The ability to jump forward and backwards in time has long fascinated science fiction writers and physicists alike. So is it really possible to travel into the past and the future?

Doctor Who is arguably one of the most famous stories about time travel. Alongside The Time Machine and Back to the Future, it has explored the temptations and paradoxes of visiting the past and voyaging into the future.

In the TV show, the Doctor travels through time in the Tardis: an advanced craft that can go anywhere in time and space. Famously, the Tardis defies our understanding of physical space: it’s bigger on the inside than it appears on the outside.

While time travel is fundamental to Doctor Who, the show never tries to ground the Tardis’ abilities in anything resembling real-world physics. It would be odd to complain about this: Doctor Who has a fairy-tale quality and doesn’t aspire to be realistic science fiction.

But what about in the real world? Could we ever build a time machine and travel into the distant past, or forward to see our great-great-great-grandchildren? Answering this question requires understanding how time actually works – something physicists are far from certain about. So far, what we can say with confidence is that travelling into the future is achievable, but travelling into the past is either wildly difficult or absolutely impossible.

Let’s start with Albert Einstein’s theories of relativity, which set out a description of space, time, mass and gravity. A key outcome of relativity is that the flow of time isn’t constant. Time can speed up or slow down, depending on the circumstances.

“This is where time travel can come in and it is scientifically accurate and there are real-world repercussions from that,” says Emma Osborne, an  astrophysicist at the University of York, in the UK.

For example, time passes more slowly if you travel at speed, though you need to start approaching the speed of light for the effect to be significant. This gives rise to the twin paradox, in which one of two identical twins becomes an astronaut and whizzes around in space at close to the speed of light, while the other stays on Earth. The astronaut will age more slowly than their Earthbound twin. “If you travel and come back, you are really younger than the twin brother,” says Vlatko Vedral, a quantum physicist at the University of Oxford, in the UK. Twins Scott and Mark Kelly did this for real when Scott spent months in space, albeit not at speeds close to that of light.

Similarly, time passes more slowly for you if you are in an intense gravitational field, such as a black hole. “Your head is ageing quicker than your feet, because Earth’s gravity is stronger at your feet,” says Osborne.

Doctor Who used this as the setup for season 10 finale World Enough and Time, in which the Twelfth Doctor and his friends are trapped on a spaceship close to a black hole. At the front of the craft, closer to the black hole, time passes more slowly than at the rear. This means the small group of Cybermen at the rear of the craft are able to develop into a huge army in, from the Doctor’s point of view, a matter of minutes. This effect of gravity on time also features in the plot of the film Interstellar.

In our everyday lives, these relativistic effects are too tiny to be noticed. But they do affect the satellites that we use for global positioning system (GPS). “The clocks above click faster than the clocks on Earth”, and must be constantly readjusted, says Osborne. “If we didn’t, Google Maps would be wrong about 10km (six miles) a day.”

Relativity means it is possible to travel into the future. We don’t even need a time machine, exactly. We need to either travel at speeds close to the speed of light, or spend time in an intense gravitational field. In relativity, these two acts are essentially equivalent. Either way, you will experience a relatively short amount of subjective time, while decades or centuries pass in the rest of the Universe. If you want to see what happens hundreds of years from now, this is how to do it.

In contrast, going backwards in time looks far, far harder.