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Topic: The Large Scale Structure of Spacetime

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	[No title]
		The spacetime forms of the PAFs, in the complete classical physical description on nature, entail, within that mathematical structure, large scale spacetime structures of visible (for example) size, and these large-scale structures are of the same conceptual kind as the large-scale spacetime structures that were idealized to form the theory.
		Structures in space and time are what the classical physicist conceives the world to be built out of, and he conceives his experiences of shapes to be (with due allowance for small errors in perceptions) experiences of features of this physical world of spacetime structures.
		This characteristic of the experience was a crucial element in the former case: the capacity of human observers to `equate' the spacetime forms in their empirical experiences of sensed objects to the spacetime form of the object as it is conceptualized in classical physics was the key tool in the former case.
	www-physics.lbl.gov /~stapp/rephayes/rephayesapr3.txt (3807 words)

	The Very Best Books : The Large Scale Structure of Space-Time (Cambridge Monographs on Mathematical Physics)
		Spacetime is assumed to be a connected 4-dimensional smooth manifold on which is defined a Lorentz metric.
		Some of the more interesting or well-written parts of this chapter include the example of a spacetime that is not inextendible, the determination of the conformal factor for the spacetime metric, and the discussion of alternative field equations.
		The next chapter is pretty much independent of the rest, and was put in no doubt for the mathematician who desires to understand the Einstein equations as a set of nonlinear second-order hyperbolic partial differential equations with initial data on a 3-dimensional manifold, the famous Cauchy problem in general relativity.
	www.elise.com /store/Reviews/ItemId/0521099064 (1414 words)

	Grand Unified Theory - New proposals for the structure of spacetime (Site not responding. Last check: 2007-11-03)
		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.
		It is in accord with Einstein's theory of general relativity that is a field theory of gravitation that acts across large scales, quantum mechanics which describes electromagnetism and the strong and weak nuclear interactions, theory of quantum gravity that resembles general relativity at the microscopic scale, simplicity principle, Heisenberg's uncertainty principle...
		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)

	Hubble's law - Wikipedia, the free encyclopedia
		However, a few scientists continued to pursue the dynamical universe and discovered that it could be characterized by a metric that came to be known after its discoverers, namely Friedmann, Lemaître, Robertson, and Walker.
		When this metric was applied to the Einstein equations, the so-called Friedmann equations emerged which characterized the expansion of the universe based on a parameter known today as the scale factor which can be considered a scale invariant form of the proportionality constant of Hubble's Law.
		However, the best way to calculate the recessional velocity and its associated expansion rate of spacetime is by considering the conformal time associated with the photon traveling from the distant galaxy.
	www.wikipedia.org /wiki/Hubble_Constant (1387 words)

	The structure of the Universe
		One of the tricky aspects of describing a spacetime geometry is that we need to describe the whole of space and the whole of time.
		Spacetime geometry is the geometry of all space and all time together as one mathematical entity.
		The Einstein equation says that the curvature in spacetime in a given direction is directly related to the energy and momentum of everything in the spacetime that isn't spacetime itself.
	superstringtheory.com /cosmo/cosmo2.html (840 words)

	the theology company > synopsis > 24 cosmology
		To the limits of instrumental precision, Einstein's field equation appears to be an exact description of the large scale structure of the spacetime in which we live.
		Gravitation also explains the formation of structure in the universe, galaxies, clusters of galaxies, stars, and planets have all formed as a result of gravitational interaction, establishing the environment for life as we know it.
		Jacket: 'Einstein's description of gravitation as curvature of spacetime led directly to that greatest of all predictions of his theory, that the universe itself is dynamic.
	www.physicaltheology.com /Synopsis/s24Cosmology.html (853 words)

	spacetime
		A spacetime interval between two events is the frame-invariant quantity analogous to distance in Euclidean space.
		Events with a spacetime interval of zero are separated by the propagation of a light signal.
		Events with a positive spacetime interval are in each other's future or past, and the value of the interval defines the proper time measured by an observer travelling between them.
	www.fact-library.com /spacetime.html (654 words)

	the theology company > synopsis > 6 Evolution
		Einstein's general theory of relativity models the large scale structure of spacetime, and shows us that spacetime is a growing structure whose roots may be traced to an initial spacetime point which is called the initial singularity.
		From the purely physical point of view, the big bang theory, as the expansion of spacetime from the initial singularity is called, is supported by a large amount of evidence.
		Further, physics is able to give a largely consistent account of the origins of matter in the universe, and the formation of galaxies, stars and planets.
	www.physicaltheology.com /Synopsis/s06Evolution.html (778 words)

