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Topic: Global spacetime structure

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Grand Unified Theory - New proposals for the structure of spacetime It offers a new insight into dynamical structure, order and measure of the quantum world of the entire universe, discrete and yet continuous on the global scale, by identifying the universal gravitational field and the metric causal structure of spacetime to which all physical events are reducible. through manifestation of gravity as the geometry of the structure of spacetime. An interesting proposition was advanced by a theoretical physicist John Wheeler, who in his model of the theory based on the geometry of spacetime, tries to unify all the forces and particles within the geometrical structures or geometrodynamics members.tripod.com /stemy27/title.html   (5552 words)

BBC - Cambridgeshire Cyber Science - A Profile or 'Brief History' of Stephen Hawking The Large Scale Structure of Spacetime with G F R Ellis Stephen Hawking's main aim is to find a way of combining Einstein's General Theory of Relativity, which describes the large scale structure of the universe, with Quantum Mechanics, which deals with nature at the sub-atomic level. He has also predicted the end of humanity as a result of either global warming, a killer virus, or the impact of a large comet. www.bbc.co.uk /cambridgeshire/science/2003/10/stephen_hawking.shtml   (801 words)

Abstracts The fact that Minkowski spacetime is a fixed structure with global symmetries, made it impossible, of course, that it could be an appropriate global structure for general relativity. In other words, the claim at the heart of Minkowski's analysis is, at the same time, extremely far- reaching and extremely modest: it is the claim that a world in which special relativity is true simply is a world with a particular spacetime structure. Even after the general decline of logical empiricism, and the widespread adoption of a model-theoretic approach to theories, the general notion of spacetime structure as a formalism requiring interpretation persisted, even if the question of the nature of interpretation no longer received the kind of attention that the logical empiricists had given it. alcor.concordia.ca /~scol/seminars/conference/DiSalle.html   (519 words)

Penrose Diagram Often in General Relativity one uses the Penrose diagram to describe the causal structure of the spacetime. The interest in this diagram is that an asymptotically flat spacetime will have the same structure as infinity and therefore the same diagram at infinity. The major feature of those diagram is to put the infinity at finite position and at the same time do so such that the null geodesics are preserved (we conserve the structure of the spacetime). www.pas.rochester.edu /~pvarni/TC/node48.html   (209 words)

Symmetry and Symmetry Breaking The extension of the concept of continuous symmetry from “global” symmetries (such as the Galilean group of spacetime transformations) to “local” symmetries is one of the important developments in the concept of symmetry in physics that took place in the twentieth century. Another reason for attributing symmetries to nature is the so-called geometrical interpretation of spatiotemporal symmetries, according to which the spatiotemporal symmetries of physical laws are interpreted as symmetries of spacetime itself, the “geometrical structure” of the physical world. In postulating the universality of the global continuous spacetime symmetries, Einstein's construction of his special theory of relativity represents the first turning point in the application of symmetry to twentieth-century physics. plato.stanford.edu /entries/symmetry-breaking   (209 words)

Algebraic approach to quantum field theory on non-globally-hyperbolic spacetimes Physically, what lie at the foundation of any formalism for quantization in curved spacetime are the canonical commutation relations, imposed on the field operators evaluated at a global Cauchy surface. When spacetime is globally hyperbolic, the theory defined by our construction coincides with the ordinary Klein--Gordon field theory on a globally hyperbolic background. The mathematical formalism for linear quantum field theory on curved spacetime depends in an essential way on the assumption of global hyperbolicity. stacks.iop.org /0264-9381/11/999   (430 words)

Kay: Application of linear hyperbolic PDE to linear quantum fields in curved spacetimes: especially black holes, time machines and a new semi-local vacuum concept Singularity structure of the two point function of the free Dirac field on a globally hyperbolic spacetime. A further aim is to introduce, and set into context, some recent advances in our understanding of the general structure of quantum fields in curved spacetimes which rely on classical results from microlocal analysis. Also, the theory of linear quantum fields propagating on a given background curved spacetime is the appropriate framework for the derivation of black-hole evaporation (Hawking effect) and for studying the question whether or not it is possible in principle to manufacture a time-machine. www.numdam.org /numdam-bin/item?id=JEDP_2000____A9_0   (430 words)

