Minichan

A tachyon /ˈtæki.ɒn/ or tachyonic particle is a hypothetical particle that always moves faster than light. The word comes from the Greek: ταχύς or tachys, meaning "swift, quick, fast, rapid", and was coined in 1967 by Gerald Feinberg. [1] The complementary particle types are called luxon (always moving at the speed of light) and bradyon (always moving slower than light), which both exist. The possibility of particles moving faster than light was first proposed by Bilaniuk, Deshpande, and George Sudarshan in 1962, although the term they used for it was "meta-particle". [2]

Most physicists think that faster-than-light particles cannot exist because they are not consistent with the known laws of physics. [3][4] If such particles did exist, they could be used to build a tachyonic antitelephone and send signals faster than light, which (according to special relativity) would lead to violations of causality. [4]

Potentially consistent theories that allow faster-than-light particles include those that break Lorentz invariance, the symmetry underlying special relativity, so that the speed of light is not a barrier.

In the 1967 paper that coined the term, [1]

Feinberg proposed that tachyonic particles could be quanta of a quantum field with negative squared mass. However, it was soon realized that excitations of such imaginary mass fields do not in fact propagate faster than light, [5] and instead represent an instability known as tachyon condensation. [3]

Nevertheless, negative squared mass fields are commonly referred to as "tachyons", [6]

and in fact have come to play an important role in modern physics.

Speed of light
From Wikipedia, the free encyclopedia
"Lightspeed" redirects here. For other uses, see Speed of light (disambiguation) and Lightspeed (disambiguation).
Speed of light
The distance from the Sun to the Earth is shown as 150 million kilometers, an approximate average. Sizes to scale.
Sunlight takes about 8 minutes 17 seconds to travel the average distance from the surface of the Sun to the Earth.
Exact values
metres per second 299792458
Planck length per Planck time
(i.e., Planck units) 1
Approximate values (to three significant digits)
kilometres per hour 1080 million (1.08×109)
miles per second 186000
miles per hour 671 million (6.71×108)
astronomical units per day 173[Note 1]
Approximate light signal travel times
Distance Time
one foot 1.0 ns
one metre 3.3 ns
from geostationary orbit to Earth 119 ms
the length of Earth's equator 134 ms
from Moon to Earth 1.3 s
from Sun to Earth (1 AU) 8.3 min
one light year 1.0 year
one parsec 3.26 years
from nearest star to Sun (1.3 pc) 4.2 years
from the nearest galaxy (the Canis Major Dwarf Galaxy) to Earth 25000 years
across the Milky Way 100000 years
from the Andromeda Galaxy (the nearest spiral galaxy) to Earth 2.5 million years
The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its value is exactly 299792458 metres per second, as the length of the metre is defined from this constant and the international standard for time.[1] According to special relativity, c is the maximum speed at which all matter and information in the universe can travel. It is the speed at which all massless particles and changes of the associated fields (including electromagnetic radiation such as light and gravitational waves) travel in vacuum. Such particles and waves travel at c regardless of the motion of the source or the inertial frame of reference of the observer. In the theory of relativity, c interrelates space and time, and also appears in the famous equation of mass–energy equivalence E = mc2.[2]

The speed at which light propagates through transparent materials, such as glass or air, is less than c. The ratio between c and the speed v at which light travels in a material is called the refractive index n of the material (n = c / v). For example, for visible light the refractive index of glass is typically around 1.5, meaning that light in glass travels at c / 1.5 ≈ 200000 km/s; the refractive index of air for visible light is about 1.0003, so the speed of light in air is about 299700 km/s or 90 km/s slower than c.

For many practical purposes, light and other electromagnetic waves will appear to propagate instantaneously, but for long distances and very sensitive measurements, their finite speed has noticeable effects. In communicating with distant space probes, it can take minutes to hours for a message to get from Earth to the spacecraft, or vice versa. The light seen from stars left them many years ago, allowing the study of the history of the universe by looking at distant objects. The finite speed of light also limits the theoretical maximum speed of computers, since information must be sent within the computer from chip to chip. The speed of light can be used with time of flight measurements to measure large distances to high precision.

