Bradyon, Luxon, Tachyon

Special relativity does not merely impose a cosmic speed limit. It divides the entire universe of possible particles into exactly three classes based on their rest mass and velocity relative to the speed of light. These classes are bradyons, luxons, and tachyons. Every particle that could exist, real or hypothetical, falls into precisely one of these categories.

1. Bradyons: The Subluminal Majority

Bradyons, sometimes called tardyons, are particles with positive real rest mass that always travel slower than the speed of light. The name derives from the Greek word "bradys," meaning slow. Every particle of ordinary matter is a bradyon: electrons, protons, neutrons, quarks, muons, tau leptons, neutrinos, and the W and Z bosons.

The defining kinematic property of a bradyon is straightforward. At rest, it possesses a real, positive mass $m$. When it moves, its total energy is given by the relativistic energy-momentum relation:

As a bradyon accelerates toward the speed of light, its relativistic mass increases without bound. The Lorentz factor $\gamma$ for a bradyon is:

As $v \to c$, the Lorentz factor $\gamma \to \infty$. This means infinite energy would be required to accelerate a bradyon to exactly the speed of light. The light barrier is therefore absolute for bradyons: they can approach $c$ asymptotically but never reach it. This is the fundamental reason particle accelerators like the Large Hadron Collider can push protons to 99.9999991% of $c$ but never to 100%.

On a spacetime diagram, bradyon worldlines are always timelike, meaning they remain inside the light cone at every point. Their four-momentum vector has a positive invariant mass squared ($m² > 0$).

2. Luxons: Riding the Light Cone

Luxons are particles with exactly zero rest mass that travel at exactly the speed of light in every reference frame. The name comes from the Latin "lux," meaning light. The photon is the prototypical luxon. Gluons, the carriers of the strong nuclear force, are also luxons. If gravitons exist as quantized carriers of gravity, they too are luxons.

For a luxon, setting $m = 0$ in the energy-momentum relation yields a beautifully simple result:

The energy of a luxon is entirely kinetic, determined solely by its momentum. A luxon has no rest frame. The concept of "stopping" a photon is physically meaningless within special relativity. If you could somehow ride alongside a photon at speed $c$, the equations of electrodynamics would become internally inconsistent. This was one of the key thought experiments that led Einstein to formulate special relativity in 1905.

The Lorentz factor for a luxon is formally undefined: $\gamma = 1/0$. This is not a mathematical failure but a reflection of the fact that luxons occupy a fundamentally different kinematic regime. On a spacetime diagram, luxon worldlines trace the boundary of the light cone itself. Their four-momentum is lightlike or null, with invariant mass squared equal to zero ($m² = 0$).

3. Tachyons: Beyond the Light Cone

Tachyons are hypothetical particles with imaginary rest mass that always travel faster than the speed of light. The name comes from the Greek "tachys," meaning swift. No tachyon has ever been directly detected, but their existence is not forbidden by special relativity. Rather, relativity predicts exactly how such a particle would behave if it existed.

For a tachyon, $m² < 0$, meaning the rest mass is an imaginary number. Despite this seemingly exotic property, the tachyon's energy and momentum remain real and observable. Setting $m² = -\mu²$ (where $\mu$ is a real number), the energy-momentum relation becomes:

The Lorentz factor for a tachyon uses $v > c$, which makes the quantity under the square root negative. The result is that $\gamma$ becomes imaginary, but when multiplied by the imaginary mass, produces a real energy. The peculiar consequence is that tachyons behave as the mirror image of bradyons: as a tachyon loses energy, it speeds up. A tachyon with zero energy would travel at infinite velocity. Conversely, infinite energy would be required to slow a tachyon down to the speed of light. The light barrier works in both directions.

Tachyon worldlines are always spacelike, lying outside the light cone. Their four-momentum has a negative invariant mass squared ($m² < 0$). To learn more about the physics of tachyons specifically, see our comprehensive guide on what tachyons are and the mathematical framework behind them.

4. The Energy-Momentum Diagram

The three particle classes are most clearly visualized on an energy-momentum diagram, where energy $E$ is plotted against momentum $p$. The diagram reveals three distinct geometric regions separated by the light cone:

This diagram makes an essential point visible: no continuous transformation can carry a particle from one region to another. A bradyon cannot be smoothly accelerated through the light cone to become a tachyon. The three classes are topologically separated. This separation is Lorentz invariant, meaning all observers in all reference frames agree on which class a given particle belongs to.

5. Who Named Them

The modern terminology was established during the 1960s renaissance of interest in superluminal particles. In 1962, physicists Olexa-Myron Bilaniuk, V. K. Deshpande, and E. C. George Sudarshan at Syracuse University published the first rigorous analysis of faster-than-light particles within the framework of special relativity. They initially referred to these as "meta-particles."

Gerald Feinberg at Columbia University coined the word "tachyon" in his landmark 1967 paper "Possibility of Faster-Than-Light Particles." He derived it from the Greek "tachys" (swift) to parallel the existing term "baryon" (from "barys," heavy). Bilaniuk and Sudarshan subsequently introduced the complementary terms "bradyon" (from "bradys," slow) and "luxon" (from Latin "lux," light) to complete the three-way classification. The alternative term "tardyon" (from Latin "tardus," slow) is occasionally used in place of bradyon.

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