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Topic: Timelike

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	Closed timelike curve - Wikipedia, the free encyclopedia
		In a Lorentzian manifold, a closed timelike curve (CTC) is a worldline of a material particle in spacetime that is closed.
		It is however possible to construct a metric for a spacetime where this is not the case, and some light cones are not pointed forward in time but rather in some spatial direction.
		If a light cone points in the x direction, then that has become the timelike coordinate, and an object placed at that location would not only be able to travel in the x direction "instantaneously", but would have to move, since its present spacial location would not be in its own future light cone.
	en.wikipedia.org /wiki/Closed_timelike_curve (711 words)

	Physics Today Review of _Time Travel in Einstein's Universe_ (Site not responding. Last check: 2007-10-30)
		The curvature of space-time, however, introduces the possibility of deforming the global geometry to allow what are called "closed timelike curves," paths that intersect themselves in the past.
		The notion of closed timelike curves in the real world is hard to reconcile with our intuitive understanding of causality.
		This was reassuring, as we could hope that both the singularity and the closed timelike curves were hidden behind an event horizon (although this was not part of the proof).
	pancake.uchicago.edu /~carroll/gottreview.html (858 words)

	Chronology Protection Conjecture Encyclopedia Article @ 209.197.89.145 (Karr Network) (Site not responding. Last check: 2007-10-30)
		Experimental observation of closed timelike curves would of course demonstrate this conjecture to be false.
		Other proposals which allow for backwards time travel but prevent time paradoxes, such as the Novikov self-consistency principle which would ensure the timeline stays consistent, or the idea that a time traveler is taken to a parallel universe while his original timeline remains intact, do not qualify as "chronology protection".
		Many attempts to generate plausible scenarios for closed timelike curves have been suggested, and all seem either implausible, contradict other principles of physical law, or appear to be contradicted by experiment.
	209.197.89.145 /encyclopedia/Chronology_protection_conjecture (495 words)

	Preposterous Universe
		But in general relativity spacetime is curved; it is therefore conceivable that a timelike curve can loop back and intersect itself in the past, in a kind of time machine.
		Bush's questioner had obviously found such a closed timelike curve, lived through the horrors of the recent recession, gone backwards in time, and cowered in fear as he lived once more through 1998 with the ever-present knowledge that the economy would tumble just about the time Bush was elected.
		Of course, it is probably necessary to violate some of the laws of physics to actually create closed timelike curves in the real world; this is the content of Hawking's Chronology Protection Conjecture.
	preposterousuniverse.blogspot.com /2004/05/acausality.html (702 words)

	Ashox Page of time travel (Site not responding. Last check: 2007-10-30)
		Phenomena known as wormholes and closed timelike curves are possible means of time travel into the future and the past.
		Timelike means that the body under consideration experiences time that increases in one direction along its worldline.2 Princeton University physicist John A. Wheeler, and Kip S. Thorne of Cal. Tech.
		Wormholes and closed timelike loops appear to be the main ways that time travel into the past would be possible.
	www.koolpages.com /ashok/Timetr.htm (2188 words)

	Time Travel (Site not responding. Last check: 2007-10-30)
		This phenomenon is due to the principal of time dilation, which states that bodies moving at high velocities experience a time that ticks slower than the time measured at zero velocity.3 Not as much time elapses for a moving body as does for everything else.
		Phenomena known as wormholes and closed timelike curves are possible means of time travel into the future and the past.4 Traveling into the past is a task which is much more difficult than traveling into the future.
		Phenomena known as wormholes and closed timelike curves are possible means of time travel into the future and the past.4 Traveling into the past is a task which is much more difficult however.
	www.iit.edu /%7Ebosabri/time.html (2322 words)

	General relativity - Wikipedia, the free encyclopedia
		The motion of objects being influenced solely by the geometry of spacetime (inertial motion) occurs along special paths called timelike and null geodesics of spacetime.
		The principle that inertial motion is geodesic motion: The world lines of particles unaffected by physical forces are timelike or null geodesics of spacetime.
		Similarly, two balls initially at rest with respect to and above the surface of the Earth (which are parallel paths by virtue of being at rest with respect to each other) come to have a converging component of relative velocity as both accelerate towards the center of the Earth due to their subsequent freefall.
	en.wikipedia.org /wiki/General_relativity (5342 words)

	Minkowski space - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-30)
		Vector fields are called timelike, spacelike or null if the associated vectors are timelike, spacelike or null at each point where the field is defined.
		Once a direction of time is chosen, timelike and null vectors can be further decomposed into various classes.
		An orthonormal basis for Minkowski space necessarily consists of one timelike and three spacelike unit vectors.
	www.sciencedaily.com /encyclopedia/minkowski_space (1130 words)

