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92
Quantum Gravity
, 2004
"... We describe the basic assumptions and key results of loop quantum gravity, which is a background independent approach to quantum gravity. The emphasis is on the basic physical principles and how one deduces predictions from them, at a level suitable for physicists in other areas such as string theor ..."
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Cited by 273 (9 self)
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We describe the basic assumptions and key results of loop quantum gravity, which is a background independent approach to quantum gravity. The emphasis is on the basic physical principles and how one deduces predictions from them, at a level suitable for physicists in other areas such as string theory, cosmology, particle physics, astrophysics and condensed matter physics. No details are given, but references are provided to guide the interested reader to the literature. The present state of knowledge is summarized in a list of 35 key results on topics including the hamiltonian and path integral quantizations, coupling to matter, extensions to supergravity and higher dimensional theories, as well as applications to black holes, cosmology and Plank scale phenomenology. We describe the near term prospects for observational tests of quantum theories of gravity and the expectations that loop quantum gravity may provide predictions for their outcomes. Finally, we provide answers to frequently asked questions and a list of key open problems.
Classical sequential growth dynamics for causal sets
 Physical Review D
, 2000
"... Starting from certain causality conditions and a discrete form of general covariance, we derive a very general family of classically stochastic, sequential growth dynamics for causal sets. The resulting theories provide a relatively accessible “half way house ” to full quantum gravity that possibly ..."
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Cited by 46 (5 self)
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Starting from certain causality conditions and a discrete form of general covariance, we derive a very general family of classically stochastic, sequential growth dynamics for causal sets. The resulting theories provide a relatively accessible “half way house ” to full quantum gravity that possibly contains the latter’s classical limit (general relativity). Because they can be expressed in terms of state models for an assembly of Ising spins living on the relations of the causal set, these theories also illustrate how nongravitational matter can arise dynamically from the causal set without having to be built in at the fundamental level. Additionally, our results bring into focus some interpretive issues of importance for causal set dynamics, and for quantum gravity more generally. 1
A Specimen of Theory Construction from Quantum Gravity, in The Creation of Ideas in
 Physics, Leplin, J. (Ed
, 1995
"... I describe the history of my attempts to arrive at a discrete substratum underlying the spacetime manifold, culminating in the hypothesis that the basic structure has the form of a partialorder (i.e. that it is a causal set). Like the other speakers in this session, I too am here much more as a wor ..."
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Cited by 19 (1 self)
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I describe the history of my attempts to arrive at a discrete substratum underlying the spacetime manifold, culminating in the hypothesis that the basic structure has the form of a partialorder (i.e. that it is a causal set). Like the other speakers in this session, I too am here much more as a working scientist than as a philosopher. Of course it is good to remember Peter Bergmann’s description of the physicist as “in many respects a philosopher in workingman’s* clothes”, but today I’m not going to change into a white shirt and attempt to draw philosophical lessons from the course of past work on quantum gravity. Instead I will merely try to recount a certain part of my own experience with this problem, explaining how I arrived at the idea of what I will call a causal set. This and similar structures have been proposed more than once as discrete replacements for spacetime. My excuse for not telling you also how others arrived at essentially the same idea [1] is naturally that my case is the only one I can hope to reconstruct with even minimal accuracy.
Quantum Measure Theory and its Interpretation
 Quantum Classical Correspondence: Proceedings of the 4 th Drexel Symposium on Quantum Nonintegrability, held Philadelphia, September 811
, 1994
"... We propose a realistic, spacetime interpretation of quantum theory in which reality constitutes a single history obeying a “law of motion ” that makes definite, but incomplete, predictions about its behavior. We associate a “quantum measure ” —S — to the set S of histories, and point out that —S — f ..."
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Cited by 17 (3 self)
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We propose a realistic, spacetime interpretation of quantum theory in which reality constitutes a single history obeying a “law of motion ” that makes definite, but incomplete, predictions about its behavior. We associate a “quantum measure ” —S — to the set S of histories, and point out that —S — fulfills a sum rule generalizing that of classical probability theory. We interpret —S— as a “propensity”, making this precise by stating a criterion for —S—=0 to imply “preclusion ” (meaning that the true history will not lie in S). The criterion involves triads of correlated events, and in application to electronelectron scattering, for example, it yields definite predictions about the electron trajectories themselves, independently of any measuring devices which might or might not be present. (In this way, we can give an objective account of measurements.) Two unfinished aspects of the interpretation involve
Discrete differential manifolds and dynamics on networks
 Journal of Mathematical Physics
, 1995
"... A discrete differential manifold we call a countable set together with an algebraic differential calculus on it. This structure has already been explored in previous work and provides us with a convenient framework for the formulation of dynamical models on networks and physical theories with discre ..."
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Cited by 17 (1 self)
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A discrete differential manifold we call a countable set together with an algebraic differential calculus on it. This structure has already been explored in previous work and provides us with a convenient framework for the formulation of dynamical models on networks and physical theories with discrete space and time. We present several examples and introduce a notion of differentiability of maps between discrete differential manifolds. Particular attention is given to differentiable curves in such spaces. Every discrete differentiable manifold carries a topology and we show that differentiability of a map implies continuity.
The case for background independence
, 2005
"... The aim of this paper is to explain carefully the arguments behind the assertion that the correct quantum theory of gravity must be background independent. We begin by recounting how the debate over whether quantum gravity must be background independent is a continuation of a longstanding argument ..."
