Open Questions
The Quantum Family Tree Theory is not a finished theory. It is a research program. These are the open problems — stated honestly, with proposed directions for each. If you can solve any of them, get in touch.
1. How does a discrete binary tree yield a smooth 4D manifold?
The logarithmic fit d = a ln(1/E) + b provides a scalar distance metric, but not a full metric tensor gμν. The "dimensionality gap" between a tree and a Riemannian manifold is the most immediate theoretical challenge.
Proposed direction: Use multidimensional scaling (MDS) or manifold learning to embed the N×N leaf-entanglement matrix into a continuous coordinate system. Compute Ricci curvature of the emergent graph and test whether it satisfies Einstein's field equations in the large-N limit.
2. Is the decay exponent α ≈ 1.678 universal?
Our simulations show entanglement decay steeper than classical kinship by a factor of 1.678. Is this a fundamental constant of quantum genealogy, or an artifact of the specific gates (CNOT, Hadamard) used in the simulation?
Proposed direction: Vary the decoherence gates, branching factor (ternary vs. binary trees), and distribution of random unitaries. If α converges across variations, it is a universality class — potentially related to holographic constants or the central charge of the boundary theory.
3. What lives in the ancestral bulk?
In our model, ancestor qubits are traced out to leave only observable leaf states. In AdS/CFT, the analogous structure is the "bulk" spacetime where gravity lives. Can we recover ancestor information from leaf entanglement patterns?
Proposed direction: Treat every internal node as a quantum gate maintaining wormhole connectivity between distant leaves. Attempt bulk reconstruction — recovering ancestor qubit states from leaf entanglement — analogous to the entanglement wedge reconstruction program in holography.
4. Can we scale to hundreds of leaves?
Sixteen leaves is a toy universe. To observe curvature, topology, and dimensional structure, we need orders of magnitude more. The current statevector method is limited to ~30 qubits by memory.
Proposed direction: Transition to tensor network approximations (Matrix Product States) which exploit the tree's natural entanglement hierarchy. This could enable depths of n > 20 (millions of leaves), testing stability of the distance-entanglement relationship as the universe expands significantly.
5. What is f?
The central equation d(i,j) = f(1/E(i,j)) requires determining the function f. Our data supports logarithmic (consistent with Ryu-Takayanagi), but power-law fits slightly better at small N. The exact functional form may depend on dimensionality and is one of the deepest questions in the program.
Proposed direction: Larger simulations with more data points (more genealogical distances) to discriminate between functional forms. Analytical derivation from first principles, starting with the known properties of von Neumann entropy and the structure of binary trees.
6. Does this reproduce Einstein's equations?
The ultimate test. If emergent geometry from entanglement is correct, the Einstein field equations must emerge in the classical limit. No one — not just this conjecture, but the entire It from Qubit program — has achieved this in full generality yet.
Proposed direction: This is the quantum gravity problem itself. The genealogical framework provides a specific structure to work with: a metric derived from entanglement, dynamics driven by tree growth. The hope is that the specificity of the mechanism — compared to abstract tensor network arguments — makes the derivation more tractable.