	Chronology protection conjecture (Site not responding. Last check: 2007-10-30)
		The chronology protection conjecture is a conjecture by the physicist Professor Stephen Hawking that the laws of physics are such as to prevent time travel (" closed timelike curve s") on all but sub-microscopic scales.
		The idea of the Chronology Protection Agency appears to be drawn playfully from ideas in science fiction, such as Isaac Asimov's novel The End of Eternity and the TV series Doctor Who and Star Trek.
		Many attempts to generate plausible scenarios for closed timelike curves have been suggested, and all seem either implausible, or contradict other principles of physical law, or appear to be contradicted by experimental observations.
	www.serebella.com /encyclopedia/article-Chronology_protection_conjecture.html (577 words)

	Tachyons, Time Travel, and Divine Omniscience
		The most incredible feature of this model was that it permitted the existence of closed, timelike loops, so that by making a round trip on a rocket ship in a sufficiently wide curve, it would be possible for some observer to travel into any region of the past or future and to return.
		In other words, timelike loops can exist in any world in which such rockets, switches, and so forth are possible but never in fact exist or function correctly; similarly for tachyons and the tachyonic antitelephone.
		Hence, if the timelike loops exist and the rocket and so forth are possible, then it seems that it would be true that, if the rocket were to exist, both the loops and the rocket would exist, which results in a self-inhibiting situation.
	www.leaderu.com /offices/billcraig/docs/tachyons.html (6496 words)

	Timelike Infinity - Wikipedia, the free encyclopedia
		Timelike Infinity is a 1992 science fiction book by Stephen Baxter.
		Set thousands of years in the future (5407AD), the human race has been conquered by the Qax, a truly alien turbulent-liquid form of life, who now rule over the few star systems of human space - adopting processes from human history to effectively oppress the resentful race.
		Timelike Infinity - Flux - Ring - Vacuum Diagrams - Reality Dust - Riding the Rock
	en.wikipedia.org /wiki/Timelike_Infinity (1249 words)

	Minkowski space (Site not responding. Last check: 2007-10-30)
		is called the timelike component of v while the other three components are the spacial components.
		Vectors are said to timelike or spacelike if their norms squared are positive negative respectively.
		An orthonormal basis for Minkowski space necessarily of one timelike and three spacelike unit If one wishes to work with non-orthonormal it is possible to have other combinations vectors.
	www.freeglossary.com /Minkowski_space (1273 words)

	Math Tutorial - Four-Vectors (Site not responding. Last check: 2007-10-30)
		Also shown in figure 5.1 is a spacetime vector or four-vector which represents the frequency and wavenumber of the wave, which we refer to as the wave four-vector.
		It is called a four-vector because it has 3 spacelike components and one timelike component when there are 3 space dimensions.
		multiplies the timelike component in this case, because that is what is needed to give it the same dimensions as the spacelike component.
	physics.nmt.edu /~raymond/classes/ph13xbook/node50.html (435 words)

	CiteULike: Quantum Computational Complexity in the Presence of Closed Timelike Curves (Site not responding. Last check: 2007-10-30)
		We argue that a model of quantum computation in the presence of closed timelike curves can be formulated which represents a valid quantification of resources given the ability to construct compact regions of closed timelike curves.
		D 44, 3197 (1991)], implies that the evolution of the chronology respecting components which interact with the closed timelike curve components is nonlinear.
		D {\bf 44}, 3197 (1991)], implies that the evolution of the chronology respecting components which interact with the closed timelike curve components is nonlinear.
	www.citeulike.org /user/aaronson/article/696699 (322 words)

	Analysis
		This is natural when thinking about the structure of Minkowski spacetime, where the ratio of the change in time to the change in 3-space defines five separate regions: timelike past, timelike future, lightlike past, lightlike future, and spacelike.
		Consider a covariant quaternion function f with a domain of H and a range of H. A future timelike derivative to be defined, the 3-vector must approach zero faster than the positive scalar.
		For timelike separated events, right and left depend on the inertial reference frame, so a timelike derivative should not depend on the direction of the 3-vector.
	world.std.com /~sweetser/quaternions/intro/analysis/analysis.html (1882 words)

	Amazon Light - Details for Timelike Infinity
		Timelike Infinity: the strange region at the end of time where the Xeelee, owners of the universe, are waiting.
		One of the author's earlier works, Timelike Infinity has both Stephen Baxter's usual flair for the original and the inspired, and his talent for writing extremely hard science fiction.
		The characters in Ring are more vivid than they are in Timelike Infinity, and the plot moves at a fast and logical clip, culminating in an explosion of ideology and hypothesis certain to expand the horizons of any reader
	www.kokogiak.com /amazon/detpage.asp?sb=s&asin=0451452437&field-keywords=stephen+baxter&schMod=books&type= (1229 words)

	Timelike and Spacelike people (God=G_uv) - Physics New Theories (Site not responding. Last check: 2007-10-30)
		Perceptual reality is described by ENPg, which are caused by the XYZt of physical reality.
		Republicans and Democrats are "spacelike separated" If I, god, can't tell the difference between republicans and democrats, you certainly can't without holding yourself out to be in contention for my heavenly barca-lounger.
		The upper and lower classes are "timelike separated" That's why I commanded man to invent things like gunpowder to cross the gap.
	www.okka.biz /Timelike_and_Spacelike_people_______________God=G_uv-1596564-290-a.html (1482 words)

