Scale relativity and Schrödinger's equation

✍ Scribed by L. Nottale

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 545 KB
• Volume: 9
• Category: Article
• ISSN: 0960-0779
• DOI: 10.1016/s0960-0779(97)00190-2

✦ Synopsis

The theory of scale relativity generalizes the application domain of Einstein's principle of relativity to scale transformations of space-time resolutions. In this theory, we no longer assume that the space-time continuum is differentiable, this implying its fractal character. Both classical and quantum laws may emerge from a unique, more profound, scale law. The effects of nondifferentiability (complex nature of wave function, new terms in differential equations of mean motion) are accounted for by a scalecovariant derivative that transforms the equations of classical mechanics into the Schr6dinger equation. Using an intermediate description in terms of a 'fractal potential', we finally establish the m ~ dependence of the Compton~ie Broglie wavelength.