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June 28, 2026Open Access

Origin of the Minkowski Metric from Complex Spacetime Manifold

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Authors

HSHarvey Sang

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Implication

Randomized trial examines a novel five-dimensional complex-time metric's implications on relativity, indicating a unifying framework for particle dynamics.

Key Points

  • To explore the geometric foundations of the Minkowski metric via a complex-time manifold and its implications for special relativity.
  • Introduced a five-dimensional complex-time manifold with an imaginary time coordinate τ.
  • Defined the metric as a holomorphic bilinear form impacting worldlines of particles.
  • Derived results like time dilation and invariant momentum through geometric conditions.
  • Unified null geodesic condition met by massive and massless particles under the five-dimensional metric.
  • Time dilation is directly derived from a velocity constraint: v² + V_τ² = c².
  • Identified charge conjugation (C) geometry correlating with matter-antimatter orientation.

Cite This Study

Harvey Sang (2026) studied this question.

synapsesocial.com/papers/6a40ba8861bb0a67205c66e8https://doi.org/10.5281/zenodo.20920611
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1A Five-Dimensional Lorentzian Manifold with a Compactified Imaginary-Time Dimension and the Geometry of Special Relativity2026
  2. 2The Time Fibre Bundle and the Geometric Interpretation of Special Relativity2026
  3. 3Special Relativity Seen from the Fifth Dimension: A Geometric Derivation of Minkowski Spacetime from Euclidean Geometry in R⁵2026
  4. 4Let Us Assume i Is Real - What a Complex Spacetime (3+1)C Can Explain2026
  5. 5Theory of Density-Time Metric (Intrinsic-Metric Time Dilation): A Thermodynamic Extension of General Relativity to Resolve Cosmological Tensions2026