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The quantum structure of spacetime at the Planck scale and quantum fields
 COMMUN. MATH. PHYS. 172, 187–220 (1995)
, 1995
"... We propose uncertainty relations for the different coordinates of spacetime events, motivated by Heisenberg’s principle and by Einstein’s theory of classical gravity. A model of Quantum Spacetime is then discussed where the commutation relations exactly implement our uncertainty relations. We outl ..."
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Cited by 337 (6 self)
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We propose uncertainty relations for the different coordinates of spacetime events, motivated by Heisenberg’s principle and by Einstein’s theory of classical gravity. A model of Quantum Spacetime is then discussed where the commutation relations exactly implement our uncertainty relations. We outline the definition of free fields and interactions over QST and take the first steps to adapting the usual perturbation theory. The quantum nature of the underlying spacetime replaces a local interaction by a specific nonlocal effective interaction in the ordinary Minkowski space. A detailed study of interacting QFT and of the smoothing of ultraviolet divergences is deferred to a subsequent paper. In the classical limit where the Planck length goes to zero, our Quantum Spacetime reduces to the ordinary Minkowski space times a two component space whose components are homeomorphic to the tangent bundle TS 2 of the 2–sphere. The relations with Connes’ theory of the standard model will be studied elsewhere.
Analogue Gravity
 Living Rev. Rel
"... Analogue models of (and for) gravity have a long and distinguished history dating back to the earliest years of general relativity. In this review article we will discuss the history, aims, results, and future prospects for the various analogue models. We start the discussion by presenting a particu ..."
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Cited by 70 (27 self)
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Analogue models of (and for) gravity have a long and distinguished history dating back to the earliest years of general relativity. In this review article we will discuss the history, aims, results, and future prospects for the various analogue models. We start the discussion by presenting a particularly simple example of an analogue model, before exploring the rich history and complex tapestry of models discussed in the literature. The last decade in particular has seen a remarkable and sustained development of analogue gravity ideas, leading to some hundreds of published articles, a workshop, two books, and this review article. Future prospects for the analogue gravity programme also look promising, both on the experimental front (where technology is rapidly advancing) and on the theoretical front (where variants of analogue models can be used as a springboard for radical attacks on the problem
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 30 (2 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.
Probing planckscale physics with quantum optics
 Nat. Phys
, 2012
"... One of the main challenges in physics today is to merge quantum theory and the theory of general relativity into a unified framework. Various approaches towards developing such a theory of quantum gravity are pursued, but the lack of experimental evidence of quantum gravitational effects thus far i ..."
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Cited by 13 (1 self)
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One of the main challenges in physics today is to merge quantum theory and the theory of general relativity into a unified framework. Various approaches towards developing such a theory of quantum gravity are pursued, but the lack of experimental evidence of quantum gravitational effects thus far is a major hindrance. Yet, the quantization of spacetime itself can have experimental implications: the existence of a minimal length scale is widely expected to result in a modification of the Heisenberg uncertainty relation. Here we introduce a scheme that allows an experimental test of this conjecture by probing directly the canonical commutation relation of the center of mass mode of a massive mechanical oscillator with a mass close to the Planck mass. Our protocol utilizes quantum optical control and readout of the mechanical system to probe possible deviations from the quantum commutation relation even at the Planck scale. We show that the scheme is within reach of current technology. It thus opens a feasible route for tabletop experiments to test possible quantum gravitational phenomena. The ongoing search for a quantum theory of gravity is one of the main challenges in modern physics. A major difficulty in the development of such theories is the lack
Causal structures and causal boundaries
, 2005
"... We give an uptodate perspective with a general overview of the theory of causal properties, the derived causal structures, their classification and applications, and the definition and construction of causal boundaries and of ..."
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Cited by 12 (0 self)
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We give an uptodate perspective with a general overview of the theory of causal properties, the derived causal structures, their classification and applications, and the definition and construction of causal boundaries and of
Minimum Distances in NonTrivial String Target Spaces
, 1994
"... The idea of minimum distance, familiar from R ↔ 1/R duality when the string target space is a circle, is analyzed for less trivial geometries. The particular geometry studied is that of a blownup quotient singularity within a CalabiYau space and mirror symmetry is used to perform the analysis. It ..."
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Cited by 9 (2 self)
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The idea of minimum distance, familiar from R ↔ 1/R duality when the string target space is a circle, is analyzed for less trivial geometries. The particular geometry studied is that of a blownup quotient singularity within a CalabiYau space and mirror symmetry is used to perform the analysis. It is found that zero distances can appear but that in many cases this requires other distances within the same target space to be infinite. In other cases zero distances can occur without compensating infinite distances.
The Search for Quantum Gravity Signals
, 2005
"... We give an overview of ongoing searches for effects motivated by the study of the quantumgravity problem. We describe in greater detail approaches which have not been covered in recent “Quantum Gravity Phenomenology ” reviews. In particular, we outline a new framework for describing Lorentz invarian ..."
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Cited by 9 (1 self)
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We give an overview of ongoing searches for effects motivated by the study of the quantumgravity problem. We describe in greater detail approaches which have not been covered in recent “Quantum Gravity Phenomenology ” reviews. In particular, we outline a new framework for describing Lorentz invariance violation in the Maxwell sector. We also discuss the general strategy on the experimental side as well as on the theoretical side for a search for quantum gravity effects. The role of test theories, kinematical and dymamical, in this general context is emphasized. The present status of controlled laboratory experiments is described, and we also summarize some key results obtained on the basis of astrophysical observations. 1 Introduction and preliminary remarks 1.1 The search for quantum gravity Our present description of the laws of physics may be characterized as obtained from two types of constituents. The first type of constituent are theoretical frameworks which apply to all physical phenomena at any instant. These “universal ” or “frame ” theories are Quantum Theory (all matter
Localization of Events in SpaceTime
, 1997
"... The present paper deals with the quantum coordinates of an event in spacetime, individuated by a quantum object. It is known that these observables cannot be described by selfadjoint operators or by the corresponding spectral projectionvalued measure. We describe them by means of a positiveopera ..."
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Cited by 6 (2 self)
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The present paper deals with the quantum coordinates of an event in spacetime, individuated by a quantum object. It is known that these observables cannot be described by selfadjoint operators or by the corresponding spectral projectionvalued measure. We describe them by means of a positiveoperatorvalued (POV) measure in the Minkowski spacetime, satisfying a suitable covariance condition with respect to the Poincaré group. This POV measure determines the probability that a measurement of the coordinates of the event gives results belonging to a given set in spacetime. We show that this measure must vanish on the vacuum and the oneparticle states, which cannot define any event. We give a general expression for the Poincaré covariant POV measures. We define the baricentric events, which lie on the worldline of the centreofmass, and we find a simple expression for the average values of their coordinates. Finally, we discuss the