Speed and nature of light

By Slawomir S. Piatek, Hamamatsu Corporation & New Jersey Institute of Technology (March 2015)


Introduction

Man has wondered about light since the beginning of time. How fast does it travel: is its speed infinite or finite? If finite, how fast is it? What is light: is it made of particles? Is it made of waves? Perhaps it is something entirely different? How do we see things around us: do eyes emit light that reflects from surroundings and comes back to the eyes, or do eyes only detect light from the surroundings? These and many other questions preoccupied the minds of countless natural philosophers, physicists, and experimenters. After millennia of debates and experiments, we now know that the speed of light, c, is finite and at 299,792,458 m/s in vacuum, it is a fundamental constant of nature. Any observer, no matter in what state of motion or location in the Universe, will always measure the speed of light to have the same value. We understand vision: eyes detect light from surroundings and produce its image in the part of the eyes called the retina. Light-sensitive nerves sample the image producing electrical signals, which the brain converts to the sensation of seeing. However, we do not yet fully understand the nature of light itself. Some phenomena such as Compton scattering or the photoelectric effect can be explained if light behaves like a stream of particles (named photons), whereas the phenomena of interference and diffraction can only be understood if we assume that light behaves like a wave. This dual behavior is known as wave-particle duality — a modern concept ascribed to light and to matter. The classical concepts of particles and waves are mutually exclusive; therefore, the idea of wave-particle duality more accurately represents the failure of the classical concepts of space, time, and matter rather than a new paradigm. The task for the future generations of scientists is to understand the nature of light and matter, and for linguists and philosophers to invent words to describe it.


This article is a brief historical account of the intellectual struggle to understand light. It focuses mainly on its two aspects, speed and nature, describing in some detail the key experiments probing these attributes.


From Antiquity, through the Dark Ages, to the Renaissance

The earliest recorded discussion of the nature and speed of light and vision dates back to Empedocles (490 – 430 BC), who argued that light travels with a finite speed, as related by Aristotle (384 – 322 BC) about a century later: "Empedocles says that the light from the Sun arrives first in the intervening space before it comes to the eye, or reaches Earth. This might plausibly seem to be the case. For whatever is moved through space, is moved from one place to another; hence, there must be a corresponding interval of time also in which it is moved from the one place to the other. But any given time is divisible into parts; so that we should assume a time when the sun's ray was not as yet seen, but was still travelling in the middle space." However, Aristotle disagreed with this view arguing that propagation is instantaneous — the speed is infinite. He based his assertion on a daily observation that the entire sky at sunrise, from the eastern to the western horizon, becomes instantaneously illuminated.


Empedocles also formulated an extramission theory of vision: one sees an object because eyes emit light which then reflects from the object and re-enters the eyes. Aristotle again disagreed, advancing an intromission theory: the act of seeing a non-luminous object occurs when light (emitted by some source) enters the eyes after reflecting from the object. Interestingly, Plato (427 – 347 BC), a teacher of Aristotle, held a view on vision that is similar to that of Empedocles.


Aristotle thought of light as a disturbance propagating through air - one of the four elements — thus, light had a wave nature. This picture of light contradicted the view of Democritus (460 – 370 BC), the founder of the atomist school of thought, who believed everything in the universe, including light, consists of some indivisible particles (atoms). Because of Aristotle's great influence on scientific thought, the majority of his contemporaries and of the future natural philosophers and scientists shared his view that the speed of light is infinite. There existed, however, several notable exceptions.


A medieval Persian natural philosopher, Avicenna (980 – 1037), made significant contributions in many branches of science, among them physics. He studied light, heat, mechanical energy, and vacuum, and wrote about concepts such as infinity. In his works, he noted, "If the perception of light is due to the emission of some sort of particles by a luminous source, the speed of light must be finite."


Avicenna's contemporary and an Arabic scholar with many interests, Alhazen (965 – 1040), studied light extensively while living in Cairo, Egypt. His major written work, The Book of Optics, had a significant impact on science. Among many phenomena and concepts considered in the book, Alhazen argued for the intromission theory of vision, finite speed and particle nature of light, and propagation of light in the form of rays. Alhazen's views on light influenced the future work of Roger Bacon (1214 – 1294), Francis Bacon (1561 – 1626), Johannes Kepler (1571 – 1630), and Pierre de Fermat (1601 – 1665).


