用户:JC1/twenty-second

光速

太阳光平均只要8分19秒即可到达地球。
准确数字
米每秒	7008299792458000000♠299792458
普朗克	1
大约数字
公里每秒	300,000
公里每小时	1,080,000,000
英里每秒	186,000
英里每小时	671,000,000
天文单位每日	173
前进某一距离所需时间
距离	时间
1英尺	1.0纳秒
1米	3.3纳秒
从地球静止轨道到地面	119毫秒
赤道长度	134毫秒
从月球到地球	1.3秒
从太阳到地球（1天文单位）	8.3分钟
从毗邻星到太阳（1.3秒差距）	4.2年
从大犬座矮星系到地球	25,000年
横越银河系	100,000年
从仙女座星系到地球	2,500,000年

光速，通常指光波传播的速度。光在真空中传播的速度，又名${\begin{smallmatrix}c\end{smallmatrix}}$，是一个于物理学中极为重要的物理常量。此值为299,792,458米每秒。其为一实数，因为秒为国际单位，而米的长度亦由光速定义。以英制单位来说，此值约为186,282尺每秒。

跟据狭义相对论，${\begin{smallmatrix}c\end{smallmatrix}}$是宇宙中所有能量、物质或信息所能达至的最高速度。${\begin{smallmatrix}c\end{smallmatrix}}$也是无质量粒子及相关的场（包括电磁波，如光）于真空中前进的速度。其亦是现时理论中预测引力波的传递速度。上述的粒子或波皆以${\begin{smallmatrix}c\end{smallmatrix}}$传递，不论来源有否运动或观察者的惯性参考系。相对论中，${\begin{smallmatrix}c\end{smallmatrix}}$与时空相关连，亦出现于质能等价公式${\begin{smallmatrix}E=mc^{2}\end{smallmatrix}}$之中。

光线传播时若通过透明的物质，如空气或水，则其速度会低于${\begin{smallmatrix}c\end{smallmatrix}}$，而该速度${\begin{smallmatrix}v\end{smallmatrix}}$与${\begin{smallmatrix}c\end{smallmatrix}}$的比例为折射率－${\begin{smallmatrix}n\end{smallmatrix}}$（${\begin{smallmatrix}n={\tfrac {c}{v}}\end{smallmatrix}}$）。例如可见光于玻璃的折射率通常约为1.5，即光于玻璃中传播时的速度为${\begin{smallmatrix}{\tfrac {c}{1.5}}\thickapprox 200,000\end{smallmatrix}}$ 公里每秒；空气的折射率约为1.0003，即光于空气中的速度比${\begin{smallmatrix}c\end{smallmatrix}}$慢约90公里每秒。

大部分情况下，光都可以被理解为“瞬间到达”，但当距离较长或要求非常精准时光的速度就显得非常重要。当与遥远的太空探测器沟通时，其需要数分钟甚至以小时计来传递讯息。由于星系之间的距离极长，所以我们看到的星光实际上由恒星于很多年前发出，使我们能借此研究宇宙的历史。光线有限的速度也限制了电脑于理论上的最高速度，因为电脑中的信息需于集成电路之间传递。最后，光速亦能用于精确测量长距离的飞行。

奥勒·罗默于1676年首次以木卫一与木星之间的掩食演示了光的速度有限。1865年，詹姆斯·克拉克·麦克斯韦提出光是一种电磁波，因此在他的理论中为光速予以${\begin{smallmatrix}c\end{smallmatrix}}$。1905年，阿尔伯特·爱因斯坦假设光速对于任何惯性系来说都是独立于其光源，并根据狭义相对论探讨了一些推论，并由此显示${\begin{smallmatrix}c\end{smallmatrix}}$不只在光和电磁方面的相关性。经过百多年来越来越精确的测量，1975年测出为约为7008299792458000000♠299792458米每秒。1983年，国际单位制将米按光速重新定义，改为每秒的299,792,458分之1。

数值、符号和单位

光在真空中传播的速度通常以${\begin{smallmatrix}c\end{smallmatrix}}$代表，而${\begin{smallmatrix}c\end{smallmatrix}}$则意为constant（常数）或拉丁文celeritas（迅捷）。一开始使用的符号为詹姆斯·克拉克·麦克斯韦于1865年发明的${\begin{smallmatrix}V\end{smallmatrix}}$。而${\begin{smallmatrix}c\end{smallmatrix}}$原本，由1856开始，鲁道夫·科尔劳施与威廉·韦伯皆用之于真空中光速的${\begin{smallmatrix}{\sqrt {2}}\end{smallmatrix}}$倍。1894年，保罗·德鲁德将其重新定义至现有意思。爱因斯坦于1905年的奇迹年论文使用${\begin{smallmatrix}V\end{smallmatrix}}$，到1907时则转用${\begin{smallmatrix}c\end{smallmatrix}}$，其后${\begin{smallmatrix}c\end{smallmatrix}}$更成为了一标准符号。

