Speed of light

A laser beam in the air traveling to about 99.97% of the speed of light in the vacuum (the air cooling rate is about 1,0003)

The speed of light in a vacuum is a universal constant with the value 299 792 458 m/s, although it is usually close to 3·10⁸ m/s. It is symbolized by the letter c, from the Latin celéritās (in Spanish, speed or speed).

The value of the speed of light in a vacuum was officially included in the International System of Units as a constant on October 21, 1983, thus making the meter a unit derived from this constant. It is also used in the definition of the light year, a unit of length equivalent to 9.46·10¹⁵ m, since the speed of light can also be expressed as 9.46·10 ¹⁵ m/year.

The speed through a medium other than a "vacuum" it depends on its electrical permittivity, its magnetic permeability, and other electromagnetic characteristics. In material media, this speed is less than c and is encoded in the refractive index. In more subtle modifications of the vacuum, such as curved spaces, the Casimir effect, thermal populations or the presence of external fields, the speed of light depends on the energy density of that vacuum.

Description

According to modern physics, all electromagnetic radiation (including visible light) propagates or moves with a constant speed in a vacuum, known —although improperly^{[citation needed]}—like "speed of light" (vector magnitude), instead of "speed of light" (scalar magnitude). This is a physical constant denoted as c. The speed c is also the speed of propagation of gravity in the general theory of relativity.

A consequence that follows from the laws of electromagnetism (such as Maxwell's equations) is that the speed c of electromagnetic radiation does not depend on the speed of the object emitting such radiation. So, for example, light emitted by a very rapidly moving light source would travel with the same speed as light from a stationary source (although the color, frequency, energy, and momentum of the light will change; phenomenon known as the Doppler effect).

If this observation is combined with the principle of relativity, it follows that all observers will measure the speed of light in a vacuum as the same quantity, regardless of the observer's frame of reference or the speed of the object emitting the light. light. Because of this, c can be viewed as a fundamental physical constant. This fact, then, can be used as a basis for the theory of special relativity. The constant is speed c, rather than light itself, which is fundamental to special relativity. Thus, if light is somehow retarded to travel at a speed less than c, this will not directly affect the theory of special relativity.

Observers traveling at high speed will find that distances and times are distorted according to the Lorentz transformation. However, the transformations distort time and distance so that the speed of light remains constant. A person traveling with a speed close to c will also find that the colors of light ahead turn blue and behind turn red.

If information could travel faster than c in one frame of reference, causality would be violated: in other frames of reference, information would be received before it was sent; thus, the cause could be observed after the effect. Due to the time dilation of special relativity, the ratio of the perceived time between an outside observer and the time perceived by an observer moving closer and closer to the speed of light approaches zero. If something could move faster than light, this ratio would not be a real number. Such a violation of causality has never been observed.

Light cone. Space-time diagram, which allows to dilute the possible causality between the event A and the event B (possible causality) and between the event A and the event C (impossible cause)

A light cone defines the location that is in causal contact and those that are not. To put it another way, information propagates to and from a point in regions defined by a light cone. The interval AB in the diagram to the right is of "time type" (i.e., there is a frame of reference in which events A and B occur at the same location in space, separated only by their occurrence at different times, and if A precedes B in that frame then A precedes B by all frames: there is no frame of reference in which event A and event B occur simultaneously). Thus, it is hypothetically possible for matter (or information) to travel from A to B, so there may be a causal relationship (with A the cause and B the effect).

On the other hand, the interval AC is of "space type"^{[citation needed]} (that is, there exists a frame of reference where the event A and event C occur simultaneously). However, there are also frames in which A precedes C, or in which C precedes A. By confining a way to travel faster than light, it will not be possible for any matter (or information) to travel from A to C or from C to A. Thus there is no causal connection between A and C.

According to the current definition, adopted in 1983, the speed of light is exactly 299,792,458 m/s (approximately 3 × 10⁸ meters per second, 300,000 km/s, or 300 m per millionth of s).

