a discrete Causal Set.

Calculate the First Quantum Corrections

The derivation shows how the GSC model reproduces General Relativity in the classical limit. The most exciting new physics lies in the corrections to that limit. The next step is to go beyond the stationary phase approximation and calculate the first-order quantum correction terms (proportional to $\hbar$). This will lead to a modified version of the Einstein equations and could produce testable predictions in regions of high curvature.

Long-Term Phenomenological Goals

These are the grand challenges that will connect the theory to observation and test its ability to solve real-world physical mysteries.

Construct a GSC Cosmological Model

Apply the full formalism to the universe as a whole. The goal is to derive the Friedmann equations from the evolution of the GSC state and show how the concepts of "entanglement density" and "computational complexity" can quantitatively explain the phenomena we attribute to dark matter and dark energy.

Model a GSC Black Hole

Use the formalism to build a complete model of a black hole. Show explicitly how the singularity is resolved at the center. Does this lead to a "Planck star" or some other exotic object? Does the model predict different observational signatures for the event horizon or for gravitational waves from merging black holes?

Derive Quantitative Astrophysical Predictions

Revisit the original motivations for the model. Use the formalized theory to derive a specific, testable equation for the rotation curve of a galaxy based on its observable properties (baryonic mass, gas content) and its location in the cosmic web (as a proxy for the local entanglement density). This would provide a "smoking gun" test that could be confronted with astronomical data.

Research Strategy

The immediate theoretical priorities establish the mathematical rigor necessary for the GSC model, while the long-term phenomenological goals connect the theory to observable phenomena. Success in both areas will transform the GSC from a speculative framework into a predictive theory of quantum gravity.