有时${\begin{smallmatrix}c\end{smallmatrix}}$用作光于任何材质中的速度，而${\begin{smallmatrix}c\end{smallmatrix}}$_{${\begin{smallmatrix}_{0}\end{smallmatrix}}$}则用于真空中的光速。此法受国际单位制官方文章认可，而同时亦存在于相关的常数，如${\begin{smallmatrix}\mu \end{smallmatrix}}$_{${\begin{smallmatrix}0\end{smallmatrix}}$}为真空磁导率、${\begin{smallmatrix}\epsilon \end{smallmatrix}}$_{${\begin{smallmatrix}0\end{smallmatrix}}$}为真空电容率、${\begin{smallmatrix}\mathrm {Z} \end{smallmatrix}}$_{${\begin{smallmatrix}0\end{smallmatrix}}$}为自由空间阻抗。此条目使用${\begin{smallmatrix}c\end{smallmatrix}}$代表真空中的光速。

国际单位制中，米定义为${\begin{smallmatrix}c\end{smallmatrix}}$的7008299792458000000♠299792458分之1秒，因此${\begin{smallmatrix}c\end{smallmatrix}}$也倒过来固定于7008299792458000000♠299792458米每秒。${\begin{smallmatrix}c\end{smallmatrix}}$的数值于不同系统也有不同数值，如英制及美制单位中，若按每寸等于2.54厘米则${\begin{smallmatrix}c\end{smallmatrix}}$为186,282英里，698码，2呎及5+21⁄127吋每秒。自然单位制中，${\begin{smallmatrix}c\end{smallmatrix}}$归一化成为${\begin{smallmatrix}c=1\end{smallmatrix}}$.在这些单位中，${\begin{smallmatrix}c\end{smallmatrix}}$并不显得精密，因为数式乘1或除1并不影响结果。

物理学中的基本作用

参见：狭义相对论

光于真空中传播的速度独立于其来源的运动模式及观察者的惯性参考系，但同时，光的频率可以因多普勒效应而改变。受到以太缺乏证据的刺激及詹姆斯·克拉克·麦克斯韦的电磁理论所激励，爱因斯坦于1905年发表光速不变性的假设，其后各项实验亦证明此理论。另外，实验只能证明光的双程速度，如从光源到镜子再反射回来，因为单程光线速度无法量度。其原因为没有方法为两边的时钟同步。然而，若使用爱因斯坦同步则可显示单程光线速度等于双程光线速度。狭义相对论利用了“各惯性参考系的物理定律相同”探讨了${\begin{smallmatrix}c\end{smallmatrix}}$不变的结果。其中之一个结果就是所有无质量粒子于太空中前进的速度固定为${\begin{smallmatrix}c\end{smallmatrix}}$。

洛伦兹因子${\begin{smallmatrix}\gamma \end{smallmatrix}}$是一个速度的函数。其由1开始，并于${\begin{smallmatrix}v\end{smallmatrix}}$接近${\begin{smallmatrix}v\end{smallmatrix}}$时接近无限。

狭义相对论有许多与直觉相反的影响，包括质能等价（${\begin{smallmatrix}E=mc^{3}\end{smallmatrix}}$）、长度收缩（当运动中的物件“测量”为较短时，他们“看来”在旋转，亦即特勒尔旋转）及时间膨胀。代表长度收缩和时间膨胀的函数${\begin{smallmatrix}\gamma \end{smallmatrix}}$称为洛伦兹因子，并由${\begin{smallmatrix}\gamma ={\frac {1}{\sqrt {1-v^{2}/c^{2}}}}\,\end{smallmatrix}}$产生，其中${\begin{smallmatrix}v\end{smallmatrix}}$是速度。当速度比${\begin{smallmatrix}c\end{smallmatrix}}$低很多时，例如日常速度，${\begin{smallmatrix}\gamma \end{smallmatrix}}$数值接近1，因此可以忽略。此时的${\begin{smallmatrix}\gamma \end{smallmatrix}}$与伽利略不变性相似，但其将于${\begin{smallmatrix}v\end{smallmatrix}}$接近${\begin{smallmatrix}c\end{smallmatrix}}$时逼近无限。