Both Roger and Francis Bacon reasoned against the idea of the speed of light being infinite. In the words of the latter, "Even in sight, whereof the action is most rapid, it appears that there are required certain moments of time for its accomplishment ... things which by reason of the velocity of their motion cannot be seen — as when a ball is discharged from a musket." Even though almost two millennia have passed since Aristotle, the preceding statement was still the voice of the minority. About the same year, Johannes Kepler expressed the view of the majority that the speed of light is infinite arguing that space could not offer resistance to its motion. Pierre de Fermat derived mathematically the laws of reflection and refraction (Snell's Law) using what is now known as Fermat's principle of least time. The principle asserts that among all possible paths light can take from some point to another, light takes the path that requires the shortest time. Implicit to this principle is the finite speed of light.


By the mid-17th century, the development of clocks, telescopes, mirrors, light sources, and other accessories made it possible to settle the questions of the speed and nature of light in a scientific way — by performing an experiment. The rest of the article discusses in approximate chronological order the key experiments performed to determine the speed of light and to unravel its nature.


Isaac Beeckman

The first person to design and perform an experiment to determine if the speed of light is finite is Dutch natural philosopher, Isaac Beeckman (1588 – 1637). The experiment, conducted together with René Descartes (1596 – 1650) around 1626, involved detonating gunpowder in a cannon, which acted as a source of both pulsed sound and light (see Figure 1). The sound is allowed to reach an observer without any obstructions, but the light must first reflect from a distant mirror before reaching the observer. The logic of the experiment is that if the observer is next to the cannon, the sound reaches him "almost instantly," whereas the light, having to cover a much larger distance to and from the mirror, would arrive after the sound. The time delay between the two pulses depends on the known distance to the mirror and the unknown speed of light. By measuring the delay, one can determine the speed of light.


The results of the experiment were inconclusive. In hindsight, this is not surprising. Suppose that the observer is 1 m away from the cannon and the mirror is a reasonable 2 km away. Assuming the speed of sound in air is 340 m/s, the pulse of sound reaches the observer about 3 ms after the explosion, while the pulse of light after 0.013 ms. The pulse of light arrived earlier than the pulse of sound! The time difference between the two arrivals was too small to be detected by any clocks existing at the time. The mirror would have to be 450 km away for the two pulses to arrive simultaneously.



Figure 1. Beeckman's experimental setup to determine whether the speed of light is finite.


Galileo Galilei

In 1638, about twelve years after Beeckman's experiment, Galileo Galilei (1564 – 1642) used a similar technique to attempt to measure the speed of light. Figure 2 illustrates the concept.



Figure 2. Galileo Galilei's method of measuring the speed of light. Although the method was conceptually correct, it failed in practice because the time of flight was too short to be measured by any existing clocks.


Two observers, A and B, are a distance d apart (about a couple of kilometers), each holding a lantern equipped with a shutter; observer A also has a clock. Both shutters are closed at the beginning of the experiment, but observer B is instructed to open his the moment he sees light from observer A. At the instant A opens his shutter, he activates the clock. The light signal travels towards B; the moment B sees the signal, he opens his shutter. The light from B's lantern travels towards A. When A sees this light, he stops the clock. The speed of light c can be calculated from the known distance d and the measured time of flight t using Equation 1:



The roundtrip time was too short for Galileo to measure accurately with the available clocks; thus, he concluded, "I have not been able to ascertain with certainty whether the appearance of the opposite light was instantaneous or not; but if not instantaneous it is extraordinarily rapid — I should call it momentary."


Galileo's experiment uses humans as the detectors, but humans are imperfect detectors having an inherent non-instantaneous reaction time. In this experiment, reaction time is a time interval between the instant of seeing the light and opening the shutter (observer B) and seeing the light and stopping or reading the clock. Modern psychological tests estimate an average reaction time for humans to be around 250 ms; therefore, what Galileo's experiment shows is that the light's roundtrip time is less than the combined reaction times, which implies the speed is greater than about 11 km/s, or about 32 times greater than the speed of sound. Galileo's method is conceptually correct and would have succeeded had he used a detector with response time much smaller than the roundtrip time and/or used a much larger distance between the observers. For example, if observer B were located on the Moon, ignoring the impossibility of such an arrangement in Galileo's times, Galileo would have measured the speed of light with reasonable accuracy, even using humans as detectors.


René Descartes

Descartes maintained throughout his life that light has to travel with infinite speed. In support of his assertion, he noted that during a lunar eclipse, both the Sun and the Moon are observed on the opposite sides of the sky with respect to the Earth, as shown in Figure 3. The green arrows indicate the directions to the Sun and Moon in the sky as perceived by a hypothetical earthbound observer. If the speed of light is infinite, the arrows are also pointing towards the true locations of the Sun and Moon.



