What Are Tachyons? A Comprehensive Guide

Tachyons are among the most fascinating and misunderstood concepts in modern physics. They are hypothetical particles that, if they exist, always travel faster than the speed of light. They have never been observed, yet they arise naturally from the mathematics of Einstein’s special relativity and play a significant role in string theory and quantum field theory. This guide provides a thorough, accessible introduction to tachyon physics from the ground up.

Etymology: Where the Name Comes From

The word tachyon derives from the Greek tachys (ταχύς), meaning “swift” or “fast.” The term was coined by the Columbia University physicist Gerald Feinberg in his 1967 paper “Possibility of Faster-Than-Light Particles,” published in Physical Review. Feinberg chose the name to contrast with “tardyon” (from the Latin tardus, meaning “slow”), the proposed name for ordinary subluminal particles. A third class, particles that always travel exactly at the speed of light, were called “luxons” (from the Latin lux, meaning “light”).

It is worth noting that the theoretical groundwork for superluminal particles predates Feinberg’s naming. In 1962, physicists Olexa-Myron Bilaniuk, V. K. Deshpande, and E. C. George Sudarshan at the University of Rochester published a paper exploring the kinematics of faster-than-light particles within the framework of special relativity. Feinberg’s contribution was to develop a quantum field theory for such particles and to give them their enduring name.

The Three Classes of Particles

Special relativity divides all particles into three kinematic classes based on their relationship to the speed of light, $c$:

Tardyons (Bradyons)

Always travel slower than $c$
Have positive real rest mass
Include all familiar matter: electrons, protons, neutrons, atoms, baseballs, planets
Gaining energy increases their speed, which approaches but never reaches $c$
The Lorentz factor $\gamma = 1/\sqrt{1 - v^2/c^2}$ is always real and greater than 1

Luxons

Always travel at exactly $c$
Have zero rest mass
Include photons and gluons
Cannot be sped up or slowed down; adding energy increases frequency (and thus energy per photon), not speed
Experience no proper time: from a photon’s “perspective,” emission and absorption are simultaneous

Tachyons

Always travel faster than $c$
Have imaginary rest mass
No confirmed examples exist
Gaining energy decreases their speed toward $c$; losing energy increases their speed toward infinity
At zero energy, a tachyon would travel at infinite speed

These three classes are separated by the speed of light, which acts as an impassable barrier. No particle in any class can cross into another class. A tardyon cannot be accelerated to $c$, and a tachyon cannot be decelerated to $c$. This is why physicists describe the light barrier as a wall, not a ceiling.

The Energy-Momentum Relation Explained Simply

The central equation governing particle kinematics in special relativity is:

$$E^2 = (pc)^2 + (mc^2)^2$$

where $E$ is total energy, $p$ is momentum, $m$ is rest mass, and $c$ is the speed of light.

For tardyons, $m$ is a positive real number. The minimum energy occurs when the particle is at rest ($p = 0$), giving $E = mc^2$, Einstein’s famous equation. As speed increases, momentum increases, and so does energy.

For tachyons, $m$ is imaginary. If we write $m = i\mu$ where $\mu$ is a real number and $i = \sqrt{-1}$, then $m^2 = -\mu^2$, and the equation becomes:

$$E^2 = (pc)^2 - (\mu c^2)^2$$

This equation still yields real values for energy and momentum, as long as the momentum is large enough. The energy is real and positive; nothing about tachyon energy is “imaginary” or unphysical. Only the rest mass parameter is imaginary, and since a tachyon can never actually be at rest, the “rest mass” is a mathematical label rather than a measurable quantity.

Why Imaginary Mass Is Not “Fake Mass”

The phrase “imaginary mass” is deeply misleading for non-physicists. In everyday language, “imaginary” means “not real” or “made up.” In mathematics, “imaginary” refers to a specific and well-defined class of numbers involving $i = \sqrt{-1}$.

Imaginary numbers are not fictitious. They are indispensable in electrical engineering (alternating current analysis), quantum mechanics (the Schrödinger equation), fluid dynamics, and signal processing. An imaginary rest mass does not mean the particle is fake. It means that the mathematical quantity we call “rest mass,” which is defined as the mass measured in the particle’s own rest frame, does not correspond to a physically realizable measurement for tachyons, because a tachyon can never be at rest.

What is physically meaningful for tachyons is their energy and momentum, and both of these are ordinary real numbers. The imaginary mass is simply a parameter in the equations, a bookkeeping device that ensures the energy-momentum relation produces the correct (superluminal) behavior.

The Inverse Energy-Speed Relationship

Perhaps the most counterintuitive property of tachyons is their inverse relationship between energy and speed. For ordinary matter, adding energy makes things go faster. For tachyons, the opposite is true.

An Everyday Analogy

Imagine a ball rolling down an infinitely long hill. As it loses energy to friction, it slows down. Now imagine the opposite: a ball that speeds up as it loses energy and slows down as it gains energy. That is how a tachyon behaves.

More precisely:

A tachyon with high energy moves just barely faster than $c$. It is “slow” by tachyon standards.
A tachyon with low energy moves enormously faster than $c$.
A tachyon with zero energy would travel at infinite speed, arriving at its destination at the same instant it departed (in some reference frame).
To slow a tachyon down to exactly $c$ would require infinite energy, just as accelerating a tardyon to $c$ requires infinite energy.

This relationship is not arbitrary. It follows directly from the Lorentz transformations when applied to particles with imaginary mass. The speed of light is an energy maximum for luxons, an asymptotic limit for tardyons, and an asymptotic limit from the other side for tachyons.

