Relational Distinguishability Framework I: Emergent Spacetime, Lorentzian Signature, and Newton's Constant from Quantum Information

Key Points

• The aim is to explore how quantum states and the geometry of spacetime are interrelated.
• Developed a relational distinguishability framework on projective Hilbert space.
• Applied the Banach fixed-point theorem to demonstrate a fixed point.
• Utilized the Hepp theorem to recover Einstein’s field equations.
• Derived Lorentzian signature from quantum decoherence and entanglement principles.
• Calculated Newton’s constant from vacuum Fisher information.
• Confirmed the existence of a unique self-consistent fixed point.
• Successfully recovered Einstein’s field equations.
• Derived the Lorentzian signature from quantum processes.
• Obtained a derivation of Newton’s gravitational constant without circular reasoning.