In general relativity, closed timelike curves can break causality with remarkable and unsettling consequences. Are geometries that contain closed timelike curves possible. An obvious necessary received by the editors june 7, 1983 and, in revised form, october 21, 1983. The rotating black hole solution, the godel universe and. These have generated much puzzlement and suspicion that they could imply paradoxes. Moreover, the godel universe is geodesically complete and it has neither a singularity nor a horizon. These include perfect discrimination of nonorthogonal states and, most intriguingly, the ability to distinguish nominally equivalent ways of preparing pure quantum states. Pdf closed timelike curves and geodesics of godeltype. Ctc allows time travel, in the sense that an observer which travels on a trajectory in spacetime along this curve, returns. 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. Curves in spacetime violate heisenbergs uncertainty principle. Closed timelike curve how is closed timelike curve.
Moreover, the godel universe is geodesically complete and it has neither a singularity nor a horizon in its original form, the godel metric reads. Mathematically, when we represent spacetime by a lorentzian manifold, the paths of physical observers must be timelike. We will equip ourselves with some mathematical tools, such as manifolds, tensors, and derivatives and then consider einsteins. It becomes clear quickly, alarmingly super crystal clear that theyre seriously outgunned. In this paper, we attempt to present a short argument, different from that of the original proofs by that of hawking, for a theorem stated that no closed timelike curves can exist. Quantum state cloning in the presence of a closed timelike. A new argument for the nonexistence of closed timelike curves sanath devalapurkar1 1physics, center for fundamental research and creative education, india abstract.
Pacs number 0420 in general relativity a timelike curve in spacetime represents a possible path of a physical object or an observer. A timelike curve is a worldline of a physical object an object traveling at a speed entanglement and closed timelike curves motivation introduction gtr allows nontrivial geometry of spacetime which can generate closed timelike curves ctcs. Similarly, a curve is null respectively, spacelike if its tangent vector at each point is null respectively, spacelike. Introduction it is well known that general relativity allows the existence of closed timelike curves ctcs, but hard selfconsistency problems arise. Since the nocloning theorem has played a central role in the development of quantum information science, it is clear that the existence of closed timelike curves that behave according to deutsch. The einstein equations allow solutions containing closed timelike curves. As legitimate solutions to einsteins field equations, they allow for time travel, which instinctively seems. Time, closed timelike curves and causality 3 imagine travelling into the past and meeting ones grandfather. The above theorem can be extended without much difficulty.
The purified state does not depend on the state of any extraneous system with which the mixed state is going to interact and on. A time machine spacetime is a time travel spacetime in which the ctcs are generated by the operation of a device the time machine. Cauchy problem in spacetimes with closed timelike curves. In fact, there are many versions of the grandfather paradox, limited only by.
If ctcs are permitted, then the semiclassical laws of physics the laws with gravity classical and other fields quantized or classical should be. View closed timelike curves research papers on academia. It follows in the same manner as the riemannian case that such a curve, if it exists, must be a closed timelike geodesic. In what follows, it is assumed that spacetimes are time orientable. Two centuries after the initial formulation of general relativity, and exactly one. A timelike curve that forms a causal loop is a closed timelike curve. So that means on crazy saturday i was at home at 10.
Closed timelike curves, superluminal signals, and free. Closed timelike curves are among the most controversial features of modern physics. Pdf killing closed timelike curves for their own good. The laws of physics might permit the existence, in the real universe, of closed timelike curves ctcs. Type iii spacetime with closed timelike curves progress in physics. Pdf closed timelike curves and causality violation researchgate. We will begin our discussing just what closed timelike curves are. Our intuition is that travel along a timelike curve will always move either forwards or backwards in time and it is the former that matches our subjective experience. Greg galloway university of miami esi summer school. Replicating the benefits of deutschian closed timelike. 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. On the inextendibility of spacetime philsciarchive. In the extended region of the spacetime, we find a topology change and nontrivial closed timelike curves both in the ordinary 3dimensional black hole and in the compactified one. Experimental simulation of closed timelike curves nature.