The value of c defines the electrical permitivity of the vacuum (ε ε 0{displaystyle varepsilon}) in SIU units like:

ε ε 0=107/4π π c2(enA2s4kg− − 1m− − 3=Fm− − 1){displaystyle varepsilon _{0}=10^{7}/4pi {text{c}{2}{2}{2}{quad mathrm {(en~A^{2},s^{4},kg^{-1},m^{-3}=F,m^{-1}}}}}}}} }}}

The magnetic permeability of the vacuum (μ μ 0{displaystyle mu _{0}}) is not dependent on c and is defined in SIU units as:

μ μ 0=4π π 10− − 7(enkgms− − 2A− − 2=NA− − 2){displaystyle mu _{0}=4,pi ,10^{-7}quad mathrm {(en~kg,m,s^{-2},A^{-2}=N,A^{-2}}}}}} }.

These constants appear in Maxwell's equations, which describe electromagnetism and are related by:

c=1ε ε 0μ μ 0{displaystyle {text{c}}={frac {1}{sqrt {varepsilon _{0}{0}}}}}}}

Astronomical distances are usually measured in light years (which is the distance light travels in one year, approximately 9.46×10¹² km (9.46 trillion km).

Meter definition

Historically, the meter had been defined as one ten-millionth of the length of the arc of the terrestrial meridian between the north pole and the equator through Paris, with reference to the standard bar, and with reference to a wavelength of a particular frequency of light.

In 1967, the XIII General Conference on Weights and Measures defined the second of atomic time as the duration of 9,192,631,770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom, which in the actuality remains the definition of the latter.

In 1983 the General Conference on Weights and Measures decided to modify the definition of the meter as a unit of length of the International System, establishing its definition based on the speed of light:

"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."
(The metro is the length of the journey through the light in the vacuum for a time interval of 1/299 792 458 of a second)

Consequently, this adjustment made to the definition of the meter allows the speed of light to have an exact value of 299,792,458 m/s when expressed in meters/second. This modification makes practical use of one of the bases of Einstein's theory of relativity, which establishes that the magnitude of the speed of light in a vacuum is independent of the reference system used to measure it.

The motivation in changing the definition of the meter, as well as all changes in the definition of units, was to provide a precise definition of the unit that could be easily used to homogeneously calibrate devices all over the world. The standard rod was impractical in this regard, as it could not be removed from its chamber or used by two scientists at the same time. It was also prone to significant changes in its length due to temperature variations, end wear, oxidation, etc., incompatible with the accuracy necessary to establish one of the base units of the International System of units.

Communications

GPS signal delay times depending on the distance of the satellites to the observer, which allows you to calculate your position

The speed of light is of great importance for telecommunications. For example, given that the Earth's perimeter is 40,075 km (at the equator) and c is theoretically the fastest speed that a piece of information can travel, the shortest period of time to reach the other end of the globe would be 0.067 s.

Actually, the travel time is a bit longer, partly because the speed of light is about 30% slower in an optical fiber, and there are rarely any straight paths in global communications; In addition, delays occur when the signal passes through electrical switches or signal generators. In 2004, the typical signal reception delay from Australia or Japan to the United States was 0.18 s. Additionally, the speed of light affects the design of wireless communications.

The finite speed of light became apparent to everyone in the communications control between Houston Ground Control and Neil Armstrong, when he became the first man to set foot on the Moon: after each question, Houston had to wait about 3 s for the return of an answer even though the astronauts responded immediately.

Similarly, instantaneous remote control of an interplanetary ship is impossible because a ship far enough from our planet could take a few hours from sending information to the ground control center and receiving instructions.

The speed of light can also have an influence over short distances. In supercomputers, the speed of light imposes a limit on how fast data can be sent between processors. If a processor is operating at 1GHz, the signal can only travel a maximum of 300mm in a single cycle. Therefore, the processors should be placed close to each other to minimize communication delays. If clock frequencies continue to increase, the speed of light will eventually become a limiting factor for the internal design of individual chips.

