The bizarre quantum paradox of 'negative time'

In the quantum world, our intuitive grasp of past, present and future may not apply. Richard Fisher explores the discombobulating concepts of "negative time" and "retrocausality".

Tony Soprano is smoking a cigar, driving home. His journey begins in Manhattan, where he enters the Lincoln Tunnel, headed towards New Jersey. There's no traffic, so he passes through in a few minutes, emerging into the daylight. 

So begins the familiar opening credits of The Sopranos TV show. 

In the physical world of mafia bosses, one event follows another. So if Tony strikes a match to light his cigar, this needs to happen before the tip ignites. Such causality appears to be fundamental to how we experience the Universe.

However, at the quantum level, temporal sequencing is not so clear or intuitive. In recent years, physicists have been exploring some seriously head-scratching behaviours at very small scales – some of which can be explained; some of which seem to throw our understanding of past, present and future into question.

To get a flavour, imagine The Sopranos opening credits featured an FBI helicopter watching Tony emerge from the Lincoln Tunnel – but they can't make sense of what they're seeing. From their perspective, the mafia boss leaves the tunnel before he enters. And when the confused FBI officers check their watches, he has spent a negative amount of time driving between Manhattan and New Jersey.

That of course is impossible. However, recently physicists were in the headlines for measuring a duration of "negative time". In quantum experiments, they sent light-pulses through the equivalent of a tunnel – but like Tony Soprano's puzzling drive, the pulses apparently spent less than zero time travelling through.

And that's not the only baffling example of temporal strangeness at very small scales – other theorists think it's conceivable that some particles could even change the past from the future, via an effect called "retrocausality". In the quantum world, it seems our familiar understanding of time quickly becomes, well, disordered. 

This year will mark 100 years since the development of quantum mechanics, and the UN has designated 2025 as the International Year of Quantum Science and Technology. Over the past century, physicists have explored all sorts of unusual behaviours in the quantum world: entanglement, superposition, uncertainty and more.

One of the lesser-known examples is a puzzling way that light tunnels through barriers, such as clouds of atoms. In the 1990s, physicists fired photons through a barrier as a "wave packet" (a bundle of waves that describes both the particle and wave nature of light). Puzzlingly, the packet's peak apparently emerged before they entered – like a car leaving a tunnel before it drove in.

Earlier theory in the mid-20th Century had predicted the effect – now known as a "negative group delay" – but observing it experimentally was another thing, because it should be impossible. It suggested that light could travel faster than itself, which is nonsensical. Moreover, events in time were apparently occurring out of order.

"We had to find a new way to reconcile that with our ideas of causality," says physicist Aephraim Steinberg of the University of Toronto.

In the intervening years, Steinberg and his fellow physicists proposed what could be happening, without violating known physical laws. In short, they argued that the wave packet was not time-travelling but reorganising itself to give the appearance of effect coming before cause.

To understand, imagine a line of cars driving between New York and New Jersey, says Steinberg. We might picture them as 100 Tony Sopranos, each driving bumper-to-bumper. These represent photons in a wave packet.

The line of Tonys depart Manhattan at 13.00. At around 13.30, the midpoint of this car-train enters the Lincoln Tunnel. This is the peak of a wave packet. You would expect this peak to emerge a few minutes later, right? However, the peak has already left the tunnel – at 13.25. Tony Soprano, apparent time-traveller.

What may actually be happening at the quantum level, inside the barrier, is that not all the photons are making it through, says Steinberg. In the car analogy, some Tonys are getting pulled over or turned back; in the experiment, they are absorbed or ejected by atoms within the barrier. When this happens, the forward tail of the wave packet reshapes itself into a new peak. It looks uncannily like the one entering.

Naturally, it's more complex than that – photons don't act like queuing cars because their position is undetermined. "The photons don't have any individual identity," says Steinberg. "That's why the tunnel is purely an analogy, but it's meant to show that there's no contradiction with causality." So what appears to be a violation of physical laws is more like a reorganisation within the light-pulse. With this explanation, no particle is experiencing negative time and there's no faster-than-light travel.

Mystery solved? Not quite.

More recent experiments from Steinberg's group have added a new twist and can't be explained (yet). Whereas physicists in the earlier work were observing an apparent negative delay – a pulse leaving a barrier before it entered – this time, a team led by physicist Daniela Angulo Murcillo calculated a negative duration.

Delay and duration sound like they should be the same: after all, if your flight has a delay, that's the same as the duration you spend waiting. But that doesn't appear to be the case at atomic scales. "It turns out quantum mechanics says there might be one process – one event – that's described by multiple time scales," says Steinberg. "So you might ask, 'when does [a photon] arrive?' You might ask, 'how long does it spend in the barrier?' You're not necessarily going to get the same answer." 

A negative measurement of duration has added a new level of strangeness. In the car analogy, Tony Soprano is spending less than zero amount of time in the tunnel, and it can't be explained by the same wave packet reshuffling that explained the negative delay.

"When the weirdness was explored in the 1990s, people made sense of it. But looking again, a little deeper, the mystery appears to be kind of irrepressible now. There's something here that is truly, seemingly paradoxical," says Josiah Sinclair, now at MIT, who worked with Steinberg and colleagues in recent years to explore this phenomenon.

It began with a seemingly simple question: how long do photons spend tunnelling through a barrier? Making this measurement is not as easy as setting a stopwatch. Unlike cars in a tunnel, photons have no fixed position or trajectory through space. "An incredibly fundamental and deep insight about the nature of photons is that they don't have the same reality," says Sinclair. "Their existence is fundamentally different to cars. We can't label and track them."

