20 research outputs found
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