The reduced Planck constant ħ = 1.0546 × 10⁻³⁴ J·s appears in every equation of quantum mechanics. Its value has been measured to eleven significant figures. It has never been derived.
Max Planck introduced it in 1900 as a fitting parameter for blackbody radiation. He called it "an act of desperation." BFUT Paper 16 shows it was not arbitrary — it is the action scale of the first stable Spaticle condensation.
The Derivation
ħ is the action of one complete circulation of a stable Spaticle condensation unit at the free-energy minimum R₀ = 1.271. One complete circulation traverses a characteristic path with momentum m_p·c:
Using m_p = 1.6726 × 10⁻²⁷ kg, c = 2.998 × 10⁸ m/s, r_p = 0.8409 fm, R₀ = 1.271: ħ_derived ≈ 1.0532 × 10⁻³⁴ J·s. Measured: 1.05457 × 10⁻³⁴ J·s. Agreement: 0.136%.
Physical Meaning
Action quantisation — the fact that physical processes exchange action in multiples of ħ — is not an axiom imposed from outside. Action is quantised because the Spaticle substrate produces condensation circulations of discrete size. Only integer multiples of the fundamental circulation are stable. The quantum of action is the circulation quantum of the condensation.
The Schrödinger Coefficient A = 1/2
If the ħ derivation is exact, the A coefficient of the condensation free-energy functional in model units is A_model = 1/2 exactly. This is precisely the coefficient in the Schrödinger kinetic energy term T = −(ħ²/2m)∇². The factor of 1/2 in quantum mechanics is not an assumption — it is the condensation localisation cost in model units.
All Planck Units From One Geometry
Paper 27 applies this derivation to all Planck units: l_P, m_P, t_P all expressed in terms of m_p, r_p, R₀, G, and c. Agreement: 0.068% (the square root of the 0.136% ħ agreement). The Planck scale is not a separate fundamental scale — it is the geometric mean of the condensation scale and the gravitational scale, derived from the same R₀.
Download BFUT papers, simulation code, and companion materials: vijayshankarsharma.com/downloads/