TIME, CLOSED TIMELIKE CURVES AND CAUSALITY

摘要

GTR has been an extremely successful theory, with a well established experimental footing, at least for weak gravitational fields. Its predictions range from the existence of black holes and gravitational radiation to the cosmological models, which predict a primordial beginning, namely the big-bang. However, it was seen that it is possible to find solutions to the EFEs, with certain ease, which generate CTCs. This implies that if we consider GTR valid, we need to include the possibility of time travel in the form of CTCs. A typical reaction is to exclude time travel due to the associated paradoxes. But the paradoxes do not prove that time travel is mathematically or physically impossible. Consistent mathematical solutions to the EFEs have been found, based on plausible physical processes. What they do seem to indicate is that local information in spacetimes containing CTCs are restricted in unfamiliar ways. The grandfather paradox, without doubt, does indicate some strange aspects of spacetimes that contain CTCs. It is logically inconsistent that the time traveller murders his grandfather. But, one can ask, what exactly prevented him from accomplishing his murderous act if he had ample opportunities and the free will to do so. It seems that certain conditions in local events are to be fulfilled for the solution to be globally self-consistent. These conditions are denoted consistency constraints. To eliminate the problem of free will, mechanical systems were developed, such as the self-collision of billiard balls in the presence of CTCs. These do not convey the associated philosophical speculations on free will related to human beings. Much has been written on two possible remedies to the paradoxes, namely the Principle of Self-Consistency and the Chronology Protection Conjecture. Igor Novikov is a leading advocate for the Principle of Self-Consistency, which stipulates that events on a CTC are self-consistent, i.e., events influence one another along the curve in a cyclic and self-consistent way. In the presence of CTCs the distinction between past and future events is ambiguous, and the definitions considered in the causal structure of well-behaved spacetimes break down. What is important to note is that events in the future can influence, but cannot change, events in the past. The Principle of Self-Consistency permits one to construct local solutions of the laws of physics, only if these can be prolonged to a unique global solution, defined throughout non-singular regions of spacetime. Therefore, according to this principle, the only solutions of the laws of physics that are allowed locally, reinforced by the consistency constraints, are those which are globally self-consistent. Hawking's Chronology Protection Conjecture is a more conservative way of dealing with the paradoxes. Hawking notes the strong experimental evidence in favour of the conjecture from the fact that "we have not been invaded by hordes of tourists from the future". An analysis reveals that the renormalized expectation value of the quantum stress-energy tensor diverges as one gets close to CTC formation. This conjecture permits the existence of traversable wormoles, but prohibits the appearance of CTCs. The transformation of a wormhole into a time machine results in enormous effects of the vacuum polarization, which destroys its internal structure. There is no convincing demonstration of the Chronology Protection Conjecture, but the hope exists that a future theory of quantum gravity may prohibit CTCs.