狭义相对论可以视时间及空间为一个统一结构－时空，并需要一个名为洛伦兹协变性的理论来达至对称性，而洛伦兹协变性中又包含${\begin{smallmatrix}c\end{smallmatrix}}$洛伦兹协变性以往是现代物理学中的必要假设，如量子电动力学、量子色动力学、粒子物理学的标准模型、广义相对论等。${\begin{smallmatrix}c\end{smallmatrix}}$于现代物理学中看似无处不在，然而大部分理论，却与光无关。其中如广义相对论预测${\begin{smallmatrix}c\end{smallmatrix}}$是引力波或重力的速度 。于非惯性参考系中，本地的光速是一个等于${\begin{smallmatrix}c\end{smallmatrix}}$的定量，而沿着一条有限长度的轨迹的光的速度却可以按定义了的时间及空间而与${\begin{smallmatrix}c\end{smallmatrix}}$有所不同。

通常来说，认知中${\begin{smallmatrix}c\end{smallmatrix}}$于整个时空都应为同一数值，即光的速度不依赖地点或时间。然而，有一些理论却认为光速可以改变。虽然没有证据指光速确会改变，但这个是最近热门的研究。

通常情况下亦会假定光速具有各向同性，即其于各方位测量的速度既一样。但核能级发放的过程却显示其可能为各向异性

速度上限

根据狭义相对论所说，某物件与其不变质量${\begin{smallmatrix}m\end{smallmatrix}}$及速度${\begin{smallmatrix}v\end{smallmatrix}}$由${\begin{smallmatrix}\gamma mc^{2}\end{smallmatrix}}$给出，${\begin{smallmatrix}\gamma \end{smallmatrix}}$则是上方的洛伦兹因子。当速度为0，${\begin{smallmatrix}\gamma \end{smallmatrix}}$为1，引出${\begin{smallmatrix}E=mc^{2}\end{smallmatrix}}$。由于${\begin{smallmatrix}\gamma \end{smallmatrix}}$于速度接近${\begin{smallmatrix}c\end{smallmatrix}}$时会逼近无限，故该物件将需要无限能量来加速至光速。亦因此，光速的上限为光速。此理论亦为许多测试所证实

三种可能性：先于、慢于、同步。

更普遍来说，信息或能量的速度不可能超过${\begin{smallmatrix}c\end{smallmatrix}}$。而其又引申出一个违反直觉的论点－同时性的相对性。如果事件A与B之间的距离大于时间的间距乘事件C，那么参照系将有三种：A先于B，B先于A或同步。因此，当一物件相对一惯性参考系来说比C快、其将于另一个参考系显得向后移动，而因果关系也将会颠倒。 In such a frame of reference, an "effect" could be observed before its "cause". Such a violation of causality has never been recorded, and would lead to paradoxes such as the tachyonic antitelephone.

Faster-than-light observations and experiments

主条目：Faster-than-light

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, but such waves do not convey any information.

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. In neither case does any matter, energy, or information travel faster than light.

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.

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.

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. This could result in a virtual particle crossing a large gap faster-than-light. However, no information can be sent using this effect.

So-called superluminal motion is seen in certain astronomical objects, 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.

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. 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.

In September 2011, physicists working on the OPERA experiment published results that suggested beams of neutrinos had travelled from CERN (in Geneva, Switzerland) to LNGS (at the Gran Sasso, Italy) faster than the speed of light. These findings, sometimes referred to as the faster-than-light neutrino anomaly, were subsequently determined—subject to further confirmation—to be the result of a measurement error.

Propagation of light

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. 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. No variation of the speed of light with frequency has been observed in rigorous testing, 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, the experimental upper bound for its mass is about 10⁻⁵⁷ grams; if photon mass is generated by a Higgs mechanism, the experimental upper limit is less sharp, m ≤ 10⁻¹⁴ eV/c²  (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 (l_P = √ħG/c³ ≈ 6965161630000000000♠1.6163×10⁻³⁵ 米) divided by 1.2.

In a medium

参见：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 v_p. 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 v_g, and its earliest part travels at the front velocity v_f.

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 v_p 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. Denser media, such as water, glass, and diamond, 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 meters per second. However, this represents absorption and re-radiation delay between atoms, as does 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.

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. 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. 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. The opposite, group velocities exceeding c, has also been shown in experiment. It should even be possible for the group velocity to become infinite or negative, with pulses travelling instantaneously or backwards in time.

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.

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.

Practical effects of finiteness

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

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厘米（1英尺） 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.

Large distances on Earth

For example, given the equatorial circumference of the Earth is about 40,075 km and c about 300,000 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. Furthermore, straight lines rarely occur in global communications situations, and delays are created when the signal passes through an electronic switch or signal regenerator.

Spaceflights and astronomy

A beam of light is depicted travelling between the Earth and the Moon in the time it takes a light pulse to move between them: 1.255 seconds at their mean orbital (surface-to-surface) distance. The relative sizes and separation of the Earth–Moon system are shown to scale.

