Share Email Print

Proceedings Paper

Bohr's indeterminacy principle in quantum holography, adaptive neural networks, cortical self-organization, molecular computers, magnetic resonance imaging, and solitonic nanotechnology
Author(s): Walter Schempp
Format Member Price Non-Member Price
PDF $17.00 $21.00

Paper Abstract

A rigorous proof of quantum parallelism cannot be based on the Heisenberg inequality because the standard deviation of self-adjoint operators in complex Hilbert space is insensitive to fine structures of the collective stationary interference distribution generated by a Mach-Zehnder interferometer from a coherent primary beam. Actually Niels Bohr's indeterminacy principle of spatio-temporal quantum electrodynamics cannot be based on any of the known uncertainty principles. It is shown how the holographic transform allows to circumvent the difficulties with the standard deviation by using a group theoretical implementation of the canonical commutation relations of quantum electrodynamics. The geometric quantization approach combined with the emitter-absorber transaction model of quantum dynamics on the whole real line R allows one to describe by a Liouville density the flow and counter-flow of single optical photons in split fan-in/fan-out coherent photonic channels. It makes the heuristic arguments concerning quantum parallelism rigorous by considering the collective stationary interference distributions of coherent wavepacket densities as symplectic spinors over the linear symplectic manifold modelled on the hologram plane. Consequently the symplectic spinorial organizational form governs photonic holograms. It implies the existence of single-photon holograms and includes the standard uncertainty inequality as a special case.

Paper Details

Date Published: 1 April 1992
PDF: 47 pages
Proc. SPIE 1658, Nonlinear Image Processing III, (1 April 1992); doi: 10.1117/12.58386
Show Author Affiliations
Walter Schempp, Univ. of Siegen (Germany)

Published in SPIE Proceedings Vol. 1658:
Nonlinear Image Processing III
Edward R. Dougherty; Jaakko T. Astola; Charles G. Boncelet Jr., Editor(s)

© SPIE. Terms of Use
Back to Top
Sign in to read the full article
Create a free SPIE account to get access to
premium articles and original research
Forgot your username?