Contact between laboratory instruments and equations of quantum mechanics

Ambiguity in the contact between laboratory instruments and equations of quantum mechanics is formulated in terms of responses of the instruments to commands transmitted to them by a Classical digital Process-control Computer (CPC); in this way instruments are distinguished from quantum-mechanical models (sets of equations) that specify what is desired of the instruments. Results include: (1) a formulation of quantum mechanics adapted to computer-controlled instruments; (2) a lower bound on the precision of unitary transforms required for quantum searching and a lower bound on sample size needed to show that instruments implement a desired model at that precision; (3) a lower bound on precision of timing required of a CPC in directing instruments; (4) a demonstration that guesswork is necessary in ratcheting up the precision of commands.Comment: 19 pages, prepared for SPIE AeroSense 200

On statements of experimental results expressed in the mathematical language of quantum theory

We note the separation of a quantum description of an experiment into a statement of results (as probabilities) and an explanation of these results (in terms of linear operators). The inverse problem of choosing an explanation to fit given results is analyzed, leading to the conclusion that any quantum description comes as an element of a family of related descriptions, entailing multiple statements of results and multiple explanations. Facing this multiplicity opens avenues for exploration and consequences that are only beginning to be explored. Among the consequences are these: (1) statements of results impose topologies on control parameters, without resort to any quantum explanation; (2) an endless source of distinct explanations forces an open cycle of exploration and description bringing more and more control parameters into play, and (3) ambiguity of description is essential to the concept of invariance in physics.Comment: 10 pages, 4 figures. Edited version of SPIE paper 6976-9 presented at the 2008 SPIE Defense & Security Conference on Quantum Information and Computation VI, March 17-20, 200