Physics

Constant velocity for all reference frames

It is important to note that the speed of light is not a speed limit in the conventional sense. An observer chasing a ray of light would measure it by moving parallel to himself traveling at the same speed as if he were a stationary observer. This is because the speed measured by this observer depends not only on the difference in the distances traveled by him and the ray, but also on his own time, which slows down with the speed of the observer. The slowing down of time or temporal dilation for the observer is such that he will always perceive a ray of light moving at the same speed.

Most individuals are used to the speed addition rule: if two cars approach each other from opposite directions, each traveling at a speed of 50 km/h, one would expect (with a high degree of accuracy) that each car would perceive the other at a combined speed of 50 + 50=100 km/h. This would be correct in all cases if we could ignore that the physical measure of elapsed time is relative to the observer's state of motion.

However, at speeds close to the speed of light, it becomes clear from experimental results that this rule cannot be applied due to time dilation. Two ships approaching each other, each traveling at 90% of the speed of light relative to a third observer between them, will miss each other at 90% + 90%=180% of the speed of light. Instead, each will perceive the other as approaching at less than 99.5% the speed of light. This result is given by Einstein's velocity addition formula:

u=v+w1+vwc2{displaystyle u={cfrac {v+w}{1+{cfrac {vw}{{{{{text{c}}}{{2}}}}}}}}}}}

where v and w are the speeds of the ships as observed by a third observer, and u is the speed of either ships observed by the other.

Contrary to natural intuition, no matter how fast one observer is moving relative to another observer, both will measure the speed of an oncoming ray of light with the same constant value, the speed of light.

The above equation was derived by Einstein from his special theory of relativity, which takes the principle of relativity as its main premise. This principle (originally proposed by Galileo Galilei) requires physical laws to act in the same way in all frames of reference.

Since Maxwell's equations directly give a speed of light, it should be the same for every observer; a consequence that sounded obviously wrong to the physicists of the 19th century, who assumed that the speed of light given by the theory of Maxwell is valid in relation to the "light ether".

But the Michelson and Morley experiment, perhaps the most famous and useful experiment in the history of physics, could not find this ether, suggesting instead that the speed of light is a constant in all frames of reference.

Although it is not known if Einstein knew the results of Michelson's and Morley's experiments, he assumed that the speed of light was constant, understood it as a reaffirmation of Galileo's principle of relativity, and deduced the consequences, now known as the theory of special relativity, which include the above self-intuitive formula.

Physical speed and coordinate speed of light

It should be kept in mind, especially if non-inertial reference frames are considered, that the experimental observation of light constancy refers to the physical speed of light. The difference between the two magnitudes caused certain misunderstandings to the theorists of the beginning of the century XX. Thus Pauli came to write:

You can no longer speak of the universal character of the record of the speed of light in the vacuum since the speed of light is constant only in Galileo's reference systems

However, that comment is true predicate of the coordinate speed of light (whose definition does not involve the metric coefficients of the metric tensor), however, an adequate definition of physical speed of light involving the components of the metric tensor of non-inertial reference systems leads to the fact that the physical speed is constant.

Interaction with transparent materials

Refrection of light

The refractive index of a material indicates how slow the speed of light is in that medium compared to a vacuum. The decrease in the speed of light in materials can cause the phenomenon called refraction, as can be observed in a prism crossed by a ray of white light, forming a spectrum of colors and producing its dispersion.

When passing through materials, light propagates at a speed less than c, expressed by the ratio called the “refractive index” of the material.

The speed of light in air is only slightly less than c. Denser media, such as water and glass, can slow light down more, to fractions such as 3/4 and 2/3 of c. This slowdown is also responsible for bending light (modifying its path according to a bend with a given angle) at an interface between two materials with different indices, a phenomenon known as refraction. This is because within transparent media, light as an electromagnetic wave interacts with matter, which in turn produces response fields, and light through the medium is the result of the initial wave and the response of The matter. This electromagnetic wave that propagates in the material has a speed of propagation less than that of light in a vacuum. The refractive index "n" of a medium is given by the following expression, where "v" is the speed of light in that medium (since, as already noted, the speed of light in a medium is less than the speed of light in a vacuum):

n=cv{displaystyle n={frac {text{c}{v}}}}

Since the speed of light in materials depends on the refractive index, and the refractive index depends on the frequency of light, light at different frequencies travels at different speeds through the same material. This can cause distortion in electromagnetic waves made up of multiple frequencies; a phenomenon called dispersion.

