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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.
		One feature of a CTC is that it opens the possibility of a worldline which is not connected to earlier times, and so the existence of events that cannot be traced to an earlier cause.
		No CTC can be continuously deformed as a CTC (is timelike homotopic) to a point, as that point would not be causally well behaved.
	en.wikipedia.org /wiki/Closed_timelike_curve (771 words)

	Timelike homotopy - Wikipedia, the free encyclopedia
		On a Lorentzian manifold, certain curves are distinguished as timelike.
		timelike homotopy between two timelike curves is a homotopy such that each intermediate curve is timelike.
		No closed timelike curve (CTC) on a Lorentzian manifold is timelike homotopic to a point (that is, null timelike homotopic); such a manifold is therefore said to be multiply connected by timelike curves (or timelike multiply connected).
	en.wikipedia.org /wiki/Timelike_homotopic (162 words)

	Closed timelike curve - Biocrawler (Site not responding. Last check: 2007-10-26)
		From the point of view of general relativity, a closed timelike curve (CTC) is a worldline of a material particle in spacetime that is closed.
		If CTCs exist, their existence would seem to imply at least the theoretical possibility of making a time machine.
		If a second time parameter is introduced to discuss a CTC, then the question "Is it possible to travel backwards in time?" becomes meaningful, since at least two different time parameters are used.
	www.biocrawler.com /encyclopedia/Closed_timelike_curve (106 words)

	Halfbakery: CTC Baking
		Employ a closed timelike curve to allow simultaneous transcontinental baking.
		A closed timelike curve (CTC) allows time travel, in the sense that an observer which travels on a trajectory in spacetime along this curve, returns to an event which coincides with the departure.
		So, a signal sent by an Englishman while he's at work, is read by an American when he shows up at work 6 hours later, is responded to and sent on the CTC back 6 hours to where the Englishman waits for responce.
	www.halfbakery.com /lr/idea/CTC_20Baking (181 words)

	FAAC - Ford Amateur Astronomy Club (Site not responding. Last check: 2007-10-26)
		Faraday's law (M. Faraday) The line integral of the electric flux around a closed curve is proportional to the instantaneous time rate of change of the magnetic flux through a surface bounded by that closed curve.
		The line integral of the electric flux around a closed curve is proportional to the instantaneous time rate of change of the magnetic flux through a surface bounded by that closed curve.
		The line integral of the magnetic flux around a closed curve is proportional to the sum of two terms: first, the algebraic sum of electric currents flowing through that closed curve; and second, the instantaneous time rate of change of the electric flux through a surface bounded by that closed curve.
	www.boonhill.net /faac/other/laws.html (8656 words)

	Science & Technology: Time Travel - a Fact or Fiction
		Timelike means that the body under consideration experiences time that increases in one direction along its worldline.
		Wormholes and closed timelike loops appear to be the main ways that time travel into the past would be possible.
		Although the aforementioned theories of general relativity are consistent for closed timelike curves and wormholes, the theories say nothing about the actual process of traveling through them.
	roshantitus.blogspot.com /2006/04/time-travel-fact-or-fiction.html (2328 words)

	articles
		A closed curve in spacetime that is permitted by a particular spacetime as a trajectory of an object.
		Two cosmic strings that pass each other with the velocity near c produce time-like close curves, hence may be considered as a TM.
		A region of space-time that permits a close time-like curves ("nonchronological region").
	www.math.siu.edu /Kocik/tm/tm-dic.htm (1480 words)

	CTC Construct Prototype (Site not responding. Last check: 2007-10-26)
		The main aim of this CTC Construct, scale model prototype is to test a hypothetical design (I discovered by accident), for a device or construct to generate closed timelike curves.
		The CTC Construct is a scale model prototype for a full-sized manned prototype, known as the Flight Test Article (FTA): Defiance.
		The CTC Construct has a specially designed skin, which acts like a capacitor and it is capable of holding a strong electrostatic charge.
	www.skybooksusa.com /time-travel/physics/tgskeggs.htm (1441 words)

	M Theory Visionists - Van Stokum Cylinder (Sol's Time Travelling Guide of Mandalics Origins)
		Tipler assumed that the energy density was never negative and showed that closed timelike curves could never arise in a local region without also creating a singularity.
		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).
		Having examined Einstein's equations more closely, physicists now realize that the river of time may be diverted into a whirlpool - called a closed timelike curve - or even a fork leading to a parallel universe.
	worldcrossing.com /WebX?14@@.1ddea281/0 (1518 words)