Figure 3. The configuration of the Sun, Earth, and Moon during a lunar eclipse. The green arrows indicate the direction where the Sun and Moon would be seen in the sky by an earthbound observer.



Figure 4. If the speed of light is finite, an earthbound observer does not see the Sun and the Moon on the opposite sides of the sky during a lunar eclipse. See the text for further discussion.


If the speed of light is finite, say, it takes one hour to cover the distance between the Earth and the Moon, then during the lunar eclipse, an earthbound observer would not see the Sun and the Moon on opposite sides. Figure 4 explains why. When the Earth is at location E, an observer on the Earth sees the Sun (assumed to be stationary) at S. Because it takes light one hour to reach location M where the Moon must be for the lunar eclipse to occur, the Moon may not be there yet; it is instead at M', one hour of orbital travel time before reaching M. When the Moon finally reaches M, it enters the Earth's shadow; however, it takes one additional hour for this information to reach the Earth, which by then moves to E', two hours of orbital motion later after being at E. To an observer on Earth when it is at E', the Sun appears to be at S and Moon at M, thus, the angle between them is less than 180 degrees — they are not on opposite sides of the sky. Because this is not observed during actual eclipses, Descartes concluded that the speed of light must be infinite.


Descartes' reasoning is correct, but the conclusion is not. The deviation of the Sun-Earth-Moon angle from 180 degrees during a lunar eclipse is very small (undetectable) because light takes a little more than one second to traverse Earth-Moon distance. The accuracy of lunar eclipse observations was not high enough to measure this deviation.


Ole Røemer

In 1675, astronomer Ole Røemer (1644 – 1710) observed that the time when Io, one of Jupiter's four Galilean moons, undergoes an eclipse depends on the configuration of the Earth, Jupiter, and the Sun. Of the four moons, Io is closest to Jupiter and has an orbital period of about 42.5 hours. Refer to Figure 5, which depicts Jupiter (red disk), Io (light brown disk) during an eclipse, Earth (blue disk) at three locations, and the Sun (yellow disk). Suppose that when Earth is closest to Jupiter (Earth-Sun-Jupiter angle is 0°), an observer on Earth sees an eclipse of Io and notes its time on an "Eclipse Clock" to be t = 0 (the arrow is straight up). If Jupiter and Earth were stationary, the eclipse would always occur at t = 0 as measured by this clock. In other words, the time between the consecutive t = 0 readings is 42.5 hours, the orbital period of Io. However, both planets revolve around the Sun with different periods; should this affect the time an eclipse is observed? Røemer found the answer to be yes.


Suppose now that the Earth-Sun-Jupiter angle is 90°. Because light from the eclipse has a longer distance to travel, the observed time of an eclipse will be delayed. The delay is greatest (about 17 minutes) when the Earth-Sun-Jupiter angle is 180° (the distance between the Earth and Jupiter is at maximum) and then decreases as the Earth moves closer to Jupiter. Røemer reasoned that the orbital period of Io should not depend on the configuration of Earth, Jupiter, and the Sun, and attributed the delay to an extra distance that light has to travel when Earth is farther from Jupiter. The maximum extra distance is the diameter of Earth's orbit; using its existing accepted value, Røemer calculated the speed of light to be around 200,000 km/s. The speed of light is finite albeit very large compared to any other speeds.



Figure 5. The observed time of the moon's eclipse depends on the distance between Earth and Jupiter because of the finiteness of the speed of light.


James Bradley

In 1728, astronomer James Bradley (1693 – 1762) discovered the aberration of stellar light while trying to detect stellar parallax (changes in the apparent positions of stars due to Earth's motion around the Sun). Despite being unsuccessful in uncovering stellar parallax, his discovery of the aberration of stellar light allowed him to estimate the speed of light to be around 301,000 km/s, a value that is much closer to the modern value than the estimate made by Røemer. The three panels in Figure 6 give a non-relativistic explanation for the aberration of starlight using falling rain as an analogy.



Figure 6. Non-relativistic explanation of the aberration of starlight discovered by James Bradley in 1728.


Refer to panel (a) in Figure 6, which shows a stationary observer experiencing a steadily falling rain with a downward speed v. In panel (b), the observer now moves to the left with a constant speed V; in the reference frame of the observer, the direction of the falling rain is no longer vertical but makes an angle α with respect to the vertical, where α is related to the two speeds by the equation tan(α) = V/v. Panel (c) depicts a star that is exactly overhead; however, because of Earth's revolution around the Sun and rotation, this star will not appear overhead. Instead, its location will be tilted in the direction of the observer's motion by an angle α. Bradley found the angle to be around 20 (1 = 1°/3600), which is at the limit of the human eye's resolution, but easily detected with a telescope. Given the observed α and knowing Earth's orbital and rotational speeds (about 30 km/s and 0.5 km/s at the equator, respectively), the speed of light can be calculated from the aforementioned equation; Bradley's estimate was 301,000 km/s, which is of the same order of magnitude as Røemer's estimate. The evidence for the finite speed of light seems convincing now, but what about light's nature? Is it a wave or a particle?


