Projection of Straintity as Mass and Energy in Space-Time: Emergence of E = mc^2 in Triogenesis
Description
We present a derivation of the mass–energy equivalence relation E = mc^2 from within the Triogenesis framework, in which mass and energy emerge as complementary projections of recursive straint structures in space-time. Unlike conventional relativistic approaches that derive this relation from inertial frame transformations, Triogenesis grounds it in the discrete, directional organization of causal interaction. Mass is interpreted as the localized recursion of certainty within a closed straint frame, while energy arises from the outward projection of recurrence asymmetry. The speed of light c is shown to be a topological constraint: the maximal propagation rate of straint traversal within the 12-Straint Frame (12SF), which defines the minimal isotropic generator of three-dimensional space-time. We further derive four-momentum conservation as a consequence of total recurrence-rate invariance across closed straint networks, recovering E = mc^2 as the rest-frame limit. This approach reframes the mass–energy equivalence not as a kinematic postulation of space-time symmetry, but as a generative necessity of recursive structure.
Notes
This paper extends the Triogenesis framework by providing a foundational derivation of Einstein’s iconic mass–energy relation E = mc^2, not from relativistic postulates, but from the internal topological structure of directional interaction.
In classical physics, E = mc^2 is derived from assumptions about inertial frames and space-time symmetry. In this work, we show that this equivalence is not merely a kinematic result, but a topological necessity that arises from the recursive organization of straint interactions — the quantized, directional relations that build the structure of space-time in Triogenesis.
We introduce the Straint Conservation Principle, a theorem demonstrating that four-momentum conservation (energy and momentum conservation) — and thus E = mc^2 — emerges directly from the symmetry of recursive straint networks, provided they remain flat and complete. The speed of light c is reinterpreted as a structural limit of causal projection across the 12-Straint Frame (12SF), the minimal configuration that generates isotropic 3D space.
This work builds directly on our previous closed-form derivation of the hydrogen atom spectrum from first principles, where physical constants such as unified electro-gravitational strength, and normalized Planck constrant were derived from recursive geometry without experimental tuning.
🔗 Related Articles:
• 🌐 Triogenesis: A Closed-Form Framework for the Emergence of Physical Order and Consciousness
The original theoretical paper introducing straints, recurrence, and the recursive emergence of matter, space, and observers.
→ https://zenodo.org/records/15123321
• 🔬 Closed-Form Derivation of the Hydrogen Spectrum (Triogenesis):
Shows that the Schrödinger energy levels and quantum constants can be derived purely from recursive geometric rules.
→ https://zenodo.org/records/15116919
• 🌌 Triogenesis: Explaining the Formation of the World with Scientific Precision
A non-technical introduction to Triogenesis for general readers, explaining how the universe might emerge from a single generative principle.
→ https://zenodo.org/records/15131013
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