What is a tachyon?
A tachyon is a pretend particle that scientists dreamed up: one that always zooms faster than light. Nobody has ever found one, and most scientists think there aren’t any. But thinking about them is a brilliant way to discover how strange and wonderful the rules of space and time really are.
A tachyon is a hypothetical particle that always travels faster than light. None has ever been detected, and most physicists think they don’t exist. They’re worth understanding anyway, because working out what they would do shows you exactly how Einstein’s relativity holds the universe’s cause and effect together.
A tachyon is a hypothetical particle that always travels faster than light. None has ever been detected, and most physicists doubt they exist. Relativity does not quite rule them out, though, and following that loophole through is one of the clearest ways to see how space, time and cause and effect fit together.
A tachyon is a hypothetical particle with spacelike four-momentum: m² < 0, so |v| > c in every inertial frame. None has been observed. Special relativity admits the kinematics; what fails is a consistent causal interpretation of tachyon signals, and in quantum field theory a tachyonic mode signals an unstable vacuum rather than a new particle.
“The limiting velocity is c, but a limit has two sides.”
1The speed limit
Light is the fastest thing there is. It could zip around the Earth more than seven times in one second.
Here’s the odd part: you can push something faster and faster, but you can never quite get it to the speed of light. It isn’t like a car running out of road. It’s more as if every push works a little less well than the one before. Near light speed, a giant push only adds a tiny bit more speed. To reach light speed exactly, you’d need a push bigger than all the energy in the universe, and then bigger than that, forever.
Light itself is allowed to go that fast only because it has no weight at all. Anything with even a speck of weight is stuck below the limit.
Where this picture is too simple: things don’t really get “heavier” or harder to push in the way a shopping trolley does. The cost goes up because of how space and time themselves work. But “each push buys less speed” is exactly right.
Light in empty space travels at about 300,000 km every second. We call that speed c. It’s fast enough to go around the Earth about seven and a half times in a second.
In everyday life, energy and speed are simply linked: double the speed, four times the energy. Near c that stops being true. Einstein’s relativity says the energy of a moving object is its rest energy (the famous mc²) multiplied by a number called gamma, γ, which depends on speed:
- At half the speed of light, γ is about 1.15.
- At 90 %, about 2.3.
- At 99 %, about 7.1.
- At 99.99 %, about 71.
The closer you get, the faster γ climbs, and at exactly c it would be infinite. No amount of energy gets you there. Light gets to travel at c only because it has no mass at all: it never had to speed up.
Light in a vacuum travels at c, exactly 299,792,458 meters per second (the meter is defined from it). Anything with mass can approach that speed but never reach it.
The reason is energy. A body of mass m moving at speed v has total energy γmc², where γ = 1/√(1 − v²/c²). At everyday speeds γ is indistinguishable from 1. Near c it grows without limit: γ is about 7 at 0.99c, about 22 at 0.999c and about 71 at 0.9999c. Each extra step toward c costs more than all the steps before it, and reaching c would cost infinite energy.
That isn’t an engineering problem to be solved with a better engine. It’s a statement about spacetime. Only massless things, like light, move at exactly c, and they always do. Particle accelerators see the effect directly: the Large Hadron Collider pours energy into protons that are already within a hair of c, and almost all of it goes into energy rather than speed.
For a particle of rest mass m, E = γmc² and p = γmv with γ = (1 − β²)−1/2, β = v/c, so E² − (pc)² = (mc²)², a Lorentz invariant. For m² > 0, E → ∞ as β → 1⁻; no finite work moves a massive particle onto the light cone, and no continuous chain of boosts carries a timelike worldline into a spacelike one.
The invariant m² sorts all particles into three classes that no interaction preserving four-momentum can mix: bradyons (m² > 0, |v| < c), luxons (m² = 0, |v| = c) and, hypothetically, tachyons (m² < 0, |v| > c).
