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1921]), A Treatise on Probability
, 2004
"... Los paradigmas económicos de Ludwig von Mises por una parte, y de John Maynard Keynes por otra, han sido correctamente reconocidos como contradictorias a nivel teórico, y como antagonistas, con respecto a sus implicancias políticas prácticas y públicas. Desde el punto de vista característico también ..."
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Cited by 358 (0 self)
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Los paradigmas económicos de Ludwig von Mises por una parte, y de John Maynard Keynes por otra, han sido correctamente reconocidos como contradictorias a nivel teórico, y como antagonistas, con respecto a sus implicancias políticas prácticas y públicas. Desde el punto de vista característico también han sido reivindicadas por sectores de oposición del espectro político. Aún así, las respectivas visiones de estos autores con respecto al significado e interpretación de la probabilidad, muestra una afinidad conceptual más estrecha que los que se ha reconocido en la literatura. Se ha argumentado especialmente que en algunos aspectos importantes, la interpretación de Ludwig von Mises del concepto de probabilidad, muestra una estrecha afinidad con la interpretación de probabilidad desarrollada por su oponente John Maynard Keynes, que con las maneras de ver la probabilidad respaldadas por su hermano Richard von Mises. Sin embargo, también existen grandes diferencias entre los puntos de vista de Ludwig von Mises y aquellos de John Maynard Keynes con respecto a la probabilidad. Uno de ellos se destaca principalmente: cuando John Maynard Keynes aboga por un punto de vista monista de la probabilidad, Ludwig von Mises defiende un punto de vista dualista de la probabilidad, de acuerdo con lo cual, el concepto de probabilidad recibe dos significados diferentes, y en donde cada uno de ellos es válido en un área o contexto en particular. Se concluye que tanto John Maynard Keynes como Ludwig von Mises presentan puntos de vista claramente diferenciados con respecto al significado e interpretación de la probabilidad.
Quantum Equilibrium and the Origin of Absolute Uncertainty
, 1992
"... The quantum formalism is a "measurement" formalisma phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what emerges from Schr6dinger's equation for a system of particles when ..."
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Cited by 112 (47 self)
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The quantum formalism is a "measurement" formalisma phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what emerges from Schr6dinger's equation for a system of particles when we merely insist that "particles " means particles. While distinctly nonNewtonian, Bohmian mechanics is a fully deterministic theory of particles in motion, a motion choreographed by the wave function. We find that a Bohmian universe, though deterministic, evolves in such a manner that an appearance of randomness emerges, precisely as described by the quantum formalism and given, for example, by "p = IV [ 2.,, A crucial ingredient in our analysis of the origin of this randomness is the notion of the effective wave function of a subsystem, a notion of interest in its own right and of relevance to any discussion of quantum theory. When the quantum formalism is regarded as arising in this way, the paradoxes and perplexities so often associated with (nonrelativistic) quantum theory simply evaporate.
Epistemic and Ontic Quantum Realities
, 2005
"... Quantum theory has provoked intense discussions about its interpretation since its pioneer days, beginning with Bohr’s view of quantum theory as a theory of knowledge. We show that such an epistemic perspective can be consistently complemented by Einstein’s ontically oriented position. ..."
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Cited by 21 (11 self)
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Quantum theory has provoked intense discussions about its interpretation since its pioneer days, beginning with Bohr’s view of quantum theory as a theory of knowledge. We show that such an epistemic perspective can be consistently complemented by Einstein’s ontically oriented position.
The Bekenstein bound, topological quantum field theory and pluralistic quantum cosmology
"... this paper a new approach to the problem of constructing a quantum theory of gravity in the cosmological context is proposed. It is founded on results from four separate directions of investigation, which are: 1) A new point of view towards the interpretation problem in quantum cosmology[1, 2, 3, 4] ..."
