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58
Bohmian mechanics as the foundation of quantum mechanics
"... In order to arrive at Bohmian mechanics from standard nonrelativistic quantum mechanics one need do almost nothing! One need only complete the usual quantum description in what is really the most obvious way: by simply including the positions of the particles of a quantum system as part of the state ..."
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Cited by 42 (13 self)
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In order to arrive at Bohmian mechanics from standard nonrelativistic quantum mechanics one need do almost nothing! One need only complete the usual quantum description in what is really the most obvious way: by simply including the positions of the particles of a quantum system as part of the state description of that system, allowing these positions to evolve in the most natural way. The entire quantum formalism, including the uncertainty principle and quantum randomness, emerges from an analysis of this evolution. This can be expressed succinctly—though in fact not succinctly enough—by declaring that the essential innovation of Bohmian mechanics is the insight that particles move! 1 Bohmian Mechanics is Minimal Is it not clear from the smallness of the scintillation on the screen that we have to do with a particle? And is it not clear, from the diffraction and interference 1 patterns, that the motion of the particle is directed by a wave? De Broglie showed in detail how the motion of a particle, passing through just one of two holes in screen, could be influenced by waves propagating through both holes.
Spin foam models of Riemannian quantum gravity, available as grqc/0202017
"... Abstract. Using numerical calculations, we compare three versions of the Barrett– Crane model of 4dimensional Riemannian quantum gravity. In the version with face and edge amplitudes as described by De Pietri, Freidel, Krasnov, and Rovelli, we show the partition function diverges very rapidly for m ..."
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Cited by 25 (4 self)
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Abstract. Using numerical calculations, we compare three versions of the Barrett– Crane model of 4dimensional Riemannian quantum gravity. In the version with face and edge amplitudes as described by De Pietri, Freidel, Krasnov, and Rovelli, we show the partition function diverges very rapidly for many triangulated 4manifolds. In the version with modified face and edge amplitudes due to Perez and Rovelli, we show the partition function converges so rapidly that the sum is dominated by spin foams where all the spins labelling faces are zero except for small, widely separated islands of higher spin. We also describe a new version which appears to have a convergent partition function without drastic spinzero dominance. Finally, after a general discussion of how to extract physics from spin foam models, we discuss the implications of convergence or divergence of the partition function for other aspects of a spin foam model. 1.
Structural Issues in Quantum Gravity
, 1995
"... A discursive, nontechnical, analysis is made of some of the basic issues that arise in almost any approach to quantum gravity, and of how these issues stand in relation to recent developments in the field. Specific topics include the applicability of the conceptual and mathematical structures of bo ..."
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Cited by 23 (1 self)
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A discursive, nontechnical, analysis is made of some of the basic issues that arise in almost any approach to quantum gravity, and of how these issues stand in relation to recent developments in the field. Specific topics include the applicability of the conceptual and mathematical structures of both classical general relativity and standard quantum theory. This discussion is preceded by a short history of the last twentyfive years of research in quantum gravity, and concludes with speculations on what a future theory might look like.
Do we really understand quantum mechanics? Strange correlations, paradoxes, and theorems
 Am. J. Phys
, 2001
"... This article presents a general discussion of several aspects of our present understanding of quantum mechanics. The emphasis is put on the very special correlations that this theory makes possible: they are forbidden by very general arguments based on realism and local causality. In fact, these cor ..."
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Cited by 20 (1 self)
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This article presents a general discussion of several aspects of our present understanding of quantum mechanics. The emphasis is put on the very special correlations that this theory makes possible: they are forbidden by very general arguments based on realism and local causality. In fact, these correlations are completely impossible in any circumstance, except the very special situations designed by physicists especially to observe these purely quantum effects. Another general point that is emphasized is the necessity for the theory to predict the emergence of a single result in a single realization of an experiment. For this purpose, orthodox quantum mechanics introduces a special postulate: the reduction of the state vector, which comes in addition to the Schrödinger evolution postulate. Nevertheless, the presence in parallel of two evolution processes of the same object (the state vector) may be a potential source for conflicts; various attitudes that are possible
Geometrical Formulation of Quantum Mechanics
, 1997
"... ..., has a very different appearance. In particular, states are now represented bypointsofasymplecticmanifold (whichhappenstohaveinadditionacomplecticowgeneratedbya Hamiltonianfunction. Thereisthusaremarkablepatible Riemannian metric), observablesarerepresentedbycertain realvalued functionsonthissp ..."
