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The idea that the future can influence the past may finally explain the inherent randomness of quantum theory and bring it in line with Einstein's space-time

If you were to break your arm tomorrow afternoon, would you suddenly find it hanging useless in a sling this morning? Of course not - the question makes no sense. Cause always precedes effect. But maybe life isn't quite so straightforward for a photon. In the subatomic realm, where the laws of quantum physics make seemingly impossible feats routine, the one thing that we always considered beyond the pale might just be true.

This idea that the future can influence the present, and that the present can influence the past, is known as retrocausality. It has been around for a while without ever catching on - and for good reason, because we never see effects happen before their causes in everyday life. But now, a fresh twist on a deep tension in the foundations of quantum theory suggests that we may have no choice but to think again.

No one is saying time travel is anything other than fantasy. But if the theorists going back to the future with retrocausality can make it stick, the implications would be almost as mind-boggling. They could not only explain the randomness seemingly inherent to the quantum world, but even remake it in a way that finally brings it into line with Einstein's ideas of space and time - an achievement that has eluded physicists for decades. "If you allow retrocausality, it is possible to have a theory of reality that's more compatible with lots of things that we think should be true," says Matthew Leifer at Chapman University in Orange, California.

To get to grips with this particular brand of time warp, we need to rewind to the 1930s, when the outlandish physics of quantum mechanics was threatening to overturn centuries of conventional wisdom. The theory seemed to imply that subatomic particles exist in a vague cloud of probabilities until they are measured, at which point they snap into a definite state. But Einstein, for one, wasn't having it. "God doesn't play dice with the universe," he insisted.

Yet despite his distaste for randomness, it was a different feature of the quantum world that Einstein found truly unbelievable. In a thought experiment, he pointed out that if the probabilistic description of the quantum world were the true state of things, then measuring one subatomic particle could instantly influence the state of another, regardless of the distance between them - a strange phenomenon that became known as entanglement.

Imagine that two particles collide and fly off in opposite directions. Under quantum rules, these particles are now entangled. Their velocities are unknown. But if you measure the velocity of one of them, you'll immediately get the velocity of the other, even though there was no way to know this in advance. So you have a choice: either the particles can instantaneously affect each other when measured, or they had definite velocities all along, even though quantum physics was incapable of determining them.

Einstein's money was on the second option. Instantaneous connections between distant particles were impossible according to his theory of special relativity, which enforced a strict speed limit for how fast signals can pass between objects - the speed of light. In fact, he was adamant that all theories must uphold this ban on instantaneous signals, a principle known as locality. Hence he damned entanglement as "spooky action at a distance", suggesting it would turn out to be a mirage once a more fundamental theory came to light.

But entanglement never did vanish. Instead, it made its presence felt in the laboratory. In the 1960s, Northern Irish physicist John Bell came up with a brilliant way to put spooky action to the test, and it has since passed with flying colours every time. The examination culminated in 2015 with a "loophole-free" Bell test hailed as the nail in the coffin for locality. Like it or not, spooky action at a distance - or non-locality - is a thing.

Or is it? Retrocausality could save us from non-locality. The trouble is that it seems absurd at first glance. It jars with everyday experience, in which time flows forward and effect follows cause. But backward causation is no harder to swallow than entanglement - and it might just solve two of the greatest conundrums in physics.

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"Certainly, John Bell himself thought his work revealed a deep tension with special relativity," says Huw Price, a philosopher of physics at the University of Cambridge. "The appeal of retrocausality is that it removes that tension." By restoring a kind of locality, retrocausality gives us the chance to rebuild quantum mechanics in a way that works with Einstein's theory of general relativity, which shows how gravity results from the warping of space-time by matter and energy.

"Most people have tried to recast gravity in quantum terms, but maybe it is the other way around," says Ken Wharton, a theorist at San Jose State University in California. "Maybe what we need to do is recast quantum theory in space and time. Retrocausality looks like one way to do that."

The notion that the present might influence the past in the quantum realm can be traced back to Paris in the late 1940s, when a young physicist called Olivier Costa de Beauregard spotted a way to explain pairs of entangled particles without invoking non-locality. Perhaps, he suggested, measuring one particle sent a signal back in time to the point in the past when the pair collided. The signal could then turn around and travel forwards in time with the other particle, ensuring its velocity was exactly in accordance with the measurement of the first one.

If a signal took this path, you could preserve locality without requiring the two entangled particles to have determined their velocities at the point of their collision. No instant communication, no violations of relativity.

At that point, no one had shown that non-locality was real. Only when Bell came along was there any reason to take de Beauregard's proposal seriously. But even then, with all manner of clever interpretations springing up to explain the perplexing results of the Bell experiments, retrocausality never really caught on.

It wasn't until 2010 that Price attempted to resuscitate the idea. His case revolved around a principle called time-reversal symmetry. This states that, mathematically speaking, the fundamental laws of physics work the same going backwards in time as they do going forwards. Of course, that doesn't tally with our everyday experience: you can't unscramble an egg, say, or unshatter a glass. (Physicists suspect that has something to do with the second law of thermodynamics, which says that entropy - the amount of disorder - always increases over time when large numbers of particles are involved.) But the fact is that fundamental physics is almost entirely indifferent to the direction of time. Nearly all physicists agree that most of the basic laws of physics obey time-reversal and they would be loath to give it up.