Try pulling the blue dot toward the line. See how the climb gets steeper and steeper? Now slide the purple one, the tachyon: the faster it goes, the less energy it has. It can never slow down to the line either. Drag the ordinary particle toward c: the energy shoots up. Now drag the tachyon: its energy is highest right next to c and falls as it speeds up. A tachyon that loses energy goes faster. Both branches blow up at c, from opposite sides. A tachyon would need infinite energy to slow down to c, and as it radiates energy away it speeds up, toward infinite speed at zero energy. Plotted: E/(|m|c²) = 1/√|1 − β²| on both branches. For the tachyon, dE/dβ < 0 everywhere on β > 1; the β → ∞ limit is the “transcendent” state with E = 0, p = |m|c, which is frame-dependent (Bilaniuk and Sudarshan, 1969).
2The other side of the barrier
In 1962, three scientists (Bilaniuk, Deshpande and Sudarshan) asked a sneaky question. The speed of light is a wall nobody can climb over. But what if something started on the other side of the wall, and had always been faster than light?
A few years later, in 1967, a scientist called Gerald Feinberg gave it a name: tachyon, from an ancient Greek word for “swift”.
A tachyon would be a backward sort of thing. It could never slow down to light speed; that’s the same wall, from the other side. And when it lost energy, it would go faster, not slower.
Important: nobody has ever seen a tachyon. They’re an idea, a “what if”, that scientists use to test their rules. And “faster when it loses energy” isn’t like anything you know: there’s no engine or brake inside it. It’s just what the rules of speed and energy say, if you run them on the far side of the wall.
Relativity says nothing with mass can be pushed to c. In 1962, Olexa-Myron Bilaniuk, V. K. Deshpande and E. C. George Sudarshan pointed out that it doesn’t forbid something that was always faster than light. In 1967, Gerald Feinberg worked out how such particles could fit into quantum theory, and named them tachyons, from the Greek tachys, “swift”.
The math gives them a very odd property: their mass would be an imaginary number, a multiple of √−1. That sounds like nonsense, but nobody ever measures a mass directly. We measure energy and momentum, and for a tachyon those come out as ordinary, real numbers.
And they would behave backward. Push energy in, and a tachyon slows down toward c. Take energy out, and it speeds up. It can never slow all the way to c: that would need infinite energy, the same barrier as before.
Relativity forbids accelerating through c. In 1962 Olexa-Myron Bilaniuk, V. K. Deshpande and E. C. G. Sudarshan pointed out that it says nothing against particles that were never slower: created already moving faster than light, as photons are created already moving at c. In 1967 Gerald Feinberg published the first quantum field theory of such particles and gave them their name, from the Greek tachys, “swift”. (Sudarshan and colleagues were developing their own quantum theory of tachyons at the same time; it appeared in 1968.)
Put v > c into E = mc²/√(1 − v²/c²) and the square root goes negative. The formula still gives a real energy if the mass itself is imaginary, m = iμ. That’s less alarming than it sounds: mass is never measured directly, only inferred from energy and momentum, and a tachyon’s energy and momentum are real.
The same formula makes tachyons run backward. The energy is E = μc²/√(v²/c² − 1): enormous just above c, falling toward zero as the speed grows. Adding energy slows a tachyon toward c (it can never reach it), and a tachyon that loses energy speeds up.
Bilaniuk, Deshpande and Sudarshan (1962) observed that the Lorentz group leaves the spacelike region of four-momentum space invariant, so a particle with spacelike pμ stays spacelike in every frame. Feinberg (1967) constructed a free, Lorentz-invariant field for spinless tachyons and found it must be quantized with Fermi statistics, with the particle number and the no-particle state both frame-dependent. With m² = −μ²:
E = μc² / √(β² − 1), p = μβc / √(β² − 1), E² − (pc)² = −(μc²)²
so dE/dβ < 0 on β > 1, with E → ∞ as β → 1⁺ and E → 0, p → μc as β → ∞. The sign of E is not Lorentz invariant for a spacelike four-momentum, which leads directly to the next section.
