190 research outputs found
Effects and Propositions
The quantum logical and quantum information-theoretic traditions have exerted
an especially powerful influence on Bub's thinking about the conceptual
foundations of quantum mechanics. This paper discusses both the quantum logical
and information-theoretic traditions from the point of view of their
representational frameworks. I argue that it is at this level, at the level of
its framework, that the quantum logical tradition has retained its centrality
to Bub's thought. It is further argued that there is implicit in the quantum
information-theoretic tradition a set of ideas that mark a genuinely new
alternative to the framework of quantum logic. These ideas are of considerable
interest for the philosophy of quantum mechanics, a claim which I defend with
an extended discussion of their application to our understanding of the
philosophical significance of the no hidden variable theorem of Kochen and
Specker.Comment: Presented to the 2007 conference, New Directions in the Foundations
of Physic
On the complementarity of the quadrature observables
In this paper we investigate the coupling properties of pairs of quadrature
observables, showing that, apart from the Weyl relation, they share the same
coupling properties as the position-momentum pair. In particular, they are
complementary. We determine the marginal observables of a covariant phase space
observable with respect to an arbitrary rotated reference frame, and observe
that these marginal observables are unsharp quadrature observables. The related
distributions constitute the Radon tranform of a phase space distribution of
the covariant phase space observable. Since the quadrature distributions are
the Radon transform of the Wigner function of a state, we also exhibit the
relation between the quadrature observables and the tomography observable, and
show how to construct the phase space observable from the quadrature
observables. Finally, we give a method to measure together with a single
measurement scheme any complementary pair of quadrature observables.Comment: Dedicated to Peter Mittelstaedt in honour of his eightieth birthda
Facts, Values and Quanta
Quantum mechanics is a fundamentally probabilistic theory (at least so far as
the empirical predictions are concerned). It follows that, if one wants to
properly understand quantum mechanics, it is essential to clearly understand
the meaning of probability statements. The interpretation of probability has
excited nearly as much philosophical controversy as the interpretation of
quantum mechanics. 20th century physicists have mostly adopted a frequentist
conception. In this paper it is argued that we ought, instead, to adopt a
logical or Bayesian conception. The paper includes a comparison of the orthodox
and Bayesian theories of statistical inference. It concludes with a few remarks
concerning the implications for the concept of physical reality.Comment: 30 pages, AMS Late
Non-Abelian Bosonization and Haldane's Conjecture
We study the long wavelength limit of a spin S Heisenberg antiferromagnetic
chain. The fermionic Lagrangian obtained corresponds to a perturbed level 2S
SU(2) Wess-Zumino-Witten model. This effective theory is then mapped into a
compact U(1) boson interacting with Z_{2S} parafermions. The analysis of this
effective theory allows us to show that when S is an integer there is a mass
gap to all excitations, whereas this gap vanishes in the half-odd-integer spin
case. This gives a field theory treatment of the so-called Haldane's conjecture
for arbitrary values of the spin S.Comment: 9 pages REVTeX, no figure
Bell Correlations and the Common Future
Reichenbach's principle states that in a causal structure, correlations of
classical information can stem from a common cause in the common past or a
direct influence from one of the events in correlation to the other. The
difficulty of explaining Bell correlations through a mechanism in that spirit
can be read as questioning either the principle or even its basis: causality.
