Speed of light
Speed of light generally refers to the propagation speed of light and other electromagnetic waves in any media. Usually, the fundamental constant of nature speed of light in vacuum is specially meant, whose meaning goes by the special theory of relativity far beyond the speed of propagation of light in vacuum.
It has been demonstrated that the speed independently of the speed of the receiver used to detect ( Michelson Morley experiment ), and the speed of the light source itself of light in a vacuum. Albert Einstein therefore postulated the vacuum speed of light c is the maximum speed at which mass can move and energy and information can be transferred in our universe. From this he developed the theory of relativity. Particles without rest mass, like the photon, always all involving mass particles move with this speed limit, always slower. As a consequence of special relativity theory (SRT ) combines the natural constant c, the previously independent concepts of energy (E) and mass (m) in the famous equivalence of mass and energy, E = mc2. Also spatial and temporal coordinates are now grouped by c spacetime and considered together in a four-dimensional space as a four-vector.
The speed of light is so high that it took a long time that the lighting of a light can be seen everywhere at once. In 1676 Ole Rømer presented a delay in the darkening of Jupiter's moon Io, depending on the position of the Earth relative to Jupiter fixed. He concluded correctly that light travels at a finite speed. The value from this deviated by only 30 % from the actual value. The measurement methods for determining the speed of light were always greater detail in the subsequent period. Since 1983, the meter is defined as the distance that light travels in 299 792 458 -th fraction of a second in a vacuum, so that the numerical value of the vacuum speed of light is permanently valid. Precise distance measurements are now directly related to the speed of light, for example, in laser rangefinders or the Global Positioning System.
The symbol ( Celeritas from Latin, speed ) is used in many cases for the different velocity of propagation in materials such as glass, air or electrical lines. Therefore, it is often made clear by word additives, if the speed of light is meant in vacuum or in a medium when it is not apparent from the context. And the index 0 () is used for the speed of light in vacuum.
Value
Before 1983, the meter was defined as the multiple of the wavelength of a specific atomic transition, and the second as the multiple of the oscillation period of the transition. The speed of light is specified in the derived units of meters per second. The 17th General Conference on Weights and Measures in 1983 this ratio is reversed. Since the relationship between the wavelength of the transition and the meter is regarded as the result of measurements. In turn, the relationship between the meter and the speed of light could be determined without measurement by a definition.
After making this determination, the speed of light in a vacuum is exactly
The exact numerical value was chosen so that it matched the best at that time measurement result. He will also remain valid if more accurate velocity measurements are possible. Such measurements then result in a more accurate determination of the length of a meter.
Natural units
Many representations of the relativistic physics enter lengths by light maturities or vice versa times through the length of the path passes through the light during this time. A light year is, then shorter one year. In these units (see Planck units) applies
And light is the dimensionless velocity of a second per second
The formula image of physical relationships simplified by this choice unit, for example, the relationship between energy and momentum of a particle of mass is no longer, but then.
Who wants to win back from an equation in natural units, the equation in the SI system, each summand must be multiplied by so many factors that both sides of the equation and each term have the same SI units. For example, in the SI system, the energy, the unit of mass times the square of a speed and a pulse, the unit of mass times a velocity. Thus, in the formula on the right side in the SI system sizes of the same unit, energy times energy, are shown on the left, you must therefore use the squared mass and the square pulse is multiplied by. Thus we obtain the valid in the SI system equation
Technical significance
Since all electromagnetic waves travel at the speed of light, it is important for telecommunications. On Earth, the maximum distance ( along the surface ) of two places Around 20 000 km (half the circumference of the earth ). The shortest time for an electromagnetic signal to go through this route, is just 67 milliseconds. The actual transmission time is longer, however. At atmospheric transmission, the wave is reflected in the different layers of the atmosphere and on the ground and has so to travel a longer path. In the transmission fiber optic cables in the speed of light is approximately 30 percent smaller than in a vacuum. In addition, delays occur through the electronic switching elements.
Microprocessors today work with clock frequencies in the order of a few gigahertz. The period of oscillation at 1 GHz is 1 nanosecond. During this time an electrical signal sets ie a maximum of just under 30 inches back - that's the order of the dimensions of a motherboard of a personal computer. Designers must therefore take into account runtime effects in the development of printed circuit boards for such electronics.
Geostationary satellites are located 35,786 km above the equator. To get an answer on telephone or television signals in this way, the signal must have at least 144 000 kilometers: from the transmitter to the satellite, then to the receiver, then the response, and the signal passes back the same way. Pure duration is about half a second.