Cherenkov Radiation and Tachyons

When a charged particle travels through a medium faster than the speed of light in that medium, it emits Cherenkov radiation, a distinctive blue glow. This is analogous to a sonic boom: the electromagnetic equivalent of breaking the sound barrier. Cherenkov radiation is routinely observed in nuclear reactors and particle detectors; it is not hypothetical.

If charged tachyons exist, they would produce vacuum Cherenkov radiation, Cherenkov radiation emitted not in a medium but in empty space, because they exceed the speed of light in vacuum. This radiation would cause the tachyon to lose energy continuously, which, because of the inverse energy-speed relationship, would cause it to speed up. The tachyon would accelerate without limit, radiating away energy as it goes, in a runaway process.

This has two implications. First, it provides a potential detection mechanism: the Cherenkov radiation produced by tachyons would have distinctive spectral and angular properties. Second, it suggests that charged tachyons may be inherently unstable, radiating away their energy almost instantaneously and accelerating to infinite speed. Some physicists have argued that this effectively makes charged tachyons unobservable, even if they exist.

The Causality Problem, Simplified

The deepest problem with tachyons is not their imaginary mass or their inverse energy relation. It is causality.

In special relativity, if Event A causes Event B, then all observers agree that A happened before B, provided the signal from A to B travels at or below the speed of light. But if the signal is superluminal, the Lorentz transformations guarantee that some observers will see B happen before A. In other words, different observers disagree about which event is the cause and which is the effect.

This is not a matter of perception or measurement error. It is a fundamental consequence of how spacetime coordinates transform between reference frames. And it leads directly to paradoxes: if you can send a tachyonic message to the past, you can instruct your past self not to send the message, creating a logical contradiction.

Physicists have proposed several resolutions: the Feinberg reinterpretation principle (reinterpret backward-in-time tachyons as forward-in-time tachyons moving in the opposite direction), the Novikov self-consistency principle (only self-consistent causal loops are permitted), and the Chronology Protection Conjecture (quantum effects prevent causal loops from forming). None of these resolutions is universally accepted, and the causality problem remains the single strongest theoretical argument against tachyon particles.

Tachyons in Quantum Field Theory

In modern theoretical physics, the word “tachyon” most often refers not to a faster-than-light particle but to a specific feature of a quantum field: a tachyonic mode, a field excitation with a negative mass-squared term.

Tachyon Condensation and the Higgs

When a scalar field has a potential with a local maximum at the origin and lower-energy minima elsewhere (a “Mexican hat” or “wine bottle” potential), small perturbations around the maximum grow exponentially. The field “rolls” downhill to a stable minimum. This process is called tachyon condensation.

The most important example in all of physics is the Higgs field. The Higgs potential has a tachyonic mode at the origin: the mass-squared parameter is negative. This instability drives the field to its nonzero vacuum expectation value, spontaneously breaking electroweak symmetry and giving mass to the W and Z bosons (and, via Yukawa couplings, to quarks and leptons).

In this context, “tachyon” does not mean a faster-than-light particle. It means the field is sitting at an unstable point and must evolve to a stable configuration. The tachyonic instability is not a problem to be solved; it is the mechanism by which the universe acquires much of its structure.

Tachyons in String Theory

In bosonic string theory, the ground state of the open string is a tachyon, a particle with negative mass-squared. For decades, this was considered a fatal flaw of bosonic string theory. In 1999, Ashoke Sen proposed that this tachyon represents the instability of the space-filling D25-brane on which the open strings end. Tachyon condensation corresponds to the decay of this brane, and Sen conjectured that at the true vacuum, the brane tension is exactly canceled by the tachyon potential energy. This conjecture has been confirmed to extraordinary precision in string field theory calculations.

The Current Scientific Consensus

The scientific consensus on tachyons can be summarized in three points:

No tachyon particle has ever been detected. Despite decades of experimental searches, including analyses of cosmic ray showers, neutrino velocity measurements, and dedicated particle physics experiments, no evidence for superluminal particles has been found.
Tachyonic fields are real and important. The tachyonic instability mechanism is central to the Higgs mechanism, string theory, and cosmology. But these “tachyons” are field instabilities, not particles that travel faster than light.
The causality problems are severe. If tachyon particles exist and can interact with ordinary matter, they would enable backward-in-time signaling, creating paradoxes that most physicists consider fatal to the particle interpretation.

Common Misconceptions Debunked

“Tachyons prove time travel is possible.” No. Tachyons are hypothetical, and even if they existed, the causality paradoxes they create are generally considered evidence against their physical reality, not evidence for time travel.

“Tachyons have been detected.” No. The 2011 OPERA experiment initially reported neutrinos traveling faster than light, but this was traced to a loose fiber optic cable and a clock synchronization error. No credible detection has ever been reported.

“Imaginary mass means tachyons aren’t real particles.” Not exactly. “Imaginary mass” is a mathematical description, not a statement about physical reality. The energy and momentum of tachyons would be perfectly real. The issue is not the mathematics but the physical consequences (causality violation).

“Tachyons are just science fiction.” Tachyons arise naturally from the mathematics of special relativity. They are a legitimate subject of theoretical physics, studied by serious researchers. The question is not whether the math works (it does) but whether nature makes use of it.

“If tachyons exist, we could use them for instant communication.” Even if tachyons exist, controlling them for communication would face enormous obstacles. The inverse energy-speed relationship means low-energy tachyons move fastest, but low-energy particles are hardest to detect. And any successful tachyonic communication scheme would create causal paradoxes.

For more on the experimental search for tachyons, see the detection page. For the mathematical framework, see physics. For common questions, see the FAQ.