	The Large Scale Structure of Space-Time (Cambridge Monographs on Mathematical Physics) (Site not responding. Last check: 2007-11-03)
		In chapter 5, the authors consider the causal structure of spacetime, namely the study of its conformal geometry.
		The consideration of the set of all metrics conformal to the physical metric allows one to discuss "geodesic completeness" of spacetime, this concept forming the basis of a later definition of a singularity in spacetime.
		The last two chapters of the book are more physical in nature wherein the singularity problem is shown to have physical relevance via the occurence of fl holes at the endpoint of evolution of massive stars.
	mo-server.no-ip.biz /lonely-nobody-want.html (1160 words)

	Amazon.com: Books: The Large Scale Structure of Space-Time (Cambridge Monographs on Mathematical Physics) (Site not responding. Last check: 2007-11-03)
		The theory of the causal structure of a general space-time is developed, and is used to study fl holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions.
		These conditions are shown to be satisfied in the vicinity of stars of more than twice the solar mass near the endpoint of their nuclear evolution, and in a time-reversed sense for the universe as a whole.
		It covers in brilliant form the gravitational collapse of a star, the theory of fl holes, the space-time singularities, the causal structure of space-time, and in its end the initial singularity of the universe, popularly known as the Big Bang.
	www.amazon.com /exec/obidos/tg/detail/-/0521099064?v=glance (2497 words)

	[No title]
		Cosmological principle: This is the glorified expression for the simplifying assumption that the universe averaged over sufficiently large scales is homogeneous (i.e., the same everywhere at one time) and isotropic (i.e, the same in all directions).
		spacetime: In relativistic physics (special relativity and general relativity) space and time become coupled (i.e., they are interdependent), and thus it is convenient to have a single word to refer to them both simultaneously: i.e., spacetime.
		The theory has two primary postulates: (1) the laws of physics are the same in all inertial frames (i.e., the relativity postulate) and (2) the vacuum speed of light is the same for all observers and is the highest physical speed.
	www.physics.unlv.edu /~jeffery/astro/glossary/glossary.html (3316 words)

	Research (Site not responding. Last check: 2007-11-03)
		While direct probes of the Planck scale are not possible, this fundamental structure could still have observable consequences.
		Whatever the fundamental structure of spacetime is, at energies much lower than the Planck scale it must reduce to the standard model plus small corrections.
		The fundamental structure of space that might give rise to Lorentz violation is, of course, what one would ideally like to discover.
	lifshitz.ucdavis.edu /~mattingly/research.htm (895 words)

	Cosmic Strings and Structure
		One of the outstanding problems in cosmology today is developing a more precise understanding of structure formation in the universe, that is, the origin of galaxies and other large-scale structures.
		Existing theories for the structure formation of the Universe fall into two categories, based either upon the amplification of quantum fluctuations in a scalar field during inflation, or upon a symmetry breaking phase transition in the early Universe which leads to the formation of topological defects.
		When strings evolve scaling from smaller scales to larger ones, they seed perturbations into the matter energy density of the universe.
	www.damtp.cam.ac.uk /user/gr/public/cs_lss.html (373 words)