Space probes are located at their destinations often many millions or billions of miles from Earth. Even with the speed of light, the radio signals from several minutes to hours to them on the go. The answer needs again as long back to Earth. Extraterrestrial vehicles such as the Mars rover Opportunity, therefore, must be able to control yourself and to recognize dangers, as the ground station can respond only minutes later to incidents.
Speed of light and electrodynamics
From the Maxwell equations it follows that the electric and magnetic fields oscillate and thereby carry energy through empty space. In this case, the fields obey a wave equation, similar to that for mechanical waves and water waves. The electromagnetic waves transfer energy and information, which is used in technical applications for radio, radar or laser.
The speed of electromagnetic waves in a vacuum, according to the Maxwell equations, the inverse of the root of the product of the electric field and the constant magnetic field constant
This resulted with the then known values for and the value of 310,740 km / s It concluded Maxwell 1865:
" This velocity is so close to the speed of light, so that we have a strong reason to believe that the light itself (including radiant heat and other radiation, if it exists ), an electromagnetic wave. "
Maxwell's conjecture has been confirmed without exception in all observations.
A medium in the two field constants are adjusted by the material, which is taken into account by the factors relative permittivity and relative permeability. Both depend on the frequency. The speed of light in the medium is therefore
The ratio of the speed of light in vacuum to that in a medium the refractive index of the medium. His connection with the relative permittivity and the relative permeability is also called Maxwellian relation:
Refers to the phase velocity in the medium. This is identical to the group velocity with which only propagates a wave packet in a vacuum. In the media, these rates can differ drastically. A refractive index less than one indicates only so that the maxima of the wave faster than progress. It does not mean that in this material information is faster than forwarded.
Speed of light in matter
In light matter is slower than that in vacuum and that is true, as has been derived above, for material with the refractive index n (> 1), that is. This is consistent with the notion that photons are absorbed by the molecules and is sent again. Although they run between the molecules as fast as in a vacuum, but the interaction with the molecules that acts as effective " breaks," she slowed down. ( However, this illustrative image can not be used to calculate the optical properties of solid or liquid body. )
In the lower atmosphere, the speed of light is about 0.28 ‰ smaller than the vacuum ( or about 299,710 km / s), in water it is approximately 225,000 km / s ( -25 %) and in glasses with a high optical density 160 000 km / s ( -47 %).
In some media, such as Bose -Einstein condensates or photonic crystals, there is a very large dispersion for certain wavelengths. Light propagates in them slowed significantly from. So could bring light in 1999 to a group velocity of about 61 km / h, the Danish physicist Lene Research Group Hau year.
Borders two transparent media each other, the light speed of the two different media causes the refraction of light at the interface. Since the speed of light in the medium also depends on the wavelength of the light, light of different colors is refracted differently and splits white light into its different color components to. This effect can be observed directly, eg by means of a prism.
In a medium particles can travel faster than light. If they are electrically charged, such as electrons or protons, while the Cherenkov effect occurs: the particles emit light, such as a supersonic fast plane drags the sonic boom behind him. This is observable for example in swimming pool reactors. In them there is water between the fuel assemblies. The beta radiation from the cleavage products is from electrons that are faster than the speed of light in water. The Cherenkov light emitted by them can turn blue the water.
The Cherenkov effect is used in particle detectors for the detection of fast charged particles.
Speed of light and particle physics
Particles without mass move always and in every inertial system the speed of light. The best-known massless particles showing this property, is the photon. It mediates the electromagnetic interaction, which determines a large part of the physics of everyday life. More massless particles are the gluons, which Vermittlerteilchen of the strong interaction in the Standard Model of particle physics. Particles with a non-zero mass are always slower than the speed of light. If it accelerates them, their energy increases due to the relativistic energy-momentum relationship in accordance
Here, the velocity of the particle in relation to the inertial system which is selected for the description of the process. The closer the absolute value of the particle velocity at the speed of light, the more the ratio is approaching a value of 1 and the root expression is getting smaller. Total energy is thus greater, the more the particle approaches the speed of light. The additional energy is needed for the operation of the acceleration. With finite high energy so you can indeed accelerate particles close to the speed of light. However, they can not reach.
The predicted by the theory of relativity context of power and speed has been demonstrated in various experiments.
He has, among other things impact on the technology of particle accelerators. The orbital period of, for example, circling in a synchrotron packet of electrons hardly changes with further acceleration; the synchronization of the individual accelerating alternating fields can therefore be constant. However, they must be continuously adapted to the increasing speed during heavy particles, which are supplied to a lower speed.