Similarly, communications between the Earth and spacecraft are not instantaneous. There is a brief delay from the source to the receiver, which becomes more noticeable as distances increase. This delay was significant for communications between ground control and Apollo 8 when it became the first manned spacecraft to orbit the Moon: for every question, the ground control station had to wait at least three seconds for the answer to arrive. The communications delay between Earth and Mars can vary between five and twenty minutes depending upon the relative positions of the two planets. As a consequence of this, if a robot on the surface of Mars were to encounter a problem, its human controllers would not be aware of it until at least five minutes later, and possibly up to twenty minutes later; it would then take a further five to twenty minutes for instructions to travel from Earth to Mars.

NASA must wait several hours for information from a probe orbiting Jupiter, and if it needs to correct a navigation error, the fix will not arrive at the spacecraft for an equal amount of time, creating a risk of the correction not arriving in time.

Receiving light and other signals from distant astronomical sources can even take much longer. For example, it has taken 13 billion (13×10⁹) years for light to travel to Earth from the faraway galaxies viewed in the Hubble Ultra Deep Field images. Those photographs, taken today, capture images of the galaxies as they appeared 13 billion years ago, when the universe was less than a billion years old. The fact that more distant objects appear to be younger, due to the finite speed of light, allows astronomers to infer the evolution of stars, of galaxies, and of the universe itself.

Astronomical distances are sometimes expressed in light-years, especially in popular science publications and media. A light-year is the distance light travels in one year, around 9461 billion kilometres, 5879 billion miles, or 0.3066 parsecs. Proxima Centauri, the closest star to Earth after the Sun, is around 4.2 light-years away.

Distance measurement

Radar systems measure the distance to a target by the time it takes a radio-wave pulse to return to the radar antenna after being reflected by the target: the distance to the target is half the round-trip transit time multiplied by the speed of light. A Global Positioning System (GPS) receiver measures its distance to GPS satellites based on how long it takes for a radio signal to arrive from each satellite, and from these distances calculates the receiver's position. Because light travels about 300,000 kilometres (186,000 miles) in one second, these measurements of small fractions of a second must be very precise. The Lunar Laser Ranging Experiment, radar astronomy and the Deep Space Network determine distances to the Moon, planets and spacecraft, respectively, by measuring round-trip transit times.

Measurement

There are different ways to determine the value of c. One way is to measure the actual speed at which light waves propagate, which can be done in various astronomical and earth-based setups. However, it is also possible to determine c from other physical laws where it appears, for example, by determining the values of the electromagnetic constants ε₀ and μ₀ and using their relation to c. Historically, the most accurate results have been obtained by separately determining the frequency and wavelength of a light beam, with their product equalling c.

In 1983 the metre was defined as "the length of the path travelled by light in vacuum during a time interval of 1⁄299,792,458 of a second", fixing the value of the speed of light at 7008299792458000000♠299792458 m/s by definition, as described below. Consequently, accurate measurements of the speed of light yield an accurate realization of the metre rather than an accurate value of c.

Astronomical measurements

Outer space is a natural setting for measuring the speed of light because of its large scale and nearly perfect vacuum. Typically, one measures the time needed for light to traverse some reference distance in the solar system, such as the radius of the Earth's orbit. Historically, such measurements could be made fairly accurately, compared to how accurately the length of the reference distance is known in Earth-based units. It is customary to express the results in astronomical units (AU) per day. An astronomical unit is approximately the average distance between the Earth and Sun; it is not based on the International System of Units. Because the AU determines an actual length, and is not based upon time-of-flight like the SI units, modern measurements of the speed of light in astronomical units per day can be compared with the defined value of c in the International System of Units.

Ole Christensen Rømer used an astronomical measurement to make the first quantitative estimate of the speed of light. When measured from Earth, the periods of moons orbiting a distant planet are shorter when the Earth is approaching the planet than when the Earth is receding from it. The distance travelled by light from the planet (or its moon) to Earth is shorter when the Earth is at the point in its orbit that is closest to its planet than when the Earth is at the farthest point in its orbit, the difference in distance being the diameter of the Earth's orbit around the Sun. The observed change in the moon's orbital period is actually the difference in the time it takes light to traverse the shorter or longer distance. Rømer observed this effect for Jupiter's innermost moon Io and deduced that light takes 22 minutes to cross the diameter of the Earth's orbit.

Aberration of light: light from a distant source appears to be from a different location for a moving telescope due to the finite speed of light.

