In the standard model of particle physics and Albert Einstein's theory of special relativity, the speed of light in a vacuum ($c$) serves as an absolute cosmic speed limit for all known forms of matter and information. However, the mathematical framework of relativity does not explicitly forbid the existence of particles that always travel faster than light. These hypothetical entities are known as tachyons.
1. The Historical Origin of Tachyons
The conceptual foundation for faster-than-light (FTL) particles dates back to the early 20th century. As early as 1917, physicist Richard Tolman recognized that FTL travel within the framework of special relativity would lead to causality violations, famously articulated through the "tachyonic antitelephone" paradox.
However, the modern formalization of the tachyon concept is primarily attributed to physicist Gerald Feinberg, who coined the term in his seminal 1967 paper published in the Physical Review, titled "Possibility of Faster-Than-Light Particles." The name itself is derived from the Greek word tachys (ταχύς), meaning "swift." Feinberg hypothesized that tachyons could exist as quanta of a quantum field with an imaginary mass. Around the same time, physicists E.C.G. Sudarshan, O.M.P. Bilaniuk, and V.K. Deshpande independently developed a rigorous kinematic framework for superluminal particles, classifying all matter into three distinct categories based on their relationship to the speed of light:
- Bradyons (or Tardyons): Particles with real rest mass that always travel slower than $c$ (e.g., protons, electrons).
- Luxons: Massless particles that travel exactly at $c$ (e.g., photons, gluons).
- Tachyons: Hypothetical particles with imaginary rest mass that always travel faster than $c$.
2. The Kinematics of Imaginary Mass
To understand tachyons, one must examine the relativistic energy-momentum equation:
For a particle traveling faster than light, its momentum ($p$) and energy ($E$) must remain mathematically real for the particle to be physically observable. According to the Lorentz transformation equations, the relativistic energy of a particle is given by $E = m₀c² / √(1 - v²/c²)$.
If the velocity ($v$) is greater than $c$, the term under the square root ($1 - v²/c²$) becomes negative, resulting in an imaginary denominator. For the total energy ($E$) to remain a real number, the rest mass ($m₀$) must also be an imaginary number. When an imaginary number is divided by an imaginary number, the result is real. Thus, tachyons are mathematically defined by possessing an imaginary rest mass (a multiple of the square root of -1, or $i$).
The Inverted Energy-Velocity Relationship
One of the most counterintuitive properties of tachyons is how they respond to energy changes. For ordinary matter (bradyons), adding energy increases velocity, pushing it closer to the speed of light. For tachyons, the relationship is inverted: losing energy increases their velocity. As a tachyon's energy approaches zero, its speed approaches infinity. Conversely, as its energy approaches infinity, its speed slows down, approaching $c$ from above. Therefore, the speed of light acts as an impassable floor for tachyons, just as it acts as an impassable ceiling for ordinary matter.
3. Tachyons in Quantum Field Theory and String Theory
While isolated tachyon particles have never been observed, tachyonic fields are a critical concept in modern theoretical physics, particularly in Quantum Field Theory (QFT) and String Theory.
In QFT, a tachyon is understood not necessarily as a particle traveling faster than light, but as an indication of an instability in the system. A field with an imaginary mass (a tachyonic field) represents a configuration sitting at the local maximum of its potential energy—like a ball balanced precariously on the top of a hill.
This instability is resolved through a process known as Tachyon Condensation. The field "rolls down" the hill to reach a stable minimum, acquiring a non-zero vacuum expectation value. The most famous example of this mechanism is the Higgs field. Before spontaneous symmetry breaking in the early universe, the Higgs field was technically tachyonic (having a negative mass-squared term). As the universe cooled, the field underwent tachyon condensation, breaking electroweak symmetry and giving mass to fundamental particles.
In Bosonic String Theory, the foundational version of string theory, the lowest energy state (the ground state) of the string is a tachyon. This "tachyon problem" indicated that bosonic string theory was unstable. The issue was later resolved by the introduction of Supersymmetry, leading to Superstring Theory, which naturally eliminates the tachyonic ground state.
4. Experimental Searches and the OPERA Anomaly
For decades, experimental physicists have conducted rigorous searches for tachyonic particles using cosmic ray detectors and particle accelerators. If charged tachyons existed, they would theoretically emit Cherenkov radiation even in a perfect vacuum, as they would be traveling faster than the local speed of light (which in a vacuum is $c$). This continuous loss of energy would cause them to accelerate toward infinite speed. No such vacuum Cherenkov radiation has ever been detected.
The most famous modern intersection of experimental physics and tachyons occurred in 2011 with the OPERA neutrino anomaly. The OPERA collaboration at the Gran Sasso National Laboratory in Italy reported that muon neutrinos fired from the CERN facility in Switzerland had arrived 60 nanoseconds earlier than light would have taken to travel the same distance. For a brief period, the physics community considered the possibility that neutrinos might be tachyonic.
However, subsequent investigations revealed that the anomaly was the result of experimental measurement errors—specifically, a loose fiber optic cable connecting a GPS receiver to an electronic card, and a clock oscillator ticking slightly too fast. Once corrected, the neutrino speeds were confirmed to be consistent with the speed of light, and the tachyon hypothesis was discarded.
5. The Causality Paradox: The Tachyonic Antitelephone
The primary theoretical objection to the existence of physical tachyons is the violation of causality. In special relativity, the sequence of events depends on the observer's frame of reference. If tachyons can transmit information faster than light, it is possible to construct reference frames where a signal is received before it is sent.
This is illustrated by the tachyonic antitelephone paradox. If Alice and Bob are moving away from each other at relativistic speeds, Alice could use a tachyon transmitter to send a message to Bob. Bob, upon receiving it, immediately replies with his own tachyon transmitter. Because of the relativity of simultaneity, the mathematics dictate that Alice would receive Bob's reply before she sent her original message. This creates a fatal causal loop—what if Alice's original message was an instruction to Bob *not* to reply?
To resolve this, physicists rely on principles like Stephen Hawking's chronology protection conjecture or the idea that even if tachyonic fields exist (as in the Higgs mechanism), they cannot be used to transmit localized information or energy faster than $c$.
Conclusion
Tachyons remain an elegant mathematical curiosity and a vital theoretical tool. While physical particles hurtling through space faster than light have never been detected—and would wreak havoc on causality if they were—the underlying mathematics of imaginary mass and tachyonic fields (tachyon condensation) are absolutely central to our modern understanding of quantum field theory and the origin of mass in the universe.