Superluminal
There are several approaches to the speculative existence of particles which are moving faster than the speed of light. One example is as a Tachyon designated hypothetical particles. According to relativity theory but tachyon can not interact with normal matter: otherwise one could not, for all observers alike to distinguish between cause and effect. The theoretical foundations of the tachyon concept are controversial. Experimental evidence of tachyons not succeeded so far.
In addition, in recent years attracted Publications special attention, have claimed to have achieved faster than light, see for example measurements of neutrino speed. But either it was shown that the apparent superluminal signal transmission by a misinterpretation of the data originated ( faster than light jets, superluminares tunnels ). In other cases, the measurements could not be reproduced independent repetitions.
Historical background
Speculation about finiteness
The question of whether the light propagates infinitely fast or if it has a finite speed, was already in the ancient philosophy of interest. Light creates a kilometers in just three microseconds. With the observation possibilities of antiquity, a light beam is thus inevitably seemingly at the moment of its creation at the same time already at his destination.
Already Empedocles ( 450 BC ) believed nevertheless already that light is something that would be in motion and therefore need time to travel distances. Aristotle said, however, the light come here from the mere presence of objects, but is not in motion. He stated that the speed must be so enormous failing that they lie beyond the human imagination. Because of its prestige and influence of Aristotle's theory met with general acceptance.
An ancient theory of vision was assumed that the light required for seeing is emitted from the eye ( still colloquially: "lose sight " for blind ). An object should therefore be seen when the light rays from the eye träfen it. Building on this idea also advocated Heron of Alexandria the Aristotelian theory. He stated that the speed of light must be infinite, since you yourself can see the distant stars, once you open your eyes.
In the Oriental world, however, the idea of a finite speed of light was prevalent. In particular, the Persian philosopher and scientist Avicenna and Alhazen believed (both around 1000 ), that the light has a finite speed. Their supporters were, however, against the followers of Aristotle's theory in the minority.
At the beginning of the 17th century believed the astronomer Johannes Kepler, that the speed of light, at least in the vacuum is infinite, since empty space for light does not represent an obstacle. Here already appears on the idea that the speed of a light beam from the crossed medium could be dependent.
Francis Bacon argued that the light need not necessarily be infinitely fast, but perhaps only faster than noticeable.
René Descartes started from an infinitely large speed of light. Sun, Moon and Earth during a solar eclipse are in a line. Descartes argued that these bodies would not be an observer at this time apparently in series when the speed of light is finite. Since such an effect has never been observed, he saw himself confirmed in his assumption. Descartes believed so strongly in an infinitely large speed of light, that he was convinced that his world view would collapse if they were finite.
This contrasts with the theories of Isaac Newton and Christiaan Huygens with finite speed of light in 1700. Newton saw light as a stream of particles, while Huygens pointed light as a wave. Both were able to explain the law of refraction, by proportional ( Newton ) or inverse proportion ( Huygens ) set off for the speed of light to the refractive index. Newton's idea was refuted after observed interference and diffraction in the 19th century and the speed in media could be measured.
Since the first measurement of the speed of light admitted Huygens time that was much too high in his opinion, as that body mass they could reach, he struck with the ether, an elastic (not visible and measurable ) background medium before, the spread of the permit of waves, similar to the sound in the air.
Measurement of the speed of light
Galileo Galilei tried in 1600 was the first to measure the speed of light using scientific methods, by positioning himself and a mate with one signal lantern on two hills with a known distance. The assistant should promptly return Galileo signal. After deduction of reaction time of his assistants he hoped to measure the speed of light, as he had already successfully measured with a similar method, the speed of sound. To his amazement, remaining after deduction of the reaction time of the agents no longer measurable time; which is also not ( measurable) changed when the distance was increased to a maximum possible sight of the lanterns. Isaac Beeckman proposed in 1629 before a modified version of the experiment, in which the light should be reflected by a mirror. Descartes criticized such experiments as superfluous as accurate observations with the help of solar eclipses had already been carried out and had provided a negative result.
Nevertheless, the Accademia del Cimento in Florence in 1667 repeated the experiment of Galileo, where the lamps were situated about a mile away from each other. Re was no delay is observed. This was confirmed by Descartes ' assumption of an infinitely fast propagation of light; Galileo and Robert Hooke suggested the result, however, so that the speed of light is very high and could not be determined with this experiment.
