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Andrzej Dragan is not one for following rules. As a photographer, he uses extensive post-production to portray worlds spinning out of control in disturbing ways: heads splitting in half; bleeding brides and long-dead celebrities reimagined in their old age.

But in Dragan’s main job as a physicist at the University of Warsaw in Poland, railing against conformity is not always appreciated. Particularly when those ideas might rock the two pillars that form our fundamental understanding of the world: general relativity and quantum mechanics.

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These theories are the crowning achievements of modern physics, describing nature exquisitely, but separately. General relativity handles the big familiar objects and events of the universe, while quantum mechanics covers the invisible and strange micro-world that surrounds us, where subatomic particles can tunnel through barriers they have no business getting past, or where two particles thousands of light-years apart can instantaneously respond to each other’s motions.

Most of the time, this setup works well. If you’re looking at how a massive star’s gravity bends light, you whip out your general relativity textbook. And if you want to understand how electrons move through a computer chip, you’ll need your trusty quantum physics hardback by your side. But there are times when a bit of both is called for. Trying to understand what happened in the very first moments of the Big Bang or what goes on in the heart of black holes, for instance.

In these situations, a glaring problem comes into focus: general relativity and quantum mechanics appear to be completely incompatible. The smooth, continuous universe general relativity describes conflicts with the discrete, chunky one of quantum physics. When you bring their equations together you get nonsense.

To try to reconcile them, physicists generally assume that quantum mechanics is more or less the true description of nature and then tinker with relativity to get it to match up. This approach has given the world rich and complex ideas like string theory. But it has also left physicists frustrated, unable to match juggernaut equations to reality. Dragan comes at this problem from a different angle, attempting to describe nature through the lens of relativity.

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Decades before he first started pondering the connections between the quantum world and relativity, a link between special relativity (Einstein’s first theory describing space and time before he added acceleration in his general theory of relativity) and quantum mechanics was already well established. In fact, quantum field theory – which forms the basis for our modern understanding of how the building blocks of matter interact – unites quantum mechanics and special relativity. But it does it in a way that regards them as two independent and distinct pieces of a wider puzzle.

Dragan felt that this connection must run deeper: “It’s more than just being part of quantum field theory, more profound,” he says. “It’s almost as if quantum theory does exactly what relativity allows and not a bit more.”

Following this line of thought, in 2008 Dragan began to dig into the maths. He remembered that special relativity’s equations allow for two branches of solutions: one that leads to the familiar world where matter travels below light speed, and another where it always travels faster than the speed of light.

Because there is no physical evidence that anything can travel faster than the speed of light, the faster-than-light solutions are always thrown away. But, mathematically, these solutions are still valid. So Dragan thought, why not keep the faster-than-light solutions and see what happens? When he did, he uncovered a world that would look more familiar to quantum theorists.

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In this world, instead of a particle following a well-defined path, its motion is hard to pin down, described by layers of complex probabilities that correspond to different possible outcomes, much like what is known as superposition in quantum physics. Moreover, if a physicist in this world tried to measure certain properties of this particle multiple times, they would not get the same result every time. Outcomes can be random, just as they are in quantum mechanics.

In essence, Dragan had shown that in a world ruled by special relativity, counterintuitive quantum effects don’t have to be accepted as fundamental. In other words, by including the wacky ‘unphysical’ parts of special relativity’s equations, patently random and distinctly quantum-like phenomena emerge naturally.

A few months later, realising the enormity of what he had discovered, Dragan got these thoughts and calculations down on paper and submitted the work to a scientific journal. But the manuscript was rejected, twice. “I got completely disappointed by this,” he says. “I just thought, ‘I’m not gonna bother anymore, I’m going to leave it behind’.”

Dragan moved on from his disappointment and was happily working in a branch of quantum computing called relativistic quantum information. Then, in 2010, he received an email from Artur Ekert that would bring him right back to his musings on relativity and quantum mechanics. Ekert was and is a leading figure in quantum information and pioneer of quantum cryptography, who has dual Polish-British nationality and holds dual professorships at the University of Oxford and National University of Singapore. The email invited Dragan to Singapore to discuss links between their respective research.

Immediately realising an intellectual affinity, over the course of several visits Ekert and Dragan developed a friendship, becoming as comfortable talking about quantum algorithms as they were teasing each other with mathematical puzzles.

