5,677 research outputs found
Location equivalence in a parametric setting
AbstractLocation equivalence has been presented in [5] as a bisimulation-based equivalence able to take into account the spatial distribution of processes.In this work, the parametric approach of [12] is applied to location equivalence. An observation domain for localities is identified and the associated equivalence is shown to coincide with the equivalence introducted in [6,16]. The observation of a computation is a forest (defined up to isomorphism) whose nodes are the events (labeled by observable actions) and where the arcs describe the sublocation relation.We show in the paper that our approach is really parametric. By performing minor changes in the definitions, many equivalences are captured: partial and mixed ordering causal semantics, interleaving, and a variation of location equivalence where the generation ordering is not evidenced. It seems difficult to modify the definitions of [6,16] to obtain the last observation. The equivalence induced by this observation corresponds to the very intuitive assumption that different locations cannot share a common clock, and hence the ordering between events occurring in different places cannot be determined.Thanks to the general results proved in [12] for the parametric approach, all the observation equivalences described in this paper come equipped with sound and complete axiomatizations
Localization and the interface between quantum mechanics, quantum field theory and quantum gravity I (The two antagonistic localizations and their asymptotic compatibility)
It is shown that there are significant conceptual differences between QM and
QFT which make it difficult to view the latter as just a relativistic extension
of the principles of QM. At the root of this is a fundamental distiction
between Born-localization in QM (which in the relativistic context changes its
name to Newton-Wigner localization) and modular localization which is the
localization underlying QFT, after one separates it from its standard
presentation in terms of field coordinates. The first comes with a probability
notion and projection operators, whereas the latter describes causal
propagation in QFT and leads to thermal aspects of locally reduced finite
energy states. The Born-Newton-Wigner localization in QFT is only applicable
asymptotically and the covariant correlation between asymptotic in and out
localization projectors is the basis of the existence of an invariant
scattering matrix. In this first part of a two part essay the modular
localization (the intrinsic content of field localization) and its
philosophical consequences take the center stage. Important physical
consequences of vacuum polarization will be the main topic of part II. Both
parts together form a rather comprehensive presentation of known consequences
of the two antagonistic localization concepts, including the those of its
misunderstandings in string theory.Comment: 63 pages corrections, reformulations, references adde
The Nature and Implementation of Representation in Biological Systems
I defend a theory of mental representation that satisfies naturalistic constraints. Briefly, we begin by distinguishing (i) what makes something a representation from (ii) given that a thing is a representation, what determines what it represents. Representations are states of biological organisms, so we should expect a unified theoretical framework for explaining both what it is to be a representation as well as what it is to be a heart or a kidney. I follow Millikan in explaining (i) in terms of teleofunction, explicated in terms of natural selection.
To explain (ii), we begin by recognizing that representational states do not have content, that is, they are neither true nor false except insofar as they both âpoint toâ or âreferâ to something, as well as âsayâ something regarding whatever it is they are about. To distinguish veridical from false representations, there must be a way for these separate aspects to come apart; hence, we explain (ii) by providing independent theories of what I call f-reference and f-predication (the âfâ simply connotes âfundamentalâ, to distinguish these things from their natural language counterparts).
Causal theories of representation typically founder on error, or on what Fodor has called the disjunction problem. Resemblance or isomorphism theories typically founder on what Iâve called the non-uniqueness problem, which is that isomorphisms and resemblance are practically unconstrained and so representational content cannot be uniquely determined. These traditional problems provide the motivation for my theory, the structural preservation theory, as follows. F-reference, like reference, is a specific, asymmetric relation, as is causation. F-predication, like predication, is a non-specific relation, as predicates typically apply to many things, just as many relational systems can be isomorphic to any given relational system. Putting these observations together, a promising strategy is to explain f-reference via causal history and f-predication via something like isomorphism between relational systems.
This dissertation should be conceptualized as having three parts. After motivating and characterizing the problem in chapter 1, the first part is the negative project, where I review and critique Dretskeâs, Fodorâs, and Millikanâs theories in chapters 2-4. Second, I construct my theory about the nature of representation in chapter 5 and defend it from objections in chapter 6. In chapters 7-8, which constitute the third and final part, I address the question of how representation is implemented in biological systems. In chapter 7 I argue that single-cell intracortical recordings taken from awake Macaque monkeys performing a cognitive task provide empirical evidence for structural preservation theory, and in chapter 8 I use the empirical results to illustrate, clarify, and refine the theory
The role of positivity and causality in interactions involving higher spin
It is shown that the recently introduced positivity and causality preserving string-local quantum field theory (SLFT) resolves most No-Go situations in higher spin problems. This includes in particular the VeloâZwanziger causality problem which turns out to be related in an interesting way to the solution of zero mass WeinbergâWitten issue. In contrast to the indefinite metric and ghosts of gauge theory, SLFT uses only positivity-respecting physical degrees of freedom. The result is a fully Lorentz-covariant and causal string field theory in which light- or space-like linear strings transform covariant under Lorentz transformation.