The first successful estimation of the speed of light, the Danish astronomer Ole Rømer succeeded in 1676. He examined the movement of Jupiter's moon Io with his telescope. From the A - or exiting Jupiter's shadow, the mean orbital period of the moon could be determined to be about 42.5 hours. This value can be the time of the eclipse of the moon predict. But Rømer observed that the calculated values did not coincide exactly with the times of the input or exit from the shadow of Jupiter: In one year the moon was going on only increasing, then increasingly after. Rømer pointed this time shift by a different transit time of the light depending on the distance between the moon Io and Earth. He concluded that the light is not instantaneous, but propagates with a finite, but very high speed. He gave to the Earth's orbit diameter for a period of light of 22 min. The correct value is shorter ( 16 min 38 s ). Rømer had to extrapolate from his measurements (without the required statement to specify ) because Jupiter and Io is not observable in the area of greatest distance from the earth, because the sun is between. Since Rømer did not know the diameter of Earth's orbit, he did not specify a value for the speed of light. This did two years later, Christiaan Huygens first. He referred the runtime specification of Rømer on the randomly about right given by Cassini in 1673 Earth's orbit diameter of 280 million kilometers, came as the speed of light, 213,000 km / s Because both values were inaccurate, more the calculated velocity by about a quarter of today's value.
James Bradley was 1728 other astronomical method by certain fluctuations in the positions of stars at an angle of 20 " during the revolution of the earth around the sun ( aberration ( astronomy) ). Its measurements was an attempt to observe the parallax of fixed stars in order to determine their distances. From Bradley calculated that the light 10 210 times faster than the Earth in its orbit is ( measurement error 2 %). Its measurement ( published in 1729 ) was at that time as further evidence for a finite speed of light and - simultaneously - regarded as the Copernican system. From his observations resulted in a value of 301,000 km / s For the calculation he needed the path velocity of the earth and for them again the Earth's orbit radius.
Cassini had determined the Earth's orbital radius from the Marsparallaxe. This was criticized at the time by Edmund Halley. He suggested instead that Venus passages 1761 and 1769 to use it. Through their analysis they did the first time, the absolute magnitude of the planetary system (see Astronomical unit ) and could be calculated by known " light Distances " the speed of light to about 5 % accuracy.
The first underground determining the speed of light succeeded Armand Fizeau with the gear method. He sent 1849 light by a rotating gear on a several kilometers distant mirror reflecting it back through the gear. Depending on how quickly rotates the gear drops the reflected light which has passed through on the way there is a gap of gear, either on a tooth, or it again passes through a gap, and only then you see it. Fizeau came then to a 5% to a high value.
Léon Foucault in 1850 improved the method further by significantly shortened the distances measured with the rotating mirror method. So that he could first prove the material dependence of the speed of light: light propagates in other media more slowly than in air. In the experiment, light is incident on a rotating mirror. From this it is deflected onto a fixed mirror, where it is reflected back to the rotating mirror. Since the rotating mirror but has been further rotated, the light beam is no longer reflected on the starting point. By measuring the displacement of the point it is possible to determine in a known rotational frequency and known intervals, the speed of light. Foucault published his results in 1862 and gave to c to 298 000 kilometers per second.
Simon Newcomb and Albert Michelson built again on Foucault apparatus and improved the principle again. 1926 Michelson used in California also rotating prism mirror to send a beam of light from Mount Wilson to Mount San Antonio and back. He received 299,796 km / s, which corresponds almost exactly to the current market value; the deviation is less than 0.002%.
For the constant velocity of light
Initial considerations
James Bradley was able to determine not only with his studies on the aberration of 1728 the speed of light itself, but also for the first time make statements about their constancy. He observed that the aberration for all stars in the same line of sight during a year varies in an identical manner. From this he concluded that the rate arrives with the starlight on the Earth, as part of its measuring accuracy of about one percent of all stars are the same.
In order to clarify whether these Eintreffgeschwindigkeit depends on whether the earth moves on its path around the sun on a star to or away from it, this measurement accuracy, however, was not enough. This question first examined François Arago in 1810 based on the measurement of the deflection of starlight in a glass prism. According to the then-accepted corpuscular theory of light he expected a change of this angle in a measurable magnitude, since adding the speed of the incident star light to the Earth on its way around the sun. However, it showed during the year no measurable variation of the deflection angle. Arago explained this result with the hypothesis that the star light is a mixture of different speeds is, while the human eye can perceive it only one. Present, however, its measurement can be regarded as the first experimental proof of the constancy of the speed of light.
