Physicists have simulated a photon interacting with an older version of itself in an experiment that could help reconcile quantum mechanics and relativity
One of the curiosities of general relativity is that it seems to allow time travel. Various physicists have discovered solutions to Einstein’s field equations that contain loops that return to the same point in space and time. Physicists call them closed time-like curves.
At first glance, these kinds of time machines seem to lead to all kinds of problems, such as the grandfather paradox. This is where somebody travels back in time and kills their grandfather meaning they could never have been born and so could not have gone back to kill the grandfather.
That’s just bizarre so physicists have attempted to find ways to prevent these paradoxes. In the early 90s, for example, cosmologists showed that a billiard ball entering a wormhole that leads to a closed time-like curve must always meet its older self coming out of the wormhole. What’s more, the resulting collision always prevents the ball entering the wormhole in the first place. In other words, the billiard ball would simply bounce off the entrance to a closed time-like curve.
So much for classical objects and time travel. But what would happen if a quantum particle entered a closed time-like curve? In the early 90s, the physicist David Deutsch showed that not only is this possible but that it can only happen in a way that does not allow superluminal signalling. So quantum mechanics plays havoc with causality but in a way that is consistent with relativity and so prevents grandfather-type paradoxes.
Deutsch’s result has extraordinary implications. It implies that closed time-like curves can be used to solve NP-complete problems in polynomial time and to violate Heisenberg’s uncertainty principle.
As far as we can tell, nobody has ever created a Deutsch closed time-like curve. So it’s easy to imagine that until we do, we will never know whether Deutsch’s predictions are true. But today Martin Ringbauer and a few pals at the University of Queensland in Australia say that it’s not necessary to create a closed time -like curve to test how it behaves.
Instead, these guys have created a quantum system that reproduces the behaviour of a photon passing through a closed time-like curve and interacting with its older self. In other words, these guys have built a time machine simulator.
That is not quite as far-fetched as it sounds. Physicists have long known that one quantum system can be used to simulate another. In fact, an emerging area of quantum science is devoted to this practice. “Although no closed time-like curves have been discovered to date, quantum simulation nonetheless enables us to study their unique properties and behaviour,” say Ringbauer and co.
The quantum system that they want to simulate is straightforward to describe. It consists of a photon interacting with an older version of itself. That’s equivalent to a single photon interacting with another trapped in a closed time-like curve.
That turns out to be straightforward to simulate using a pair of entangled photons. These are photon pairs created from a single photon and so therefore share the same existence in the form of a wave function.
Ringbauer and co send these photons through an optical circuit which gives them arbitrary polarisation states and then allows them to interfere when they hit a partially polarising beam splitter. By carefully setting the experimental parameters, this entangled system can simulate the behaviour of a photon interacting with an older version of itself.
The result of this interaction can be determined by detecting the pattern of photons that emerges from the beam splitter.
The results make for interesting reading. Ringbauer and co say they can use the system to distinguish between quantum states that are prepared in seemingly identical ways, something that is otherwise not possible. They can also use the time machine simulator to tell apart quantum states that are ordinarily impossible to distinguish.
But perhaps most significant is that all their observations are compatible with relativity. At no point does the time machine-simulator lead to grandfather-type paradoxes, regardless of the tricks it plays with causality. That’s just as Deutsch predicted.
There are some curious wrinkles in these results too. For example, Ringbauer and co say that quantum inputs can change the output in a non-linear way but only for some experimental set ups. In other words, they can control the way the experiment twists causality, which is an interesting avenue for exploring just how far it is possible to distort cause and effect.
That’s a fascinating experiment which leads to some tantalising new ways to probe the link between quantum mechanics and relativity. As Ringbauer and co conclude: “Our study of the Deutsch model provides insights into the role of causal structures and non-linearities in quantum mechanics, which is essential for an eventual reconciliation with general relativity.”
There’s plenty more work to be done here, even before they fire up their Delorean. Worth watching.
Ref: arxiv.org/abs/1501.05014 : Experimental Simulation of Closed Timelike Curves