	Geodesic Surfaces and Conjugate Loci in the Heisenberg Group (Site not responding. Last check: 2007-10-30)
		From outside in, we have spacelike, null, and timelike geodesic surfaces, cut away to reveal their interiors.
		Between the two stacks of spiked sheets is the central part, which has the same timelike spikes up and down, but stays spacelike bounded, passing smoothly through the central plane.
		Shown are the null "cone," three timelike (spacelike for relativists) and two spacelike (timelike for relativists) surfaces.
	www.math.wichita.edu /~pparker/research/h3geos+cjl.htm (364 words)

	Modern Physics:Special Relativity Spacetime Thinking - Wikibooks, collection of open-content textbooks
		Notice that it is physically possible for an object to have world line which connects event O at the origin and the events A and D in figure 4.3, since the slope of the resulting world line would exceed unity, and thus represent a velocity less than the speed of light.
		On the other hand, event O cannot be connected to events B and C by a world line, since this would imply a velocity greater than the speed of light.
		If two events have timelike, spacelike, or lightlike separation for any inertial observer then it turns out that they have that kind of separation for all observers.
	en.wikibooks.org /wiki/Modern_Physics:Special_Relativity_Spacetime_Thinking (421 words)

	SpaceTime
		Their meanings of the terms "spacelike" and "timelike" are consequently the reverse of ours here with regard to signtaure signs.
		We colour timelike edges pink rather than red and so imagine a spacial 2-simplex as appearing to any observers as an instantaneous white flash, a pink dot travelling at sublight speed for a while before vanishing in a white flash.
		is a timelike 1-vector representing the wordline direction of an observer percieving all four events as cotemporaneous.
	www.iancgbell.clara.net /maths/spctime.htm (2905 words)

	Re: Tiny Dimensions
		And, indeed, in addition >to compactifying along spacelike and timelike directions, one can also >compactify along a lightlike direction.
		And compactifying along a timelike dimension seems fine too (especially if you start with more than one timelike dimension).
		If you start with an N+M-dimensional Minkowski spacetime (N spacelike and M timelike dimensions) and compactify in a spacelike direction, then on scales much larger than the length of the compact dimension, things look just like (N-1)+M-dimensional Minkowski space.
	www.lns.cornell.edu /spr/2002-06/msg0041962.html (351 words)

	Science News Online (4/11/98): Evading quantum barrier to time travel by I. Peterson
		A traveler moving along such a path would find that his or her watch always runs forward, even though the traveler eventually ends up where -- and when -- he or she started.
		However, the possible existence of closed timelike curves under certain extreme conditions may offer a solution to the problem of what came before the Big Bang, which most cosmologists believe started our universe.
		Li and Gott speculate that a universe undergoing the rapid early expansion known as inflation could give rise to baby universes, one of which (by means of a closed timelike curve) would turn out to be the original universe.
	www.sciencenews.org /sn_arc98/4_11_98/fob3.htm (606 words)

	Wormholes and Exotic Matter
		Without FTL, all particles travel along timelike geodesics in spacetime ((the simplest such timelike path is the one you get by just sitting in one place and letting time pass).
		In spacetimes with wormholes or other topological oddities, it's sometimes possible for these timelike paths to form loops, which are called "closed timelike curves".
		Visser and co have conjectured that at the moment this happens the virtual particles streaming around the closed timelike curve overwhelm the negative energy density that you need to keep the wormhole open and so it collapses.
	www.orionsarm.com /intro/wormholes_and_exotic_matter.html (1340 words)

	1.3 The Einstein-Vlasov system
		The worldline of a particle with non-zero rest mass m is a timelike curve and the unit future-directed tangent vector
		The possible values of the four-momentum are all future-directed unit timelike vectors and they constitute a hypersurface P in the tangent bundle TM, which is called the mass shell.
		A timelike vector is future directed if and only if its zero component is positive.
	relativity.livingreviews.org /Articles/lrr-2002-7/node4.html (1002 words)

	Modern Physics:Math:Four Vectors - Wikibooks, collection of open-content textbooks
		It is called a four-vector because it has 3 spacelike components, forming a vector, and one timelike component when there are 3 space dimensions.
		when there are 3 space dimensions, while the timelike component is ω / c where the c is in the denominator to give the timelike component the same dimensions as the spacelike component.
		The c multiplies the timelike component in this case, because that is what is needed to give it the same dimensions as the spacelike component.
	en.wikibooks.org /wiki/Modern_Physics:Math:Four_Vectors (994 words)

	Citebase - Closed Timelike Curves Re-Examined
		Following Gödel's prescription, it is seen that flat spacetime can produce closed timelike curves with structure similar to that of Gödel. In this context, coordinate identifications rather than exotic gravitational effects of general relativity are shown to be the source of closed timelike curves.
		Removing the periodic time coordinate restriction, the modified Gödel family of curves is expressed in a form that retains the timelike and spacelike character of the coordinates.
		A helicoidal surface unifies the families of timelike, spacelike and null curves.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:gr-qc/0405114 (210 words)

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