On 23 August, actor Peter Capaldi starts as the new Dr Who. Which prompts an obvious question: is time travel possible? The surprising answer is: nobody knows. Physicists, despite trying for almost a century to rule it out, have so far failed. The known laws of physics do not forbid time travel. In fact, they appear to make it easy - at least in principle.
It's all down to Einstein. In his "general theory of relativity" of 1915, he showed that time flows at different rates in different gravity: slower in strong gravity, faster in weak gravity. So, all you need for a time machine is a region of space where gravity is weak and time flows normally - say the Earth - and one where gravity is strong and time flows more slowly - say close to a black hole.
Now imagine clocks which start ticking in both locations on, say, Monday. By the time it's Friday on the Earth, it's still only Wednesday by the black hole. If there is a way to go instantaneously from the black hole to the Earth, it is possible to travel from Friday back to Wednesday. So, is there? Remarkably, yes. Einstein's theory permits a tunnel or short-cut through space-time. It's called a "wormhole".
The recipe for a time machine is therefore this: Take the Earth and a region near a black hole, and connect them with a wormhole.
But there is a snag (Isn't there always?). Wormholes have the annoying habit of snapping shut in the merest blink of an eye. To stop this, they must be propped open by stuff with repulsive gravity - stuff that blows rather than sucks. Such material is known to exist. The expansion of the Universe is currently being speeded up by "dark energy". This is invisible, fills all of space and has repulsive gravity. In fact, it's the repulsive gravity that is speeding up cosmic expansion. The trouble with the dark energy, however, is that it is far too dilute and feeble to prop open a wormhole. To keep a wormhole open wide enough for, say, a person to crawl through requires material packed full of energy - equivalent to the energy pumped out by an appreciable fraction of the stars in our Galaxy during their lifetimes.
So let's recap. The recipe for a time machine is a black hole; a wormhole; type of matter with repulsive gravity that we don't know exists; and the energy emitted by appreciable fraction of the stars in our Milky Way during their lifetimes. Nobody said making a practical time machine was easy!
The point is not that it is possible to build a time machine in practice. It's mind-bogglingy hard. Except for a super-advanced technological civilisation it would appear impossible. The point is that it is possible to build a time machine in principle. This fact keeps physicists awake at night because it opens the door to all sorts of crazy things. If a time machine existed, for instance, someone could use it go back in time and shoot their grandfather before their mother was born. Not anything most people would want to do, admittedly, but it only takes one nutter. And that's enough for physicists. The question would then be: How did the person go back in time and bump off their grandfather if they had never been born?
To avoid the so-called Grandfather Paradox, Stephen Hawking has proposed the Chronology Protection Conjecture. It's really just a fancy way of saying time travel is impossible. In other words, some as-yet-unknown law of physics must intervene and prevent time travel and its associated paradoxes. Hawking's argument is a simple observational one: "Where", he says, "are the time travellers from the future?"
Marcus Chown is author of What A Wonderful World: Life, the Universe and Everything, Faber & Faber, the paperback of which is published on 4 September. It has been long-listed for the 2014 Royal Society Book Prize.