	STARpod.org TIME MACHINE
		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 {\bf 44}, 3197 (1991)], implies that the evolution of the chronology respecting components which interact with the closed timelike curve components is nonlinear.
		In particular we demonstrate that a quantum computer which has access to closed timelike curve qubits can solve NP-complete problems with only a polynomial number of quantum gates.
	www.starstreamresearch.com /time_machine.htm (198 words)

	randomthought: Time travel is no longer regarded as str
		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.
		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.
		Time dilation is the easiest method because it merely requires high velocity motion to experience time travel.3 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.
	community.livejournal.com /randomthought/15674872.html (2321 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal
		The exterior gravitational field is shown to contain closed timelike lines.
		The presence of closed timelike lines indicates the possibility of time travel into the past.
		which demonstrated that according to general relativity it should be impossible to create closed timelike curves in any finite region that satisfies the weak energy condition, meaning that the region contains no exotic matter with negative energy.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Ronald_Mallett (994 words)

	Formation of Closed Timelike Curves with Morris-Thorne wormholes
		The CTC C\'CC\' consists of\na segment from C\' to C through the throat of the wormhole together with\na timelike segment from C to C\' external to the wormhole.\n\nBecause the throat of the wormhole is short (and thin), Every event on\nthe worldline of mouth 1 is identified with a corresponding event on the\nworldline of mouth 2.
		A and A\' are one such pair of identified points.\n\nSuppose the mouths of the wormhole are initially close together and at\nrest with respect to a particular inertial reference frame for the\nexternal flat spacetime.
		a timelike segment from C to C' external to the wormhole.
	www.physicsforums.com /showthread.php?p=462677 (5127 words)

	Chapter 8 Questions
		What we are looking for when we are trying to do time travel, is a timelike worldline through space-time that moves into the future of some event A and ends up in the past of event A without ever exceeding the speed of light.
		This is called a ``closed timelike curve.'' Remarkably, there are solutions of Einstein's equations that contain such curves.
		Some think that solutions to Einstein's equations that admit closed timelike curves are forbidden, that is, while mathematically they are solutions to the equations, physically they are impossible.
	www.astro.virginia.edu /~jh8h/Foundations/questions/questions8.html (962 words)

	Re: Formation of Closed Timelike Curves with Morris-Thorne wormholes
		In other words, there has to be a (future-directed) timelike worldline joining C to C' for Han to traverse.
		The CTC C'CC' consists of a segment from C' to C through the throat of the wormhole together with a timelike segment from C to C' external to the wormhole.
		Suppose the mouths of the wormhole are initially close together and at rest with respect to a particular inertial reference frame for the external flat spacetime.
	www.lns.cornell.edu /spr/2005-02/msg0067015.html (1120 words)

	Schemes Time Travel
		There are certain solutions that contain curves that would allow some observer to travel into his future but arrive in his past.
		Some solutions to the equations of Einstein’s general theory of relativity lead to situations in which space-time curves back on itself, theoretically allowing travellers to loop back in time and meet younger versions of themselves.
		His original paper on this stuff 3 years ago was about how solutions to the Einstein field equations containing closed timelike curves can be found when considering the gravitational field of a cylinder of light.
	www.meta-religion.com /Physics/Relativity/schemes_time_travel.htm (2014 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)

	"Light cones tipping over"
		Well, unquestionably, if we define the term 'timelike' as any coordinate that contributes positively (assuming the + - - - convention) to g it follows that this would indeed be a closed timelike loop.
		Depending on the exact dynamics, it will probably be pretty easy to perturb a true CTC into a less-pathological but more recongnizable form of time travel, the self-intersecting timelike curve.
		if we define the term 'timelike' as any coordinate that contributes positively (assuming the + - - - convention) to g it follows that this would indeed be a closed timelike loop.
	www.physicsforums.com /showthread.php?p=1204486#post1204486 (2852 words)

	The laws list: C
		The concept that the formation of any closed timelike curve will automatically be destroyed by quantum fluctuations as soon as it is formed.
		A law which states that, in a closed system, the total quantity of something will not increase or decrease, but remain exactly the same; that is, its rate of change is zero.
		There are several other laws that deal with particle physics, such as conservation of baryon number, of strangeness, etc., which are conserved in some fundamental interactions (such as the electromagnetic interaction) but not others (such as the weak interaction).
	www.alcyone.com /max/physics/laws/c.html (1543 words)

