Misc,
The Unreasonable Success of Quantum Probability II: Quantum Measurements as Universal Measurements
(2014)cite arxiv:1401.2650Comment: 29 pagesa, 6 figures.
Abstract
In the first part of this two-part article, we have introduced and analyzed a
multidimensional model, called the 'general tension-reduction' (GTR) model,
able to describe general quantum-like measurements with an arbitrary number of
outcomes, and we have used it as a general theoretical framework to study the
most general possible condition of lack of knowledge in a measurement, so
defining what we have called a 'universal measurement'. In this second part, we
present the formal proof that universal measurements, which are averages over
all possible forms of fluctuations, produce the same probabilities as
measurements characterized by 'uniform' fluctuations on the measurement
situation. Since quantum probabilities can be shown to arise from the presence
of such uniform fluctuations, we have proven that they can be interpreted as
the probabilities of a first-order non-classical theory, describing situations
in which the experimenter lacks complete knowledge about the nature of the
interaction between the measuring apparatus and the entity under investigation.
This same explanation can be applied -- mutatis mutandis -- to the case of
cognitive measurements, made by human subjects on conceptual entities, or in
decision processes, although it is not necessarily the case that the structure
of the set of states would be in this case strictly Hilbertian. We also show
that universal measurements correspond to maximally 'robust' descriptions of
indeterministic reproducible experiments, and since quantum measurements can
also be shown to be maximally robust, this adds plausibility to their
interpretation as universal measurements, and provides a further element of
explanation for the great success of the quantum statistics in the description
of a large class of phenomena.
