4,427 research outputs found
On the Unpredictability of Individual Quantum Measurement Outcomes
Abstract. We develop a general, non-probabilistic model of prediction which is suitable for assessing the (un)predictability of individual physical events. We use this model to provide, for the first time, a rigorous proof of the unpredictability of a class of individual quantum measurement outcomes, a well-known quantum attribute postulated or claimed for a long time. We prove that quantum indeterminism-formally modelled as value indefiniteness-is incompatible with the supposition of predictability: measurements of value indefinite observables are unpredictable. The proof makes essential use of a strengthened form of the Kochen-Specker theorem proven previously to identify value indefinite observables. This form of quantum unpredictability, like the Kochen-Specker theorem, relies on three assumptions: compatibility with quantum mechanical predictions, non-contextuality, and the value definiteness of observables corresponding to the preparation basis of a quantum state. We explore the relation between unpredictability and incomputability and show that the unpredictability of individual measurements of a value indefinite quantum observable complements, and is independent of, the global strong incomputability of any sequence of outcomes of this particular quantum experiment. Finally, we discuss a real model of hypercomputation whose computational power has yet to be determined, as well as further open problems
A Non-Probabilistic Model of Relativised Predictability in Physics
Little effort has been devoted to studying generalised notions or models of
(un)predictability, yet is an important concept throughout physics and plays a
central role in quantum information theory, where key results rely on the
supposed inherent unpredictability of measurement outcomes. In this paper we
continue the programme started in [1] developing a general, non-probabilistic
model of (un)predictability in physics. We present a more refined model that is
capable of studying different degrees of "relativised" unpredictability. This
model is based on the ability for an agent, acting via uniform, effective
means, to predict correctly and reproducibly the outcome of an experiment using
finite information extracted from the environment. We use this model to study
further the degree of unpredictability certified by different quantum
phenomena, showing that quantum complementarity guarantees a form of
relativised unpredictability that is weaker than that guaranteed by
Kochen-Specker-type value indefiniteness. We exemplify further the difference
between certification by complementarity and value indefiniteness by showing
that, unlike value indefiniteness, complementarity is compatible with the
production of computable sequences of bits.Comment: 10 page
A Quantum-Bayesian Route to Quantum-State Space
In the quantum-Bayesian approach to quantum foundations, a quantum state is
viewed as an expression of an agent's personalist Bayesian degrees of belief,
or probabilities, concerning the results of measurements. These probabilities
obey the usual probability rules as required by Dutch-book coherence, but
quantum mechanics imposes additional constraints upon them. In this paper, we
explore the question of deriving the structure of quantum-state space from a
set of assumptions in the spirit of quantum Bayesianism. The starting point is
the representation of quantum states induced by a symmetric informationally
complete measurement or SIC. In this representation, the Born rule takes the
form of a particularly simple modification of the law of total probability. We
show how to derive key features of quantum-state space from (i) the requirement
that the Born rule arises as a simple modification of the law of total
probability and (ii) a limited number of additional assumptions of a strong
Bayesian flavor.Comment: 7 pages, 1 figure, to appear in Foundations of Physics; this is a
condensation of the argument in arXiv:0906.2187v1 [quant-ph], with special
attention paid to making all assumptions explici
Neural Unpredictability, the Interpretation of Quantum Theory, and the Mind-Body Problem
It has been suggested, on the one hand, that quantum states are just states
of knowledge; and, on the other, that quantum theory is merely a theory of
correlations. These suggestions are confronted with problems about the nature
of psycho-physical parallelism and about how we could define probabilities for
our individual future observations given our individual present and previous
observations. The complexity of the problems is underlined by arguments that
unpredictability in ordinary everyday neural functioning, ultimately stemming
from small-scale uncertainties in molecular motions, may overwhelm, by many
orders of magnitude, many conventionally recognized sources of observed
``quantum'' uncertainty. Some possible ways of avoiding the problems are
considered but found wanting. It is proposed that a complete understanding of
the relationship between subjective experience and its physical correlates
requires the introduction of mathematical definitions and indeed of new
physical laws.Comment: 27 pages, plain TeX, v2: missing reference inserted, related papers
from http://www.poco.phy.cam.ac.uk/~mjd101
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