What does this research mean for the field?

A lightcone-like causal boundary and Lorentzian spacetime structure can be mathematically derived from a primitive relational orientation algebra without assuming a prior Minkowski metric, reinterpreting photon masslessness as null-rank protection. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.ESTABLISHES_NEW_DIRECTION.

What question did this study set out to answer?

To determine whether Lorentzian spacetime geometry and lightcone causal boundaries emerge from primitive relational orientation algebra rather than being presupposed.

September 3, 2026Open Access

THE LIGHTCONE AS A CLOSURE BOUNDARY Minimal Relational Orientation, Grade-Dual Lorentzian Structure, and Null-Rank Protection

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Authors

PLPhilip Lilien

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Overview

Theoretical analysis demonstrates that Lorentzian lightcone geometry arises from minimal algebraic closure, indicating causal boundaries precede metric assumptions.

Key Points

To determine whether Lorentzian spacetime geometry and lightcone causal boundaries emerge from primitive relational orientation algebra rather than being presupposed.
Formulated a minimal relational orientation model using the compact Lie algebra su(2) equipped with its negative Killing form carrier.
Constructed the Clifford completion Cl(3,0) and mapped its trivector-bivector sector to scalar-vector paravectors using grade-dual isomorphisms.
Evaluated invariant paravector quadratic forms, matrix rank stratification in 2x2 Hermitian representations, and electromagnetic gauge transversality.
Derived the standard Lorentzian quadratic form without presupposing a Minkowski metric signature.
Stratified the causal structure into invariant closure ranks, showing nonzero null matrices exhibit rank one while timelike matrices exhibit rank two.
Demonstrated that unbroken gauge symmetry and Ward-Takahashi transversality dynamically protect the photon on the rank-one causal boundary.

Cite This Study

Philip Lilien (2026) studied this question.

synapsesocial.com/papers/6a9935f3636c6408cfa7eaa2 https://doi.org/10.5281/zenodo.22218350

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September 3, 2026Open Access

THE LIGHTCONE AS A CLOSURE BOUNDARY Minimal Relational Orientation, Grade-Dual Lorentzian Structure, and Null-Rank Protection

View Full Paper

Ask AI

Bookmark

Authors

PLPhilip Lilien

Discussion

Member takes

Overview

Theoretical analysis demonstrates that Lorentzian lightcone geometry arises from minimal algebraic closure, indicating causal boundaries precede metric assumptions.

Key Points

To determine whether Lorentzian spacetime geometry and lightcone causal boundaries emerge from primitive relational orientation algebra rather than being presupposed.
Formulated a minimal relational orientation model using the compact Lie algebra su(2) equipped with its negative Killing form carrier.
Constructed the Clifford completion Cl(3,0) and mapped its trivector-bivector sector to scalar-vector paravectors using grade-dual isomorphisms.
Evaluated invariant paravector quadratic forms, matrix rank stratification in 2x2 Hermitian representations, and electromagnetic gauge transversality.
Derived the standard Lorentzian quadratic form without presupposing a Minkowski metric signature.
Stratified the causal structure into invariant closure ranks, showing nonzero null matrices exhibit rank one while timelike matrices exhibit rank two.
Demonstrated that unbroken gauge symmetry and Ward-Takahashi transversality dynamically protect the photon on the rank-one causal boundary.

Cite This Study

Philip Lilien (2026) studied this question.

synapsesocial.com/papers/6a9935f3636c6408cfa7eaa2 https://doi.org/10.5281/zenodo.22218350

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