Analysis: many researchers have highlighted the existence of systems incorporating self-consistent time travel since the 1990s

Hungarian logician, mathematician and philosopher Kurt Gödel revolutionised our view of mathematical truth with his incompleteness theorems. He also drew up the blueprints for a working time machine. He left Vienna shortly after the outbreak of the Second World War and started work at the Institute of Advanced Studies in Princeton from late 1939.

There, Gödel befriended another European émigré, Albert Einstein.The two men regularly walked home together – Einstein claimed that he continued to work at the Institute primarily to enjoy these walks – and the discussion often turned to General Relativity, Einstein's theory of space, time and gravitation.

This theory sets aside Newton's universal concept of time ticking away in the background at the same rate for all observers at all points of the universe. In Einstein’s theory, as verified by countless experiments, the measured time interval between two events depends on the motion of the observer and on the local gravitational field.

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From RTÉ Radio 1's History Show in 2015, a look at 100 years of Einstein's Theory of General Relativity

Motivated by philosophical questions – is the Kantian subjectivity of time in General Relativity maintained when considering the apparently objective, universal clock provided by the motions of the galaxies? – Gödel proved an astonishing result that gave birth to the scientific study of time travel. In a paper published in 1949 as part of a celebratory review marking Einstein’s 70th birthday, he produced a universe model within Einstein’s theory in which there are observers who travel back in time to events of their own past (moving on trajectories known as closed timelike curves).

Gödel’s mathematical solution of Einstein’s equations of General Relativity constitutes a blueprint for a working time-machine. However, it would be difficult to construct (to understate the case), requiring infinitely long cylinders of rigid material, with radii on the scale of galaxies. One could argue that this is simply an engineering problem: there is a sharp contrast with the description of, for example, the time machine in HG Wells' novel of that name, which makes vague references to ebony rods, crystals and a velvet covered seat. No blueprints, though.

Although unrealistic, Gödel's universe raises fundamental questions about time travel. Einstein’s theory is remarkably successful, correctly predicting a wide variety of phenomena from the bending of starlight by the sun's gravitational field to recently observed black hole collisions and their gravitational wave emissions. The theory underpins the accuracy of the Global Positioning System that we use every day.

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From RTÉ Radio 1's Drivetime in 2019, Prof Peter Gallagher from DIAS on how the first ever image taken of a black hole supports Einstein's theory of relativity

It’s a pretty good theory. So if this theory allows for gravitational fields generated by exotic sources that produce closed time-like curves, can it also allow for the generation of such curves – and time travel to the past – with realistic sources? Does Einstein’s theory tell us that time travel is possible?

This question has been studied intensively since the 1990s, with early work by Igor Novikov, Kip Thorne and others highlighting the existence of systems incorporating self-consistent time travel. The results obtained by these physicists (describing, for example, systems of colliding billiards) provide support for the views of the American philosopher David Lewis. In an influential essay published in 1976, he set out his stall unequivocally: "Time travel, I maintain, is possible."

Using the rigorous calculations required in physics, Novikov and others highlighted the possibility of avoiding the usual paradoxes of time travel. Most famous among these is perhaps the Grandfather Paradox: the time-traveller travels back in time to assassinate their own grandfather prior to his meeting their grandmother, thereby preventing their own birth. The thrust of the arguments of Lewis and of Novikov is that not all time travel entails such paradoxes and indeed may be possible when such paradoxes are avoided.

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From Science Time, Neil deGrasse Tyson explains how time travel into the future is possible through Einstein's general relativity theory

But are these paradoxes avoidable? In a recent paper, we considered this question by studying the behaviour of a gyroscope carried along a closed timelike curve. The axis of rotation of a gyroscope maintains its orientation as the gyroscope as a whole moves, and so provides a useful tool for navigation.

However, according to Einstein’s theory, this axis is subject to a precession as it moves through a variable gravitational field. This precession is not detectable for a gyroscope carried by an ocean-going ship, but when carried around a complete loop of a closed timelike curve (generated by a strong gravitational field), the axis of rotation may not be the same as it was at the beginning of the loop.

This leads to a contradiction: we have the same object, the gyroscope, at the same point in space and time, but with two different orientations of its axis of rotation. This contradiction is all but unavoidable (for every self-consistent gyroscope, there is an uncountable infinity of inconsistent ones). This result may offer a route to ruling out closed timelike curves - and hence time-travel - entirely, providing a proof of Stephen Hawking's Chronology Protection Conjecture that the laws of physics do not permit closed timelike curves.

The views expressed here are those of the author and do not represent or reflect the views of RTÉ