3Arriving before it leaves
Here is one of the strangest true facts about the universe. Two people zooming past each other very fast don’t agree about what is happening “right now” far away. It isn’t that one of them is fooled, or that light is slow to reach them. Even after both of them work everything out carefully, their answers are different, and both are right.
That sounds as if the universe could get muddled, but there’s a rule that keeps it tidy. If something could travel between two events while going slower than light, everyone agrees which came first. A ball is thrown before it’s caught. A cake goes into the oven before it comes out baked. Nobody, however fast they’re going, sees it the other way round.
A tachyon would break that rule, because it’s faster than light. Throw one across a room, and some very fast travelers would count it landing before it was thrown.
Where this picture is too simple: you’d never notice any of this in everyday life. The disagreement only gets big for someone moving at a large slice of the speed of light, far faster than any rocket.
Picture two events. A: a flash here, at noon exactly. B: a flash on a spaceship 3 light-seconds away (about 900,000 km, more than twice as far as the Moon), one second later.
Light would need three seconds to get from A to B, so nothing slower than light could carry a message from A to B in time. Only something going three times the speed of light could make the trip.
Now relativity steps in. Observers moving relative to each other slice space and time differently: what one calls “the same moment”, the other doesn’t. For someone flying from A toward B at half the speed of light, B happens about 0.6 seconds before A. For them, the tachyon arrives before it was sent.
Compare a slower pair. Event C happens 1 light-second away, 3 seconds after A, close enough for a signal at a third of the speed of light. Every observer, at every possible speed, puts A before C. That’s the pattern: when something slower than light could link two events, their order is fixed. When only something faster than light could, the order depends on who’s watching.
This isn’t about light taking time to reach your eyes. Each observer has already subtracted that delay; the disagreement is what’s left.
In special relativity, simultaneity is relative: observers in relative motion disagree about which distant events happen at the same time. That alone doesn’t threaten cause and effect, because the disagreement has a limit. If a signal at or below the speed of light could pass between two events, so that the events are timelike or lightlike separated, every observer agrees on their order. Only spacelike events, too far apart for light to bridge in the time between them, have an order that depends on the observer.
A tachyon is exactly what would connect spacelike events. Take one sent from A at noon that reaches B, 3 light-seconds away, one second later: it is traveling at 3c. An observer moving from A toward B at more than c/3 finds that B happens before A. At c/2 the arrival comes about 0.58 s before the departure; at exactly c/3 the trip is instantaneous.
So in some frames the tachyon’s history runs backward: absorbed at B, then emitted at A. The answer Bilaniuk, Deshpande and Sudarshan gave in 1962, later called the reinterpretation principle, reads that history as an ordinary tachyon traveling from B to A, with emission and absorption swapped. Every frame’s description then stays self-consistent. But it moves the problem rather than solving it: which end sent the signal is no longer something observers agree on.
Two events separated by (Δt, Δx), seen by an observer with velocity v along x:
Δt′ = γ(Δt − vΔx/c²), γ = (1 − v²/c²)−1/2
Δt′ changes sign at v = c²Δt/Δx, which a subluminal boost can reach only if |Δx| > c|Δt|: the interval s² = c²Δt² − Δx² is negative (spacelike). For s² > 0, sgn Δt′ = sgn Δt in every inertial frame. A tachyon worldline with speed u > c has Δx = uΔt, so Δt′ = γΔt(1 − uv/c²) < 0 for v > c²/u; equivalently u′ = (u − v)/(1 − uv/c²) diverges at v = c²/u and changes sign beyond it. For u = 3c the threshold is c/3, and at v = c/2, Δt′ = (2/√3)(−½)(1 s) ≈ −0.577 s.
The energy flips in the same frames: p = Eu/c² for any particle, so E′ = γ(E − vp) = γE(1 − uv/c²) < 0 exactly when v > c²/u. The reinterpretation principle (Bilaniuk, Deshpande and Sudarshan, 1962) maps a negative-energy tachyon running backward in t′ onto a positive-energy one running forwards in the opposite direction, with emission and absorption exchanged.