The angles of incidence (i) and refraction (r) between two media, and the refractive indices, are related by Snell's Law. Angles are measured with respect to the normal vector to the surface between the media:

ni⋅ ⋅ sen α α i=nr⋅ ⋅ sen α α r{displaystyle n_{i}cdot operatorname {sen} {alpha _{i}=n_{r}cdot operatorname {sen} {s} {alpha _{r}}}}

At a microscopic scale, considering electromagnetic radiation as a particle, refraction is caused by a continuous absorption and re-emission of the photons that make up the light through the atoms or molecules through which it is passing. In a sense, light itself travels only through the void between these atoms, and is impeded by the atoms. Alternatively, considering electromagnetic radiation as a wave, the charges of each atom (primarily electrons) interfere with the electric and electromagnetic fields of the radiation, retarding its progress.

Faster than light

Recent experimental evidence shows that it is possible for the group speed of light to exceed c. An experiment made the group velocity of laser beams travel extremely short distances through cesium atoms at 300 times c. However, it is not possible to use this technique to transfer information faster than c: the speed of information transfer depends on the forward velocity (the speed at which the first increment of a pulse above zero moves it forward) and the product of the bundled velocity and the forward velocity is equal to the square of the normal speed of light in the material.

Exceeding the group speed of light in this way is comparable to exceeding the speed of sound by placing people in an equidistantly spaced line, and asking everyone to shout out a word one after the other at short intervals, each measuring the time by looking at their own watch so they don't have to wait to hear the previous person's scream.

The speed of light may also appear to be exceeded in certain phenomena involving evanescent waves, such as quantum tunneling. Experiments indicate that the phase velocity of evanescent waves can exceed c; however, it would appear that neither the bundled velocity nor the forward velocity exceed c, so, again, it is not possible for information to be transmitted faster than c.

In some interpretations of quantum mechanics, quantum effects can be relayed at speeds greater than c (actually, action at a distance has long been perceived as a problem with quantum mechanics: see RPE paradox). For example, the quantum states of two particles can be linked, so that the state of one particle determines the state of another particle (in other words, one must have a spin of +½ and the other of -½). Until the particles are observed, they exist in a superposition of two quantum states (+½, –½) and (–½, +½). If the particles are separated and one of them is observed to determine its quantum state, then the quantum state of the second particle is determined automatically. If, in some interpretations of quantum mechanics, information about the quantum state is assumed to be local to a particle, then it must be concluded that the second particle takes its quantum state instantaneously, as soon as the first observation is made. However, it is impossible to control what quantum state the first particle will take when it is observed, so no information can be transmitted in this way. The laws of physics also seem to prevent information from being transmitted in more cunning ways, and this has led to the formulation of rules such as the no-cloning theorem.

The so-called superluminal motion is also seen in certain astronomical objects, such as active galaxy jets, active galaxies, and quasars. However, these jets do not actually move at speeds exceeding the speed of light: the apparent superluminal motion is a projection of the effect caused by objects moving close to the speed of light at a small angle to the viewing horizon.

Although it may sound paradoxical, shock waves may have been formed by electromagnetic radiation, since a charged particle traveling through an insulated medium disrupts the local electromagnetic field in the medium. The electrons in the atoms in the middle are displaced and polarized by the field of the charged particle, and the photons that are emitted as electrons restore themselves to equilibrium after the interruption has passed (in a conductor, the interruption can be restored without emitting a photon).

Under normal circumstances, these photons destructively interfere with each other and no radiation is detected. However, if the disruption travels faster than the photons themselves, the photons will interfere constructively and intensify the observed radiation. The result (analogous to a sonic boom) is known as Cherenkov radiation.