Caroline is accidentally sent to the future by the latest big bad and requests help from future. Closed timelike curves, superluminal signals, and free will in universal quantum mechanics. At some point in its history, it will reach a point on its worldline that it previously occupied. Closed timelike curves california institute of technology caltech. It is crucial to have analysis that the above ctc evolve from a spacelike t constant hypersurface and thus t is a ahmed faizuddin. I show that puzzlement and paradoxes disappears if we discuss carefully the physics of the irreversible phenomena in the. Recall that timelike geodesies locally maximize arc length. Some of these solutions refer to ordinary materials in situ. Normally such a curve will run from past to future, but in some spacetimes timelike curves can intersect themselves, giving a loop, or a closed timelike curve ctc. However, in the quantum regime these paradoxes can be resolved leaving closed timelike curves consistent with relativity. Macroscopic ctcs might be a semiclassical consequence of planckscale, quantum gravitational, lorentzian foam, if such foam exists.
A timelike curve represents a possible spatiotemporal path carved out by material objects, a socalled worldline. A curve is everywhere timelike, or simply timelike, if the tangent vectors to the curve are timelike at each point of the curve. Pdf godels contention that closed timelike curves ctcs are a necessary consequence of the einstein equations for his metric is challenged. 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. A new argument for the nonexistence of closed timelike curves. One of the most intriguing aspects of einsteins theory of gravitation is that solutions of field equations admit closed timelike curves ctc. A closed timelike curve ctc allows time travel, in the sense that an observer that. 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. Nurturing homicidal tendencies, the time traveller murders his grandfather, impeding the birth of his father, therefore making his own birth impossible. In ordinary quantum theory any mixed state can be purified in an enlarged hilbert space by bringing an ancillary system. 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. Using the deutsch model of closed timelike curves, we show that a universal cloner can be constructed that when acting on a completely arbitrary qubit state, exceeds the nocloning bound for fidelity.
The closed timelike curve can be utilized to extract quantum entanglement in the form shared by the stationary observer and the uniformly accelerated observer while avoiding decoherence due to the. Especially, in the case of the compactified 3dimensional black hole, we show an example of topology change from one double torus to eight spheres with three punctures. A closed timelike curve sometimes abbreviated ctc is a theoretical solution to the general field equations of the theory of general relativity. By the logic that we believe that all physically realistic spacetimes are globally hyperbolic, i can invoke 8. Steinberg4 1xqit, massachusetts institute of technology, 77 massachusetts avenue, cambridge, massachusetts. A closed time like curve connects back on itself, for example, in the presence of a spacetime wormhole that could link a future spacetime point with a past.
In addition, if fw is an illusion, then qm on a closed timelike curve can be made consistent even without the deutch nonlinear consistency constraint. Physical observers in spacetime seem to travel only slower than the speed of light. Many solutions of einsteins field equations contain closed timelike curves ctc. Finally, we examine the dependence of these effects on the initial qubit state, the form of the unitary interaction and the in. The cauchy horizon is generated by closed null geodesics. Compact spacetimes have limited interest in general relativity since they all violate the chronology condition. This is a spacetime curve as it shows where i was both in space and time. Rozema,4 ardavan darabi,4 yasaman soudagar,4 lynden k. As legitimate solutions to einsteins eld equations, they allow for time travel, which instinctively seems paradoxical. At the classical level, they induce causal paradoxes disturbing enough to. Do the laws of physics prevent ctcs from ever forming. The topic of time machines is the subject of a sizable and growing physics literature, some of which has filtered down to popular and semipopular presentations. But this is impossible since a has maximal length among all timelike curves from a point in s to the corresponding point in s.
The feat should be possible based on einsteins theory of general relativity, which describes gravity as the warping of spacetime by energy and matter. A physical object following a ctc goes back in time. A closed timelike curve is perhaps the closest thing to time travel that general relativity allows. 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.
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