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.