Another method is to use the aberration of light, discovered and explained by James Bradley in the 18th century. This effect results from the vector addition of the velocity of light arriving from a distant source (such as a star) and the velocity of its observer (see diagram on the right). A moving observer thus sees the light coming from a slightly different direction and consequently sees the source at a position shifted from its original position. Since the direction of the Earth's velocity changes continuously as the Earth orbits the Sun, this effect causes the apparent position of stars to move around. From the angular difference in the position of stars (maximally 20.5 arcseconds) it is possible to express the speed of light in terms of the Earth's velocity around the Sun, which with the known length of a year can be easily converted to the time needed to travel from the Sun to the Earth. In 1729, Bradley used this method to derive that light travelled 10,210 times faster than the Earth in its orbit (the modern figure is 10,066 times faster) or, equivalently, that it would take light 8 minutes 12 seconds to travel from the Sun to the Earth.

Nowadays, the "light time for unit distance"—the inverse of c, expressed in seconds per astronomical unit—is measured by comparing the time for radio signals to reach different spacecraft in the Solar System, with their position calculated from the gravitational effects of the Sun and various planets. By combining many such measurements, a best fit value for the light time per unit distance is obtained. 截至2009年 (2009-Missing required parameter 1=month!), the best estimate, as approved by the International Astronomical Union (IAU), is:

light time for unit distance: 7002499004783836000♠499.004783836(10) s

c =  = 7002173144632674000♠173.144632674(3) AU/day.

The relative uncertainty in these measurements is 0.02 parts per billion (2×10^-11), equivalent to the uncertainty in Earth-based measurements of length by interferometry. Since the metre is defined to be the length travelled by light in a certain time interval, the measurement of the light time for unit distance can also be interpreted as measuring the length of an AU in metres.

Time of flight techniques

A method of measuring the speed of light is to measure the time needed for light to travel to a mirror at a known distance and back. This is the working principle behind the Fizeau–Foucault apparatus developed by Hippolyte Fizeau and Léon Foucault.

Diagram of the Fizeau apparatus

The setup as used by Fizeau consists of a beam of light directed at a mirror 8千米（5英里） away. On the way from the source to the mirror, the beam passes through a rotating cogwheel. At a certain rate of rotation, the beam passes through one gap on the way out and another on the way back, but at slightly higher or lower rates, the beam strikes a tooth and does not pass through the wheel. Knowing the distance between the wheel and the mirror, the number of teeth on the wheel, and the rate of rotation, the speed of light can be calculated.

The method of Foucault replaces the cogwheel by a rotating mirror. Because the mirror keeps rotating while the light travels to the distant mirror and back, the light is reflected from the rotating mirror at a different angle on its way out than it is on its way back. From this difference in angle, the known speed of rotation and the distance to the distant mirror the speed of light may be calculated.

Nowadays, using oscilloscopes with time resolutions of less than one nanosecond, the speed of light can be directly measured by timing the delay of a light pulse from a laser or an LED reflected from a mirror. This method is less precise (with errors of the order of 1%) than other modern techniques, but it is sometimes used as a laboratory experiment in college physics classes.

Electromagnetic constants

An option for deriving c that does not directly depend on a measurement of the propagation of electromagnetic waves is to use the relation between c and the vacuum permittivity ε₀ and vacuum permeability μ₀ established by Maxwell's theory: c² = 1/(ε₀μ₀). The vacuum permittivity may be determined by measuring the capacitance and dimensions of a capacitor, whereas the value of the vacuum permeability is fixed at exactly 6993400000000000000♠4π×10⁻⁷ H*m-1 through the definition of the ampere. Rosa and Dorsey used this method in 1907 to find a value of 7008299710000000000♠299710±22 km/s.

Cavity resonance

Electromagnetic standing waves in a cavity.

Another way to measure the speed of light is to independently measure the frequency f and wavelength λ of an electromagnetic wave in vacuum. The value of c can then be found by using the relation c = fλ. One option is to measure the resonance frequency of a cavity resonator. If the dimensions of the resonance cavity are also known, these can be used determine the wavelength of the wave. In 1946, Louis Essen and A.C. Gordon-Smith establish the frequency for a variety of normal modes of microwaves of a microwave cavity of precisely known dimensions. The dimensions were established to an accuracy of about ±0.8 μm using gauges calibrated by interferometry. As the wavelength of the modes was known from the geometry of the cavity and from electromagnetic theory, knowledge of the associated frequencies enabled a calculation of the speed of light.

The Essen–Gordon-Smith result, 7008299792000000000♠299792±9 km/s, was substantially more precise than those found by optical techniques. By 1950, repeated measurements by Essen established a result of 7008299792500000000♠299792.5±3.0 km/s.

A household demonstration of this technique is possible, using a microwave oven and food such as marshmallows or margarine: if the turntable is removed so that the food does not move, it will cook the fastest at the antinodes (the points at which the wave amplitude is the greatest), where it will begin to melt. The distance between two such spots is half the wavelength of the microwaves; by measuring this distance and multiplying the wavelength by the microwave frequency (usually displayed on the back of the oven, typically 2450 MHz), the value of c can be calculated, "often with less than 5% error".