Grand Unified Theory - New proposals for the structure of spacetime It offers a new insight into dynamical structure, order and measure of the quantum world of the entire universe, discrete and yet continuous on the global scale, by identifying the universal gravitational field and the metric causal structure of spacetime to which all physical events are reducible. When observed and studied in their geometrodynamic interaction and within the interval of 1-5-9-13 cells of references, we notice the importance of a dynamic equilibrium of the composite states of matter as experienced by us the observers and participants, the phenomena that emanate throughout the various scales of the resolution of cellular structure of spacetime. Structures as vast as the superclusters and the voids are an accurate reflection of the original distribution of matter, as opposed to smaller scales which have been perturbed by mixing and subsequent interactions between galaxies, literally erasing the initial conditions." members.tripod.com /stemy27/title.html   (5552 words)

Citebase - Polarized Spacetime Foam It is shown that the global structure of the spacetime depends on the relation between the ``electrical'' and ``magnetic'' Kaluza-Klein fields. It is supposed that in the spacetime foam each quantum handle is like to an electric dipole and therefore the spacetime foam is similar to a dielectric. An approximate model of a spacetime foam is presented. citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:gr-qc/0109050   (5552 words)

Applications of Sheaf Cohomology in Twistor Theory The extra mathematical structure in the complex number field, giving rise to theorems like Cauchy's integral formula, represents an interplay between local and global properties, totally absent in the real number system, which has been exploited to great effect in twistor theory. Perhaps these results depending essentially on the structure of complex numbers give some clues towards an under- standing of the fundamental role of complex structures in physics but a full understanding, which perhaps incorporates the union of quantum mechanics and relativity, is yet to emerge. In the following work, among other results it will be seen how zero rest mass fields on spacetime, originally described as real spinor fields satisfying field equations, later by arbitrary holomorphic functions of one twistor, are now interpreted as elements of a sheaf cohomology group. users.ox.ac.uk /~tweb/00003/index.shtml   (5552 words)

thread It also furnishes a very nice illustration of dynamic versus static coordinate patches (again providing a very nice foil to the analogous patches in the Kruskal vacuum), and of the use of Kruskal-like coordinates and a Penrose diagram to understand the (surprising!) global geometry and causal structure. Verify that m = 1/(1 + q^2 r^2) (e_t + e_r) is another congruence of null geodesics, for which the expansion scalar is 1/[(2r)(1 + q^2 r^2)^2] and the shear scalar is [1 - 3 q^2 r^2]/[(2r) (1 + q^2 r^2)^2] Compare with analogous congruences of null geodesics in Minkowski spacetime in cylindrical coordinates. Compare with the analogous congruence k = 1/t (e_t + e_x) in the Kasner metric for a wedge shaped piece of Minkowski spacetime, ds^2 = -dt^2 + t^2 dx^2 + dy^2 + dz^2 (The "wedge" is T > X^2 > 0 in the Cartesian metric. math.ucr.edu /home/baez/PUB/thread   (5552 words)

Kay: Application of linear hyperbolic PDE to linear quantum fields in curved spacetimes: especially black holes, time machines and a new semi-local vacuum concept Singularity structure of the two point function of the free Dirac field on a globally hyperbolic spacetime. Also, the theory of linear quantum fields propagating on a given background curved spacetime is the appropriate framework for the derivation of black-hole evaporation (Hawking effect) and for studying the question whether or not it is possible in principle to manufacture a time-machine. The aim is to give a sketch-impression of the whole subject of Quantum Field Theory in Curved Spacetime, focussing on work with which the author has been personally involved, and also to mention some ideas and work-in-progress by the author and collaborators towards a new ''semi-local'' vacuum construction for this subject. www.numdam.org /numdam-bin/item?id=JEDP_2000____A9_0   (839 words)