Ole Rømer first demonstrated in 1676 that light travels at a finite speed (as opposed to instantaneously) by studying the apparent motion of Jupiter's moon Io. In 1865, James Clerk Maxwell proposed that light was an electromagnetic wave, and therefore travelled at the speed c appearing in his theory of electromagnetism.[3] In 1905, Albert Einstein postulated that the speed of light with respect to any inertial frame is independent of the motion of the light source,[4] and explored the consequences of that postulate by deriving the special theory of relativity and showing that the parameter c had relevance outside of the context of light and electromagnetism. After centuries of increasingly precise measurements, in 1975 the speed of light was known to be 299792458 m/s with a measurement uncertainty of 4 parts per billion. In 1983, the metre was redefined in the International System of Units (SI) as the distance travelled by light in vacuum in 1/299792458 of a second. As a result, the numerical value of c in metres per second is now fixed exactly by the definition of the metre.[5]

Contents [hide]
1 Numerical value, notation, and units
2 Fundamental role in physics
2.1 Upper limit on speeds
3 Faster-than-light observations and experiments
4 Propagation of light
4.1 In a medium
5 Practical effects of finiteness
5.1 Small scales
5.2 Large distances on Earth
5.3 Spaceflights and astronomy
5.4 Distance measurement
5.5 High-frequency trading
6 Measurement
6.1 Astronomical measurements
6.2 Time of flight techniques
6.3 Electromagnetic constants
6.4 Cavity resonance
6.5 Interferometry
7 History
7.1 Early history
7.2 First measurement attempts
7.3 Connections with electromagnetism
7.4 "Luminiferous aether"
7.5 Special relativity
7.6 Increased accuracy of c and redefinition of the metre and second
7.7 Defining the speed of light as an explicit constant
8 See also
9 Notes
10 References
11 Further reading
11.1 Historical references
11.2 Modern references
12 External links
Numerical value, notation, and units[edit]
The speed of light in vacuum is usually denoted by a lowercase c, for "constant" or the Latin celeritas (meaning "swiftness"). Originally, the symbol V was used for the speed of light, introduced by James Clerk Maxwell in 1865. In 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch had used c for a different constant later shown to equal √2 times the speed of light in vacuum. In 1894, Paul Drude redefined c with its modern meaning. Einstein used V in his original German-language papers on special relativity in 1905, but in 1907 he switched to c, which by then had become the standard symbol.[6][7]

Sometimes c is used for the speed of waves in any material medium, and c0 for the speed of light in vacuum.[8] This subscripted notation, which is endorsed in official SI literature,[5] has the same form as other related constants: namely, μ0 for the vacuum permeability or magnetic constant, ε0 for the vacuum permittivity or electric constant, and Z0 for the impedance of free space. This article uses c exclusively for the speed of light in vacuum.

Since 1983, the metre has been defined in the International System of Units (SI) as the distance light travels in vacuum in 1/299792458 of a second. This definition fixes the speed of light in vacuum at exactly 299792458 m/s.[9][10][11] As a dimensional physical constant, the numerical value of c is different for different unit systems.[Note 2] In branches of physics in which c appears often, such as in relativity, it is common to use systems of natural units of measurement or the geometrized unit system where c = 1.[13][14] Using these units, c does not appear explicitly because multiplication or division by 1 does not affect the result.

Fundamental role in physics[edit]
See also: Introduction to special relativity, Special relativity and One-way speed of light
The speed at which light waves propagate in vacuum is independent both of the motion of the wave source and of the inertial frame of reference of the observer.[Note 3] This invariance of the speed of light was postulated by Einstein in 1905,[4] after being motivated by Maxwell's theory of electromagnetism and the lack of evidence for the luminiferous aether;[15] it has since been consistently confirmed by many experiments. It is only possible to verify experimentally that the two-way speed of light (for example, from a source to a mirror and back again) is frame-independent, because it is impossible to measure the one-way speed of light (for example, from a source to a distant detector) without some convention as to how clocks at the source and at the detector should be synchronized. However, by adopting Einstein synchronization for the clocks, the one-way speed of light becomes equal to the two-way speed of light by definition.[14][16] The special theory of relativity explores the consequences of this invariance of c with the assumption that the laws of physics are the same in all inertial frames of reference.[17][18] One consequence is that c is the speed at which all massless particles and waves, including light, must travel in vacuum.