The ability to communicate or travel faster than light is a popular subject in science fiction. Particles traveling faster than light, tachyons, bent^{[citation needed]} by particle physics have been proposed, although they have never been observed.

Some physicists (including João Magueijo and John Moffat) have proposed that light traveled much faster in the past than it does today. This theory is known as variable speed of light, and its proponents claim that this phenomenon has the ability to better explain many cosmological puzzles than its rival theory, the inflationary model of the universe. However, this theory has not gained sufficient acceptance.

In September 2011, at the CERN facilities in Geneva, from the underground laboratory of Gran Sasso (Italy), neutrinos were observed that apparently exceeded the speed of light, reaching (60.7 ± 6.9 (stat.) ± 7.4 (sys.)) nanoseconds earlier (corresponding to about 18 meters over a total distance of 732 kilometers). From the outset, the scientific community was skeptical of the news, since several years earlier, the Milos project Fermilab in Chicago had obtained similar results that were discarded because the margin of error was too high. And sure enough, in this case, too, it turned out to be a measurement error. In February 2012, CERN scientists announced that the measurements they had been wrong due to a faulty connection.

Experiments to retard light

Refractive phenomena such as rainbows tend to slow down the speed of light in a medium (such as water, for example). In a sense, any light that travels through a medium other than a vacuum travels at a speed less than c as a result of refraction. However, certain materials have an exceptionally high refractive index: in particular, the optical density of the Bose-Einstein condensate can be very high.

In 1999, a team of scientists led by Lene Hau were able to slow a beam of light to about 17 m/s, and in 2001 they were able to momentarily stop a beam of light.

In 2003, Mikhail Lukin, together with scientists from Harvard University and the Lebedev Institute of Physics (Moscow), succeeded in completely stopping light by directing it at a mass of hot rubidium gas, whose atoms, in the words of Lukin, behaved like "small mirrors" due to interference patterns in two control beams.

It is important to mention that the speed of light tends to slow down as it travels through a medium with a density greater than vacuum, this applies to light moving through a medium such as air, water, oil, among others...

History

Until relatively recent times, the speed of light was a subject of great conjecture. Empedocles believed that light was something in motion, and that therefore some time had to elapse in his journey.

In contrast, Aristotle believed that "light is subject to the presence of something, but it is not motion." Furthermore, if light has a finite speed, it had to be immense. Aristotle stated: "The strain on our power of belief is too great to believe this."^{[citation needed]}

One of the ancient theories of vision is that light is emitted by the eye, rather than being generated by a source and reflected back at the eye. In this theory, Heron of Alexandria advanced the argument that the speed of light should be infinite, since when one opens one's eyes distant objects such as stars appear immediately. During the VI century, Boethius attempted to document the speed of light.

Islamic

The Islamic philosophers Avicenna and Alhazen believed that light had a finite speed, although other philosophers agreed with Aristotle on this point.^{[citation needed]}

Hinduism

The Ayran school of philosophy in ancient India also held that the speed of light was finite.^{[citation needed]}

Europe

Johannes Kepler believed that the speed of light is finite since empty space is not an obstacle to it. Francis Bacon argued that the speed of light is not necessarily finite, since something can travel fast enough to be perceived.

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. Because such a misalignment has not been observed, Descartes concluded that the speed of light is infinite. In fact, Descartes was convinced that if the speed of light was finite, his entire system of philosophy would be refuted.

Measuring the speed of light

The history of measuring the speed of light begins in the 12th century at the dawn of the scientific revolution. A landmark study concerning measurements of the speed of light points to a dozen different methods for determining the value of "c". Most of the early experiments to try to measure the speed of light failed. due to its high value, and only indirect measurements could be obtained from astronomical phenomena. In the XIX century, the first direct experiments to measure the speed of light could be carried out, confirming its electromagnetic nature and the equations from Maxwell.