Penrose Diagram The major feature of those diagram is to put the infinity at finite position and at the same time do so such that the null geodesics are preserved (we conserve the structure of the spacetime). The interest in this diagram is that an asymptotically flat spacetime will have the same structure as infinity and therefore the same diagram at infinity. Often in General Relativity one uses the Penrose diagram to describe the causal structure of the spacetime. www.pas.rochester.edu /~pvarni/TC/node48.html   (839 words)

Anzhong Wang - Publications A.Z. Wang and P.S. Letelier, Local and Global Structure of a Plane Domain Wall Spacetime, gr-qc/9411020, Phys. P.S. Letelier and A.Z. Wang, "Dynamical Lorentz Wormholes" in Gravitation: The Spacetime Structure,” SILARG VIII, July 25 -- 30, 1993, edited by P.S. Letelier and W.A. Rodrigues Jr. P.S. Letelier and A.Z. Wang, "Cosmic Bubbles and Rotating Black Holes" in Gravitation: The Spacetime Structure, SILARG VIII, July 25 -- 30, 1993, edited by P.S. Letelier and W.A. Rodrigues Jr. www3.baylor.edu /~Anzhong_Wang/publications.htm   (839 words)

Algebraic approach to quantum field theory on non-globally-hyperbolic spacetimes Physically, what lie at the foundation of any formalism for quantization in curved spacetime are the canonical commutation relations, imposed on the field operators evaluated at a global Cauchy surface. The mathematical formalism for linear quantum field theory on curved spacetime depends in an essential way on the assumption of global hyperbolicity. In the algebraic formulation of linear quantum field theory, the canonical commutation relations are restated in terms of a well-defined symplectic structure on the space of smooth solutions, and the local field algebra is constructed as the Weyl algebra associated to this symplectic vector space. stacks.iop.org /0264-9381/11/999   (839 words)

Mathematics of general relativity - Wikipedia, the free encyclopedia Measurements in physics are performed in a relatively small region of spacetime and this is one reason for studying the local structure of spacetime in general relativity, whereas determining the global spacetime structure is important, especially in cosmological problems. In general relativity, it is assumed that inertial motion occurs along timelike and null geodesics of spacetime as parameterized by proper time. The mathematics of general relativity refers to various mathematical structures and techniques that are used in Einstein's theory of general relativity. en.wikipedia.org /wiki/Mathematics_of_general_relativity   (3764 words)

EaCurved.txt The transition had to be immediate, as otherwise the Minkowski spacetime structure would decay on its own (and on an entirely global scale). Eru, of course, was aware that to regain stability in the world, he would need to introduce a metric structure on spacetime that would allow singularities and yet maintain the orbits of the Sun and Moon, and that General Relativity was the best candidate for the job. However, the creation of a singularity was completely at odds with Minkowski structure; Iluvatar managed to create a temporary stabalization for the situation, but needed a more permanant solution. tolkien.slimy.com /newsgroups/EaCurved.txt   (3764 words)

Mathematics of general relativity - Wikipedia, the free encyclopedia Measurements in physics are performed in a relatively small region of spacetime and this is one reason for studying the local structure of spacetime in general relativity, whereas determining the global spacetime structure is important, especially in cosmological problems. The mathematics of general relativity refers to various mathematical structures and techniques that are used in Albert Einstein's theory of general relativity. The principle of general covariance states that the laws of physics should take the same mathematical form in all reference frames and was one of the central principles in the development of general relativity. en.wikipedia.org /wiki/Mathematics_of_general_relativity   (3786 words)