γ starts at 1 when v equals zero and stays nearly constant for small v's, then it sharply curves upwards and has a vertical asymptote, diverging to positive infinity as v approaches c.
The Lorentz factor γ as a function of velocity. It starts at 1 and approaches infinity as v approaches c.
Special relativity has many counterintuitive and experimentally verified implications.[19] These include the equivalence of mass and energy (E = mc2), length contraction (moving objects shorten),[Note 4] and time dilation (moving clocks run more slowly). The factor γ by which lengths contract and times dilate is known as the Lorentz factor and is given by γ = (1 − v2/c2)−1/2, where v is the speed of the object. The difference of γ from 1 is negligible for speeds much slower than c, such as most everyday speeds—in which case special relativity is closely approximated by Galilean relativity—but it increases at relativistic speeds and diverges to infinity as v approaches c.

The results of special relativity can be summarized by treating space and time as a unified structure known as spacetime (with c relating the units of space and time), and requiring that physical theories satisfy a special symmetry called Lorentz invariance, whose mathematical formulation contains the parameter c.[22] Lorentz invariance is an almost universal assumption for modern physical theories, such as quantum electrodynamics, quantum chromodynamics, the Standard Model of particle physics, and general relativity. As such, the parameter c is ubiquitous in modern physics, appearing in many contexts that are unrelated to light. For example, general relativity predicts that c is also the speed of gravity and of gravitational waves.[23][24] In non-inertial frames of reference (gravitationally curved space or accelerated reference frames), the local speed of light is constant and equal to c, but the speed of light along a trajectory of finite length can differ from c, depending on how distances and times are defined.[25]

It is generally assumed that fundamental constants such as c have the same value throughout spacetime, meaning that they do not depend on location and do not vary with time. However, it has been suggested in various theories that the speed of light may have changed over time.[26][27] No conclusive evidence for such changes has been found, but they remain the subject of ongoing research.[28][29]

It also is generally assumed that the speed of light is isotropic, meaning that it has the same value regardless of the direction in which it is measured. Observations of the emissions from nuclear energy levels as a function of the orientation of the emitting nuclei in a magnetic field (see Hughes–Drever experiment), and of rotating optical resonators (see Resonator experiments) have put stringent limits on the possible two-way anisotropy.[30][31]

Upper limit on speeds[edit]
According to special relativity, the energy of an object with rest mass m and speed v is given by γmc2, where γ is the Lorentz factor defined above. When v is zero, γ is equal to one, giving rise to the famous E = mc2 formula for mass–energy equivalence. The γ factor approaches infinity as v approaches c, and it would take an infinite amount of energy to accelerate an object with mass to the speed of light. The speed of light is the upper limit for the speeds of objects with positive rest mass. This is experimentally established in many tests of relativistic energy and momentum.[32]

Three pairs of coordinate axes are depicted with the same origin A; in the green frame, the x axis is horizontal and the ct axis is vertical; in the red frame, the x′ axis is slightly skewed upwards, and the ct′ axis slightly skewed rightwards, relative to the green axes; in the blue frame, the x′′ axis is somewhat skewed downwards, and the ct′′ axis somewhat skewed leftwards, relative to the green axes. A point B on the green x axis, to the left of A, has zero ct, positive ct′, and negative ct′′.
Event A precedes B in the red frame, is simultaneous with B in the green frame, and follows B in the blue frame.
More generally, it is normally impossible for information or energy to travel faster than c. One argument for this follows from the counter-intuitive implication of special relativity known as the relativity of simultaneity. If the spatial distance between two events A and B is greater than the time interval between them multiplied by c then there are frames of reference in which A precedes B, others in which B precedes A, and others in which they are simultaneous. As a result, if something were travelling faster than c relative to an inertial frame of reference, it would be travelling backwards in time relative to another frame, and causality would be violated.[Note 5][34] In such a frame of reference, an "effect" could be observed before its "cause". Such a violation of causality has never been recorded,[16] and would lead to paradoxes such as the tachyonic antitelephone.[35]

Faster-than-light observations and experiments[edit]
Main article: Faster-than-light
Further information: Superluminal motion
There are situations in which it may seem that matter, energy, or information travels at speeds greater than c, but they do not. For example, as is discussed in the propagation of light in a medium section below, many wave velocities can exceed c. For example, the phase velocity of X-rays through most glasses can routinely exceed c,[36] but phase velocity does not determine the velocity at which waves convey information.[37]