Slide to the right to fly toward B. Watch B sink below A’s dotted “now” line: for you, B happened first! C never sinks, however fast you go. The dotted line is “the moment of A” for the moving observer. Past a third of the speed of light, B drops below it. C stays above at every speed, because a slower-than-light signal could reach it. This is the “active” view: the observer’s coordinates are drawn square and the events move. B (spacelike from A) crosses A’s line of simultaneity at v = c/3. C (timelike from A) cannot, because it stays inside A’s light cone, and the cone is the same for everyone. Events are Lorentz-transformed, (t′, x′) = γ(t − βx, x − βt) in units with c = 1, and slide along their invariant hyperbolae s² = const. The light cone is boost-invariant; only the spacelike event's time ordering is frame-dependent.
4The paradox: a reply before the question
So what’s the harm in a tachyon arriving a little early? Here’s the trick that makes scientists nervous.
Two friends, Alice and Bob, each have a tachyon phone. Bob is on a spaceship zooming away. Alice sends a tachyon message: “Did you get this?” Bob answers straight away with his own tachyon phone.
Because of the strange “who-goes-first” rule, Bob’s fast reply could reach Alice before she sent her question. Now imagine the reply says “Don’t send it!”, and she listens. Then she never asks, so Bob never answers, so she never gets told not to ask… This kind of puzzle is called a paradox: a story that can’t make sense whichever way you tell it.
Most scientists think the universe simply doesn’t allow it. That means tachyons can’t be used to send messages, or more likely don’t exist at all.
One tachyon arriving “early” for some observer isn’t a disaster by itself. The trouble starts when you send one back.
Alice is at home. Bob is on a ship flying away from her fast. Alice sends a tachyon message to Bob. Bob replies at once, also by tachyon. Each message is faster than light in the sender’s own frame, which is all a tachyon needs. But in Alice’s frame, Bob’s reply can travel backward in time and arrive before she sent the question.
Physicists call this the tachyonic antitelephone. Richard Tolman described the problem in 1917, and the name comes from a 1970 paper by Gregory Benford, David Book and William Newcomb. Their conclusion: if you could switch a tachyon beam on and off to send a message, you’d get exactly this paradox. So either tachyons can’t carry messages at all, or they don’t exist.
Try it below: send the message, then the reply, and watch where it lands.
A single tachyon whose emission and absorption swap order in some frame is not yet a contradiction. The reinterpretation principle can relabel that. The trouble comes from a round trip.
Alice sends a tachyon signal to Bob, who is moving away from her. Bob immediately replies by tachyon. Both signals are faster than light in their sender’s rest frame, which is all anyone could build into a transmitter. But a signal that is instantaneous in Bob’s frame runs backward in Alice’s. If Bob is moving fast enough, and the signals are fast enough, the reply reaches Alice before she sent the question.
The argument goes back to Richard Tolman in 1917. Benford, Book and Newcomb sharpened it in 1970 under the name tachyonic antitelephone: any experiment that can modulate tachyon emission, and so send a message, would produce a closed causal loop. The reinterpretation principle doesn’t save it, because it decides who sent what by the energy sign each observer sees, and the observers disagree. Alice can still decide, after receiving the reply, not to send the question. That is the grandfather paradox in miniature, and it is the main reason most physicists think tachyons cannot carry information, or do not exist.
Tolman’s argument (1917), as formalized by Benford, Book and Newcomb (1970). Units with c = 1. A is at rest at x = 0; B moves along x = L + βt. A emits a tachyon of speed u > 1 (in A’s frame) at t = 0; it reaches B at t₁ = L/(u − β). B immediately replies with speed u in B’s own frame, which by velocity addition is w = (β − u)/(1 − uβ) in A’s frame. The reply reaches x = 0 at
t₂ = L (2u − (1 + u²)β) / (u − β)²
so t₂ < 0, a reply received before the question was sent, exactly when β > 2u/(1 + u²). For u = 3 that is β > 0.6; for signals instantaneous in each sender’s frame (u → ∞) the threshold vanishes and t₂ → −βL: any relative motion at all closes the loop.