Preface to GKBH Chapter 2 establishes the basic geometry of the Kerr metric; Chapter 3 constructs maximal analytic extensions and examines their global structure; and Chapter 4 (the longest) is a detailed study of Kerr geodesics. This book is an account of the global geometry of Kerr spacetime, the relativistic model of the gravitational field of a rotating central mass. Actually, the Kerr exact solution is a family of spacetimes depending on parameters m (mass) and a (angular momentum per unit mass). www.math.ucla.edu /~bon/kerrpreface.html   (3786 words)

Award#0104042 - Metric Differential Geometry and Mathematical Gravity These theories provide a method for studying the relationship among three fundamental aspects of the spacetime universe: curvature (i.e., the bending of space or spacetime), topology (i.e., the global shape and complexity of space or spacetime) and causal structure (i.e., the large scale behavior of light rays and light cones). In more general terms, this project is concerned with the study of certain features of gravity of current scientific interest from this geometric point of view, utilizing the tools of Riemannian geometry, a mathematical theory of space, and Lorentzian geometry, a mathematical theory of spacetime. DMS-0104042 Gregory G. Galloway Research under this award will be conducted in the areas of Lorentzian and Riemannian geometry, with applications to General Relativity and String Theory. www.fastlane.nsf.gov /servlet/showaward?award=0104042   (3786 words)

Parcellular Inflation/Gravitation & the Space of Local Forces It is because of the global symmetry of that projection at every here-and-now, dramatised in the metaphor of a democratic cosmic inflation of spacetime, that "the gravitational field", which is spacetime, operates both as a constraint which we call an "attraction" between proximate masses and as a "repulsion" between remote masses. Inflation, we will soon see, is cognate with a combinatorial (or decombinatorial) procedure, the exponential numerical enlargement by parcellular "mitosis" of a set of non-local topological relations, defining an abstract, complex projective spacetime that has no intrinsic spatial or temporal scale or orientation. Cosmic inflation per se, on the other hand, does not begin to interpret the meaning of quantum non-locality at the present epoch, nor does it explain why an enormous cosmological constant is not visibly distorting spacetime on the scale of the room you are in - or the scale of this page, or even less. www.parcellular.fsnet.co.uk /parc.mech.12.htm.htm   (7451 words)

New Physics Reviews 1, 1 This preferred cosmological global frame appears to be analogous to spontaneous broken symmetry in classical flat spacetime quantum theories where the lowest energy solution to a set of field equations does not have the full symmetry of those equations. The spatial 3- geometry is compact with fixed topology and differential structure. A) The measurement theory must be fully 4D spacetime diffeomorphism invariant. www.qedcorp.com /pcr/pcr/NPR1.htm   (3395 words)

Superstrings: Penrose Diagram A Penrose Diagram shows the global causal structure of a spacetime. It is a spacetime diagram in which all light rays travel in 45 degree angles. In the following diagram the causal structure of a spherically symmetric "Schwarzchild" type black hole is shown. www.physics.ucsb.edu /~strings/superstrings/penrose.htm   (132 words)

Applications of Sheaf Cohomology in Twistor Theory For example, in the representation of zero rest mass fields on spacetime, by means of twistor functions, the field equations are essentially replaced merely by a condition of holomorphicity (Penrose 1975, 1969) and in the nonlinear graviton (Penrose 1976) curved vacuum spacetimes are generated by deforming the complex structure of flat twistor space. The extra mathematical structure in the complex number field, giving rise to theorems like Cauchy's integral formula, represents an interplay between local and global properties, totally absent in the real number system, which has been exploited to great effect in twistor theory. Also, It will be seen how deformations of complex structures, described in terms of sheaf cohomology, can be used to generate the general half flat solution of Einstein's vacuum equations. users.ox.ac.uk /~tweb/00003/index.shtml   (132 words)