If a laser beam is swept quickly across a distant object, the spot of light can move faster than c, although the initial movement of the spot is delayed because of the time it takes light to get to the distant object at the speed c. However, the only physical entities that are moving are the laser and its emitted light, which travels at the speed c from the laser to the various positions of the spot. Similarly, a shadow projected onto a distant object can be made to move faster than c, after a delay in time.[38] In neither case does any matter, energy, or information travel faster than light.[39]

The rate of change in the distance between two objects in a frame of reference with respect to which both are moving (their closing speed) may have a value in excess of c. However, this does not represent the speed of any single object as measured in a single inertial frame.[39]

Certain quantum effects appear to be transmitted instantaneously and therefore faster than c, as in the EPR paradox. An example involves the quantum states of two particles that can be entangled. Until either of the particles is observed, they exist in a superposition of two quantum states. If the particles are separated and one particle's quantum state is observed, the other particle's quantum state is determined instantaneously (i.e., faster than light could travel from one particle to the other). However, it is impossible to control which quantum state the first particle will take on when it is observed, so information cannot be transmitted in this manner.[39][40]

Another quantum effect that predicts the occurrence of faster-than-light speeds is called the Hartman effect; under certain conditions the time needed for a virtual particle to tunnel through a barrier is constant, regardless of the thickness of the barrier.[41][42] This could result in a virtual particle crossing a large gap faster-than-light. However, no information can be sent using this effect.[43]

So-called superluminal motion is seen in certain astronomical objects,[44] such as the relativistic jets of radio galaxies and quasars. However, these jets are not moving at speeds in excess of the speed of light: the apparent superluminal motion is a projection effect caused by objects moving near the speed of light and approaching Earth at a small angle to the line of sight: since the light which was emitted when the jet was farther away took longer to reach the Earth, the time between two successive observations corresponds to a longer time between the instants at which the light rays were emitted.[45]

In models of the expanding universe, the farther galaxies are from each other, the faster they drift apart. This receding is not due to motion through space, but rather to the expansion of space itself.[39] For example, galaxies far away from Earth appear to be moving away from the Earth with a speed proportional to their distances. Beyond a boundary called the Hubble sphere, the rate at which their distance from Earth increases becomes greater than the speed of light.[46]

Propagation of light[edit]
In classical physics, light is described as a type of electromagnetic wave. The classical behaviour of the electromagnetic field is described by Maxwell's equations, which predict that the speed c with which electromagnetic waves (such as light) propagate through the vacuum is related to the electric constant ε0 and the magnetic constant μ0 by the equation c = 1/√ε0μ0.[47] In modern quantum physics, the electromagnetic field is described by the theory of quantum electrodynamics (QED). In this theory, light is described by the fundamental excitations (or quanta) of the electromagnetic field, called photons. In QED, photons are massless particles and thus, according to special relativity, they travel at the speed of light in vacuum.

Extensions of QED in which the photon has a mass have been considered. In such a theory, its speed would depend on its frequency, and the invariant speed c of special relativity would then be the upper limit of the speed of light in vacuum.[25] No variation of the speed of light with frequency has been observed in rigorous testing,[48][49][50] putting stringent limits on the mass of the photon. The limit obtained depends on the model used: if the massive photon is described by Proca theory,[51] the experimental upper bound for its mass is about 10−57 grams;[52] if photon mass is generated by a Higgs mechanism, the experimental upper limit is less sharp, m ≤ 10−14 eV/c2 [51] (roughly 2 × 10−47 g).

Another reason for the speed of light to vary with its frequency would be the failure of special relativity to apply to arbitrarily small scales, as predicted by some proposed theories of quantum gravity. In 2009, the observation of the spectrum of gamma-ray burst GRB 090510 did not find any difference in the speeds of photons of different energies, confirming that Lorentz invariance is verified at least down to the scale of the Planck length (lP = √ħG/c3 ≈ 1.6163×10−35 m) divided by 1.2.[53]

In a medium[edit]
See also: Refractive index
In a medium, light usually does not propagate at a speed equal to c; further, different types of light wave will travel at different speeds. The speed at which the individual crests and troughs of a plane wave (a wave filling the whole space, with only one frequency) propagate is called the phase velocity vp. An actual physical signal with a finite extent (a pulse of light) travels at a different speed. The largest part of the pulse travels at the group velocity vg, and its earliest part travels at the front velocity vf.