So, the physicists measured the spent time indirectly, by analysing the excitation of atoms within the barrier, as photons pass through or strike them. To return to the car-tunnel analogy, Sinclair says it's a bit like analysing passing vehicles using only their emissions. If you installed a carbon monoxide monitor inside the Lincoln Tunnel, you couldn't track individual cars but you could maybe figure out how long the passing vehicles spent in there.

"The shocking thing is that when you design something that measures how long are the cars in the tunnel – this carbon monoxide monitor – it turns out that the monitor in this kind of quantum mechanical situation will read negative minutes," says Sinclair.

"We understand mathematically why it's happening, but we don't know how to talk about the physical meaning of it," he continues. "There's no clear correspondence to the world that we know: the physical world we experience. And so we're just left saying, 'Okay, well, I guess quantum mechanics are just different'."

If you think that is strange though, quantum mechanics has even more bewilderment in store. In recent years, some theorists have proposed that particles may be able to change the past from the future – so-called "retrocausality".

While this idea doesn't have the observational evidence of the quantum tunnel experiments, it's a prospect taken seriously by physicists. The reason is that such temporal weirdness would help to solve an apparent impossibility they have observed, dubbed "spooky action at a distance".

This spooky action happens when two particles are "entangled", which means they are strongly connected, regardless of how far apart they are physically. In principle, they could be at opposite sides of the Universe, but when scientists measure, say, the spin or polarisation of one entangled particle, a corresponding property of its entangled partner becomes instantly determined. 

To return to The Sopranos, it's a bit like if Tony had a twin brother who lived in California. If Tony orders veal at Vesuvio's restaurant in New Jersey, his brother's order at a Los Angeles restaurant instantly becomes veal too (or perhaps fish; the property needn't be identical, but the key point is that the brother's meal is not determined until that moment). 

What makes it spooky is that particles don't have these properties until they are measured; until then, they exist in multiple states simultaneously. In the Soprano twin analogy, there's no pre-planning about their meal choices; it's as if some influence is passing instantaneously between them as the waiter takes Tony's order, faster than light.

"It's possible to show mathematically that those correlations are not explainable in terms of a common cause in the past," says physicist Emily Adlam at Chapman University in California. "It looks naively as though there's some kind of instantaneous signal going from one particle to the other telling this particle what measurement you performed, or vice versa. That's pretty weird. Physicists don't think that signals should be able to send faster than light."

One way to get round the spooky-action-at-a-distance problem – also known as non-locality – is to invoke retrocausality. In this scenario, information does not need to pass instantaneously between the particles across space; it happens across time. 

If true, it would mean that a measured particle passes information into the past – to the moment it was entangled with its pair – and then forwards to the moment at which the measurement happens. Or in the Sopranos analogy, Tony's meal order in New Jersey goes back to when the two twins were in the womb, and then forwards to the California restaurant.

More like this:

• Why does time go forward, not backward?

• Is time travel really possible? Here's what physics says

• Time: The Ultimate Guide

This is admittedly a counterintuitive concept to get your head around, and it seemingly replaces one impossibility with another – a cure that seems worse than the disease. And that's not to mention the fact that it would seem to open the door to paradoxes of time travel, where influencing the past alters the present. However, it wouldn't be the first time quantum mechanics has defied common sense.

In its defence, retrocausality's supporters have pointed out that it only seems unlikely because we – at the macroscopic scale – experience time in one direction. At very small scales, it's long been believed that the physical laws are time-symmetric (with some exceptions). And as for the apparent time-travel problem, that only applies if the particle was measured in the past, they say. That doesn't happen; instead, it stays in its quantum underdetermined state.

Still, if it's true, the Universe would have to work differently than we currently imagine, says Adlam. In one scenario, two timelines would essentially sit side-by-side. "When people mention retrocausality, what they seem to have in mind is a picture in which there's a forward evolution and a backwards evolution of the Universe. It's a picture with two separate and independent causal arrows," she says. "That's a kind of 'dynamical' picture of retrocausality, where you have literal forwards and backwards processes happening in some combination."

Adlam, however, doubts this scenario. "It is not a very appealing way of thinking about retrocausality, because you can very easily get inconsistencies, contradictions and paradoxes," she says. 

Instead, she argues that retrocausality is more plausible if we live in what's known as a "block universe". This is a hypothetical (and philosophically controversial) model of existence, where all moments in time – past, present, and future – exist in a four-dimensional object. 

If this block is filled with every event that ever has or will happen, then it's easier to see how some hypothetical influence could pass between particles within it, says Adlam. To explain the spooky actions of entangled particles, information would not need to travel backward on some alternative retrocausal timeline. "There's no temporal flow," she says. "Time is just another dimension within the block, rather than being a material thing that moves."

If that is the case, we have arrived at what may be the most troubling implication of all about quantum mechanics and its weird temporal behaviour. If you accept the most fatalistic interpretation of the block universe, then, like Tony Soprano, we're all just characters in some cosmic TV series. We may experience life episodically, but our future is just as determined as our past. So while you're currently in the middle of your story, here's a spoiler alert: your own finale – the moment where the scene cuts to black – may already be written.

*Richard Fisher is the author of The Long View: Why We Need to Transform How the World Sees Time, and a senior editor for Aeon.

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