Topic
Spacetime
About: Spacetime is a research topic. Over the lifetime, 19503 publications have been published within this topic receiving 362052 citations. The topic is also known as: space–time continuum & space–time.
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TL;DR: In this paper, the authors present a plan of the present work, from absolute space to abstract space, from the Contradictions of Space to Differential Space, and from Contradictory Space to Social Space.
Abstract: Translatora s Acknowledgements. 1. Plan of the Present Work. 2. Social Space. 3. Spatial Architectonics. 4. From Absolute Space to Abstract Space. 5. Contradictory Space. 6. From the Contradictions of Space to Differential Space. 7. Openings and Conclusions. Afterword by David Harvey. Index.
10,114 citations
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TL;DR: The standard model of particle physics is valid to distances as small as 10−16 cm, and there is some evidence (such as that obtained by extrapolating the strengths of the four forces to determine the distance scale at which they might become indistinguishable) that the next level of structure will be detected only at a distance scale of roughly 10−32 cm as discussed by the authors.
Abstract: Particle physicists have spent much of this century grappling with one basic question in various forms: what are the fundamental degrees of freedom needed to describe nature, and what are the laws that govern their dynamics? First molecules, then atoms, then “elementary particles” such as protons and neutrons all have been revealed to be composite objects whose constituents could be studied as more fundamental degrees of freedom. The current “standard model” of particle physics—which is nearly 25 years old, has much experimental evidence in its favor and is comprised of six quarks, six leptons, four forces, and the as yet unobserved Higgs boson—contains internal indications that it, too, may be just another step along the path toward uncovering the truly fundamental degrees of freedom. The standard model is valid to distances as small as 10−16 cm, and there is some evidence (such as that obtained by extrapolating the strengths of the four forces to determine the distance scale at which they might become indistinguishable) that the next level of structure will be detected only at a distance scale of roughly 10−32 cm, far beyond our abilities to measure in the laboratory.
The study of motion and gravity also has undergone several revisions during this century. Reconciling the Newtonian theory of motion with the experimentally observed constancy of the speed of light required the introduction of special relativity, which quite remarkably insists that space and time are intimately related, much as different faces of the same …
2,812 citations
TL;DR: In this paper, it is shown that the ignorance principle holds for the quantum-mechanical evaporation of black holes, where the black hole creates particles in pairs, with one particle always falling into the hole and the other possibly escaping to infinity.
Abstract: The principle of equivalence, which says that gravity couples to the energy-momentum tensor of matter, and the quantum-mechanical requirement that energy should be positive imply that gravity is always attractive. This leads to singularities in any reasonable theory of gravitation. A singularity is a place where the classical concepts of space and time break down as do all the known laws of physics because they are all formulated on a classical space-time background. In this paper it is claimed that this breakdown is not merely a result of our ignorance of the correct theory but that it represents a fundamental limitation to our ability to predict the future, a limitation that is analogous but additional to the limitation imposed by the normal quantum-mechanical uncertainty principle. The new limitation arises because general relativity allows the causal structure of space-time to be very different from that of Minkowski space. The interaction region can be bounded not only by an initial surface on which data are given and a final surface on which measurements are made but also a "hidden surface" about which the observer has only limited information such as the mass, angular momentum, and charge. Concerning this hidden surface one has a "principle of ignorance": The surface emits with equal probability all configurations of particles compatible with the observers limited knowledge. It is shown that the ignorance principle holds for the quantum-mechanical evaporation of black holes: The black hole creates particles in pairs, with one particle always falling into the hole and the other possibly escaping to infinity. Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state. This means there is no $S$ matrix for the process of black-hole formation and evaporation. Instead one has to introduce a new operator, called the superscattering operator, which maps density matrices describing the initial situation to density matrices describing the final situation.
2,226 citations
TL;DR: In this paper, the authors developed a method for renormalizing the AdS/CFT prescription for computing correlation functions, which involves regularizing the bulk on-shell supergravity action in a covariant way, computing all divergences, adding counterterms to cancel them and then removing the regulator.
Abstract: We develop a systematic method for renormalizing the AdS/CFT prescription for computing correlation functions. This involves regularizing the bulk on-shell supergravity action in a covariant way, computing all divergences, adding counterterms to cancel them and then removing the regulator. We explicitly work out the case of pure gravity up to six dimensions and of gravity coupled to scalars. The method can also be viewed as providing a holographic reconstruction of the bulk spacetime metric and of bulk fields on this spacetime, out of conformal field theory data. Knowing which sources are turned on is sufficient in order to obtain an asymptotic expansion of the bulk metric and of bulk fields near the boundary to high enough order so that all infrared divergences of the on-shell action are obtained. To continue the holographic reconstruction of the bulk fields one needs new CFT data: the expectation value of the dual operator. In particular, in order to obtain the bulk metric one needs to know the expectation value of stress-energy tensor of the boundary theory. We provide completely explicit formulae for the holographic stress-energy tensors up to six dimensions. We show that both the gravitational and matter conformal anomalies of the boundary theory are correctly reproduced. We also obtain the conformal transformation properties of the boundary stress-energy tensors.
1,795 citations
TL;DR: The holographic principle as mentioned in this paper asserts that the fundamental degrees of freedom involved in a unified description of spacetime and matter must be manifest in an underlying quantum theory of gravity, and it has yet to be explained.
Abstract: There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at $1.4\ifmmode\times\else\texttimes\fi{}{10}^{69}$ bits per square meter. This article reviews the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black holes. The construction of light sheets, which associate relevant spacetime regions to any given surface, is discussed in detail. This article explains how the bound is tested, and its validity is demonstrated in a wide range of examples. A universal relation between geometry and information is thus uncovered. It has yet to be explained. The holographic principle asserts that its origin must lie in the number of fundamental degrees of freedom involved in a unified description of spacetime and matter. It must be manifest in an underlying quantum theory of gravity. This article surveys some successes and challenges in implementing the holographic principle.
1,706 citations