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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
Matched detectors as definers of force
Although quantum states nicely express interference effects, outcomes of
experimental trials show no states directly; they indicate properties of
probability distributions for outcomes. We prove categorically that probability
distributions leave open a choice of quantum states and operators and
particles, resolvable only by a move beyond logic, which, inspired or not, can
be characterized as a guess. By recognizing guesswork as inescapable in
choosing quantum states and particles, we free up the use of particles as
theoretical inventions by which to describe experiments with devices, and
thereby replace the postulate of state reductions by a theorem. By using the
freedom to invent probe particles in modeling light detection, we develop a
quantum model of the balancing of a light-induced force, with application to
models and detecting devices by which to better distinguish one source of weak
light from another. Finally, we uncover a symmetry between entangled states and
entangled detectors, a dramatic example of how the judgment about what light
state is generated by a source depends on choosing how to model the detector of
that light.Comment: 30 pages, 4 figs, LaTeX; new Introduction; new material in Secs. 4 &
5; new Sec. 6; 1 new figure, added reference
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