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Cited by 15 (0 self)
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..., has a very different appearance. In particular, states are now represented bypointsofasymplecticmanifold (whichhappenstohaveinadditionacomplecticowgeneratedbya Hamiltonianfunction. Thereisthusaremarkablepatible Riemannian metric), observablesarerepresentedbycertain realvalued functionsonthisspaceandthe Schrödingerevolutioniscapturedbythesym similaritywiththestandardsymplecticformulationofclassicalmechanics. FeaturessuchasuncertaintiesandstatevectorreductionswhicharespeclassicalconsiderationsandtheWKBapproximation.Moreimportantly,it Thegeometricalformulationshedsconsiderablelightonanumberofissues cictoquantummechanicscanalsobeformulatedgeometricallybutnowrefer totheRiemannianmetricastructurewhichisabsentinclassicalmechanics. ture.Thegeometricalreformulationprovidesauniedframeworktodiscuss suggestsgeneralizationsofquantummechanics. Thesimplestamongtheseare suchasthesecondquantizationprocedure,theroleofcoherentstatesinsemi theseandtocorrectamisconception. Finally,italsosuggestsdirectionsin equivalenttothedynamicalgeneralizations thathaveappearedintheliterahasanastonishingrangeofapplicationsfromquarksandleptonstoneutronstarsand Quantummechanicsisprobablythemostsuccessfulscientictheoryeverinvented.It whichmoreradicalgeneralizationsmaybe found.
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 Mereotopology
 Annals of Mathematics and Artificial Intelligence
, 2000
"... While mereotopology  the theory of boundaries, contact and separation built up on a mereological foundation  has found fruitful applications in the realm of qualitative spatial reasoning, it faces problems when its methods are extended to deal with those kinds of spatial and nonspatial reas ..."
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Cited by 13 (5 self)
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While mereotopology  the theory of boundaries, contact and separation built up on a mereological foundation  has found fruitful applications in the realm of qualitative spatial reasoning, it faces problems when its methods are extended to deal with those kinds of spatial and nonspatial reasoning which involve a factor of granularity. This is because granularity cannot easily be represented within a mereologybased framework. We sketch how this problem can be solved by means of a theory of coarsegrained partitions, drawing on methods developed for the manipulation of partitions in the spatial realm and applying these to a range of partitions of nonspatial sorts. We then show how these same methods can be extended to apply to finite sequences of partitions evolving over time, or to what we shall call coarse and finegrained histories. Keywords: mereotopology, granularity, ontology, partitions, histories 1. Introduction As a result of a series of important contribut...
Aspects of the Decoherent Histories Approach to Quantum Mechanics
 ARXIV:QUANTPH/9805062]; PHYS. REV. D 60, 105031
, 1995
"... I review the decoherent (or consistent) histories approach to quantum mechanics, due to Griffiths, to GellMann and Hartle, and to Omnès. This is an approach to standard quantum theory specifically designed to apply to genuinely closed systems, up to and including the entire universe. It does not d ..."
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Cited by 13 (0 self)
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I review the decoherent (or consistent) histories approach to quantum mechanics, due to Griffiths, to GellMann and Hartle, and to Omnès. This is an approach to standard quantum theory specifically designed to apply to genuinely closed systems, up to and including the entire universe. It does not depend on an assumed separation of classical and quantum domains, on notions of measurement, or on collapse of the wave function. Its primary aim is to find sets of histories for closed systems exhibiting negligble interference, and therefore, to which probabilities may be assigned. Such sets of histories are called consistent or decoherent, and may be manipulated according to the rules of ordinary (Boolean) logic. The approach provides a framework from which one may discuss the emergence of an approximately classical domain for macroscopic systems, together with the conventional Copenhagen quantum mechanics for microscropic subsystems. In the special case in which the total closed system naturally separates into a distinguished subsystem coupled to an environment, the decoherent histories approach is
Discrete Quantum Causal Dynamics
 International Journal of Theoretical Physics
, 2003
"... We give a mathematical framework to describe the evolution of an open quantum systems subjected to nitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems which evolve independently but may also interact. This evolut ..."
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Cited by 10 (5 self)
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We give a mathematical framework to describe the evolution of an open quantum systems subjected to nitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems which evolve independently but may also interact. This evolution, driven both by unitary operators and measurements, is coded in a precise mathematical structure in such a way that the crucial properties of causality, covariance and entanglement are faithfully represented. We show how our framework may be expressed using the language of (poly)categories and functors. Remarkably, important physical consequences  such as covariance  follow directly from the functoriality of our axioms. We establish strong links between the physical picture we propose and linear logic. Specifically we show that the rened logical connectives of linear logic can be used to describe the entanglements of subsystems in a precise way. Furthermore, we show that there is a precise correspondence between the evolution of a given system and deductions in a certain formal logical system based on the rules of linear logic. This framework generalizes and enriches both causal posets and the histories approach to quantum mechanics. 1
Progress in the manyminds interpretation of quantum mechanics
, 1999
"... abstract This paper is a response to some recent discussions of manyminds interpretations in the philosophical literature. After an introduction to the manyminds idea, the complexity of quantum states for macroscopic objects is stressed. Then it is proposed that a characterization of the physical ..."
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Cited by 7 (2 self)
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abstract This paper is a response to some recent discussions of manyminds interpretations in the philosophical literature. After an introduction to the manyminds idea, the complexity of quantum states for macroscopic objects is stressed. Then it is proposed that a characterization of the physical structure of observers is a proper goal for physical theory. It is argued that an observer cannot be defined merely by the instantaneous structure of a brain, but that the history of the brain’s functioning must also be taken into account. Next the nature of probability in manyminds interpretations is discussed and it is suggested that only discrete probability models are needed. The paper concludes with brief comments on issues of actuality and identity over time.