This week’s episode of Doctor Who features a fascinating concept: a 400-mile long and 100-mile wide spaceship that has to reverse away from a black hole, with the resulting change in gravity meaning that the bottom of the ship (furthest away from the black hole) runs in a much faster timeline than the top (nearest to the black hole).

In simple terms laid out in the episode, this means that for 2 days passed on the slower top floor over 1,000 years pass on the bottom, and while this might sound like convenient sci-fi mumbo-jumbo intended to drive an interesting story it’s actually based on real-life science that we all experience in our day-to-day lives.

Yep, that’s right – even as you read this parts of your body are ageing faster than the others, all thanks to the powers of time dilation. 

“It certainly [could happen], depending on the gravitational gradient, you can get very big time differences particularly close to a black hole,” Dr Marek Kukula, Public Astronomer at the Royal Observatory Greenwich, says of this week's episode.

“Basically just over 100 years ago, a bloke – you've probably heard of him – called Albert Einstein came up with his general and special theories of relativity,” adds writer Simon Guerrier, who co-authored a book called The Scientific Secrets of Doctor Who with Kukula.

“Einstein came up with an idea that said the larger a body is, like a planet or a star, the more it warped space/time and the effect of it warping space/time is that around masses that have large bodies, time slows down.

“The basic idea is rather than everything being clockwork parts that put together, time isn't a fixed quantity, it's relative to where you're moving and to other objects around you.”

Apparently around black holes and their increased gravitational mass the effect is even more pronounced, meaning that this episode’s depiction of time dilation isn’t too far off the money.

“The closer you get to a something like a black hole the slower time will pass for you,” Kukula says.

“The nearer you get to the black hole, the deeper you go into the black hole's gravitational field, the more slowly time will pass for you, relative to people who are far away from the black hole.”

Both agree, then, that the events in this week’s Doctor Who episode are scientifically possible – though they were keen to point out that a black hole is not essential for time dilation, with even the comparatively weak gravitational field of the Earth making time pass at slightly different rates depending on your proximity to it.

“The example that we use in our book is Sat Nav,” Guerrier tells me. “So on your telephone you have an app that has a map on it that can tell you where you are and give you directions. And the way that works is the map that your mobile phone pings up to a satellite that orbits around the Earth which can tell you where you are and where other things are relative to you.

“Now, the odd thing about that is because the satellites are in orbit, they're further away from the centre of mass of the earth so they are moving at a slightly different speed, so the length of a second to them is slightly different. So what that means is that satellite navigation systems have to correct, they have to take that difference into account. It's about a ten millionth of a second difference, but if they don't take that into account your Sat Nav won't work.”

And even our own bodies aren’t safe from time dilation, with Earth's gravitational field apparently strong enough to create time differences within the proximity of our extremities. Yes, you read that right.

“Your head has aged more than your feet since you were born because your feet have spent more time deeper in the earths gravitational field,” Dr Kukula tells me. “It’s a tiny fraction of a second but its measurable with very accurate atomic clocks.

“And a black hole, of course has a much stronger gravitational field, so the effects would be much, much greater.”

We know, Missy. We know.

But we’d all better try and wrap our rapidly-ageing heads around this, because Guerrier and Kukula also believe that time dilation could actually have some practical applications in the future – especially when it comes to space travel.

“The classic sci-fi idea is that the spaceship goes away, and because they're travelling so close to the speed of light, that for the people on the spaceship it feels like a year has passed, or 10 years has passed,” Guerrier says. “But when they get back to Earth it turns out that centuries have passed, or 1000s of years have passed.”

“This means that although we can't go faster than the speed of light, so journeys between stars will still take years or decades, for the people actually making the journey it'll feel like a lot less time, perhaps just a few weeks or months,” Kukula explains.

“So a journey that takes 100 years could still be done in a human lifetime if you travelled close to the speed of light because the time passing for you on board that very fast spaceship would be much slower, so you wouldn't experience 100 years, you'd just experience a few months.

“The homecoming would be a bit of a downer because you'd get back, 100 years out, 100 years back, perhaps 6 months has passed for you and you'd get back and find that everyone had aged 200 years, so it's a bit of a one-way ticket for you into the future if you'd like.”

All in all, then, we’d say this week’s Doctor Who has pulled off the rare feat of including some highbrow science in a relatively simple way that also manages to be accurate to the real-life theory, and we should commend them for that.

However, according to Guerrier, this week’s episode doesn’t get everything quite right – because while the storyline sees the Doctor affected by the slower timeline, previous episodes of the classic series established that he should have some resistance to the process.

“There's a 1974 Jon Pertwee story called Invasion of the Dinosaurs in which there's some people who've built a time machine and their idea is that they can bring dinosaurs back to the present day, basically from 65 million years ago,” Guerrier tells me.

“And at the end of the story they settle for this system which sends time back, they effectively rewrite history so the dinosaurs are never wiped out, and civilisation as we know it is overwritten.

“The effect is that, for all the humans in the room they all stand completely still as for them, time is frozen. But the Doctor, as he's a Time Lord, is able to hurry over to the controls and reverse the effect.

Jon Pertwee in 1974's Invasion of the Dinosaurs

“So, there's a precedent that whatever these relativistic effects, the Doctor is immune to them, or affected differently from them, to us. We kind of discuss in our book whether that's related to the Tardis, because the r in Tardis stands for relative, so this kind of relativism seems to be fundamental for the Doctor or for the Tardis.”

So while Doctor Who might have managed to pull off flawless scientific accuracy this week it has instead committed a far more grievous sin – not lining up with incredibly obscure and arcane parts of Doctor Who canon that no-one’s thought about for years. How they’ll be able to show their faces at the next big convention is beyond us.

Doctor Who airs on BBC1 on Saturday evenings