Quantum Theory as a Biconformal Measurement Theory
International Journal of Geometric Methods in Modern Physics
Biconformal spaces contain the essential elements of quantum mechanics, making the independent imposition of quantization unnecessary. Based on three postulates characterizing motion and measurement in biconformal geometry, we derive standard quantum mechanics, and show how the need for probability amplitudes arises from the use of a standard of measurement. Additionally, we show that a postulate for unique, classical motion yields Hamiltonian dynamics with no measurable size changes, while a postulate for probabilistic evolution leads to physical dilatations manifested as measurable phase changes. Our results lead to the Feynman path integral formulation, from which follows the Schrödinger equation. We discuss the Heisenberg uncertainty relation and fundamental canonical commutation relations.
Anderson, L. B. and Wheeler, J. T., Quantum theory as a biconformal measurement theory, Int.J.Geom.Meth.Mod.Phys. 3 (2006) 315, (35pp.) http://arxiv.org/pdf/hep-th/0406159