In Albert Einstein’s theory of general relativity, which connects gravity with time and space, time can indeed become distorted. For instance, clocks close to a compact mass will go slower than clocks that are further away. Time travelling into the future like this could work in principle, but the effect for all masses that we will realistically be able to reach in the foreseeable future will be very small.
Even more speculative than work on travelling forwards in time are a series of studies that are investigating whether we could travel into the past. From a physics perspective, this is highly problematic as it brings up the issue of paradoxes: what would happen if a time traveller went back to the past and then did something that meant he or she was never conceived or born? Uncertainty surrounds many of the details here, as they enter into territory that concerns both general relativity and quantum theory (physics at the microscopic level). As yet, physics offers no convincing frameworks or theories for these kinds of borderline areas. However, the work that has so far tried to explore the territory suggests that the laws of nature would make it impossible to travel into the past.
This question was answered by Dr Markus Pössel of the Haus der Astronomie in Heidelberg.