The dead end was partly built by the formalism itself.
For more than half a century, faster-than-light particles known as tachyons have haunted the edges of theoretical physics — promising and paradoxical in equal measure. Researchers from Warsaw and Oxford now argue that the real obstacle was never the particles themselves, but the mathematical language used to describe them. By extending quantum field theory into a broader formal structure that treats past and future states together, they propose that tachyons may coexist with special relativity after all — not by bending causality's rules, but by revealing that those rules were always more subtle than assumed.
- Decades of dismissal are being challenged: a new paper in Physical Review D argues that tachyons were never truly forbidden by relativity — only by an inadequate mathematical framework.
- The old theory broke down catastrophically, producing unstable vacuums, unbounded energies, and reference-frame-dependent contradictions that made faster-than-light particles seem logically toxic.
- The proposed fix expands the mathematical space from standard Fock space into a 'twin space' that unifies incoming and outgoing particle states, restoring the symmetries relativity demands.
- Rather than erasing causality paradoxes, the framework reframes them as 'disturbances of causality' — strange but familiar features already present in quantum mechanics.
- No tachyon has ever been detected, and the authors make no such claim — but the work reopens questions about time symmetry, the Higgs mechanism, and the deep structure of quantum field theory.
For more than fifty years, tachyons — hypothetical particles that travel faster than light — have occupied an uncomfortable corner of physics. They seemed to threaten causality itself: if something outruns light, effects might arrive before their causes, unraveling the orderly sequence on which science depends. The question was troubling enough that tachyons were quietly shelved, treated as a thought experiment rather than a serious physical possibility.
Now researchers from the University of Warsaw and the University of Oxford are challenging that consensus — not by claiming tachyons exist, but by arguing that the mathematics used to describe them was always the wrong tool. In a paper published in Physical Review D, Andrzej Dragan and Artur Ekert propose a revised quantum field theory that they say resolves the old contradictions without abandoning relativity.
The trouble with earlier attempts, they argue, traces back to Gerald Feinberg's 1960s framework, which assigned tachyons imaginary mass to keep them permanently beyond light speed. The approach was elegant but unstable: different observers could disagree about the order of events, energy spectra grew unbounded, and the symmetries at the heart of relativity collapsed. Standard quantum field theory's Fock space, designed for ordinary particles, simply couldn't accommodate the strange behavior of faster-than-light ones.
The new proposal enlarges that mathematical space into what the authors call a twin space — a unified structure combining input and output states. Because a Lorentz boost can flip a tachyon from positive energy moving forward in time to negative energy moving backward, the boundary between past and future becomes observer-dependent. Merging those states restores the covariance relativity requires, stabilizes the vacuum, and bounds the energy spectrum from below.
What makes the framework philosophically striking is its alignment with quantum mechanics' two-state formalism, which describes processes using both past and future boundary conditions. The authors argue this isn't a choice but a necessity: a consistent relativistic theory of tachyons forces future and past states to be treated together. Rather than producing logical paradoxes, superluminal particles would generate what they call disturbances of causality — unusual but not incoherent features already present in quantum theory.
Tachyons already appear quietly throughout modern physics — in string theory, in tachyonic fields in cosmology, and in the mathematics underlying the Higgs mechanism. A cleaner theoretical treatment could therefore matter well beyond the question of faster-than-light travel, potentially touching time symmetry, CP violation, and the matter-antimatter asymmetry of the universe. The authors are careful not to overclaim. But they have pushed a long-dismissed idea back into serious territory — and asked whether the door was ever truly closed, or merely built from the formalism itself.
For more than fifty years, physicists have circled around a stubborn problem: faster-than-light particles called tachyons. They seemed to offer a way to test the boundaries of Einstein's relativity, but they came with a terrible cost. If something could outrun light itself, what would prevent effects from arriving before their causes? The question was so troubling that tachyons drifted to the margins of serious physics, treated less as a real prediction than as a useful thought experiment—a way to stress-test theory without expecting nature to cooperate.
Now a team from the University of Warsaw and the University of Oxford is arguing that the problem was never the particles themselves, but the mathematical language physicists were using to describe them. In a paper published in Physical Review D, researchers led by Andrzej Dragan and Artur Ekert propose a revised quantum field theory for tachyons that they say sidesteps the old contradictions. They are not claiming to have found tachyons in nature. They are claiming something more modest and more interesting: that tachyons may not be forbidden by special relativity in the way most physicists have assumed.