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Cited by 16 (1 self)
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The aim of this paper is to explain carefully the arguments behind the assertion that the correct quantum theory of gravity must be background independent. We begin by recounting how the debate over whether quantum gravity must be background independent is a continuation of a longstanding argument in the history of physics and philosophy over whether space and time are relational or absolute. This leads to a careful statement of what physicists mean when we speak of background independence. Given this we can characterize the precise sense in which general relativity is a background independent theory. The leading background independent approaches to quantum gravity are then discussed, including causal set models, loop quantum gravity and dynamical triangulations and their main achievements are summarized along with the problems that remain open. Some first attempts to cast string/M theory into a background independent formulation are also mentioned. The relational/absolute debate has implications also for other issues such as unification and how the parameters of the standard models of physics and cosmology are to be explained. The recent issues concerning the string theory landscape are reviewed and it is argued that they can only be resolved within the context of a background independent formulation. Finally, we review some recent proposals to make quantum theory more relational. This is partly based on the text of a talk given to a meeting of the British Association for the Philosophy of Science, in July 2004, under the title ”The relational idea in physics and cosmology.”
Algebraic Quantization of Causal Sets
 International Journal of Theoretical Physics
, 2000
"... A scheme for an algebraic quantization of the causal sets of Sorkin et al. is presented. The suggested scenario is along the lines of a similar algebraization and quantum interpretation of finitary topological spaces due to Zapatrin and this author. To be able to apply the latter procedure to causal ..."
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Cited by 15 (12 self)
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A scheme for an algebraic quantization of the causal sets of Sorkin et al. is presented. The suggested scenario is along the lines of a similar algebraization and quantum interpretation of finitary topological spaces due to Zapatrin and this author. To be able to apply the latter procedure to causal sets Sorkin’s ‘semantic switch ’ from ‘partially ordered sets as finitary topological spaces ’ to ‘partially ordered sets as locally finite causal sets ’ is employed. The result is the definition of ‘quantum causal sets’. Such a procedure and its resulting definition is physically justified by a property of quantum causal sets that meets Finkelstein’s requirement from ‘quantum causality ’ to be an immediate, as well as an algebraically represented, relation between events for discrete locality’s sake. The quantum causal sets introduced here are shown to have this property by direct use of a result from the algebraization of finitary topological spaces due to Breslav, Parfionov and Zapatrin. 1.
Algebraic description of spacetime foam
 Classical and Quantum Gravity
, 2001
"... A mathematical formalism for treating spacetime topology as a quantum observable is provided. We describe spacetime foam entirely in algebraic terms. To implement the correspondence principle we express the classical spacetime manifold of general relativity and the commutative coordinates of its eve ..."
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Cited by 13 (10 self)
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A mathematical formalism for treating spacetime topology as a quantum observable is provided. We describe spacetime foam entirely in algebraic terms. To implement the correspondence principle we express the classical spacetime manifold of general relativity and the commutative coordinates of its events by means of appropriate limit constructions. Physical Motivation In this paper we present an algebraic model of spacetime foam. The notion of spacetime foam has manifold and somewhat ambiguous meaning in the literature if only because the models vary. There is no unanimous agreement about what foam ‘really ’ pertains to mainly due to the fact that each of the mathematical models highlights different aspects of that concept. Here we use the term ‘foam ’ along the concrete but general lines originally introduced by Wheeler [42] who intended to refer to a spacetime with a dynamically variable, because quantally fluctuating, topology. The basic intuition is that at quantum scales even the topology of spacetime is subject to dynamics and interference. This conception of foam is in glaring contrast with general relativity, the classical theory of gravity, where spacetime is fixed to a topological manifold once and forever so that the sole dynamical variable is a higher level structure, namely, the spacetime geometry. It seems theoretically lame and rather ad hoc to regard the geometry of spacetime as being a dynamical variable that can in principle be measured (ie, an observable), while at the same time to think of its topology as a structure a priori fixed by the theoretician, an inert etherlike absolute background that is not liable to experimental investigation thus effectively an unobservable theoretical entity [9]. Especially in the quantum realm where everything seems
Quantum Theory from Quantum Gravity
 grqc/0311059, Phys.Rev. D70
, 2004
"... We provide a mechanism by which, from a background independent model with no quantum mechanics, quantum theory arises in the same limit in which spatial properties appear. Starting with an arbitrary abstract graph as the microscopic model of spacetime, our ansatz is that the microscopic dynamics can ..."
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Cited by 13 (4 self)
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We provide a mechanism by which, from a background independent model with no quantum mechanics, quantum theory arises in the same limit in which spatial properties appear. Starting with an arbitrary abstract graph as the microscopic model of spacetime, our ansatz is that the microscopic dynamics can be chosen so that 1) the model has a low low energy limit which reproduces the nonrelativistic classical dynamics of a system of N particles in flat spacetime, 2) there is a minimum length, and 3) some of the particles are in a thermal bath or otherwise evolve stochastically. We then construct simple functions of the degrees of freedom of the theory and show that their probability distributions evolve according to the Schrödinger equation. The nonlocal hidden variables required to satisfy the conditions of Bell’s theorem are the links in the fundamental graph that connect nodes adjacent in the graph but distant in the approximate metric of the low energy limit. In the presence of these links, distant stochastic fluctuations are transferred into universal quantum fluctuations.