First attempts

In 1629 Isaac Beeckman, a friend of René Descartes, proposed an experiment in which a cannon muzzle could be observed reflecting off a mirror located one mile (1.6 km) from the first. In 1638, Galileo proposed an experiment to measure the speed of light, attempting to detect a possible lapse in uncovering a lantern when viewed from a distance. René Descartes criticized this attempt as superfluous, since eclipse observation, a procedure with much greater potential for detecting a finite speed of light, had given a negative result. The Accademia del Cimento in Florence put into practice in 1667 the experiment that Galileo had devised, with the lanterns separated by one mile from each other, without observing any delay. Robert Hooke explained the negative results just as Galileo had done: by pointing out that such observations would not establish the infinite speed of light, just that it must be very great.

First measurements

In 1676 Ole Rømer made the first quantitative estimate of the speed of light by studying the motion of Jupiter's satellite Io with a telescope. It is possible to time Io's revolution due to its movements in and out of the shadow cast by Jupiter at regular intervals. Rømer observed that Io revolves around Jupiter every 42.5 h when Earth is closest to Jupiter. He also observed that, as Earth and Jupiter move apart, Io's departure from the shadow projection began progressively later than predicted. Detailed observations showed that these exit signals needed longer to reach Earth, as Earth and Jupiter drifted further apart. In this way the extra time taken by light to reach Earth could be used to deduce its speed. Six months later, Io's entries into the shadow projection were brought forward, as Earth and Jupiter moved closer to each other. Based on these observations, Rømer estimated that it would take light 22 min to cross the diameter of the Earth's orbit (that is, twice the astronomical unit); modern estimates are closer to the figure of 16 min 40 s.

At around the same time, the astronomical unit (radius of Earth's orbit around the Sun) was estimated to be about 140 million km. This data and Rømer's time estimate were combined by Christian Huygens, who considered that the speed of light was close to 1,000 Earth diameters per minute, that is, about 220,000 km/s, well below the current value. accepted, but much faster than any other physical phenomenon then known.

Isaac Newton also accepted the concept of finite velocity. In his book Opticks he exposes the most precise value of 16 minutes for light to travel the diameter of the Earth's orbit,^{[citation required]} value which he apparently deduced by himself (whether this was from Rømer's data or in some other way is unknown).

The same effect was subsequently observed by Rømer at a point in rotation with the surface of Jupiter. Later observations also showed the same effect with the other three Galilean moons, which were more difficult to observe as these moons were farther from Jupiter and cast lesser shadows on the planet.

Although by means of these observations the finite speed of light was not established to everyone's satisfaction (notably Jean-Dominique Cassini), after the observations of James Bradley (1728), the infinite speed hypothesis was fully considered. discredited. Bradley deduced that the light from stars arriving on Earth would appear to come from a slight angle, which could be calculated by comparing the speed of the Earth in its orbit with the speed of light. This so-called aberration of light was observed, estimated to be 1/200 of a degree.

Bradley calculated the speed of light to be about 301,000 km/s. This approximation is only slightly higher than the currently accepted value. The aberration effect was extensively studied in subsequent centuries, notably by Friedrich Georg Wilhelm Struve and Magnus Nyren.

Direct measurements

Fizeau-Foucault device diagram

The second successful measurement of the speed of light, the first using a terrestrial apparatus, was made by Hippolyte Fizeau in 1849. Fizeau's experiment was conceptually similar to those proposed by Beeckman and Galileo. A ray of light was directed at a mirror hundreds of meters away. On its way from the source to the mirror, the beam passed through a rotating gear. At a certain level of rotation, the beam would pass through one hole on its way out and another on its way back. But at slightly lower levels, the spoke would project onto one of the teeth and not pass through the wheel. Knowing the distance to the mirror, the number of teeth on the gear, and the rate of rotation, the speed of light could be calculated. Fizeau reported the speed of light as 313,000 km/s. Fizeau's method was later refined by Marie Alfred Cornu (1872) and Joseph Perrotin (1900), but it was the French physicist Léon Foucault who further improved Fizeau's method by replacing the gear with a rotating mirror. The value estimated by Foucault, published in 1862, was 298,000 km/s. Foucault's method was also used by Simon Newcomb and Albert Michelson, who began his long career replicating and improving this method.

