Planck's Radiation Law in the Quantized Universe

Abstract

Physical research looks for clues to quantum properties of the gravitational field. On the basis of the common Schr\"odinger theory, a simple model of the quantization of a Friedmann universe comprising dust and radiation is investigated. With regard to energy quantization, the result suggests a universal limitation of the energy spacing between neighbouring quantum states by the Planck energy. Applied to black-body radiation, a modified Planck radiation law follows. If this could be verified in the laboratory, it would provide a direct hint at quantum properties of the space-time manifold.