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Cited by 19 (12 self)
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this paper a new approach to the problem of constructing a quantum theory of gravity in the cosmological context is proposed. It is founded on results from four separate directions of investigation, which are: 1) A new point of view towards the interpretation problem in quantum cosmology[1, 2, 3, 4], which rejects the idea that a single quantum state, or a single Hilbert space, can provide a complete description of a closed system like the universe. Instead, the idea is to accept Bohr's original proposal that the quantum state requires for its interpretation a context in which we distinguish two subsystems of the universethe quantum system and observer. However, we seek to relativize this split, so that the boundary between the part of the universe that is considered the system and that which might be considered the observer may be chosen arbitrarily. The idea is then that a quantum theory of cosmology is specified by giving an assignment of a Hilbert space and algebra of observables to every possible boundary that can be considered to split the universe into two such subsystems. A quantum state of the universe is then an assignment of a statistical state to every one of these Hilbert spaces, subject to certain conditions of consistency. Each of these states is interpreted to contain the information that an observer on one side of each boundary might have about the system of the other side. This formulation then accepts the idea that each observer can only have incomplete information about the universe, so that the most complete description possible of the universe is given by the whole collection of incomplete, but mutually compatible quantum state descriptions of all the possible observers. At the same time, the information of different observers is, to some extent, ...
Computations via experiments with kinematic systems
, 2004
"... Consider the idea of computing functions using experiments with kinematic systems. We prove that for any set A of natural numbers there exists a 2dimensional kinematic system BA with a single particle P whose observable behaviour decides n ∈ A for all n ∈ N. The system is a bagatelle and can be des ..."
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Cited by 14 (5 self)
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Consider the idea of computing functions using experiments with kinematic systems. We prove that for any set A of natural numbers there exists a 2dimensional kinematic system BA with a single particle P whose observable behaviour decides n ∈ A for all n ∈ N. The system is a bagatelle and can be designed to operate under (a) Newtonian mechanics or (b) Relativistic mechanics. The theorem proves that valid models of mechanical systems can compute all possible functions on discrete data. The proofs show how any information (coded by some A) can be embedded in the structure of a simple kinematic system and retrieved by simple observations of its behaviour. We reflect on this undesirable situation and argue that mechanics must be extended to include a formal theory for performing experiments, which includes the construction of systems. We conjecture that in such an extended mechanics the functions computed by experiments are precisely those computed by algorithms. We set these theorems and ideas in the context of the literature on the general problem “Is physical behaviour computable? ” and state some open problems.
Between classical and quantum
, 2005
"... The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, inclu ..."
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Cited by 14 (3 self)
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The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, including over 500 references. For example, we sketch how certain intuitive ideas of the founders of quantum theory have fared in the light of current mathematical knowledge. One such idea that has certainly stood the test of time is Heisenberg’s ‘quantumtheoretical Umdeutung (reinterpretation) of classical observables’, which lies at the basis of quantization theory. Similarly, Bohr’s correspondence principle (in somewhat revised form) and Schrödinger’s wave packets (or coherent states) continue to be of great importance in understanding classical behaviour from quantum mechanics. On the other hand, no consensus has been reached on the Copenhagen Interpretation, but in view of the parodies of it one typically finds in the literature we describe it in detail. On the assumption that quantum mechanics is universal and complete, we discuss three ways in which classical physics has so far been believed to emerge from quantum physics, namely
Quantum Theory Without Observers
 I and II, Physics Today
, 1997
"... Introduction Despite its extraordinary predictive successes, quantum mechanics has, since its inception some seventy years ago, been plagued by conceptual difficulties. The basic problem, plainly put, is this: It is not at all clear what quantum mechanics is about. What, in fact, does quantum mecha ..."
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Cited by 13 (1 self)
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Introduction Despite its extraordinary predictive successes, quantum mechanics has, since its inception some seventy years ago, been plagued by conceptual difficulties. The basic problem, plainly put, is this: It is not at all clear what quantum mechanics is about. What, in fact, does quantum mechanics describe? It might seem, since it is widely agreed that the state of any quantum mechanical system is completely specified by its wave function, that quantum mechanics is fundamentally about the behavior of wave functions. Quite naturally, no physicist wanted this to be true more than did Erwin Schrodinger, the father of the wave function. Nonetheless, Schrodinger ultimately found this impossible to believe. His difficulty was not so much with the novelty of the wave function [2, page 156 of [3]]: "That it is an abstract, unintuitive mathematical construct is a scruple that almost always surfaces against new aids to thought and that carries no great message." Rather, it was that
A Topos for Algebraic Quantum Theory
 COMMUNICATIONS IN MATHEMATICAL PHYSICS
, 2009
"... The aim of this paper is to relate algebraic quantum mechanics to topos theory, so as to construct new foundations for quantum logic and quantum spaces. Motivated by Bohr’s idea that the empirical content of quantum physics is accessible only through classical physics, we show how a noncommutative C ..."