In 1926, Michelson used rotating mirrors to measure the time it took for light to travel between Wilson Mountain and San Antonio Mountain in California and back. From increasingly accurate measurements, a speed of 299,796 km/s resulted.

Stationary electromagnetic waves in a resonance cavity

Another way to get the speed of light is to independently measure the frequency f{displaystyle f} and wavelength λ λ {displaystyle lambda } of an electromagnetic wave in the vacuum. The value of c can then be calculated using the relationship [chuckles]c=fλ λ ]{displaystyle [{text{c}}=flambda]. One option is to measure resonance frequency in a Resonance cavity. If your dimensions are accurately known, they can be used to determine the wavelength of a beam of light. In 1946, Louis Essen and AC Gordon-Smith used this method (the dimensions of the resonance cavity were established with a precision of about ± 0.8 microns using gauges calibrated by interferometry), obtaining a result of 299 792 ±9 kilometers/s, substantially more accurate than the values calculated using optical techniques. In 1950, repeated measurements established a result of 299 792,5 ±3.0 km/s.

Interferometric determination of length. Left: constructive interference; Right: destructive interference.

Interferometry is another method to find the wavelength of electromagnetic radiation to determine the speed of light. A coherent beam of light (e.g. a laser), with a known frequency f{displaystyle f}, it is divided following two different routes and then recombine. By adjusting the length of the route as the interference pattern is observed, carefully measuring the change in the length of the trajectory, the wavelength of light can be determined λ λ {displaystyle lambda }.

The speed of light is calculated as in the previous case, using the equation [chuckles]c=fλ λ ]{displaystyle [{text{c}}=flambda].

Before the advent of laser technology, radio coherent sources were used for interferometry measurements of the speed of light. However the interferometric method becomes less precise at short wavelengths, and the experiments were therefore limited to the precision of the long wavelength (~0.4 cm) of radio waves. Accuracy can be improved by using light with a shorter wavelength, but then it becomes difficult to directly measure its frequency. One way to avoid this problem is to start with a low-frequency signal (whose value can be accurately measured), and from this signal progressively synthesize higher-frequency signals, whose frequency can then be related to the original signal. The frequency of a laser can be set with remarkable precision, and its wavelength can then be determined using interferometry. This technique was developed by a group at the National Bureau of Standards (NBS) (later to become NIST). It was used in 1972 to measure the speed of light in a vacuum with a fractional uncertainty of 3.5 × 10^-9.

Relativity

Based on the work of James Clerk Maxwell, it is known that the velocity of electromagnetic radiation is a constant defined by the electromagnetic properties of a vacuum (dielectric constant and permeability).

In 1887, physicists Albert Michelson and Edward Morley performed the influential Michelson-Morley experiment to measure the speed of light relative to the motion of the Earth. The goal was to measure the speed of the Earth through the ether, the medium thought at the time necessary for the transmission of light. As shown in the Michelson interferometer diagram, a mirror with a silver half face was used to split a ray of monochromatic light into two rays traveling at right angles to each other. After leaving the split, each ray was reflected back and forth between the mirrors several times (the same number for each ray to give a long but equal path length; the current Michelson-Morley experiment uses more mirrors) then once. recombined produce a pattern of constructive and destructive interference.

Any minor change in the speed of light in each arm of the interferometer would change the amount of time spent in its transit, which would be observed as a change in the interference pattern. During the tests carried out, the experiment gave a null result.

Ernst Mach was among the first physicists to suggest that the result of the experiment was a refutation of the ether theory. Developments in theoretical physics had begun to provide an alternative theory, the Lorentz contraction, which explained the null result of the experiment.

It is uncertain whether Einstein knew the results of the Michelson and Morley experiments, but their null result contributed greatly to the acceptance of his theory of relativity. Einstein's theory did not require an etheric element but was completely consistent with the null result of the experiment: the ether does not exist and the speed of light is the same in every direction. The constant speed of light is one of the fundamental postulates (together with the principle of causality and the equivalence of inertial frames) of special relativity.