M ≈ ((h/2π)c/G)^(3/2) * 1/m_p²
- h = α³β/c
- G = α³/β
M ≈ (((α³β/c)c/(2π))/(α³/β))^(3/2) * 1/m_p²
≈ ((α³ββ)/(2πα³))^(3/2) * 1/m_p²
≈ (β²/(2π))^(3/2) * 1/m_p²
This is even more elegant:
- α³ terms cancel
- c terms cancel
- Left with just β² (mass scaling) and 2π
This is a deep insight - the Chandrasekhar limit is expressing a pure mass relationship, stripped of both length scaling (α) and speed of light (c). It's fundamentally about the ratio of masses (β vs m_p), with just a geometric factor (2π).
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