We formalize a framework in which geometry, distance, and dynamical behavior emerge from entanglement structure in a finite quantum system. By controlling subsystem correlations, one induces an effective metric space and associated physics within the system. This yields a constrained “reality sandbox”: a physically real substrate whose internal observables obey emergent geometric laws derived from information-theoretic quantities rather than pre-existing spacetime.
Let the system be a composite quantum many-body system: