封閉類時曲線
维库，知识与思想的自由文库
[编辑] 光錐
下方光錐是平直時空中典型的光錐模樣——所有包含在光錐裡的時空座標具有較遲的時間. 上方光錐不僅是於同時間點包含了其他空間位置，它也不包含未來時間的x=0，而包含了早先的時間。
當在廣義相對論中討論一系統的演進，或將討論限定在閔可夫斯基時空，物理學家常提及「光錐」。一個光錐表示一給定現在狀態的物體未來任何可能的演進，或給定現在位置之下，未來任何可能的位置。一個物體的未來可能位置受限於該物體能移動的速度，最快只能到光速。舉例而言，一個物體於時間t0位於位置p，於時間t1時，僅能移動到c(t1 − t0)之內的位置。 This is commonly represented on a graph with physical locations along the horizontal axis and time running vertically, with units of t for time and ct for space. Light cones in this representation appear as lines at 45 degrees centered on the object, as light travels at ct per t. On such a diagram, every possible future location of the object lies within the cone. Additionally, every space location has a future time, implying that an object may stay at any location in space indefinitely. Any single point on such a diagram is known as an event. Separate events are considered to be timelike if they are separated across the time axis, or spacelike if they differ along the space axis. If the object were in free fall it would travel up the t axis, if it accelerates it moves across the x axis as well. The actual path an object takes through spacetime, as opposed to the ones it could take, is known as the worldline. Another definition is that the light cone represents all possible worldlines. In "simple" examples of spacetime metrics the light cone is directed forward in time. This corresponds to the common case that an object cannot be in two places at once, or alternately that it cannot move instantly to another location. In these spacetimes, the worldlines of physical objects are, by definition, timelike. However this orientation is only true of "locally flat" spacetimes. In curved spacetimes the light cone will be "tilted" along the spacetime's geodesic. For instance, while moving in the vicinity a star, the star's gravity will "pull" on the object, affecting its worldline, so its possible future positions lie closer to the star. This appears as a slightly tilted lightcone on the corresponding spacetime diagram. An object in free fall in this circumstance continues to move along its local t axis, but to an external observer it appears it is accelerating in space as well – a common situation if the object is in orbit, for instance. In extreme examples, in spacetimes with suitably high-curvature metrics, the light cone can be tilted beyond 45 degrees. That means there are potential "future" positions, from the object's frame of reference, that are spacelike separated to observers in an external rest frame. From this outside viewpoint, the object can move instantaneously through space. In these situations the object would have to move, since its present spacial location would not be in its own future light cone. Additionally, with enough of a tilt, there are event locations that lie in the "past" as seen from the outside. With a suitable movement of what appears to it its own space axis, the object appears to travel though time as seen externally. A closed timelike curve can be created if a series of such light cones are set up so as to loop back on themselves, so it would be possible for an object to move around this loop and return to the same place and time that it started. Orbits around high-density objects with extreme gravitational forces are an example of such a closed loop. An object in such an orbit would repeatedly return to the same point in spacetime if it stays in free fall. Returning to the original spacetime location would be only one possibility; the object's future light cone would include spacetime points both forwards and backwards in time, and so it should be possible for the object to engage in time travel under these conditions. This is the mechanism the Tipler Cylinder would use to be a time machine. [编辑] 廣義相對論CTC有著令人難安的習性：會出現在廣義相對論的核心——愛因斯坦場方程式所得「局域上」無可異議的精確解，其為幾個最重要解中的數個。包括有：
這些例子中的幾個如同提普勒柱體，相當斧鑿而不自然，但克爾解的「外面」部份則被認為某種程度上是一般性的，所以一旦得知其「內部」含有CTC，則令人相當不安。多數物理學家感覺這樣的解中的CTC是人為客體(artifact)。 [编辑] 結果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. Ordinarily, causality demands that each event in spacetime is preceded by its cause in every rest frame. This principle is critical in determinism, which in the language of general relativity states complete knowledge of the universe on a spacelike Cauchy surface can be used to calculate the complete state of the rest of spacetime. However, in a CTC, causality breaks down, because an event can be "simultaneous" with its cause – in some sense an event may be able to cause itself. It is impossible to determine based only on knowledge of the past whether or not something exists in the CTC that can interfere with other objects in spacetime. A CTC therefore results in a Cauchy horizon, and a region of spacetime that cannot be predicted from perfect knowledge of some past time. No CTC can be continuously deformed as a CTC is timelike homotopic to a point, as the manifold would not be causally well behaved at that point. The topological feature which prevents the CTC from being deformed to a point is known as a timelike topological feature. Existence of CTCs places restrictions on physically allowable states of matter-energy fields in the universe. Propagating a field configuration along the family of closed timelike wordlines must eventually result in the state that is identical to the original one. This has been explored by some scientists as a possible approach towards disproving the existence of CTCs. [编辑] 相關條目[编辑] 參考文獻
[编辑] 外部連結
|