When Dragan finally shared his ideas on how quantum randomness might emerge from special relativity, Ekert was keen to get involved. “I thought it was beautiful,” he says. Up to then, Dragan had only explored his ideas in a toy world with one space dimension and time. Ekert encouraged and assisted Dragan to go further, and see if it still worked in the real world of four-dimensional spacetime.

“Like two jazz players meeting every now and then and having a gig together,” Ekert says of the pair’s meetings in Singapore. Over the summer of 2019, Dragan and Ekert wrote up a paper summarising their new theory.

With memories of rejection swirling around his mind, before submitting it to New Journal of Physics, Dragan gave Ekert one final opportunity to back out before publishing their results: “Are you not afraid to endanger your reputation?” asked Dragan. Ekert was blunt in his response: “Screw reputation.”

Unlike Dragan’s previous solo attempts, the paper passed through its first test with the journal’s academic reviewers unscathed. And though it went viral upon publication in 2020 and has amassed over 30,000 downloads and counting – by far the most out of all the papers published last year in the journal – the duo had (and still have) a fight on their hands to be taken seriously by the court of scientific opinion.

One physicist who was immediately attracted to Dragan and Ekert’s ideas is quantum information scientist Vlatko Vedral. After reading the article, Vedral — whose unofficial PhD mentor was Ekert in the past — invited Dragan to present a virtual talk to his group at the University of Oxford. “It generated a lot of excitement,” he says. “What I like about the approach is that frequently we think about imposing quantum mechanics on everything else; how do we make relativity comply with quantum mechanics? But they are trying to twist this around.”

Yet for every Vedral open to hearing out unorthodox ideas, there are many others who are suspicious of any approach that doesn’t place quantum physics front and centre. Not only are crackpots with wild unphysical concepts rife in this area of physics, but deeply rooted in the community is the idea that the mind-bending elements in quantum physics simply cannot be explained any further. They just are.

Critics from this camp question both the assumptions and methods used by the Polish pair to come to their conclusions. For instance, when Dragan discussed these ideas with one of the founding fathers of string theory, Holger Nielsen, the Danish physicist’s main criticism was that faster-than-light matter would be unstable and therefore unphysical. Another theoretical physicist, who asked to remain anonymous, thought that the pair had used mathematics that changes the vantage point from which you observe the physics in order to change the actual underlying physics itself, which it should never do.

Often though, these criticisms boil down to two points: that no one has ever detected anything racing beyond light speed, and that if anything did travel that fast, time travel is possible. Time travel leads to what is known as causal paradoxes. The most famous of these is the grandfather paradox — the idea that if you travel back in time and kill your grandfather, your own birth will be impossible.

Dragan and Ekert argue that these critics miss the point. “We’re not saying there are any objects that travel faster than light; there might be, but that doesn’t enter our arguments,” Ekert says. “What we are saying is that you can look on the world from a perspective that is beyond light speed.”

From this faster-than-light vantage point, you can swap the order of cause and effect. This is a key result because the underlying physics must remain the same regardless of whether you’re watching events unfold above or below the cosmic speed limit. And if this is true, the pair argue that the order of events no longer plays a fundamental role in the theory.

Dragan says all of this means that there are no paradoxes to answer for at all. “If you look at it carefully, you find that the rules of causality are changed. But they are not completely destroyed, they are modified in precisely the way quantum theory tells us.”

Both Dragan and Ekert admit that the paper is far from the end of the story, and that they don’t know whether they will be able to truly derive quantum theory from special relativity. But, if they can, it will transform the way researchers approach reconciling special relativity’s big brother, general relativity, with quantum mechanics. “If you convince me that quantum mechanics follows from relativity, then maybe I should reconsider what the fundamental entities are in my theory,” Vedral says. “And maybe the road to a quantum version of general relativity is very different.”

Had Covid-19 not thrown the world into turmoil, Dragan and Ekert would be working on this right now in Singapore. But, for the time being, they are happy that simply railing against conformity has renewed interest in finding alternative ways to solve one of the most pernicious problems in modern physics. “More work has to be done, for sure, but what I like about this paper is that it’s not boring, right?” says Ekert. “It will create emotions one way or another, and serve as an opening paper for further investigation.”

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