Atomic Physics and the Dimensionality of Space
The extremely high precision reached in QED experiments provides stringent bounds for any change in the standard framework of low energy physics (i.e. for energies close to the electron mass). In his contribution J. Reinhardt discusses e.g. such bounds for the coupling to a new light particle. In this lecture I want to discuss a rather different possibility, namely to derive from the Lamb-shift a bound for the deviation of the spatial dimension from the integer value three. Before doing so it is obviously necessary to discuss the concept of fractal dimensions and to explain their possible origin.
KeywordsFractal Dimension Lamb Shift Schroedinger Equation Stringent Bound Koch Curve
Unable to display preview. Download preview PDF.
- Bhanst C., Neuberger H., and Shapiro J., 1984: “Simulation of a Critical Ising Fractal” Phys. Rev. Lett. 53: 2277.Google Scholar
- Davydov A. S., 1965: “Quantum Mechanics,” Pergamon, Oxford.Google Scholar
- deMesa A. G., Guzman A., and Yndurain F. J., 1985: Determination of the Number of Non-Compact Dimensions,’ University of Madrid preprint 17/85.Google Scholar
- Gefen, Y., Meir, Y., Mandelbrot, B. B., and Aharony, A., 1983: ‘Geometric Implementation of Hypercubic Lattices with Noninteger Dimensionality by Use of Low Lacunarity Fractal Lattices’ Phys. Rev. Lett. 50: 145.Google Scholar
- Mandelbrot, B. B., 1977: ‘Fractals: Form Chance and Dimension’, Freeman, San Francisco, 1985: ‘The Fractal Geometry of Nature’, Freeman, San Francisco.Google Scholar
- Müller, B., and Schafer, A., 1986: ‘Improved Bounds on the Dimension of Space-Time’, Phys. Rev. Lett. 56: 1215.Google Scholar
- Schäfer, A., and Müller, B., 1986: ‘Bounds for the Fractal Dimension of Space’ to be published in J. Phys. A.Google Scholar
- Wetterich, C., 1985: ‘Kaluza-Klein Cosmology and the Inflationary Universe’, Nucl. Phys. B252: 309.Google Scholar
- Zeilinger, A., and Svozil, K., 1985: ‘Measuring the Dimension of Space-Time’, Phys. Rev. Lett. 54: 2553.Google Scholar