When Seth Lloyd first published his ideas about quantum time loops, he hadn’t considered all the consequences. For one thing, he hadn’t anticipated the countless emails he would get from would-be time travellers asking for his help. If he could have his time over again, he jokes, he “probably wouldn’t have done it”.
Sadly, Lloyd, a physicist at the Massachusetts Institute of Technology, won’t be revisiting years gone by. Spoiler alert: no one will go back in time during the course of this article. But particles? That is another matter.
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Theoretical routes to the past called time loops have long been hypothesised by physicists. But because they are plagued by impracticalities and paradoxes, they have been dismissed as impossible for just as long. But now Lloyd and other physicists have begun to show that in the quantum realm, these loops to the past are not only possible, but even experimentally feasible. In other words, we will soon effectively try to send a particle back in time.
If that succeeds, it raises the possibility of being able to dispatch, if not people, then at least messages in the form of quantum signals, back in time. More importantly, studying this phenomenon takes us to the heart of how cause and effect really work, what quantum theory means and perhaps even how we can create a successor theory that more fully captures the true nature of reality.
In physics, time loops are more properly known as closed time-like curves (CTCs). They first arose in Albert Einstein’s theory of general relativity, which says space-time can bend. Hypothetically, if you could curve it enough, it would close in on itself, creating a pathway to the past. The only fly in the ointment is that generating such extreme curvature would require something with a heck of a lot of mass rotating very fast. In practice, that probably means a black hole – not exactly something we could create in a lab.
Then again, all of that applies to relatively large time loops, the sort of thing a human could – in principle – jump into. But what about something that instead operates at the tiniest scales? Breakthrough experiments in quantum mechanics, the strange set of laws that governs reality at the subatomic level, have shown we could conceivably make the mathematical equivalent of a time loop in this domain. It would be called a quantum CTC.
For a long time, physicists snorted at the idea of a time loop in the quantum realm, largely because it isn’t compatible with the way time is thought to operate in this framework. Time is believed to work startlingly differently in quantum mechanics compared with general relativity. Indeed, this disjoint is one of the biggest hurdles physicists face in trying to unite relativity and quantum mechanics, to find a theory that describes reality on every scale.
In relativity, time and space are intertwined in the fabric of space-time, so time can contract and stretch under the influence of gravity. In quantum mechanics, on the other hand, time is usually conceived of as a clock that ticks immutably in the background – and cause always precedes effect.
It might sound like that rules out quantum CTCs altogether. But an increasingly popular take on quantum mechanics sees time in a different way. This approach, called retrocausality, came about because of disagreements over how to think about another peculiar feature of quantum mechanics called entanglement.
When two particles are entangled, they share a quantum state even if they are light years apart. Measure one’s momentum, for example, and you instantly know that of the other. If these entangled particles were communicating with each other, this exchange must happen at faster-than-light speed, which relativity forbids. Einstein – who was suspicious of entanglement – argued that the , but this has been ruled out again and again in experiments.
The result is usually taken to mean that entanglement challenges our notion of locality – the idea that the space between objects matters. In other words, it is taken as proof that quantum mechanics is “non-local”: it doesn’t care about distances.
In contrast, retrocausality casts entanglement as a connection through time. In this interpretation, when you measure one entangled particle, a signal is sent back to the time it was entangled and simply carried forwards with the other particle, doing away with the need for instantaneous information transfer over vast distances. Locality is preserved, but standard causality is ditched.
Although we don’t know which interpretation is correct, the prevailing view has long been that quantum mechanics is non-local, while retrocausality has remained mostly philosophical. But this has started to change, and with it the possibilities for quantum time loops have opened up.
In 1991, , a theoretical physicist at the University of Oxford, used retrocausality to propose a Deutsch tried to use aspects of quantum physics to get around any paradoxes involving cause and effect, such as the grandfather paradox, which throws up the conundrum of a time traveller going back in time and killing their own ancestor, thus negating their own existence. Deutsch’s version was inspired by the many-worlds interpretation of quantum mechanics: he argued that a time-travelling particle that went back and destroyed itself would simply enter another strand of the multiverse. But others felt this didn’t resolve the paradox.
Quantum trick
Fast forward to 2010, when and his colleagues published an without the need to invoke other universes. Their version works using a trick in quantum computing called ‼Dz-پDz”, which means running a lot of computations or measurements and throwing out the ones without the result you wanted. In the quantum world, there is always an element of uncertainty – particles exist in a cloud of possible states until someone measures them. So, the team proposed a way to use post-selection and entanglement to go back and change things that were never measured in the past. It is important to note, says Lloyd, that something with a definite outcome in the past can’t be changed. Bad news for the many people who email him wanting to dabble in time travel.
It turns out that Lloyd’s version of a quantum CTC can be incredibly useful, albeit in what at first seems like a more mundane domain. Its utility is related to metrology, the science of measurement. This is an area in which quantum mechanics has become increasingly handy in recent years. Using quantum mechanical systems, we can measure things like magnetic fields, light and even gravitational waves to accuracies we could never reach using classical physics.
But one big question is how to set up such measurement experiments. Often, you don’t have the information you need to do this, like the direction of a magnetic field, for example. Without this knowledge, you don’t know how to prepare a particle to best measure it. “It would be awfully nice if we could teleport that information backward in time,” says at the University of Maryland. Halpern was working on this dilemma, along with at the Hitachi Cambridge Laboratory and at the Swiss Federal Institute of Technology in Zurich, when she came across Lloyd’s CTC idea.
