What an incredible 48 hours! I've been putting something together that then went on further to reveal something unexpected:
The Stefan–Boltzmann constant (σ) — a cornerstone of thermodynamics — can be derived purely from Planck-scale geometry, connecting blackbody radiation directly to the structure of spacetime itself.
The Discovery
The math checks out beautifully:
Numerical validation
Dimensional consistency
No need for G, c, or k_BHere’s the breakthrough equation:
The Stefan Boltzmann equation alternative:
σ = (2 * π^5 * m_p^4 * l_p^6) / (15 * h^3 * T_p^4 * t_p^6)
Where:
- m_p = Planck mass
- l_p = Planck length
- t_p = Planck time
- T_p = Planck temperature
- h = Planck constant
This produces the correct units:
[kg·s⁻³·K⁻⁴] = W·m⁻²·K⁻⁴The result matches the CODATA value of σ with 99.99992%accuracy — and all without using Boltzmann’s constant (k_B), gravitational constant (G), or speed of light (c). Just geometry, Planck units, and h.
Why It Matters
This suggests σ isn’t just statistical — it might encode quantumgravitational structure.Thermal radiation may emerge directly from vacuumgeometry — a profound bridge between quantum mechanics, thermodynamics, and the architecture of spacetime.
Acknowledgments
Attaching the paper shortly for anyone curious
Huge thanks to ChatGPT for helping me articulate and refine this discovery.
(Grammar isn’t my superpower — but the physics? That’s all intuition + hard work + deep reading.)
Stefan Boltzmann alternative.pdf