In the former case, the principle can be replaced by its quantum version,
accepting as a common cause an entangled state, leaving the phenomenon as
mysterious as ever on the classical level (on which, after all, it occurs). If,
more radically, the causal structure is questioned in principle, closed
space-time curves may become possible that, as is argued in the present note,
can give rise to non-local correlations if to-be-correlated pieces of classical
information meet in the common future --- which they need to if the correlation
is to be detected in the first place. The result is a view resembling Brassard
and Raymond-Robichaud's parallel-lives variant of Hermann's and Everett's
relative-state formalism, avoiding "multiple realities."Comment: 8 pages, 5 figure
Active Brownian Particles. From Individual to Collective Stochastic Dynamics
We review theoretical models of individual motility as well as collective
dynamics and pattern formation of active particles. We focus on simple models
of active dynamics with a particular emphasis on nonlinear and stochastic
dynamics of such self-propelled entities in the framework of statistical
mechanics. Examples of such active units in complex physico-chemical and
biological systems are chemically powered nano-rods, localized patterns in
reaction-diffusion system, motile cells or macroscopic animals. Based on the
description of individual motion of point-like active particles by stochastic
differential equations, we discuss different velocity-dependent friction
functions, the impact of various types of fluctuations and calculate
characteristic observables such as stationary velocity distributions or
diffusion coefficients. Finally, we consider not only the free and confined
individual active dynamics but also different types of interaction between
active particles. The resulting collective dynamical behavior of large
assemblies and aggregates of active units is discussed and an overview over
some recent results on spatiotemporal pattern formation in such systems is
given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte
Linguistics and natural logic
Evidence is presented to show that the role of a generative grammar of a natural language is not merely to generate the grammatical sentences of that language, but also to relate them to their logical forms. The notion of logical form is to be made sense of in terms a ânatural logicâ, a logical for natural language, whose goals are to express all concepts capable of being expressed in natural language, to characterize all the valid inferences that can be made in natural language, and to mesh with adequate linguistic descriptions of all natural languages. The latter requirement imposes empirical linguistic constraints on natural logic. A number of examples are discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43819/1/11229_2004_Article_BF00413602.pd
The Metaphysics of the Thin Red Line
There seems to be a minimal core that every theory wishing to accommodate the intuition that the future is open must contain: a denial of physical determinism (i.e. the thesis that what future states the universe will be in is implied by what states it has been in), and a denial of strong fatalism (i.e. the thesis that, at every time, what will subsequently be the case is metaphysically necessary). 1 Those two requirements are often associated with the idea of an objective temporal flow and the non-reality of the future. However, at least certain ways to frame the âopennessâ intuition do not rely on any of these. Branching Time Theory (BTT) is one such: it is compatible with the denial that time flow is objective and it is couched in a language with a (prima facie) commitment to an eternalist ontology. BTT, though, urges us to resist certain intuitions about the determinacy of future claims, which arguably do not lead either to physical determinism or to fatalism. Against BTT, supporters of the Thin Red Line Theory (TRL) argue that their position avoids determinism and fatalism, while also representing the fact that there is a future which is âspecial â because it is the one that will be the case. But starting with Belnap and Green 1994, some have objected to the tenability of TRL, mainly on metaphysical grounds. In particular, those argue that âpositing a thin red line amounts to giving up objective indeterminism, â 2 and that âhas unacceptable consequences, ranging from a mistreatment of actuality to an inability to talk coherently about what would have happened had what is going to happen not taken place. â 3 In this paper, we wish to reframe the 1 Hence, strong fatalism implies physical determinism, while the latter does not imply the former, thus being compatible with the world having been otherwise, assuming that the initial condition of the world could have been otherwise. Also, strong fatalism is intended as opposed to weak fatalism, according to which, whatever I will do now wonât affect what will be the case. Weak fatalism, instead, does not imply, nor is implied, by physical determinism
Miocene waterfowl and other birds from central Otago, New Zealand
Copyright © The Natural History Museum 2007Abundant fossil bird bones from the lower Bannockburn Formation, Manuherikia Group, an Early-Middle Miocene lacustrine deposit, 16â19 Ma, from Otago in New Zealand, reveal the âSt Bathans Faunaâ (new name), a first Tertiary avifauna of land and freshwater birds from New Zealand. At least 23 species of birds are represented by bones, and probable moa, Aves: Dinornithiformes, by eggshell. Anatids dominate the fauna with four genera and five species described as new: a sixth and largest anatid species is represented by just one bone. This is the most diverse Early-Middle Miocene duck fauna known worldwide. Among ducks, two species of dendrochenines are most numerous in the fauna, but a tadornine is common as well. A diving petrel (Pelecanoididae: Pelecanoides) is described, so extending the geological range of this genus worldwide from the Pliocene to the Middle Miocene, at least. The remaining 16 taxa are left undescribed but include: a large species of gull (Laridae); two small waders (Charadriiformes, genus indet.), the size of Charadrius bicinctus and Calidris ruficollis, respectively; a gruiform represented by one specimen similar to Aptornis; abundant rail (Rallidae) bones, including a common flightless rail and a rarer slightly larger taxon, about the size of Gallirallus philippensis; an ?eagle (Accipitridae); a pigeon (Columbidae); three parrots (Psittacidae); an owlet nightjar (Aegothelidae: Aegotheles sp.); a swiftlet (Apodidae: Collocalia sp.); and three passerine taxa, of which the largest is a member of the Cracticidae. The absence of some waterbirds, such as anserines (including swans), grebes (Podicipedidae) and shags (Phalacrocoracidae), among the abundant bones, indicates their probable absence from New Zealand in the Early-Middle Miocene.T. H. Worthy, A. J. D. Tennyson, C. Jones, J. A. McNamara and B. J. Dougla
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