40,219 research outputs found
Quantum Structure in Economics: The Ellsberg Paradox
The 'expected utility hypothesis' and 'Savage's Sure-Thing Principle' are
violated in real life decisions, as shown by the 'Allais' and 'Ellsberg
paradoxes'. The popular explanation in terms of 'ambiguity aversion' is not
completely accepted. As a consequence, uncertainty is still problematical in
economics. To overcome these difficulties a distinction between 'risk' and
'ambiguity' has been introduced which depends on the existence of a
Kolmogorovian probabilistic structure modeling these uncertainties. On the
other hand, evidence of everyday life suggests that context plays a fundamental
role in human decisions under uncertainty. Moreover, it is well known from
physics that any probabilistic structure modeling contextual interactions
between entities structurally needs a non-Kolmogorovian framework admitting a
quantum-like representation. For this reason, we have recently introduced a
notion of 'contextual risk' to mathematically capture situations in which
ambiguity occurs. We prove in this paper that the contextual risk approach can
be applied to the Ellsberg paradox, and elaborate a sphere model within our
'hidden measurement formalism' which reveals that it is the overall conceptual
landscape that is responsible of the disagreement between actual human
decisions and the predictions of expected utility theory, which generates the
paradox. This result points to the presence of a quantum conceptual layer' in
human thought which is superposed to the usually assumed classical logical
layer', and conceptually supports the thesis of several authors suggesting the
presence of quantum structure in economics and decision theory.Comment: 8 pages, 1 figure. arXiv admin note: substantial text overlap with
arXiv:1105.1814, arXiv:1104.1459, arXiv:1105.181
Consistent Histories and Quantum Reasoning
A system of quantum reasoning for a closed system is developed by treating
non-relativistic quantum mechanics as a stochastic theory. The sample space
corresponds to a decomposition, as a sum of orthogonal projectors, of the
identity operator on a Hilbert space of histories. Provided a consistency
condition is satisfied, the corresponding Boolean algebra of histories, called
a {\it framework}, can be assigned probabilities in the usual way, and within a
single framework quantum reasoning is identical to ordinary probabilistic
reasoning. A refinement rule, which allows a probability distribution to be
extended from one framework to a larger (refined) framework, incorporates the
dynamical laws of quantum theory. Two or more frameworks which are incompatible
because they possess no common refinement cannot be simultaneously employed to
describe a single physical system.Comment: Latex, 31 page
Causality re-established
Causality never gained the status of a "law" or "principle" in physics. Some
recent literature even popularized the false idea that causality is a notion
that should be banned from theory. Such misconception relies on an alleged
universality of reversibility of laws of physics, based either on determinism
of classical theory, or on the multiverse interpretation of quantum theory, in
both cases motivated by mere interpretational requirements for realism of the
theory. Here, I will show that a properly defined unambiguous notion of
causality is a theorem of quantum theory, which is also a falsifiable
proposition of the theory. Such causality notion appeared in the literature
within the framework of operational probabilistic theories. It is a genuinely
theoretical notion, corresponding to establish a definite partial order among
events, in the same way as we do by using the future causal cone on Minkowski
space. The causality notion is logically completely independent of the
misidentified concept of "determinism", and, being a consequence of quantum
theory, is ubiquitous in physics. In addition, as classical theory can be
regarded as a restriction of quantum theory, causality holds also in the
classical case, although the determinism of the theory trivializes it. I then
conclude arguing that causality naturally establishes an arrow of time. This
implies that the scenario of the "Block Universe" and the connected "Past
Hypothesis" are incompatible with causality, and thus with quantum theory: they
both are doomed to remain mere interpretations and, as such, not falsifiable,
similar to the hypothesis of "super-determinism". This article is part of a
discussion meeting issue "Foundations of quantum mechanics and their impact on
contemporary society".Comment: Presented at the Royal Society of London, on 11/12/ 2017, at the
conference "Foundations of quantum mechanics and their impact on contemporary
society". To appear on Philosophical Transactions of the Royal Society
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