Critical research directions for transforming the Ground State Configuration model from a formal framework into a predictive physical theory.
This is the most direct path to proving the theory's core claim. The task is to rigorously demonstrate the central equation proposed in Section 4.1:
$$\int_H T_{\mu\nu}^{eff} k^\mu d\Sigma^\nu = \left(\frac{2\pi ck_B}{\hbar a}\right) \delta S_E$$To progress this, you need to:
Start with a simplified GSC state that corresponds to a flat, empty spacetime. Then, model a uniformly accelerating observer and the causal (Rindler) horizon they perceive.
Introduce a small amount of effective stress-energy ($T_{\mu\nu}^{eff}$) representing a flow of information/entanglement, and calculate its flux across the horizon.
Determine how this flux of information changes the entanglement structure of the underlying GSC state. This requires calculating the change in the microscopic entanglement entropy, $\delta S_E$, by tracing out the degrees of freedom behind the horizon.
Demonstrate that these two independently calculated quantities are proportional, with the Unruh temperature as the constant of proportionality. This would be the "smoking gun" proof that the GSC model's microscopic dynamics give rise to the thermodynamics of spacetime.
The derivation relies on several mathematical objects that are currently defined only conceptually. Making them concrete is a critical prerequisite for any calculation.
How do you extract a continuous metric tensor value from a discrete Causal Set? This is a known challenge in Causal Set Theory. A key next step is to propose and justify a specific operator for this task. For example, it could be based on the density of causal links or the volume of causal diamonds around an event $x$.
The path integral $g_{\mu\nu}(x) = \frac{1}{Z} \int \mathcal{D}C \, ...$ requires a well-defined measure on the space of all possible causal sets. The next step is to define this measure, which is essential for making the path integral calculable, at least in principle.
A successful theory of quantum gravity must not only reproduce General Relativity but also predict new physics. The first place to look for this is in the quantum corrections to the classical limit.
Go beyond the stationary phase approximation for the metric's path integral. The next terms in the expansion (the first-order corrections in $\hbar$) will represent quantum modifications to the geometry.
These corrections will lead to a modified version of the Einstein Field Equations, something like:
$$G_{\mu\nu} = \kappa T_{\mu\nu}^{eff} + \mathcal{O}(\hbar)$$The research task is to calculate the form of this correction term, $\mathcal{O}(\hbar)$.
These correction terms would be most significant in regions of high curvature. The next step would be to calculate how they affect phenomena like the event horizon of a black hole or the gravitational waves from a binary merger. This could lead to a specific, falsifiable prediction that distinguishes the GSC model from classical General Relativity.
Tackling these three areas—executing the thermodynamic proof, defining the fundamental operators, and calculating the first quantum corrections—is the most direct way to advance the GSC model from a formal framework to a predictive physical theory.