	Scaling the universe: Gravitational lenses and the Hubble constant -- Myers 96 (8): 4236 Data Supplement - Supplemental ... (Site not responding. Last check: 2007-11-03)
		Cosmology as a field of astrophysics is concerned with (in the words of Hawking and Ellis) the large-scale structure of spacetime.
		When related to astronomical observations (such as the gravitational lensing, distant supernovae and galaxies that are discussed in these articles), cosmology relates the times, distances, brightnesses, and angular sizes of observed objects to the overall geometry, topology, matter and energy content in the Universe, and the time evolution of these quantities.
		Should the compact components prove to be variable, the large number of constraints upon the lens gravitational potential by the arcs and ring would make this an important system for cosmology.
	www.pnas.org /cgi/content/full/96/8/4236/DC1 (3149 words)

	Outline of the course Geometry of SpaceTime (Site not responding. Last check: 2007-11-03)
		Relation between the operational definition of the concepts of space and time, the exchange of signals between observers and the causal structure of spacetime.
		Basics of the structural analysis of Einstein equations and their characterization with respect to the associated Cauchy problem.
		mathematical formulation of spacetime as a Lorentzian manifold; physical interpretation of geometrical entities associated with the concept of manifold: exponential map, geodesics, normal coordinate systems and their relations with the physical concepts of free motion, causal structure and equivalence principle.
	www-dft.ts.infn.it /~ansoldi/Didactics/Teaching/SpaceTimeCourse/Web/ProgEng.html (1059 words)

	The Truth Seeker - Throwing Einstein for a Loop
		We can understand this concept by gazing upward and knowing that there are countless stars we cannot see because not enough time has passed since the birth of the universe for their light to shine our way; they are beyond our light cone.
		Markopoulou Kalamara found that by attaching light cones to the nodes of the networks, their evolution becomes finite and causal structure is preserved.
		If spacetime is in fact discrete, then individual photons should travel at slightly different speeds, depending on their wavelength.
	www.thetruthseeker.co.uk /article.asp?ID=346 (1298 words)

	Cosmological Inflation and Large-Scale Structure
		Enormous progress has been made in inflationary cosmology in the past few years and this book is the first to provide a modern and unified overview of the subject.
		Coverage examines every aspect of inflationary cosmology and carefully compares predictions with the latest observations, including those of the cosmic microwave background, the clustering and velocities of galaxies and the epoch of structure formation.
		I think Peter D'Eath has a book of this sort, published by CUP.) There is a "beyond the slow roll approximation" section, which is good, and the chapter of inflationary model building is the best I have seen.The level of mathematics is pretty much nil, anyone with basic algebra could cope.
	mountainstatestech.com /bookstore/item_0521575982.html (370 words)

	Lengths
		On the scale of the Planck length, it's possible that the structure of spacetime becomes quite different from the four-dimensional manifold we know and love.
		Spacetime itself becomes a foam (according to Wheeler) or a bucket of dust (according to Wheeler) or a bubbling sea of virtual fl holes (according to Hawking) or a weave of knots or tangles (according to Ashtekar, Rovelli, and Smolin).
		Note that in all the previous three examples a length scale was proportional on the inverse of a mass - in particular, the electron mass.
	math.ucr.edu /home/baez/lengths.html (2893 words)

	Brian A. Hopkins -- "FTL Travel: The Realities of an SF Cliche"
		The Casimir capacitor must provide a large quantity of negative energy, perhaps a Jupiter-sized mass, and this must be in delicate balance with the equivalent positive energy of the wormhole's spatial curvature.
		By a purely local expansion of spacetime behind the spaceship and an opposite contraction in front of it, motion faster than the speed of light is possible.
		Perhaps wormholes or expansions of spacetime or even the sheer human power of wishing on a star hold the key, but until such time as one of these methods is founded on demonstrated science and materials, FTL travel remains unlikely.
	www.sff.net /people/Brian_A_Hopkins/ftl.htm (2203 words)

	The Large Scale Structure of Spacetime - Wikipedia, the free encyclopedia
		The Large Scale Structure of Space-Time is a book written by Stephen Hawking and George Ellis, published in 1973 by Cambridge University Press.
		(The title has no hyphen in "large scale", unlike another book on a similar topic by the same publisher.)
		This article about a non-fiction book is a stub.
	en.wikipedia.org /wiki/The_Large_Scale_Structure_of_Spacetime (88 words)