Reinterpretation fails as a resolution because it assigns emission to whichever end sees positive energy, while the experimenter’s choice to modulate the source is frame-independent. Hence the standard conclusion: tachyons, if they exist, cannot be produced or absorbed in a controllable way. In QFT the obstruction appears as noncommuting spacelike observables, or as an unstable vacuum (section 6).
3D view: drag to turn
Press the buttons one, two, three, four. Then try making Bob slower, or the messages slower, and see if you can stop the reply getting back too early. Lower the speeds and you can find settings where the reply arrives after the question. But some setting always breaks causality, and one is enough. All drawn in Alice’s frame. For signals at speed u (in each sender’s own frame), the reply arrives before the question whenever Bob’s speed exceeds 2u/(1 + u²) times c: 0.6c for signals at 3c. With instantaneous signals, any speed at all is enough. Exact two-leg calculation in A's frame with B on x = L + βct; each leg uses relativistic velocity addition from its emitter's frame. The 3D view adds a spatial axis perpendicular to the motion, so the worldlines live in (x, y, t).
5Cherenkov light: the real cousin
Nothing beats light in empty space. But light is slower inside water: it travels at only about three quarters of its top speed there. And some tiny particles can zoom through water faster than that.
When they do, they leave a glow, a beautiful blue light, because they’re outrunning light in the water. It’s a bit like a speedboat going faster than its own waves, so the waves pile up into a V shape behind it. The particle’s light piles up into a cone.
You can see this glow for real: it’s the blue light in the pools of water around some nuclear reactors. It’s named after Pavel Cherenkov, who studied it and won a Nobel Prize in 1958, sharing it with Ilya Frank and Igor Tamm, who explained it.
Remember: this is not a tachyon. The particles are still slower than light in empty space. They’re only faster than light that’s been slowed down by the water.
Light slows down in materials. In water it travels at about 75 % of c; in glass, about two thirds. A charged particle, such as a fast electron, can be slower than c but faster than light in the water.
When that happens, the particle outruns its own light, and the light piles up into a cone, just as a boat outrunning its own waves leaves a V-shaped wake, or a jet faster than sound makes a sonic boom. The cone shows up as blue light. It’s the glow in the cooling water around some research reactors and spent nuclear fuel.
It’s called Cherenkov radiation, after Pavel Cherenkov, who discovered it in 1934. He shared the 1958 Nobel Prize with Ilya Frank and Igor Tamm, who explained it.
Physicists have used this idea to hunt for tachyons. A charged tachyon would be faster than light even in empty space, so it might glow there. Searches in the 1960s and 1970s looked for faster-than-light particles in several ways; none has ever been found.
Nothing outruns light in a vacuum, but light is slower in a medium. Its speed is c/n, where n is the refractive index: about 1.33 for water, so light there travels at about 0.75c. A charged particle moving faster than c/n, but still slower than c, outruns the electromagnetic disturbance it creates. The wavefronts pile up into a cone, like a boat’s bow wave or a sonic boom, and the medium emits light, strongest toward the blue and ultraviolet. This is the blue glow around reactor cores and spent fuel in water.
Pavel Cherenkov observed it in 1934; Ilya Frank and Igor Tamm explained it in 1937, and the three shared the 1958 Nobel Prize in Physics. The light leaves at an angle θ to the particle’s path given by cos θ = 1/(nβ): no light at all below β = 1/n, and as the particle approaches c, θ opens out toward a maximum of about 41° in water. The shock front itself, the edge of the cone in the diagram, makes the complementary angle 90° − θ with the path, so it gets sharper as the light’s angle widens.
It’s the closest real thing to a tachyon, and a guide for looking for one. A charged tachyon would be faster than light even in a vacuum, so it might radiate there. Experimental searches in the 1960s and 1970s, for charged tachyons, for tachyons with missing energy and momentum, and for “precursors” arriving ahead of cosmic-ray showers, all came back empty.