Interferometry

An interferometric determination of length. Left: constructive interference; Right: destructive interference.

Interferometry is another method to find the wavelength of electromagnetic radiation for determining the speed of light. A coherent beam of light (e.g. from a laser), with a known frequency (f), is split to follow two paths and then recombined. By adjusting the path length while observing the interference pattern and carefully measuring the change in path length, the wavelength of the light (λ) can be determined. The speed of light is then calculated using the equation c = λf.

Before the advent of laser technology, coherent radio sources were used for interferometry measurements of the speed of light. However interferometric determination of wavelength becomes less precise with wavelength and the experiments were thus limited in precision by the long wavelength (~0.4 cm) of the radiowaves. The precision can be improved by using light with a shorter wavelength, but then it becomes difficult to directly measure the frequency of the light. One way around this problem is to start with a low frequency signal of which the frequency can be precisely measured, and from this signal progressively synthesize higher frequency signals whose frequency can then be linked to the original signal. A laser can then be locked to the frequency, and its wavelength can be determined using interferometry. This technique was due to a group at the National Bureau of Standards (NBS) (which later became NIST). They used it in 1972 to measure the speed of light in vacuum with a fractional uncertainty of 6991350000000000000♠3.5×10⁻⁹.

History

History of measurements of c (in km/s)

1675	Rømer and Huygens, moons of Jupiter	7005220000000000000♠220000
1729	James Bradley, aberration of light	7005301000000000000♠301000
1849	Hippolyte Fizeau, toothed wheel	7005315000000000000♠315000
1862	Léon Foucault, rotating mirror	7005298000000000000♠298000±500
1907	Rosa and Dorsey, EM constants	7005299710000000000♠299710±30
1926	Albert Michelson, rotating mirror	7005299796000000000♠299796±4
1950	Essen and Gordon-Smith, cavity resonator	7005299792500000000♠299792.5±3.0
1958	K.D. Froome, radio interferometry	7005299792500000000♠299792.50±0.10
1972	Evenson et al., laser interferometry	7005299792456200000♠299792.4562±0.0011
1983	17th CGPM, definition of the metre	7005299792458000000♠299792.458 (exact)

Until the early modern period, it was not known whether light travelled instantaneously or at a very fast finite speed. The first extant recorded examination of this subject was in ancient Greece. The ancient Greeks, Muslim scholars and classical European scientists long debated this until Rømer provided the first calculation of the speed of light. Einstein's Theory of Special Relativity concluded that the speed of light is constant regardless of one's frame of reference. Since then, scientists have provided increasingly accurate measurements.

Early history

Empedocles was the first to claim that light has a finite speed. He maintained that light was something in motion, and therefore must take some time to travel. Aristotle argued, to the contrary, that "light is due to the presence of something, but it is not a movement". Euclid and Ptolemy advanced the emission theory of vision, where light is emitted from the eye, thus enabling sight. Based on that theory, Heron of Alexandria argued that the speed of light must be infinite because distant objects such as stars appear immediately upon opening the eyes.

Early Islamic philosophers initially agreed with the Aristotelian view that light had no speed of travel. In 1021, Alhazen (Ibn al-Haytham) published the Book of Optics, in which he presented a series of arguments dismissing the emission theory in favour of the now accepted intromission theory of vision, in which light moves from an object into the eye. This led Alhazen to propose that light must have a finite speed, and that the speed of light is variable, decreasing in denser bodies. He argued that light is substantial matter, the propagation of which requires time, even if this is hidden from our senses. Also in the 11th century, Abū Rayhān al-Bīrūnī agreed that light has a finite speed, and observed that the speed of light is much faster than the speed of sound.

In the 13th century, Roger Bacon argued that the speed of light in air was not infinite, using philosophical arguments backed by the writing of Alhazen and Aristotle. In the 1270s, Witelo considered the possibility of light travelling at infinite speed in vacuum, but slowing down in denser bodies.

In the early 17th century, Johannes Kepler believed that the speed of light was infinite, since empty space presents no obstacle to it. René Descartes argued that if the speed of light were finite, the Sun, Earth, and Moon would be noticeably out of alignment during a lunar eclipse. Since such misalignment had not been observed, Descartes concluded the speed of light was infinite. Descartes speculated that if the speed of light were found to be finite, his whole system of philosophy might be demolished.

