Some of these solutions refer to ordinary materials in situ. Many solutions of einsteins field equations contain closed timelike curves ctc. A widely accepted quantum theory of ctcs was proposed by deutsch. In a closed timelike curve, the worldline of an object through spacetime follows a curious path where it eventually returns to the exact same coordinates in space and time that it was at previously.
A time machine spacetime is a time travel spacetime in which the ctcs are generated by the operation of a device the time machine. Do the laws of physics prevent ctcs from ever forming. It is seen that the imposition of periodicity in a timelike coordinate is the actual source of ctcs rather than the physics of general relativity. In principe, general relativity seems to allow the existence of closed timelike curves ctc. We ask, and answer, the question of whats computable by turing machines equipped with time travel into the past. The feat should be possible based on einsteins theory of general relativity, which describes gravity as the warping of spacetime by energy and matter. View the article pdf and any associated supplements and figures for a period of 48 hours. As legitimate solutions to einsteins eld equations, they allow for time travel, which instinctively seems paradoxical. Broome, matthew a myers, casey r white, a experimental simulation of closed timelike curves.
General relativity allows solutions exhibiting closed timelike curves. A different line of research has sought to understand the implications of ctcs, supposing they existed, for quantum mechanics, computation and. In mathematical physics, a closed timelike curve ctc is a world line in a lorentzian manifold, of a material particle in spacetime that is. If ctcs are permitted, then the semiclassical laws of physics the laws with gravity classical and other fields quantized or classical should. These have generated much puzzlement and suspicion that they could imply paradoxes. Pdf closed timelike curves and causality violation. Or one could do a few steps of a computation, then \set back the clock and do a few more steps, and so on, reusing the same time interval as often as one liked. In principe, general relativity seems to allow the existence of closed timelike. Ctcs appear in many solutions of einsteins field equations and any future quantum version of general relativity will have to reconcile them with the requirements of quantum mechanics and of quantum. The effects of selfinteraction in classical physics, in the presence of closed timelike curves, are probed by means of a simple model problem.
Experimental simulation of closed timelike curves martin ringbauer1,2, matthew a. These definitions only apply to causal chronological or null curves because only timelike or null tangent vectors can be assigned an orientation with respect to time. October 26, 2018 abstract closed timelike curves ctcs appear in many solutions of the einstein equation, even with reasonable matter sources. I show that puzzlement and paradoxes disappears if we discuss carefully the physics of the irreversible phenomena in the context of these solutions.
Closed timelike curves and chronology protection in. Until today many papers have been published concerning physical, logical and philosophical consequences of these results and the existence of closed timelike worldlines in the general theory of relativity. Closed timelike curves ctcs are valid solutions of einsteins equations in general relativity. However, in principle it is quite possible for a timelike curve to be closed. A timelike curve is a worldline of a physical object an object traveling at a speed ctcs. The einstein equations allow solutions containing closed timelike curves.
Pdf closed timelike curves reexamined researchgate. We will begin our discussing just what closed timelike curves are. Macroscopic ctcs might be a semiclassical consequence of planckscale, quantum gravitational, lorentzian foam, if such foam exists. General relativity is contaminated with nontrivial geometries which generate closed timelike curves. Closed timelike curves the source of time travel speculation lies in the fact that our best physical theories seem to contain no prohibitions on traveling backward through time. However, in the quantum regime these paradoxes can be resolved leaving closed timelike curves consistent with relativity. Rozema,4 ardavan darabi,4 yasaman soudagar,4 lynden k. This metric has been the subject of intense study and quite. The curves t 0 are timelike and the null curves t t 0 0 form the chronology horizon. Theory and experimental test of consistency seth lloyd,1 lorenzo maccone,1 raul garciapatron,1 vittorio giovannetti,2 yutaka shikano,1,3 stefano pirandola,1 lee a.
The curves t t 0, where t 0 is a constant, are closed since x is periodic. Locally, we are always travelling into the future when following such a curve in the futureoriented direction, but after some time we find ourselves back. A closed timelike curve is a timelike curve that forms a closed loop rather than a line that stretches off indefinitely into the past and future. A physical object following a ctc goes back in time. As time is incorporated into the proper structure of the fabric of spacetime, it is interesting to note that. We will equip ourselves with some mathematical tools, such as manifolds, tensors, and derivatives and then consider einsteins. If so, by what physical mechanism are cics prevented. Steinberg4 1xqit, massachusetts institute of technology, 77 massachusetts. The motion and selfcollisions of a nonrelativistic, classical billiard ball in a space endowed with a wormhole that takes the ball backward in time. By the logic that we believe that all physically realistic spacetimes are globally hyperbolic, i can invoke 8. Closed timelike curves ctcs are trajectories in spacetime that effectively travel backwards in time. Time, closed timelike curves and causality 5 imposing an exotic metric g. The laws of physics might permit the existence, in the real universe, of closed timelike curves ctcs. The second type of curves, namely, t t 0 0 are closed timelike curves ctc.
