Chronology protection conjecture
The chronology protection conjecture is a conjecture by the physicist Professor Stephen Hawking that the laws of physics are such as to prevent time travel on all but sub-microscopic scales. Mathematically, the permissibility of time travel is represented by the existence of closed timelike curves. The chronology protection conjecture should be distinguished from chronological censorship under which every closed timelike curve passes through an event horizon, which might prevent an observer from detecting the causal violation.
In a 1992 paper, Hawking uses the metaphorical device of a "Chronology Protection Agency" as a personification of the aspects of physics which make time travel impossible at macroscopic scales, thus apparently preventing time paradoxes. He says:
It seems that there is a Chronology Protection Agency which prevents the appearance of closed timelike curves and so makes the universe safe for historians.
The idea of the Chronology Protection Agency appears to be drawn playfully from the Time Patrol or Time Police concept present in works of science fiction such as Isaac Asimov's novel The End of Eternity.
Quantum corrections 
Many attempts to generate scenarios for closed timelike curves have been suggested, and the theory of general relativity does allow them in certain circumstances (for example, it would allow for a time machine constructed from a wormhole – see Wormholes and time travel). But attempts to incorporate quantum effects into general relativity using semiclassical gravity seem to make it plausible that vacuum fluctuations would drive the energy density on the boundary of the time machine (the Cauchy horizon of the region where closed timelike curves become possible) to infinity, destroying the time machine at the instant it was created or at least preventing anyone outside it from entering it. The question then arises: is this apparent censorship of closed timelike curves a global constraint of physics, in the same way as a conservation law, or is it a series of accidental coincidences?
A definite theoretical decision on the status of the chronology protection conjecture would require a full theory of quantum gravity as opposed to the semiclassical arguments that have been mainly used to support it (there are also some arguments from string theory which seem to support chronology protection, but string theory is not yet a complete theory of quantum gravity). Experimental observation of closed timelike curves would of course demonstrate this conjecture to be false, but short of that, if physicists had a theory of quantum gravity whose predictions had been well-confirmed in other areas, this would give them a significant degree of confidence in the theory's predictions about the possibility or impossibility of time travel.
Other proposals which allow for backwards time travel but prevent time paradoxes, such as the Novikov self-consistency principle which would ensure the timeline stays consistent, or the idea that a time traveler is taken to a parallel universe while his original timeline remains intact, do not qualify as "chronology protection".
See also 
- Hawking, S.W., (1992) The chronology protection conjecture. Phys. Rev. D46, 603-611.
- Matt Visser, "The quantum physics of chronology protection" in The Future of Theoretical Physics and Cosmology: Celebrating Stephen Hawking's 60th Birthday by G. W. Gibbons (Editor), E. P. S. Shellard (Editor), S. J. Rankin (Editor)
- Li-Xin Li, "Must Time Machine Be Unstable against Vacuum Fluctuations?", Class.Quant.Grav. 13 (1996) 2563-2568.
- http://plus.maths.org/content/time-travel-allowed — Kip Thorne discusses time travel in general relativity, and the basis in quantum physics for the chronology protection conjecture