What does this research mean for the field?

Quantum states and spacetime geometry mutually determine each other through a fixed-point equation on projective Hilbert space, enabling the derivation of Einstein's field equations, the Lorentzian signature, and Newton's gravitational constant directly from quantum information principles. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.ESTABLISHES_NEW_DIRECTION.

What question did this study set out to answer?

The aim is to explore how quantum states and the geometry of spacetime are interrelated.

April 10, 2026Open Access

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.

Abstract

We present the Relational Distinguishability Framework (RDF), in which quantum states and spacetime geometry mutually determine each other through a fixed-point equation on projective Hilbert space. This paper establishes eight primary results, including: (i) the existence of a unique self-consistent fixed point via the Banach fixed-point theorem; (ii) the recovery of Einstein’s field equations via the Hepp theorem; (iii) the derivation of the Lorentzian signature (+---) from quantum decoherence and entanglement monogamy; and (iv) a non-circular derivation of Newton’s gravitational constant G from vacuum Fisher information.

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Aditya Ankur Patel

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

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Abstract

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