A charge moving uniformly with β > 1/n(ω) in a dielectric radiates (Frank–Tamm, 1937):
d²E/dx dω = (q²/4π) μ(ω) ω (1 − 1/(β²n²(ω))), cos θc = 1/(nβ)
The ω-linear spectrum is why the light is blue. In vacuum n = 1, so radiation requires β > 1; a charged tachyon would radiate in free space, losing energy and therefore accelerating, which is one of several self-consistency problems for charged tachyons. Searches include Alväger and Kreisler (1968, photoproduction in lead, cross-section < 3 × 10−30 cm²), Baltay et al. (1970, missing mass in p̄p annihilation), cosmic-ray shower precursors and an earlier β-decay search by Alväger and Erman (1965, an unpublished Nobel Institute report; see Crowell); all were negative.
Slide the speed down until the cone disappears. That’s the moment the particle stops beating the water’s light. Now pick “empty space”: no cone, ever, because nothing ordinary beats light there. The cone appears only above the speed of light in the material, and gets more pointed as the particle gets faster, while the light it sends out leaves at a wider angle. In a vacuum it never appears: only a tachyon could make one there. Threshold β = 1/n: 0.75 in water, about 0.67 in glass, and 1 in vacuum, which an ordinary particle can never reach. θc = arccos(1/(nβ)); maximum arccos(1/n) as β → 1: 41.4° in water, 48.2° for n = 1.5.
6What “tachyonic” means today
Scientists still use the word “tachyon”, but these days it usually means something different: not a speedy particle, but a wobbly situation that can’t last.
Picture a ball balanced on top of a hill. It could sit there for a moment, but the tiniest nudge sends it rolling down to the bottom. When scientists’ equations show a “tachyon”, it usually means “you’ve balanced the ball on a hilltop”. The real answer is wherever the ball ends up after it rolls.
Something like this happens with the Higgs field, an invisible something that fills all of space. Its “hilltop” would be at zero. It rolled away from there in the very early universe, and where it settled is part of why tiny particles have weight.
In modern physics, “tachyonic” usually describes an instability, not a faster-than-light particle. When the equations for a field give a negative mass-squared around some state, that state isn’t stable: like a ball on top of a hill, any small wobble grows. The field then rolls down to a new, stable state, and the tachyon goes away.
The best-known example is the Higgs field. Around the value zero, its equations have exactly this negative mass-squared, so zero is a hilltop. The field settles at a non-zero value instead, and that settled value is what gives particles like the W and Z bosons, and the electron, their mass. The Higgs boson that was discovered at CERN in 2012 is a ripple around the settled value, and it has an ordinary, positive mass. It is not a tachyon.
In quantum field theory, a “tachyon” is usually a sign that you are expanding around the wrong state. A field whose mass-squared is negative near some value doesn’t produce faster-than-light particles; its small fluctuations grow exponentially instead of oscillating, like a ball balanced on a hilltop. The physical vacuum lies where the field rolls to.
The Higgs field is the textbook example. Its potential has a negative mass-squared term at zero field, so the symmetric point is unstable, and the field settles at a non-zero value throughout space. That value is what gives the W and Z bosons, and the quarks and charged leptons, their masses. The Higgs boson found at CERN in 2012 is an excitation around the settled value, with a positive mass of about 125 GeV/c². It is not a tachyon.
The same idea, called tachyon condensation, appears in string theory: the open strings attached to certain unstable configurations of branes have a tachyonic mode, and Ashoke Sen and others showed in the late 1990s how its rolling describes the decay of those branes.
For a scalar with V(φ) = −½μ²φ² + ¼λφ⁴, the quadratic term at φ = 0 is a tachyonic mass, m² = −μ². Linearized about φ = 0, the dispersion relation ω² = k² − μ² makes modes with k < μ grow exponentially. Modes with k > μ oscillate with group velocity k/ω > 1, yet nothing propagates outside the light cone: the retarded Green’s function of the tachyonic Klein–Gordon equation still vanishes for spacelike separation, so the instability is local in time, not a superluminal signal. The tachyon says that φ = 0 is a maximum. Expanding around the true vacuum v = μ/√λ gives a positive mass m² = 2μ².