With that in mind, Price pointed out that if the laws of quantum physics obey time-reversal symmetry, as they seem to, then retrocausality is inevitable. Yet there was a loophole in his argument. Price had assumed that the quantum description of a particle, known as the quantum state, corresponded to a real thing in the world, as opposed to being a mathematical tool for handling our own ignorance of said particle. For many, this was reason enough to ignore Price because the true status of the quantum state remains debatable.

But retrocausality is becoming harder to avoid. In 2017, Leifer and Matthew Pusey, now at the University of Oxford, found a way to close the loophole in Price's argument. By merging Price's ideas with Bell's, Leifer and Pusey managed to show that retrocausality is necessary to save time-reversal symmetry regardless of whether the quantum state is real. This leaves another tricky choice: abandon time-reversal symmetry or embrace the idea that in the fuzzy quantum realm, the future really can influence the past.

Leifer is among those attempting to make good on the second option. The key might be a feature of relativity called the block universe.

In its marriage of space and time, Einstein's great theory fatally undermines the concept of "now". What is happening "now" in a particular location depends on where you are and how fast you're moving, so two different observers may see different things at the same time in the exact same spot. This makes "now" an illusion. Time doesn't really pass at all, and our perception that it does is due to our limited perspective on the world. In reality, past, present and future form a single, ever-existing block.

In a block universe, quantum retrocausality wouldn't look so strange. If the past and the future coexist - if past events don't fade away before future ones come into being - the future could easily influence the past.

What we need now, says Leifer, is a new version of quantum theory that incorporates the block universe to allow for retrocausality to emerge naturally. "The idea here is that you would formulate a theory of quantum physics over all of space-time, all at once," he says, urging us to think of quantum cause and effect like a jigsaw puzzle. "When you do a jigsaw, you don't do the bottom row first, and then the next. Each piece imposes constraints on the ones around it. So physics could be like that: each region of space-time could impose constraints on the neighbouring regions."

But if the quantum world is a block universe shot through with retrocausality, why don't we see retrocausality in our everyday lives? After all, we are all made of quantum stuff. The answer boils down to quantum uncertainty. Heisenberg's uncertainty principle states that it is impossible to know both the position and momentum of a particle at the same time. So there are features of the quantum world that are persistently hidden from us, and this is ultimately what allows for retrocausation without letting us send signals to the past. "If my choice a minute from now determines one of these things that I don't know, then I can't send a signal back to myself," says Wharton. "And yet it's still retrocausal."

Wharton is among those who argue that when you really think about it, retrocausality is no crazier than entanglement. And besides, he says, it brings plenty of advantages - not least the opportunity it affords physicists to remake quantum theory in a way that works with space-time. By restoring a form of locality, retrocausality might even lead to the long-sought explanation of how gravity manifests at the quantum scale.

God plays sudoku

"A lot of avenues have been left unexplored because people have been taught to think in this Newtonian picture of states evolving forwards," says theorist Emily Adlam at the University of Cambridge. "Retrocausality is going to open up many new possibilities that might hopefully get us out of the rut we're in."

It might also help to explain where the randomness in quantum physics that never sat right with Einstein comes from. According to Adlam, retrocausality suggests a neat solution: quantum randomness is an illusion that appears because we're only seeing part of the picture at any one time.

In that case, Einstein was right. "God doesn't play dice, he plays sudoku," says Adlam. If you were doing a sudoku and you started on the left and moved towards the right, it would look as if you were seeing random events, she says. "But if you look at the whole thing at once... you can see all the rules, you can see that there's actually a unique deterministic solution from these global constraints to the whole grid."

Similarly, in a retrocausal version of quantum physics, what happens here and now could have effects on the distant past of a far-flung galaxy, effects that only make sense in the context of the "all-at-once" picture of the block universe. This may seem like a drastic departure from the ordinary laws of physics as we think of them, but to Adlam, that's not a problem. "It's quite naive of us to suppose that the laws of nature would take the form that is most convenient for us," she says. "To me, it's not in fact extreme or weird at all to go to this retrocausal picture."

Not everyone shares Adlam's enthusiasm. While it is true that time-reversal symmetry is a cherished property of nearly all the fundamental laws of physics, the version Leifer and Pusey use isn't the usual one. Rather than time-reversing the laws of physics themselves, they time-reversed the setup of their thought experiment, and showed that the results remained the same. This distinction gives sceptical physicists pause.

What's more, retrocausality doesn't answer every question facing quantum physics - at least not yet. "The next chapter in this story is just starting," says Wharton. The hard work begins now, he adds, as researchers attempt to develop a complete retrocausal theory, one that reproduces all the usual results of the hugely successful standard quantum theory.

But if recent work by Sally Shrapnel and Fabio Costa at the University of Queensland in Australia is anything to go by, even a fully retrocausal quantum theory wouldn't solve all the problems that niggle away at other interpretations of quantum physics. Although retrocausality handily accounts for the results of the Bell experiments, there is another issue, known as quantum contextuality, which may yet stop it in its tracks. Contextuality says that the outcomes of quantum experiments depend on what other experiments are conducted at the same time - a strange idea that physicists would prefer to be rid of. Now, Shrapnel and Costa have shown that retrocausality cannot easily dismiss it.

Although Shrapnel agrees with Leifer that retrocausality is worth investigating, she sounds a word of warning. "The retrocausal interpretation is not the free lunch that perhaps you might think it is," she says. "It's not going to be as simple as postulating backwards-in-time causal influences. We're going to need something even more exotic than that, and I think that's kind of cool."
Adam Becker is a writer based in Oakland, California, and author of What is Real? The unfinished quest for the meaning of quantum physics