455 research outputs found
Many worlds and modality in the interpretation of quantum mechanics: an algebraic approach
Many worlds interpretations (MWI) of quantum mechanics avoid the measurement
problem by considering every term in the quantum superposition as actual. A
seemingly opposed solution is proposed by modal interpretations (MI) which
state that quantum mechanics does not provide an account of what `actually is
the case', but rather deals with what `might be the case', i.e. with
possibilities. In this paper we provide an algebraic framework which allows us
to analyze in depth the modal aspects of MWI. Within our general formal scheme
we also provide a formal comparison between MWI and MI, in particular, we
provide a formal understanding of why --even though both interpretations share
the same formal structure-- MI fall pray of Kochen-Specker (KS) type
contradictions while MWI escape them.Comment: submitted to the Journal of Mathematical Physic
Correlations, deviations and expectations: the Extended Principle of the Common Cause
The Principle of the Common Cause is usually understood to provide causal explanations for probabilistic correlations obtaining between causally unrelated events. In this study, an extended interpretation of the principle is proposed, according to which common causes should be invoked to explain positive correlations whose values depart from the ones that one would expect to obtain in accordance to her probabilistic expectations. In addition, a probabilistic model for common causes is tailored which satisfies the generalized version of the principle, at the same time including the standard conjunctive-fork model as a special case
Bayesian Conditioning, the Reflection Principle, and Quantum Decoherence
The probabilities a Bayesian agent assigns to a set of events typically
change with time, for instance when the agent updates them in the light of new
data. In this paper we address the question of how an agent's probabilities at
different times are constrained by Dutch-book coherence. We review and attempt
to clarify the argument that, although an agent is not forced by coherence to
use the usual Bayesian conditioning rule to update his probabilities, coherence
does require the agent's probabilities to satisfy van Fraassen's [1984]
reflection principle (which entails a related constraint pointed out by
Goldstein [1983]). We then exhibit the specialized assumption needed to recover
Bayesian conditioning from an analogous reflection-style consideration.
Bringing the argument to the context of quantum measurement theory, we show
that "quantum decoherence" can be understood in purely personalist
terms---quantum decoherence (as supposed in a von Neumann chain) is not a
physical process at all, but an application of the reflection principle. From
this point of view, the decoherence theory of Zeh, Zurek, and others as a story
of quantum measurement has the plot turned exactly backward.Comment: 14 pages, written in memory of Itamar Pitowsk
A geometric proof of the Kochen-Specker no-go theorem
We give a short geometric proof of the Kochen-Specker no-go theorem for
non-contextual hidden variables models. Note added to this version: I
understand from Jan-Aake Larsson that the construction we give here actually
contains the original Kochen-Specker construction as well as many others (Bell,
Conway and Kochen, Schuette, perhaps also Peres).Comment: This paper appeared some years ago, before the author was aware of
quant-ph. It is relevant to recent developments concerning Kochen-Specker
theorem
Jump-like unravelings for non-Markovian open quantum systems
Non-Markovian evolution of an open quantum system can be `unraveled' into
pure state trajectories generated by a non-Markovian stochastic (diffusive)
Schr\"odinger equation, as introduced by Di\'osi, Gisin, and Strunz. Recently
we have shown that such equations can be derived using the modal (hidden
variable) interpretation of quantum mechanics. In this paper we generalize this
theory to treat jump-like unravelings. To illustrate the jump-like behavior we
consider a simple system: A classically driven (at Rabi frequency )
two-level atom coupled linearly to a three mode optical bath, with a central
frequency equal to the frequency of the atom, , and the two side
bands have frequencies . In the large limit we
observed that the jump-like behavior is similar to that observed in this system
with a Markovian (broad band) bath. This is expected as in the Markovian limit
the fluorescence spectrum for a strongly driven two level atom takes the form
of a Mollow triplet. However the length of time for which the Markovian-like
behaviour persists depends upon {\em which} jump-like unraveling is used.Comment: 11 pages, 5 figure
Degree of explanation
Partial explanations are everywhere. That is, explanations citing causes that explain some but not all of an effect are ubiquitous across science, and these in turn rely on the notion of degree of explanation. I argue that current accounts are seriously deficient. In particular, they do not incorporate adequately the way in which a cause’s explanatory importance varies with choice of explanandum. Using influential recent contrastive theories, I develop quantitative definitions that remedy this lacuna, and relate it to existing measures of degree of causation. Among other things, this reveals the precise role here of chance, as well as bearing on the relation between causal explanation and causation itself
Remarks on Causality in Relativistic Quantum Field Theory
It is shown that the correlations predicted by relativistic quantum field
theory in locally normal states between projections in local von Neumann
algebras \cA(V_1),\cA(V_2) associated with spacelike separated spacetime
regions have a (Reichenbachian) common cause located in the union of
the backward light cones of and . Further comments on causality and
independence in quantum field theory are made.Comment: 10 pages, Latex, Quantum Structures 2002 Conference Proceedings
submission. Minor revision of the order of definitions on p.
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