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Cited by 9 (1 self)
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The aim of this paper is to relate algebraic quantum mechanics to topos theory, so as to construct new foundations for quantum logic and quantum spaces. Motivated by Bohr’s idea that the empirical content of quantum physics is accessible only through classical physics, we show how a noncommutative C*algebra of observables A induces a topos T (A) in which the amalgamation of all of its commutative subalgebras comprises a single commutative C*algebra A. According to the constructive Gelfand duality theorem of Banaschewski and Mulvey, the latter has an internal spectrum �(A) in T (A), which in our approach plays the role of the quantum phase space of the system. Thus we associate a locale (which is the topostheoretical notion of a space and which intrinsically carries the intuitionistic logical structure of a Heyting algebra) to a C*algebra (which is the noncommutative notion of a space). In this setting, states on A become probability measures (more precisely, valuations) on �, and selfadjoint elements of A define continuous functions (more precisely, locale maps) from � to Scott’s interval domain. Noting that open subsets of �(A) correspond to propositions about the system, the pairing map that assigns a (generalized) truth value to a state and a proposition assumes an extremely simple categorical form. Formulated in this way, the quantum theory defined by A is essentially turned into a classical theory, internal to the topos T (A). These results were inspired by the topostheoretic approach to quantum physics proposed by Butterfield and Isham, as recently generalized by Döring and Isham.
Contexts in quantum, classical and partition logic
 In Handbook of Quantum Logic
, 2006
"... Contexts are maximal collections of comeasurable observables “bundled together ” to form a “quasiclassical miniuniverse. ” Different notions of contexts are discussed for classical, quantum and generalized urn–automaton systems. PACS numbers: 02.10.v,02.50.Cw,02.10.Ud ..."
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Cited by 8 (7 self)
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Contexts are maximal collections of comeasurable observables “bundled together ” to form a “quasiclassical miniuniverse. ” Different notions of contexts are discussed for classical, quantum and generalized urn–automaton systems. PACS numbers: 02.10.v,02.50.Cw,02.10.Ud
Probabilistic theories with dynamic causal structure: A new framework for quantum gravity
, 509
"... Quantum theory is a probabilistic theory with fixed causal structure. General relativity is a deterministic theory but where the causal structure is dynamic. It is reasonable to expect that quantum gravity will be a probabilistic theory with dynamic causal structure. The purpose of this paper is to ..."
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Cited by 8 (3 self)
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Quantum theory is a probabilistic theory with fixed causal structure. General relativity is a deterministic theory but where the causal structure is dynamic. It is reasonable to expect that quantum gravity will be a probabilistic theory with dynamic causal structure. The purpose of this paper is to present a framework for such a probability calculus. We define an operational notion of spacetime, this being composed of elementary regions. Central to this formalism is an object we call the causaloid. This object captures information about causal structure implicit in the data by quantifying the way in which the number of measurements required to establish a state for a composite region is reduced when there is a causal connection between the component regions. This formalism puts all elementary regions on an equal footing. It does not require that we impose fixed causal structure. In particular, it is not necessary to assume the existence of a background time. The causaloid formalism does for probability theory something analogous to what Riemannian calculus does for geometry. Remarkably, given the causaloid, we can calculate all relevant probabilities and so the causaloid is sufficient to specify the predictive aspect of a physical theory. We show how certain causaloids can be represented by suggestive diagrams and we show how to represent both classical probability theory and quantum theory by a causaloid. We do not give a causaloid formulation for general relativity though we speculate that this is possible. The causaloid formalism is likely to be very powerful since the basic equations remain unchanged when we go between different theories the differences between these theories being contained in the specification of the causaloid alone. The work presented here suggests a research program aimed at finding a theory of quantum gravity. The idea is to use the causaloid formalism along with principles taken from the two theories to marry the dynamic causal structure of general relativity with the probabilistic structure of quantum theory. 1 1