A weird elephantine noise appears, the wind sweeps around your feet, and a small, old-fashioned, blue British police box appears before you. A curiously dressed person steps out of it through the creaky front doors and says: “So – all of time and space, everything that ever happened or ever will – where do you want to start?”

The idea of traveling through time (and space) with the man (or woman) from Gallifrey is a magical idea, and one that currently remains in the realm of science fiction and fantasy. However, a new study in the journal Classical and Quantum Gravity has highlighted, once again, that it’s certainly mathematically possible.

“In this paper,” it begins, “we present geometry which has been designed to fit a layperson's description of a ‘time machine’. It is a box which allows those within it to travel backwards and forwards through time and space, as interpreted by an external observer.”

^{This paper mathematically describes a TARDIS. Doctor Who via YouTube}

That certainly sounds like a time machine to us – and fans of Doctor Who will notice that the study’s title, “Traversable acausal retrograde domains in spacetime” can be acronymized to TARDIS, the very name of the Time Lord’s own time machine. How wonderfully geeky.

So what do the pair of mathematicians from the Universities of British Columbia and Maryland propose, then? Well, as has been suggested before, time machines will need to be able to warp the fabric of spacetime itself. In this sense, it’s best to think of spacetime as a unifying point for all three physical dimensions (width, height, depth) and time.

^{Special Relativity in a nutshell. Doctor Who via YouTube}

Time only appears to go forwards to us thanks to a quirk of the decidedly pesky second law of thermodynamics. However, the warping of spacetime does appear to do some rather curious things to time. If you place a huge mass on it, it forms a huge gravitational well, and time does slow down considerably within this well.

Time still ticks forever onwards though – it won’t go backwards. For that to happen, you need to invoke a little bit of the theories of special and general relativity.

Say you’re in a TARDIS-like box, and you want to go back in time. Outside of this box, there happens to be a clock that’s ticking onwards – that will be our “reference frame”, something that we will be measuring our journey in time and space against.

Now, if you continually accelerate forwards, time will still appear normal to you inside the box, but outside of it, something strange will begin to happen. As the light emerging from the clock and entering your eye will take increasingly longer to get there, the length of each second will increase for you, but not for the clock.

Time slows down for you, but to you, it looks like time is speeding up on the clock outside the TARDIS. So, you age slower, and when you stop the TARDIS’s movement, it will have looked like time on the outside has moved on quite considerably – you have travelled into the future. That’s “time dilation” as described by special relativity.

What this paper adds is a general relativity feature. By moving faster than light in a “bubble” of spacetime, around in a circle, you will eventually catch up with your own TARDIS. When the future time machine meets the one ahead of it, which is in the past, you will be able to see the past and future at the same time, and choose which point to stop and get off at.

 

^{The person moving around the spacetime bubble would eventually catch up with their past selves. Tippett & Tsang, 2017/Classical and Quantum Gravity}

As spacetime can be described entirely mathematically, this means that this type of TARDIS is entirely possible. For it to happen in real life, however, the researchers note that we’d need some extremely “exotic” materials, as of yet undiscovered or unforged.