The Fractal Structure of the Quantum Space-Time

摘要: We report here on the present state of an attempt at understanding micro-physics by basing ourselves a ‘principle scale relativity’, according to which laws physics should apply systems reference whatever their scale. The continuity but non differentiability quantum mechanical particle paths, occurrence infinities in field theories and universal length time dependence measurement results implied Heisenberg’s relations have led us, among other arguments, suggest achievement such principle using mathematical tool fractals (Nottale 1989). concept continuous self-avoiding fractal space-time is worked out: arguments are given for generally describing them as families Riemannian space-times whose curvature tends infinity when approaches zero. recall some basic already obtained this quest: dimension trajectories jumps from 1 2 all 4 coordinates, with fractal/non transition occurring around de Broglie’s time; conversely Heisenberg may be consequence assumed structures; point particles following curves naturally endowed spin. develop interpretation wave-particle duality property geodesical lines examplify it Young’s hole Einstein-Podolsky-Rosen experiments. Finally possible consequences concerning gravitation recalled, suggestion that Newton’s law break down active gravitational masses smaller than Planck mass.