	Einstein's "Mistake" is Revived (Site not responding. Last check: 2007-11-03)
		Large stars die in supernova explosions, leaving long-lasting traces like this remnant in the constellation Cygnus (imaged here in the x-ray band).
		The most popular explanation is an exotic "dark energy" that on a cosmic scale overcomes the tendency to decelerate.
		To constrain the value of w and thus discriminate among dark energy models, Perlmutter and his colleagues used recent data of three types: measurements of the small variations in the cosmic microwave background; the density of galaxies over large distances; and the expansion speed versus distance relations gained from observing distant supernovae.
	focus.aps.org /v4/st6.html (682 words)

	EMU Dept of Physics and Astronomy -- Lunch Time Physics 19Mar03
		One alternative to string theory is the proposition that spacetime is discrete with an inherent causal structure.
		In order for a causal set to describe the fundamental structure of spacetime, it must possess the large-scale manifold properties that spacetime exhibits, such as dimension.
		Before a causal set can be said to represent a spacetime, it must be shown to have the same manifold properties that spacetime exhibits.
	www.physics.emich.edu /LTP/Ltp_w03/lunchtimephysics_w03_0319.html (332 words)

	natural theology > essays > physical theology
		Incorporating this idea in a mathematical model, Einstein was able to extrapolate from the local structure of spacetime to the structure of the whole universe.
		Since the velocity of light is simply the velocity of communication, we see that the large scale structure of spacetime reflects the network of gravitational communication which binds the universe.
		The structuring effects of communication are everywhere to be seen.
	www.naturaltheology.net /Essays/physTheolOct02.html (3344 words)

	The Arrow of Time (Site not responding. Last check: 2007-11-03)
		Spacetime however does exist as a history of an entire universe, that is, the set of all of the events that happened (past tense) in that universe.
		Feynman described a history track composed of frames which we "observe" in succession in a "forward" direction (the prime requisite of consciousness -- if the arrow is "halted" or moved backward, no conscious observation is made).
		G.F.R. (1973) The Large Scale Structure of Spacetime (Cambridge University Press, Cambridge, England).
	www.kheper.net /cosmos/arrow.htm (184 words)

	Re: What causes gravitational pull?
		For example, the far field of the Kerr vacuum retains the imprint of the angular acceleration as well as the mass of the source, regardless of whether or not the source is an ordinary star or a rotating fl hole.
		We can assert that there is a > physical entity called spacetime which curls up in various ways - we > might even hope that the structure of matter might eventually be > explained in terms of its curliques.
		For 3, the best source remains the classic monograph by Hawking and Ellis, The Large Scale Structure of Spacetime, University of Cambridge Press, 1973 (still in print as an inexpensive paperback).
	www.lns.cornell.edu /spr/2000-07/msg0026817.html (1162 words)

	Open Questions: Large-scale Structure of the Universe
		Galaxies group together in clusters and superclusters, but there seem to be no further structures of scale larger than 400 or 500 million light years.
		It depends on the topology of spacetime, and observations of the cosmic background radiation that will be feasible in just a few years should make it possible to determine the topology.
		The structure probably results from density fluctuations of matter which gave rise to flattened clouds of gas resembling flattened pancakes.
	www.openquestions.com /oq-co006.htm (947 words)

	Citebase - Towards a Canonical Formalism of Field Theory on Discrete Spacetime (Site not responding. Last check: 2007-11-03)
		It is shown that the difficulties in formulating the quantum field theory on discrete spacetime appear already in classical dynamics of one degree of freedom on discrete time.
		We formulate a quantum field theory canonically on discrete spacetime in the case where the field equation is derived from an action, though there may be no exactly conserved quantity.
		Starting from the hypothesis that both physics, in particular space-time and the physical vacuum, and the corresponding mathematics are discrete on the Planck scale we develop a certain framework in form of a '{\it cellular network}' consisting of cells interacting with each other via bonds.
	citebase.eprints.org /cgi-bin/citations?archiveID=oai:arXiv.org:hep-th/9307112 (853 words)

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