Strategic research directions for advancing the Ground State Configuration model from theoretical foundations to observational validation.
These tasks are essential for placing the theory on a fully rigorous mathematical footing.
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.
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:
Define a precise mathematical measure over the space of all possible Causal Sets.
Propose a specific, well-motivated operator that extracts a continuous metric value from a discrete Causal Set.
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.
These are the grand challenges that will connect the theory to observation and test its ability to solve real-world physical mysteries.
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.
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?
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.
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.