A modulated wave moves from left to right. There are three points marked with a dot: A blue dot at a node of the carrier wave, a green dot at the maximum of the envelope, and a red dot at the front of the envelope.
The blue dot moves at the speed of the ripples, the phase velocity; the green dot moves with the speed of the envelope, the group velocity; and the red dot moves with the speed of the foremost part of the pulse, the front velocity
The phase velocity is important in determining how a light wave travels through a material or from one material to another. It is often represented in terms of a refractive index. The refractive index of a material is defined as the ratio of c to the phase velocity vp in the material: larger indices of refraction indicate lower speeds. The refractive index of a material may depend on the light's frequency, intensity, polarization, or direction of propagation; in many cases, though, it can be treated as a material-dependent constant. The refractive index of air is approximately 1.0003.[54] Denser media, such as water,[55] glass,[56] and diamond,[57] have refractive indexes of around 1.3, 1.5 and 2.4, respectively, for visible light. In exotic materials like Bose–Einstein condensates near absolute zero, the effective speed of light may be only a few metres per second. However, this represents absorption and re-radiation delay between atoms, as do all slower-than-c speeds in material substances. As an extreme example of this, light "slowing" in matter, two independent teams of physicists claimed to bring light to a "complete standstill" by passing it through a Bose–Einstein Condensate of the element rubidium, one team at Harvard University and the Rowland Institute for Science in Cambridge, Mass., and the other at the Harvard–Smithsonian Center for Astrophysics, also in Cambridge. However, the popular description of light being "stopped" in these experiments refers only to light being stored in the excited states of atoms, then re-emitted at an arbitrarily later time, as stimulated by a second laser pulse. During the time it had "stopped," it had ceased to be light. This type of behaviour is generally microscopically true of all transparent media which "slow" the speed of light.[58]

In transparent materials, the refractive index generally is greater than 1, meaning that the phase velocity is less than c. In other materials, it is possible for the refractive index to become smaller than 1 for some frequencies; in some exotic materials it is even possible for the index of refraction to become negative.[59] The requirement that causality is not violated implies that the real and imaginary parts of the dielectric constant of any material, corresponding respectively to the index of refraction and to the attenuation coefficient, are linked by the Kramers–Kronig relations.[60] In practical terms, this means that in a material with refractive index less than 1, the absorption of the wave is so quick that no signal can be sent faster than c.

A pulse with different group and phase velocities (which occurs if the phase velocity is not the same for all the frequencies of the pulse) smears out over time, a process known as dispersion. Certain materials have an exceptionally low (or even zero) group velocity for light waves, a phenomenon called slow light, which has been confirmed in various experiments.[61][62][63][64] The opposite, group velocities exceeding c, has also been shown in experiment.[65] It should even be possible for the group velocity to become infinite or negative, with pulses travelling instantaneously or backwards in time.[66]

None of these options, however, allow information to be transmitted faster than c. It is impossible to transmit information with a light pulse any faster than the speed of the earliest part of the pulse (the front velocity). It can be shown that this is (under certain assumptions) always equal to c.[66]

It is possible for a particle to travel through a medium faster than the phase velocity of light in that medium (but still slower than c). When a charged particle does that in a dielectric material, the electromagnetic equivalent of a shock wave, known as Cherenkov radiation, is emitted.[67]

Practical effects of finiteness[edit]
The speed of light is of relevance to communications: the one-way and round-trip delay time are greater than zero. This applies from small to astronomical scales. On the other hand, some techniques depend on the finite speed of light, for example in distance measurements.

Small scales[edit]
In supercomputers, the speed of light imposes a limit on how quickly data can be sent between processors. If a processor operates at 1 gigahertz, a signal can only travel a maximum of about 30 centimetres (1 ft) in a single cycle. Processors must therefore be placed close to each other to minimize communication latencies; this can cause difficulty with cooling. If clock frequencies continue to increase, the speed of light will eventually become a limiting factor for the internal design of single chips.[68]

Large distances on Earth[edit]
For example, given the equatorial circumference of the Earth is about 40075 km and c about 300000 km/s, the theoretical shortest time for a piece of information to travel half the globe along the surface is about 67 milliseconds. When light is travelling around the globe in an optical fibre, the actual transit time is longer, in part because the speed of light is slower by about 35% in an optical fibre, depending on its refractive index n.[69] Furthermore, straight lines rarely occur in global communications situations, and delays are created when the signal passes through an electronic switch or signal regenerator.[70]