Traveling forwards in time is surprisingly easy. Einstein’s special theory of relativity, developed in 1905, shows that time passes at different rates for people who are moving relative to one another – although the effect only becomes large when you get close to the speed of light.
If one were to leave Earth in a spacecraft traveling at an appreciable fraction of light-speed, turn around and come back, only a few years might have passed on board but many years could have gone by on Earth. This is known as the “twins paradox”, since a traveller undertaking such a journey would return to find herself much younger than her twin.
There’s only one problem from anyone wishing to get a glimpse of the future – getting back. It would mean traveling faster than light – and that’s not possible.
But there may be an out to be found in general relativity, Einstein’s theory of gravity that unites space and time as “space-time”, which curves in the presence of mass. It allows for the possibility of wormholes – a kind of tunnel through space-time connecting otherwise very distant parts of the universe.
If the “mouths” of the wormhole are moving relative to one another, then traversing the bridge between different points in space would also take a traveler to a different point in time to that in which she started.
However it would still be impossible to go back further in time than the point at which the wormhole was created, limiting the options for travel somewhat – and possibly explaining why we haven’t encountered any visitors from the future. If any natural wormholes were formed in the Big Bang, it might be possible to travel to a limited number of points in the past and in the distant universe, but wouldn’t enable one to flit around the cosmos at will as the Doctor seems to do.
More restrictively still, theoretical work by Kip Thorne of Caltech using a partial unification of general relativity with quantum physics suggested that any wormhole that allows time travel would collapse as soon as it formed.
Thorne did, however, resolve an apparent issue that could arise due to by time travel (within the confines of general relativity). The “grandfather paradox” involves going back in time and accidentally killing one’s grandfather before one’s father is conceived – preventing one’s own birth, making it impossible to go back in time and kill one’s grandfather. Thorne found that for point masses traversing a wormhole, no initial conditions create this type of paradox.