The history of tachyons begins in the 1960s with physicist Gerald Feinberg, who tried to give faster-than-light particles a formal mathematical home. His solution was elegant and strange: he assigned them imaginary mass, a mathematical trick that would keep them forever beyond light speed, unable to slow down and cross the barrier that traps ordinary matter below the speed of light. But this move came with a price. Under certain conditions, different observers could disagree about the order of events. A particle emitted in one reference frame could appear, in another, to have been absorbed before it was ever sent. That kind of reversal threatened to unravel causality itself. Other problems accumulated too: tachyon field equations produced unbounded energy spectra, unstable vacuum states, and mathematics that broke down when viewed from different inertial frames. The symmetries at the heart of relativity simply would not hold.
The new proposal attacks these failures directly. The researchers argue that earlier attempts failed because they were working in too small a mathematical space. Standard quantum field theory uses something called Fock space, a structure designed to handle changing particle numbers while preserving the symmetries of ordinary particles. For tachyons, the authors contend, this space is insufficient. Because a Lorentz boost can flip a tachyon from positive energy moving forward in time to negative energy moving backward in time, the distinction between incoming and outgoing states becomes dependent on the observer's reference frame. To solve this, the team extends the mathematical space to what they call a twin space, combining input and output states into a single unified structure. This enlargement, they argue, restores the covariance that relativity demands, preserves the commutation relations that quantum mechanics requires, keeps the vacuum stable and Lorentz-invariant, and produces an energy spectrum with a lower bound—addressing one of the oldest mathematical complaints about tachyons.
What makes this proposal striking is how closely it aligns with the two-state formalism in quantum mechanics, an approach developed by Yakir Aharonov, Peter Bergmann, and Joel Lebowitz. That formalism describes quantum processes using both pre-selected states from the past and post-selected states from the future. In ordinary quantum theory, this approach has been treated as unusual, even exotic. Here, the authors argue it becomes necessary. Dragan explained the shift this way: the idea that the future can influence the present rather than the present determining the future is not new in physics, but until now it has been at best an unorthodox interpretation of certain quantum phenomena. This time, the theory itself forced them to this conclusion. The paper does not claim to prove that retrocausality is real in everyday life. It means that if tachyons are described in a relativistically consistent quantum theory, then future and past states may have to be treated together as part of the formalism. Rather than producing logical paradoxes, the authors suggest that superluminal particles would produce what they call disturbances of causality—odd features already familiar from quantum mechanics.
Tachyons have kept surfacing in theoretical physics even without experimental evidence. They appear in string theory as unwanted artifacts, in cosmology through tachyonic fields, in discussions of the Casimir effect, and in models of spontaneous symmetry breaking. Fields with negative mass squared, often described as tachyonic fields, are already built into important areas of physics, including the Higgs mechanism. That broader context explains why a cleaner mathematical treatment matters. A consistent theory of tachyons would not simply revive an old science fiction favorite. It could reshape how physicists think about time symmetry, Lorentz invariance, and the structure of quantum field theory itself. The authors are careful not to overstate their work. It does not settle interpretational debates around the two-state vector formalism. It does not show that tachyons exist. It leaves open whether ideas from the framework could help illuminate the Higgs phase transition, CP violation, or the baryon asymmetry of the universe. But it does push a long-dismissed idea back into territory many physicists had written off as a dead end. Instead of treating faster-than-light particles as a closed question, it asks whether the closure was partly built by the formalism itself.
Citações Notáveis
The idea that the future can influence the present rather than the present determining the future is not new in physics. However, until now, this kind of view has been at best an unorthodox interpretation of certain quantum phenomena, and this time we were forced to this conclusion by the theory itself.— Andrzej Dragan, University of Warsaw
A Conversa do Hearth Outra perspectiva sobre a história
Why does it matter if we can write down a consistent math for something we've never observed?
Because the math we use shapes what we're allowed to think. For fifty years, physicists assumed tachyons were forbidden. But that assumption was built into the mathematical framework, not necessarily into nature. If you change the framework and the contradictions disappear, you've learned something about your tools, not just about particles.
So they're saying the old paradoxes were artifacts of bad mathematics?
Partly. The old framework couldn't handle the fact that a tachyon's energy direction flips depending on who's observing it. They tried to force tachyons into a space designed for ordinary particles. When you use the right space—one that treats past and future together—the paradoxes dissolve.
This two-state formalism sounds like retrocausality. Are they saying the future influences the past?
Not quite. They're saying that if tachyons exist and obey relativity, then your mathematical description has to include both past and future states simultaneously. Whether that means causality actually runs backward is a different question—one they're deliberately not answering.
Has anyone actually found a tachyon?
No. And the paper doesn't claim they have. What it does is remove one of the main theoretical objections to their existence. It says: the old reasons we ruled them out may have been mathematical artifacts, not physical laws.
What happens if this framework is right?
It opens the door to asking whether tachyon-like behavior might already be hiding in physics we know—in the Higgs field, in symmetry breaking, in other places where physicists already use tachyonic mathematics as a tool. Right now those are just mathematical conveniences. If this framework holds, they might mean something deeper.