With the rise of the idea of light as a wave phenomenon formulated Augustin Fresnel in 1818 a different interpretation of the Arago experiment. Then the analogy concluded between mechanical waves and light waves an the idea that light waves must propagate in a certain medium, the ether so-called, as also water waves propagate in the water. The ether should remain representative of the reference point of a preferred inertial frame. Fresnel declared the result of Arago by assuming that the ether will carried inside of matter in part, in this case in the prism used. The degree of entrainment would depend appropriately on the refractive index.
Michelson - Morley experiment
1887 resulted Albert Michelson and Edward Morley a significant experiment for determining the speed of the earth relative to this assumed by ether. To the dependence of the light transit times was examined by the state of motion of the ether. The experiment showed, contrary to expectation always the same lifetimes. Repetitions of the experiment at different stages of the Erdumlaufs around the sun always lead to the same result. An explanation based on a long-range Äthermitführung through the earth as a whole failed because there is no aberration in stars would be perpendicular to the direction of motion of the earth in this case.
A compatible with Maxwell's electrodynamics solution was reached with the length contraction proposed by George FitzGerald and Hendrik Lorentz. Lorentz and Henri Poincaré developed this hypothesis by introducing the time dilation on, however, they combined this with the assumption of a hypothetical ether whose state of motion would have been in principle not be determined. This means that in this theory, the velocity of light is "real" only in the ether system is constant regardless of the movement of the source and the observer. This means, among other things, that the Maxwell's equations should take the usual form only in the ether system. However, this was considered from the Lorentz and Poincaré by the introduction of the Lorentz transformation, that the "apparent" speed of light is constant in all other frames of reference and thus each can claim to rest in the ether. ( The Lorentz transformation was therefore interpreted as a mathematical construction, while Einstein ( 1905) on their basis should revolutionize the entire previous ideas about the structure of space-time, see below). Poincaré introduced in 1904 yet fixed, the main feature of Lorentz 's theory was the Unüberschreitbarkeit the speed of light for all observers, regardless of their state of motion relative to the ether (see Lorentz ether theory ). This means that even for Poincaré existed the ether.
However, was a theory in which the ether system was indeed accepted as existent, but remained undetectable, very unsatisfactory. A solution to the dilemma was Einstein ( 1905) with the special theory of relativity, by giving up the conventional notions of space and time and replaced by the principle of relativity and the constancy of light as starting points or postulates of his theory. This solution was formally identical with the theory of HA Lorentz, however, she came as an emission theory with no "ether" from. The constant light he took the lorentz between ether, as he stated in 1910, where he declared contrary to Poincaré and Lorentz, that precisely because of the equality of the reference systems and thus the Undetectability of the ether, the ether concept was at all pointless. In 1912, he summed up this way:
"It is well known that the principle of relativity alone a theory of transformation laws of space and time can not be established. This depends known to the relativity of the terms " simultaneity " and " shape of moving bodies " together. To fill this gap, I led the HA Lorentz's theory of the stationary luminiferous ether borrowed principle of the constancy of the speed of light one that contains as well as the principle of relativity, a physical condition, which appeared justified by the relevant experiences (experiments of Fizeau, Rowland, etc.). "
The independence of the speed of light, the speed of the uniformly moving observer is thus based on the theory of relativity. This theory has been widely accepted for decades because of many very accurate experiments.
Independence of the source
With the Michelson - Morley experiment, although the constancy of the speed of light for a comoving observer with the light source was confirmed, however. No way for a non- comoving with the source observer Because the experiment can also be explained by an emission theory that the speed of light in all reference systems only constant relative to the emission source ( ie, in systems where the source moves at ± v, the light would thus with c ± v spread ). Albert Einstein also moved before 1905 such a hypothesis briefly considering what the reason was that he was the MM experiment, although always used as a confirmation of the principle of relativity, but not as a confirmation of the constancy of light in his writings.
However, an emission theory would require a complete reformulation of electrodynamics, while the great success of Maxwell's theory said. The emission theory was disproved experimentally. For example, would have to turn out distorted from the Earth observed orbits of double stars at different speeds of light, but this was not observed. The decay of with approximately c moving π0 mesons the resulting photons would assume the velocity of the mesons and should move almost double the speed of light, but this was not the case. And the Sagnac effect demonstrates the independence of the speed of light by the movement of the source. All of these experiments can be explained by the special theory of relativity, which states, inter alia: recon light does not light.