What question did this study set out to answer?

This research aims to derive three interrelated emergent mechanisms from a discrete four-dimensional lattice model of space-time.

June 12, 2026Open Access

4D Discrete Lattice Proof of Concept: Emergent Relativistic Kinematics, Low-Energy Quantum Dynamics, and Regge-Based Gravitational Dynamics

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This research aims to derive three interrelated emergent mechanisms from a discrete four-dimensional lattice model of space-time.
Developed a discrete four-dimensional lattice model with a fundamental update step.
Applied a nearest-neighbor tight-binding Hamiltonian to recover the Schrödinger equation.
Utilized Regge calculus to recover Einstein dynamics from link-tension fields.
Relativistic kinematics derived from structural transition constraints with velocity bound and time dilation emerging kinematically.
Schrödinger equation recovered with effective inertial mass proportional to inverse of parameters from the lattice model.
Full Einstein dynamics achieved by extremizing a simplicial action from the link-tension field.

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Implication

Proof of concept shows linked mechanisms of relativistic kinematics, quantum dynamics, and gravitational dynamics in a discrete framework, indicating a new direction for understanding gravity.

Cite This Study

Ismael Montero Vázquez (2026) studied this question.

synapsesocial.com/papers/6a2ba2448101cf8926f014f7 https://doi.org/10.5281/zenodo.20244458

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Implication

Proof of concept shows linked mechanisms of relativistic kinematics, quantum dynamics, and gravitational dynamics in a discrete framework, indicating a new direction for understanding gravity.

4D Discrete Lattice Proof of Concept: Emergent Relativistic Kinematics, Low-Energy Quantum Dynamics, and Regge-Based Gravitational Dynamics

Key Points

Discussion

Implication

Cite This Study

4D Discrete Lattice Proof of Concept: Emergent Relativistic Kinematics, Low-Energy Quantum Dynamics, and Regge-Based Gravitational Dynamics

Key Points

Discussion

Implication

Cite This Study

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