In the Standard Model, the Higgs doublet’s potential has this form, with v ≈ 246 GeV, giving mW, mZ and the fermion Yukawa masses; the physical Higgs has mH ≈ 125 GeV. In open string theory, the tachyon on non-BPS D-branes and brane–antibrane pairs condenses; Sen’s conjectures (1998–99), checked in string field theory (Sen and Zwiebach, 1999, and later work), identify the condensed vacuum with the closed-string vacuum without the brane.
7Myths and headlines
- “Neutrinos broke the speed of light.” (OPERA, 2011)
- In 2011, a team timing tiny particles called neutrinos on a 730 km trip under the mountains, from Switzerland to Italy, thought they’d arrived about 60 billionths of a second too early. Everyone checked very carefully. It turned out to be a loose cable and a clock that ticked slightly wrong. When they fixed them, the neutrinos were exactly as fast as light, not faster. In September 2011, the OPERA experiment reported neutrinos arriving about 60 nanoseconds earlier than light would over the 730 km from CERN to Gran Sasso in Italy. The team asked others to check, and the cause turned out to be equipment: a badly connected optical fiber in the timing system and a miscalibrated clock oscillator. Repeated in 2012 with the faults fixed, the neutrinos traveled at the speed of light, within the measurement error. In September 2011 the OPERA collaboration reported muon neutrinos from CERN arriving at Gran Sasso, 730 km away, about 60.7 ns earlier than light in vacuum would. They published it as an anomaly and asked for scrutiny. In early 2012 the collaboration identified two equipment faults: a poorly connected optical fiber in the GPS timing chain, and a clock oscillator out of calibration. Measurements in 2012 with a dedicated beam found the neutrinos consistent with c, as did other Gran Sasso experiments. OPERA (arXiv:1109.4897v1) reported δt = (60.7 ± 6.9 stat ± 7.4 sys) ns, (v − c)/c = (2.48 ± 0.28 stat ± 0.30 sys) × 10−5. Its 2012 dedicated run (JHEP 01 (2013) 153) found δt = (0.6 ± 0.4 stat ± 3.0 sys) ns, −1.8 × 10−6 < (v − c)/c < 2.3 × 10−6 at 90 % CL. Independently, Cohen and Glashow (2011) showed that superluminal neutrinos would lose energy by a Cherenkov-like emission of e⁺e⁻ pairs; ICARUS (2011), on the same beam, saw none and set δ < 2.5 × 10−8 (90 % CL).
- “Cherenkov light proves things can beat light.”
- Only light that’s been slowed down by water or glass. Nothing beats light in empty space. It shows particles beating light in a material, where light is slowed. They are still slower than c. Cherenkov particles are faster than light in the medium, c/n, and always slower than c. β > 1/n, never β > 1; the radiating particle is a bradyon.
- “Quantum entanglement is faster than light.”
- Two linked particles can show matching results however far apart they are, but you can’t use that to send a message, so it doesn’t break the speed limit. Measurements on entangled particles are correlated across any distance, but neither side can choose the outcome, so no message gets through. It needs no tachyons. Entangled measurements are correlated across any distance, but the no-communication theorem shows that no choice on one side changes the statistics on the other. No information, and no tachyons, travel faster than light. Local observables at spacelike separation commute (microcausality), so the reduced density matrix on one side is independent of operations on the other: no-signaling, without any superluminal carrier.
- “Warp drives and wormholes are tachyons.”
- Those are different ideas from science fiction and math, not tachyons, and nobody has made one. Those are different hypothetical ideas about bending space itself, not particles faster than light, and none has been shown to be possible. Those are separate speculations about curved spacetime (and they need exotic negative energy); they are not tachyons, and neither is known to be physically possible. Alcubierre metrics and traversable wormholes are geometric, require violations of the energy conditions, and are unrelated to spacelike four-momentum.
