August 12, 2022

The science magazine of Imperial College

# New mathematical model for time machine proposed

Physicists have proposed a new mathematical model for a time machine that permits forwards and backwards time travel.

Physicists have proposed a new mathematical model for a time machine. The research, published in Classical and Quantum Gravity, proposes a theoretical framework that permits forwards and backwards time travel.

In order to understand their idea, the concept of ‘spacetime’ must be explained. In physics, we cannot refer to space ‘on its own’ or time ‘on its own’; we have to consider them together as ‘spacetime’. Spacetime is the fundamental concept in Einstein’s theory of General Relativity, which is our best understanding of gravity.

The theory states that objects tend to follow shortest paths or ‘geodesics’ through spacetime. On Earth, we say that spacetime is flat, and the shortest path between two objects is a straight line. However, near an object with huge mass (like a star), the shortest path can actually be an ellipse. This is because the spacetime near stars is not flat, but curved, as stars distort the spacetime in their vicinity.

The key idea is that the paths objects take through spacetime depend on the geometry of spacetime itself. The physicists, Tippett and Tsang, propose a particularly exotic geometry, called the TARDIS geometry (no coincidence there), that allows forwards and backwards time travel. TARDIS stands for ‘traversable acausal retrograde domains in spacetime’. It makes use of the existence of ‘closed timelike curves’ (CTCs), that are closed paths in spacetime.

They propose a particular ‘bubble’ of geometry that can move along a circular loop. Observers travelling within this bubble would move forwards and backwards in time. External observers would be able to watch the time travellers within the bubble, evolving backwards in time by ‘unbreaking eggs’ and ‘separating milk from their tea’.

However, along a CTC, causality breaks down. The trajectory is a closed loop, allowing an event to be simultaneous with its cause. This gives rise to paradoxes where event A causes event B but, through time travel, event B goes on to cause event A. For example, I could travel back in time to prevent my brother being shot yet, once in the past, I end up accidentally shooting my brother. In this way, my own shooting of my brother causes my future self to go back in time to prevent it. This is very confusing.

This breakdown of causality offers some possible legroom with regard to free will. However, this inevitably becomes very philosophical.

Tippett and Tsang’s maths is not merely a fanciful notion of science fiction writers; there aren’t any physical laws preventing the possibility of time travel. Unfortunately, it is still extremely difficult to build a real-life time machine, as we first need to discover a method of manipulating spacetime into the configurations we desire. Nevertheless, time travel remains a captivating topic for physicists and non-physicists alike.

Peter Shatwell is a research student in the Mathematics of Planet Earth CDT

Banner image: time distortion, HypnoArt