Year: 2001
Type: preprint
Abstract: It is shown that in two-state quantum theory, a generic quantum state can be described by a non-computable real number. In terms of this, the criterion for measurement outcome is simply and deterministically defined. This demonstration is based on a construction of the Riemann sphere whose points represent, not complex numbers, but divergent sequences with bivalent elements. Complex structure arises from self-similar properties of a set of operators which generate these sequences. In general, a rotation of (the coordinates of) the sphere maps a computable real to a non-computable real. This is interpreted physically as a mapping of a physically-measurable state to a counterfactual state. Implications for non-locality, null measurements, many worlds and so on, are discussed. The possible role of the Euler equation as the counterpart of the Schrodinger equation for real-number quantum state evolution is also outlined.
Source: arXiv (Cornell University)
Author: Palmer, T. N.
Institution: European Centre for Medium-Range Weather Forecasts
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1619562964