The cooperation of causality and quantum positivity in the presence of interacting
particles leads to remarkable conceptual changes. It turns out that the presence of H-selfinteractions in the Higgs model is not the result of SSB on a postulated Mexican hat potential, but solely the consequence of the implementation of positivity and causality. These principles (and not the imposed gauge symmetry) account also for the Lie-algebra structure of the leading contributions of selfinteracting vector mesons.
Second order consistency of selfinteracting vector mesons in SLFT requires the presence of H-particles; this, and not SSB, is the raison d'ĂȘtre for H.
The basic conceptual and calculational tool of SLFT is the S-matrix. Its string-independence is a powerful restriction which determines the form of interaction densities in terms of the model-defining particle content and plays a fundamental role in the construction of pl observables and sl interpolating fields
The topology and geometry of causality
Quantum theory is manifestly in tension with the classical notion of causality. How do we recover causal reasoning in the quantum regime? In this dissertation, we propose a framework where such causal idiosyncrasies are identified as obstructions to the existence of global sections for presheaves of causal data. We do so by extending the Abramsky- Brandenburger framework for non-locality and contextuality [6] to situations where measurement contexts are allowed to be signalling. This results in a theory-independent phenomenology of causality, which can be used to reason about causal structure in any theory exhibiting contextuality.
In the first part of this dissertation, we study the specific phenomenology of coherent control of quantum channels, giving rigorous operational meaning to the superposition of causal order. We pursue a bottom-up approachâalternative to the process matrix formalismâby investigating how indefiniteness of causality emerges from specific characteristics of operational theories. This provides the recipe for building processes with indefinite causality, which are then causally analysed using tools described in the second part of the thesis.
The second, more substantial part of this dissertation is devoted to building the sheaf- theoretic framework unifying non-locality, contextuality and indefinite causality. We provide a combinatorial description of the operational assumptions underlying definite and indefinite causal order, and characterise the emergent topologies of classical contexts. We explain how to associate causal data to such topologies and detail the relationship between the covers for a topological space and varying degrees of classicality. We develop a complementary geometric understanding of the space of empirical models for this presheaf, and show how it can be used to perform theory-independent causal analysis of empirical data. We conclude by providing novel examples of such causal analysis, showcasing the existence of the phenomenon of contextual causality. Importantly, our examples demonstrate that such phenomenon can be witnessed in quantum theory, as long as coherently control of causal order is allowed for quantum processes
Black Holes: Eliminating Information or Illuminating New Physics?
Black holes, initially thought of as very interesting geometric constructions
of nature, over time, have learnt to (often) come up with surprises and
challenges. From the era of being described as merely some interesting and
exotic solutions of \gr, they have, in modern times, really started to test our
confidence in everything else, we thought we know about the nature. They have
in this process, also earned a dreadsome reputation in some corners of
theoretical physics. The most serious charge on the black holes is that they
eat up information, never to release and subsequently erase it. This goes
absolutely against the sacred principles of all other branches of fundamental
sciences. This realization has shaken the very base of foundational concepts,
both in quantum theory and gravity, which we always took for granted. Attempts
to exorcise black holes of this charge, have led us to crossroads with
concepts, hold dearly in quantum theory. The sphere of black hole's tussle with
quantum theory has readily and steadily grown, from the advent of the Hawking
radiation some four decades back, into domain of quantum information theory in
modern times, most aptly, recently put in the form of the firewall puzzle. Do
black holes really indicate something sinister about their existence or do they
really take the lid off our comfort with ignoring the fundamental issues, our
modern theories are seemingly plagued with? In this review, we focus on issues
pertaining to black hole evaporation, the development of the information loss
paradox, its recent formulation, the leading debates and promising directions
in the community.Comment: Published in Univers
Weighted logics for artificial intelligence : an introductory discussion
International audienceBefore presenting the contents of the special issue, we propose a structured introductory overview of a landscape of the weighted logics (in a general sense) that can be found in the Artificial Intelligence literature, highlighting their fundamental differences and their application areas
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