	Printer friendly version
		"If you had a closed, timelike curve, that means that something could run around it forever and ever, always going to the future but always coming back to the beginning," says Ted Jacobson, professor of physics at the University of Maryland.
		That means that, in principle, a closed, timelike curve could happen naturally, possibly through cataclysmic astronomical collisions in the abyss of space.
		It is difficult for experts to imagine the exact conditions, but extremes in the universe, such as very dense fl holes, could create the conditions necessary for the formation of a time machine.
	www.tucsoncitizen.com /print/living/073005d1_timetravel (499 words)

	Alternate View--Analog
		Having found a space-time metric to describe a plausible brane universe, PPW consider a path that leaves the brane, travels some distance in the extra-dimensional bulk outside, and then re-enters the brane.
		A third model, based loosely on the many-worlds interpretation of quantum mechanics, is that a scenario (b) event produces a branch universe in which history follows a different path.
		“Closed timelike curves in asymmetrically warped brane universes,” Heinrich Päs, Sandip Pakvasa, and Thomas J. Weiler, ArXiv preprint gr-qc/0603045 (March 13, 2006).
	www.analogsf.com /0610/altview.shtml (1776 words)

	Encyclopedia Galactica - Cl to Cn - Human (Anglic) Revised 351st Edition
		Generally, a binary pair close enough that a terrestrial planet in the comfort zone orbits both.
		From the perspective of a planet orbiting a close binary, the two suns appear very close in the sky, usually as a single shining glare in the sky during the day, usually with a noticeable elongation and maybe even two disks if observed briefly.
		The life history of close binary systems is quite complicated; variations arise from the initial masses and separation of the components, and from the transfer of mass from one component to the other.
	www.orionsarm.com /eg/c/Cl-Cn.html (3381 words)

	closed timelike curve@Everything2.com
		Closed timelike curve (abbreviated CTC) is physics jargon for a solution of general relativity that describes time travel.
		The 'curve' means a world line of somebody, 'timelike' means that the world line does not exceed the speed of light, so it is a 'valid' world line, 'closed' means that the world line is a loop, which means that it meets itself at an earlier time.
		It may be that general relativity is not valid in the conditions where CTC:s would occur.
	www.everything2.com /index.pl?node_id=811453 (219 words)

	USATODAY.com - Physicist throws time-travel theories a curve (Site not responding. Last check: 2007-10-26)
		You can travel around the curve — sing the song — but when you get to the end, you are also at the beginning.
		That means that, in principle, a closed, timelike curve could even happen naturally, possibly through cataclysmic astronomical collisions in the abyss of space.
		It is difficult for experts to imagine the exact conditions, but extremes in the universe, such as super-dense fl holes, could create the conditions necessary for the formation of a time machine.
	www.usatoday.com /tech/science/2005-07-27-time-travel_x.htm (577 words)

	Amazon.com: "closed timelike curve": Key Phrase page (Site not responding. Last check: 2007-10-26)
		See all pages with references to closed timelike curve.
		This is not what is meant by a closed timelike curve because if such a curve has a discontinuity in its tangent vector at some point the two tangent vectors must...
		A time machine is just a closed timelike curve.
	www.amazon.com /phrase/closed-timelike-curve (564 words)

	Time Physics Thoughts
		The CTC construct has a drag reduction skin to reduce friction and wave drag, in a process known as, "Plasma Magic".
		For anyone to design a device capable of creating closed timelike curves, (time travel into the past) would need to design and build a practical device which is capable of holding worm holes open long enough, so a device can safely pass through it.
		Which states gravity is curved space, caused by the presence of mass.
	www.bibliotecapleyades.net /ciencia/time_travel/esp_ciencia_timetravel04.htm (9768 words)

	The schemes for time travel (Site not responding. Last check: 2007-10-26)
		There are certain solutions that contain curves that would allow some observer to travel into his future but arrive in his past.
		With that in mind you should realize that until this kind of thing (aside from time dilation) can be demonstrated experimentally every scheme for time travel will necessarily be "cold calculations"--that is the nature of theoretical work.
		His original paper on this stuff 3 years ago was about how solutions to the Einstein field equations containing closed timelike curves can be found when considering the gravitational field of a cylinder of light.
	www.unexplainable.net /artman/publish/printer_3344.shtml (2024 words)

	Time Travel
		Such a construct is called a closed timelike curve (CTC).
		The real problem with this paradox is that it violates the principle of autonomy which says that you can have any configuration of matter that laws of physics permit locally, without worrying about what it is like in the rest of the universe.
		So if the first CTC was created in 2099, then you can't expect to see time travelers before then.
	www.ram.org /ramblings/science/time_travel.html (1547 words)

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