This provided the spark that allowed the trio to resolve this metrology problem. In 2023, they published a outlining how you could effectively use particles to create the kind of time loop Lloyd had suggested. It involves four qubits, the quantum computing equivalent of a classical bit. Qubits can be individual particles or groups of atoms, but, for the sake of argument, let’s make them electrons and call them A, B, C and D.
The thought experiment involves this set of particles being entangled and measured in a special sequence (see diagram, below). To simplify things, the team likes to think of it using the analogy of someone planning to send a gift to their friend, knowing it will take three days to deliver. They send the gift on day one, but, annoyingly, receive their friend’s wish list on day two. They then send a message back in time to tweak the gift that was dispatched, meaning the friend gets what they wanted through the power of time travel.
In the real thought experiment, the gift is particle A, while the “wish list” corresponds to knowledge of a quantum mechanical property of particle C called spin. Once this is known, the experimenters use particle D to connect backwards in time and influence the properties of particle A so that it aligns with those of particle C.
For technical reasons, this process actually only works 1 in 4 times. The other results are thrown out in the post-selection process. This might seem like cheating, but still, the researchers argue, the thought experiment involves making a measurement that determines something in the past. In quantum mechanics, this is mathematically equivalent to sending the state back in time. Particle A’s past state is determined by a condition set in a future experiment.
“I like what they’re doing,” says , a philosopher at Chapman University in California. But it isn’t truly retrocausal, she says – if it were, it would work all of the time. “What’s really going on is that you threw away all the experiments that had the wrong result.”
Adlam also notes that this result is only a thought experiment – nothing has really been sent back in time. But since Arvidsson-Shukur and his colleagues published this idea, they have designed an actual experiment with physicist at the University of Toronto in Canada. This will involve sending real individual photons through a quantum time loop.
In the meantime, Arvidsson-Shukur and his colleagues have made great progress on their original goal. They are starting to make better measurements using quantum time loops.
In an experiment , they showed it is possible to improve the efficiency of a quantum processor using a CTC simulation. To get the gist of the experiment, imagine you are stargazing with a friend and they spot a shooting star that you miss. This latest experiment is like you going back in time to look in the right direction. And this time, they did it without throwing away any results.
Unknown fields
To do that, Arvidsson-Shukur and his colleagues designed an experiment involving two atoms set up as superconducting qubits and an unknown field that could be electric, magnetic or something else. They wanted to monitor changes in one of the qubits’ spin, to estimate the unknown field’s strength. If they didn’t know the field’s direction, they didn’t know how to prepare the spin. The solution to these kinds of problems is normally to prepare many different qubits with different spins and to use that to work out the field. But this approach involves time-consuming preparation of many electrons that are discarded before the measurement.
A better approach is to send that state back in time using entanglement. In the experiment, one of two entangled qubits was placed under the influence of the field. Then, the researchers prepared a measurement on the entangled partner to send that optimal state back in time to the qubit in the field.
Lloyd, for one, is impressed. Physicists have long talked about sending quantum information to the past, he says. “What’s great about this paper is it’s not talk – it’s action.”
He points out that this could have all sorts of technological advantages, including in quantum computing. He also says it could be useful in game theory, a type of mathematics that models strategic decisions. He suggests a game with several players, or particles that make interdependent decisions. With access to a simulated time loop, he says, the players couldn’t cheat.
Zooming out, this work may be a reason to take the retrocausal interpretation of quantum mechanics more seriously. “It’s great that people in quantum information are recognising the benefits of thinking about these experiments in this alternate way of interpreting entanglement as influences that extend back in time,” says , a quantum physicist at San José State University in California who has long been an advocate of retrocausality. “It is telling that they are being inspired by this alternate viewpoint and getting some neat results.” If retrocausality is correct, it means time travel is already ubiquitous in the quantum realm.
Retrocausality has the added benefit of being a step towards aligning the approaches to time taken in quantum mechanics and general relativity – something that has to be done if we are ever to come up with a theory of quantum gravity that unites the two. Having a good model of how CTCs work in quantum mechanics would be a huge step towards creating and testing models of quantum gravity, since researchers believe any such theory has to treat time on an equal footing both in relativity and quantum mechanics.
Tweak the past
If researchers succeed in creating quantum time loops, could we send people back in time one day? That is the sort of question Lloyd gets often, and unfortunately he has to be a killjoy. Quantum states, including entanglement, are extremely fragile. This is why quantum experiments are often carried out on single atoms in a vacuum – even a passing air molecule could disrupt a state. To correlate the millions of atoms in our bodies in the present and entangle all of them with the millions of atoms in our self in the past is completely unrealistic. “I would say it will be impossible to ever build a lab good enough,” says Arvidsson-Shukur.
We may, however, be able to use quantum time travel to subtly but usefully tweak the past. Imagine setting up a pair of entangled particles and preserving them in perpetuity. This could act as a kind of waymarker in time. Physicists in the future could use retrocausality to tweak the state of the particles, influencing the result that physicists in the past would get if they measured them. This could never directly alter an awful past event in the real world, like an accident. But perhaps you could link the outcome of the quantum measurement to the real world and so – in theory – change the course of history.
Imagine, for example, a quantum CTC version of the Schrödinger’s cat thought experiment. The cat is in a box with a vial of poison that is controlled by a quantum particle in a superposition of two states, only one of which will release the toxin. The cat is considered dead and alive at the same time, until the box is opened, at which point we have measured the particle and it assumes one of its two possible states. There is a chance a quantum CTC could change the outcome and hence the cat’s fate. If we could send the optimal state back in time, we could potentially save our furry friend.
Miriam Frankel is a freelance journalist based in London
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