Eotvos and Novel Equivalence Principle Tests Metric theories of gravitation[1] (General Relativity) postulate the Equivalence Principle (EP): local bodies in vacuum free fall identically regardless of composition and internal structure, requiring spacetime curvature. The Strong Equivalence Principle embraces all laws of nature; all reference frames accelerated or not, in a gravitational field or not, rotating or not, anywhere at any time (frame covariance; global diffeomorphism invariance aside from the Big Bang). Metric theories of gravitation postulate[64] spacetime is a Lorentzian manifold, test particles pursue space-time geodesics (all sufficiently small bodies subject only to gravitational interactions and starting with the same initial positions and velocities follow identical spacetime trajectories), and the Strong Equivalence Principle obtains. www.mazepath.com /uncleal/eotvos.htm   (7763 words)

Eotvos and Novel Equivalence Principle Tests Metric theories of gravitation[1] (General Relativity) postulate the Equivalence Principle (EP): local bodies in vacuum free fall identically regardless of composition and internal structure, requiring spacetime curvature. The Strong Equivalence Principle embraces all laws of nature; all reference frames accelerated or not, in a gravitational field or not, rotating or not, anywhere at any time (frame covariance; global diffeomorphism invariance aside from the Big Bang). Metric theories of gravitation postulate[64] spacetime is a Lorentzian manifold, test particles pursue space-time geodesics (all sufficiently small bodies subject only to gravitational interactions and starting with the same initial positions and velocities follow identical spacetime trajectories), and the Strong Equivalence Principle obtains. www.mazepath.com /uncleal/eotvos.htm   (7763 words)

Eotvos and Novel Equivalence Principle Tests Metric theories of gravitation[1] (General Relativity) postulate the Equivalence Principle (EP): local bodies in vacuum free fall identically regardless of composition and internal structure, requiring spacetime curvature. The Strong Equivalence Principle embraces all laws of nature; all reference frames accelerated or not, in a gravitational field or not, rotating or not, anywhere at any time (frame covariance; global diffeomorphism invariance aside from the Big Bang). Metric theories of gravitation postulate[64] spacetime is a Lorentzian manifold, test particles pursue space-time geodesics (all sufficiently small bodies subject only to gravitational interactions and starting with the same initial positions and velocities follow identical spacetime trajectories), and the Strong Equivalence Principle obtains. www.mazepath.com /uncleal/eotvos.htm   (7763 words)

Symmetry and Symmetry Breaking The extension of the concept of continuous symmetry from “global” symmetries (such as the Galilean group of spacetime transformations) to “local” symmetries is one of the important developments in the concept of symmetry in physics that took place in the twentieth century. Another reason for attributing symmetries to nature is the so-called geometrical interpretation of spatiotemporal symmetries, according to which the spatiotemporal symmetries of physical laws are interpreted as symmetries of spacetime itself, the “geometrical structure” of the physical world. Symmetries may be used to explain (i) the form of the laws, and (ii) the occurrence (or non-occurrence) of certain events (this latter in a manner analogous to the way in which the laws explain why certain events occur and not others). www.science.uva.nl /~seop/entries/symmetry-breaking   (7763 words)

03-416.amstex.mime Note that \`{a} priori there is no relation between the tangent space and the internal space of the vector bundle $B$ associated to the spinor structure\footnote{If a (non compact) spacetime manifold, $M$ admits a global null tetrad it has a spinor-structure ${PB}$ defined on it. It is in fact the local expression of the pullback of the Sparling form to the spin-frame bundle from the bundle of null tetrads, \cite{Fraud3}. The tensor product of these two bundles can be identified with the complexified tangent bundle. www.ma.utexas.edu /mp_arc/e/03-416.amstex.mime   (7763 words)

Stephen Hawking 60th Birthday Symposium Recently retired from the Rouse Ball Chair of Mathematics at Oxford University his professional work has varied from seminal contributions to our understanding of the global structure of spacetime which underpin our current view of black holes and the Big Bang. His popular books, describing his unique view point and insights on the relationship of mathematics to physics, and indeed the structure of thought itself have received worldwide attention, most notably The Emperor's New Mind. For many years he has been developing the Twistor approach to the quantization of gravity. www.damtp.cam.ac.uk /user/hawking60/programme.html   (663 words)

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