Computability theory of closed timelike curves scott aaronson mohammad bavariany giulio gueltriniz abstract we ask, and answer, the question of whats computable by turing machines equipped with time travel into the past. Among various surprising properties this universe allows closed timelike curves ctc, i. Closed timelike curves and effective superluminal travel. We focus on a model for ctcs due to deutsch, which imposes a probabilistic consistency condition to avoid grandfather paradoxes. These apparently violate causality, producing timetravel paradoxes. Nurturing homicidal tendencies, the time traveller murders his grandfather, impeding the birth of his father, therefore making his own birth impossible. The rotating black hole solution, the godel universe and. Closed timelike curves and chronology protection in quantum and. Elsevier physics letters a 248 1998 412414 16 november 1998 physics letters a closed timelike curves in superfluid 3 he pedro f.
Pdf closed timelike curves and causality violation researchgate. Time travel generates paradoxes and quantum mechanics generalizations were proposed to solve those paradoxes. Moreover, the godel universe is geodesically complete and it has neither a singularity nor a horizon. A closed timelike curve ctc allows time travel, in the sense that an observer that travels on a trajectory in spacetime along this curve, may return to an event. Wormholes and closed timelike curves physics stack exchange. Whether or not some are, in addition, time machine spacetimes is still open to debate. It is claimed that wormholes can be used to create closed timelike curves, and this is a widely accepted in the literature and b a problem because ctcs create real problems for physics. If it was the worldline of an object, it would describe a case where the object revisited the same location in the past and took over the worldline again from its own past self.
The fact that you need exotic matter to keep the wormhole open isnt a theoretical problem, its just a practical problem. Cauchy problem in spacetimes with closed timelike curves. A closed timelike curve sometimes abbreviated ctc is a theoretical solution to the general field equations of the theory of general relativity. Determinism and indeterminism on closed timelike curves. No closed timelike curve is contractible to a point by a timelike homotopy among timelike curves, as that point would not be causally well behaved. The central question asked is whether the cauchy problem is well posed for this model. Geometry, physics and perception nato arw, proceedings of a conference held 2124 may, 2002 at tatranska lomnica, slovak republic. Time, closed timelike curves and causality 3 imagine travelling into the past and meeting ones grandfather. At some point in its history, it will reach a point on its worldline that it previously occupied. Pdf godels contention that closed timelike curves ctcs are a necessary consequence of the einstein equations for his metric is challenged. Time, time travel, and closed timelike curves page 3. Pdf examples are given of the creation of closed timelike curves by choices of coordinate identifications. Closed timelike curves and effective superluminal travel with naked line singularities to cite this article.
Can the laws of physics be adapted in any reasonable way to a. Our main result is that computers with ctcs can solve exactly the problems that. A closed timelike curve is a closed curve which is everywhere futuredirected timelike or everywhere pastdirected timelike. The consistency condition is now enforced by symmetry. Roberts december 5, 2008 1 introduction in this paper, we explore the possibility that closed timelike curves might be allowed by the laws of physics. Closed timelike curves are among the most controversial features of modern physics. The chronology violating set is the set of points through which ctcs pass. Related content a time machine for free fall into the past davide fermi and livio pizzoccheroscanning the parameter space of. Replicating the benefits of deutschian closed timelike. The possibility of closed timelike curves ctcs within general relativity and quantum gravity theories has been studied for almost a century van stockum 1937. Edited by rosolino buccheri, metod saniga, and william mark stuckey.
The conceptual definition and understanding of time, both quantitatively and qualitatively is of the utmost difficulty and importance. Recent work on this question arose in consideration of closed timelike curves ctcs and their possible role in quantum computers. The cauchy horizon is generated by closed null geodesics. We shall briefly discuss these geometries and analyze some of their physical. Closed timelike curves in superfluid 3he sciencedirect.
A closed timelike curve is perhaps the closest thing to time travel that general relativity allows. Are geometries that contain closed timelike curves. Billiard balls in wormhole spacetimes with closed timelike. The implications of selfconsistent interactions on acausal region of. In fact, there are many versions of the grandfather paradox, limited only by. Special relativity provides us with important quantitative elucidations of the fundamental processes related to time dilation e. Is it a question of the meaning associated with a state. Experimental simulation of closed timelike curves nature.
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