First measurement attempts

In 1629, Isaac Beeckman proposed an experiment in which a person observes the flash of a cannon reflecting off a mirror about one mile (1.6 km) away. In 1638, Galileo Galilei proposed an experiment, with an apparent claim to having performed it some years earlier, to measure the speed of light by observing the delay between uncovering a lantern and its perception some distance away. He was unable to distinguish whether light travel was instantaneous or not, but concluded that if it were not, it must nevertheless be extraordinarily rapid. Galileo's experiment was carried out by the Accademia del Cimento of Florence, Italy, in 1667, with the lanterns separated by about one mile, but no delay was observed. The actual delay in this experiment would have been about 11 microseconds.

Rømer's observations of the occultations of Io from Earth

The first quantitative estimate of the speed of light was made in 1676 by Rømer (see Rømer's determination of the speed of light). From the observation that the periods of Jupiter's innermost moon Io appeared to be shorter when the Earth was approaching Jupiter than when receding from it, he concluded that light travels at a finite speed, and estimated that it takes light 22 minutes to cross the diameter of Earth's orbit. Christiaan Huygens combined this estimate with an estimate for the diameter of the Earth's orbit to obtain an estimate of speed of light of 7008220000000000000♠220000 km/s, 26% lower than the actual value.

In his 1704 book Opticks, Isaac Newton reported Rømer's calculations of the finite speed of light and gave a value of "seven or eight minutes" for the time taken for light to travel from the Sun to the Earth (the modern value is 8 minutes 19 seconds). Newton queried whether Rømer's eclipse shadows were coloured; hearing that they were not, he concluded the different colours travelled at the same speed. In 1729, James Bradley discovered the aberration of light. From this effect he determined that light must travel 10,210 times faster than the Earth in its orbit (the modern figure is 10,066 times faster) or, equivalently, that it would take light 8 minutes 12 seconds to travel from the Sun to the Earth.

Connections with electromagnetism

参见：History of electromagnetic theory和History of special relativity

In the 19th century Hippolyte Fizeau developed a method to determine the speed of light based on time-of-flight measurements on Earth and reported a value of 7008315000000000000♠315000 km/s. His method was improved upon by Léon Foucault who obtained a value of 7008298000000000000♠298000 km/s in 1862. In the year 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch measured the ratio of the electromagnetic and electrostatic units of charge, 1/√ε₀μ₀, by discharging a Leyden jar, and found that its numerical value was very close to the speed of light as measured directly by Fizeau. The following year Gustav Kirchhoff calculated that an electric signal in a resistanceless wire travels along the wire at this speed. In the early 1860s, Maxwell showed that according to the theory of electromagnetism which he was working on, that electromagnetic waves propagate in empty space at a speed equal to the above Weber/Kohrausch ratio, and drawing attention to the numerical proximity of this value to the speed of light as measured by Fizeau, he proposed that light is in fact an electromagnetic wave.

"Luminiferous aether"

Hendrik Lorentz with Albert Einstein.

It was thought at the time that empty space was filled with a background medium called the luminiferous aether in which the electromagnetic field existed. Some physicists thought that this aether acted as a preferred frame of reference for the propagation of light and therefore it should be possible to measure the motion of the Earth with respect to this medium, by measuring the isotropy of the speed of light. Beginning in the 1880s several experiments were performed to try to detect this motion, the most famous of which is the experiment performed by Albert Michelson and Edward Morley in 1887. The detected motion was always less than the observational error. Modern experiments indicate that the two-way speed of light is isotropic (the same in every direction) to within 6 nanometres per second. Because of this experiment Hendrik Lorentz proposed that the motion of the apparatus through the aether may cause the apparatus to contract along its length in the direction of motion, and he further assumed, that the time variable for moving systems must also be changed accordingly ("local time"), which led to the formulation of the Lorentz transformation. Based on Lorentz's aether theory, Henri Poincaré (1900) showed that this local time (to first order in v/c) is indicated by clocks moving in the aether, which are synchronized under the assumption of constant light speed. In 1904, he speculated that the speed of light could be a limiting velocity in dynamics, provided that the assumptions of Lorentz's theory are all confirmed. In 1905, Poincaré brought Lorentz's aether theory into full observational agreement with the principle of relativity.

Special relativity

In 1905 Einstein postulated from the outset that the speed of light in vacuum, measured by a non-accelerating observer, is independent of the motion of the source or observer. Using this and the principle of relativity as a basis he derived the special theory of relativity, in which the speed of light in vacuum c featured as a fundamental constant, also appearing in contexts unrelated to light. This made the concept of the stationary aether (to which Lorentz and Poincaré still adhered) useless and revolutionized the concepts of space and time.