8The four orbit animations
On the home page, a little light zooms around the ring next to the picture. There are four ways it can move. Here’s the idea behind each one:
The ring around the screenshot on the home page plays one of four animations. Each nods to an idea on this page; the first is a playful nod rather than tachyon physics.
- Escape velocityA drift, then a break along the tangent. Gravity, not relativity: a nod to the speed limit in section 1.Play it on the home page
- Arrives before it leavesThe far end lights up first. What some observers would see of a tachyon: section 3.Play it on the home page
- Escape, arriving firstThe same flip, applied to the jump: the reply that lands before the question in section 4.Play it on the home page
- Cherenkov lapA particle outrunning light and shedding a cone: section 5.Play it on the home page
9And the editor?
Tachyon is also the name of a computer program for writing notes. It’s named after the particle because it’s built to be super quick: it opens in the blink of an eye.
Tachyon, the Markdown editor, borrows the name for its one obsession: getting there before you do. It opens into a resident instance in 20–35 ms and paints every keystroke inside a single frame. No physics is broken in the process.
Meet the editor10Sources and further reading
- O. M. P. Bilaniuk, V. K. Deshpande, E. C. G. Sudarshan, “Meta Relativity”, American Journal of Physics 30, 718–723 (1962). doi:10.1119/1.1941773
- G. Feinberg, “Possibility of Faster-Than-Light Particles”, Physical Review 159, 1089–1105 (1967). doi:10.1103/PhysRev.159.1089
- O. M. P. Bilaniuk, E. C. G. Sudarshan, “Particles beyond the light barrier”, Physics Today 22(5), 43 (1969). doi:10.1063/1.3035574
- R. C. Tolman, The Theory of the Relativity of Motion, University of California Press (1917). archive.org
- G. A. Benford, D. L. Book, W. A. Newcomb, “The Tachyonic Antitelephone”, Physical Review D 2, 263 (1970). doi:10.1103/PhysRevD.2.263
- T. Alväger, M. N. Kreisler, “Quest for Faster-Than-Light Particles”, Physical Review 171, 1357 (1968). doi:10.1103/PhysRev.171.1357
- C. Baltay, G. Feinberg, N. Yeh, R. Linsker, “Search for Uncharged Faster-Than-Light Particles”, Physical Review D 1, 759 (1970). doi:10.1103/PhysRevD.1.759
- J. Dhar, E. C. G. Sudarshan, “Quantum Field Theory of Interacting Tachyons”, Physical Review 174, 1808 (1968). doi:10.1103/PhysRev.174.1808
- B. Crowell, Special Relativity, §4.7 “Tachyons and Faster-than-Light”, LibreTexts. phys.libretexts.org (a clear, free overview of the arguments and the experimental searches)
- The Nobel Prize in Physics 1958: P. A. Cherenkov, I. M. Frank, I. Y. Tamm. nobelprize.org
- IAEA, “What is Cherenkov Radiation?” (2026). iaea.org
- OPERA Collaboration, “Measurement of the neutrino velocity with the OPERA detector in the CNGS beam”, first version (September 22, 2011). arXiv:1109.4897v1
- OPERA Collaboration, “…using the 2012 dedicated data”, JHEP 01 (2013) 153. INSPIRE
- E. S. Reich, “Timing glitches dog neutrino claim”, Nature 483, 17 (2012). doi:10.1038/483017a
- A. G. Cohen, S. L. Glashow, “Pair Creation Constrains Superluminal Neutrino Propagation”, Physical Review Letters 107, 181803 (2011). arXiv:1109.6562
- ICARUS Collaboration, “A search for the analogue to Cherenkov radiation by high energy neutrinos at superluminal speeds in ICARUS” (2011). arXiv:1110.3763
- A. Sen, B. Zwiebach, “Tachyon condensation in string field theory”, JHEP 03 (2000) 002. arXiv:hep-th/9912249
- “tachyon”, Online Etymology Dictionary: 1967, from tachy- “swift”. etymonline.com