Quantum mechanics as a measurement theory on biconformal space

Details Quantum mechanics as a measurement theory on biconformal space Quantum mechanics as a measurement theory on biconformal space

2004-06-18

arxiv.org/abs/hep-th/0406159v2

Int.J.Geom.Meth.Mod.Phys.3:315-340,2006

Physics

High Energy Physics

High Energy Physics - Theory

34 pages; replaced discussion of multiparticle Hamiltonian dynamics

Scientific paper

10.1142/S0219887806001168

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 Schroedinger equation. We discuss the Heisenberg uncertainty relation and fundamental canonical commutation relations.

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