Increased accuracy of c and redefinition of the metre

参见：History of the metre

In the second half of the 20th century much progress was made in increasing the accuracy of measurements of the speed of light, first by cavity resonance techniques and later by laser interferometer techniques. In 1972, using the latter method and the 1960 definition of the metre in terms of a particular spectral line of krypton-86, a group at NBS in Boulder, Colorado determined the speed of light in vacuum to be c = 7008299792456200000♠299792456.2±1.1 m/s. This was 100 times less uncertain than the previously accepted value. The remaining uncertainty was mainly related to the definition of the metre. Since similar experiments found comparable results for c, the 15th Conférence Générale des Poids et Mesures (CGPM) in 1975 recommended using the value 7008299792458000000♠299792458 m/s for the speed of light.

In 1983 the 17th CGPM redefined the metre thus, "The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second." As a result of this definition, the value of the speed of light in vacuum is exactly 7008299792458000000♠299792458 m/s and has become a defined constant in the SI system of units. Improved experimental techniques do not affect the value of the speed of light in SI units, but instead allow for a more precise realization of the definition of the metre.

See also

• Light-second

Further reading

Historical references

• Rømer, O. Démonstration touchant le mouvement de la lumière trouvé par M. Römer de l'Academie Royale des Sciences. Journal des sçavans. 1676: 223–36. （原始内容存档于2007-07-29） （French）.  引文格式1维护：未识别语文类型 (link)
  • Translated as A Demonstration concerning the Motion of Light. Philosophical Transactions of the Royal Society. 1677, (136): 893–4. （原始内容存档于2007-07-29）. 
• Halley, E. Monsieur Cassini, his New and Exact Tables for the Eclipses of the First Satellite of Jupiter, reduced to the Julian Stile and Meridian of London. Philosophical Transactions of the Royal Society. 1694, 18 (214): 237–56. doi:10.1098/rstl.1694.0048. 
• Fizeau, HL. Sur une expérience relative à la vitesse de propagation de la lumière (PDF). Comptes rendus de l'Académie des sciences. 1849, 29: 90–92, 132 （French）.  引文格式1维护：未识别语文类型 (link)
• Foucault, JL. Détermination expérimentale de la vitesse de la lumière: parallaxe du Soleil. Comptes rendus de l'Académie des sciences. 1862, 55: 501–503, 792–796 （French）.  引文格式1维护：未识别语文类型 (link)
• Michelson, AA. Experimental Determination of the Velocity of Light. Proceedings of the American Association of Advanced Science. 1878, 27: 71–77. 
• Michelson, AA; Pease, FG; Pearson, F. Measurement of the Velocity of Light in a Partial Vacuum. Astrophysical Journal. 1935, 82: 26–61. Bibcode:1935ApJ....82...26M. doi:10.1086/143655. 
• Newcomb, S. The Velocity of Light. Nature. 1886, 34 (863): 29–32. Bibcode:1886Natur..34...29.. doi:10.1038/034029c0. 
• Perrotin, J. Sur la vitesse de la lumière. Comptes rendus de l'Académie des sciences. 1900, 131: 731–4 （French）.  引文格式1维护：未识别语文类型 (link)

Modern references

• Brillouin, L. Wave propagation and group velocity. Academic Press. 1960. 
• Jackson, JD. Classical Electrodynamics 2nd. John Wiley & Sons. 1975. ISBN 0-471-30932-X. 
• Keiser, G. Optical Fiber Communications 3rd. McGraw-Hill. 2000: 32. ISBN 0-07-232101-6. 
• Ng, YJ. Quantum Foam and Quantum Gravity Phenomenology. Amelino-Camelia, G; Kowalski-Glikman, J (编). Planck Scale Effects in Astrophysics and Cosmology. Springer. 2004: 321ff. ISBN 3-540-25263-0. 
• Helmcke, J; Riehle, F. Physics behind the definition of the meter. Quinn, TJ; Leschiutta, S; Tavella, P (编). Recent advances in metrology and fundamental constants. IOS Press. 2001: 453. ISBN 1-58603-167-8. 
• Duff, MJ. Comment on time-variation of fundamental constants. 2004. arXiv:hep-th/0208093  . 

External links

• Speed of light in vacuum (National Institute of Standards and Technology, NIST)
• Definition of the metre (International Bureau of Weights and Measures, BIPM)
• Data Gallery: Michelson Speed of Light (Univariate Location Estimation) (download data gathered by A.A. Michelson)
• Subluminal (Java applet demonstrating group velocity information limits)
• De Mora Luminis at MathPages
• Light discussion on adding velocities
• Speed of Light (University of Colorado Department of Physics)
• c: Speed of Light (Sixty Symbols, University of Nottingham Department of Physics [video])
• Usenet Physics FAQ
• The Fizeau "Rapidly Rotating Toothed Wheel" Method

Template:Link FA Template:Link FA Template:Link FA zh:光速