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Dr Who Meets Professor Heisenberg

Example of a CTC.

A space-time structure exhibiting closed time-like curves. Here a wormhole connects two points at the same location in space (horizontal) but at different times (vertical). A quantum particle travelling on such a path might interact with its older self.

By Martin Ringbauer

Researchers have simulated in the laboratory how quantum particles could overcome the “grandfather paradox” of time travel.

From HG Wells through to Dr Who, the possibility of time travel is ubiquitous in science fiction. Yet it poses puzzling questions for physicists and philosophers alike.

According to Einstein’s theory of general relativity, space and time are not two separate concepts but one and the same thing: coordinates in four-dimensional space-time. Gravity is a consequence of the curvature of this space-time. A very heavy body, such as a star or a black hole, can bend space-time around it, causing other nearby objects to fall towards it.

General relativity also tells us that nothing can move faster than the speed of light. As a consequence, all the paths that a photon can take from a given point lie on the surface of a four-dimensional “light cone”. Since nothing can move faster than light, any massive object must follow a path within this light cone.

In normal space-time this means that we can always only go forward in time following a time-like path. But if we are close to a heavy object, space-time is bent a little and our light cone tilts towards this object. If at the same time this object spins very fast then it can drag space-time, including our light cone, with it – just like a wisp of smoke caught in a current around a fan. These effects can be so extreme that they cause time-like paths to wrap back onto themselves, creating a closed time-like curve (CTC).

Travelling Back in Time

Following a CTC, an object travels on a time-like path, going forward in its own time. But the space-time around it is deformed in such a way that it ends up where it started, not only in space but also in time! Hence the object has travelled back in time.

From a philosophical point of view this causes paradoxes. The most famous of these is the grandfather paradox, where the time traveller prevents his or her grandparents from meeting, thus preventing his or her own birth. This means that the time traveller could not have set out in the first place, so the grandparents could meet and the time traveller would be born and so on. This and other paradoxes seem to make CTCs implausible.

The Quantum Grandfather

But general relativity is one of the most successful of all the theories of physics and seems to agree remarkably well with observations. So why should it go wrong here? There is no known physical principle that precludes the existence of CTCs, and they have been discovered in many solutions of the equations of general relativity since the early 1900s.

The other extremely successful theory of physics is quantum mechanics, which is an excellent description of the world from the small scale of atoms and photons to the very small scale of sub-atomic particles, such as electrons and quarks. Quantum particles such as these exhibit strange counterintuitive features, such as the ability to exist in several states at once. In 1991 British physicist David Deutsch thus asked: what would happen if one puts a quantum particle, rather than a classical object, into a CTC?

Remarkably, he found that the counterintuitive properties of quantum particles might save the day and avoid the classical paradoxes. The quantum time traveller can end up in a so-called mixed state – a probabilistic mixture of the state of existing, travelling back in time and preventing the grandparents from meeting, and the state of non-existing that allows the grandparents to meet. In the future these two possibilities can swap roles while still comprising the same state of the quantum time traveller, thus allowing for consistent evolution.

In a similar fashion all other time travel paradoxes vanish when quantum particles travel through closed time-like curves, and the theory can be formulated in a consistent way. This, however, does not solve one important problem: we have not yet observed any closed time-like curves in nature. So how could we test our theory?

Time Travel in the Laboratory

My colleagues and I have found a way around the need to generate an actual CTC, which would demand the huge gravitational fields of objects like black holes. Instead we have studied this phenomenon by emulating it in the lab on a well-understood and controllable quantum system: we used two photons, where the second photon played the role of the past incarnation of the first. Relying on Deutsch’s consistency condition we were able to prepare this second photon in just the right way for our quantum simulator to resemble the case of a single photon travelling back in time and interacting with itself.

We then studied this system in a variety of different configurations of the time-travelling photon and interaction with its future self. The findings show that quantum systems can evolve consistently in situations that might lead to paradoxes in classical systems. At the same time, the results suggest that many of the characteristic features of quantum mechanics seem to change when CTCs are involved.

It becomes possible, for example, to perfectly clone quantum states or perfectly distinguish any pair of quantum states. The latter can be achieved by exploiting the CTC interaction to perform a non-linear transformation of any two quantum states into so-called orthogonal states, which can always be distinguished in regular quantum mechanics.

If this occurred outside a simulation it would have dramatic consequences for quantum cryptography, which is based on the fact that in standard quantum mechanics a secret quantum key shared between two people such as Alice and Bob cannot be copied without them noticing. With access to a CTC, an eavesdropper could perfectly copy the secret key and quantum cryptography would be broken.

Many Open Questions

General relativity and quantum mechanics are the two most successful and most tested physical theories describing the Universe to date. Both offer remarkably accurate descriptions of the world in their respective regimes – relativity at the large scales of stars and galaxies, and quantum mechanics at the very small scales of atoms and molecules – yet they do not seem to fit together.

Closed time-like curves are but one of many fascinating features that occur at the interface of these two theories. Very little is known about quantum mechanics in regimes where the effects of general relativity play a role. Studying phenomena such as closed time-like curves can provide important insights into where and how our theories of the world might change in such extreme regimes. This understanding is essential on the path towards unifying these two great theories.

Martin Ringbauer is a PhD student at The University of Queensland’s Quantum Technology Laboratory (http://quantum.technology).