Fractal Phase-Space Uncertainty: A Logical-Spectral Reformulation of the Heisenberg Principle

Ijaz Durrani

Masanao Ozawa

Enrique Vidal Silvente

We develop a fractal-spectral reformulation of the Heisenberg uncertainty principle within a nonlinear phase-space framework motivated by the Quantum Fractal-Logical Unified Field architecture. Instead of working on the standard Hilbert space L 2 (R) with Lebesgue measure and linear position/momentum operators, we consider a fractal Hilbert space H F = L 2 (F, µ H) built on a Cantor-type metric-measure substrate with Hausdorff measure µ H and a self-adjoint fractal Hamiltonian. Within this setting we define effective position and momentum observables (X F , P F) adapted to the fractal geometry and derive a generalized uncertainty relation

Salvatore Capozzıello, Wladimir-Georges Boskoff

Mohamed Saladin El Naschie, Otto E. Rössler, Ilya Prigogine

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Robert Prevedel, Bose-Einstein Condensate