Christian Huygens, Isaac Newton & Thomas Young

By the 17th century, two competing pictures of the nature of light emerged. Christian Huygens (1629 – 1695) proposed a theory that the speed of light is finite and that light propagates as a wave in a medium permeating all space called ether, first introduced by Descartes. Huygens introduced the idea of a wavefront and that the propagation of light could be envisioned as an emission of spherical waves along the wavefront (now known as Huygens' principle). Isaac Newton (1642 – 1726) held an opposing view in which light consists of a stream of non-spherical particles, called corpuscles, which travel along straight paths and obey laws of mechanics. In the Newtonian picture, every source of light emits a large number of corpuscles into the medium surrounding the source. A Newtonian corpuscle is perfectly elastic, rigid, and weightless. Its speed depends on the density of a medium, being larger in a denser material.



Figure 7. Simplified and modernized version of Thomas Young's double slit experiment.


The Huygens-Newton debate about the nature of light continued until Thomas Young (1773 – 1829) demonstrated the concept of wave interference using a water ripple tank, showing in a series of experiments that light also exhibits interference. His experiments supported Huygens' picture of light as a wave. Figure 7 shows a simplified and modern version of Young's well-known double slit experiment. Collimated and monochromatic light illuminates two infinitesimally narrow slits cut in a screen. If light is a wave, an interference pattern will form on a viewing screen, as depicted in the middle panel of Figure 7. In contrast, if light is a stream of corpuscles, two light shadows of the slits will form instead. Young observed the interference pattern — light is a wave. If light is a wave, what kind of wave is it?


James Clark Maxwell (1831 – 1879) summarized the existing laws of electromagnetism, uncovered by his contemporaries such as Michael Faraday (1791 – 1867) or Karl Friedrich Gauss (1777 – 1855), within four differential equations, known as Maxwell equations. The equations predict the existence of electromagnetic waves that propagate in a vacuum with the speed given by Equation 2:



where ε0 and µ0 are electric and magnetic permittivity of free space, respectively. Their values can be determined experimentally and were known to Maxwell. Substituting them into Equation 2 yields a speed that is very close to the then-known speed of light. Maxwell identified light as an electromagnetic wave whose propagation would be supported by luminiferous ether.


Maxwell's theoretical prediction soon received experimental confirmation. Heinrich Hertz (1857 – 1894) proved electromagnetic waves' existence by constructing a wave transmitter (an oscillatory discharge between two sharp metallic tips) and a receiving antenna (a loop of wire terminated at one point with a small metallic sphere and at the other, with a sharp point close to the sphere). When the transmitter and receiver are close to each other, sparks in the transmitter cause sparks in the antenna. Electromagnetic energy from the transmitter travels through air to the antenna, causing the discharge. Electromagnetic waves are real, and the only remaining issue is empirical confirmation of the luminiferous ether. Probably very few at the time suspected that future experiments would show that there is no ether and that light, unlike other waves, requires no medium to propagate through, and that its measured speed is a constant, independent of how fast an observer or the source of light is moving.


Armand Fizeau

The techniques of Røemer and Bradley for measuring the speed of light relied on astronomical phenomena. However, is it possible to modify Galileo's conceptually correct and simple terrestrial setup to make the measurement? The answer proved to be yes. In 1849, physicist Armand Fizeau (1819 – 1896) made the first successful terrestrial measurement with an apparatus depicted in Figure 8.



Figure 8. Fizeau's rotating toothed wheel apparatus to measure the speed of light. This is a time-of-flight method — similar to Galileo's — where the wheel is effectively a clock.


Using a lens and a semitransparent mirror, light from the source, S, is focused in the plane of the rotating toothed wheel. If the light encounters a lagging edge of a tooth (or leading edge of a gap), it continues to a collimating lens and then to a reflecting mirror a distance, l, away. The reflected light comes back along the same path to the semi-transparent mirror; an observer behind the mirror monitors the brightness of the returned light. The concept of this setup is that the pulse of light that passes through a given gap between teeth will pass back through the same gap if the gap does not have time to move over (be replaced by a tooth) during the roundtrip time to and from the mirror. The experimenter adjusts the rotational speed of the wheel so that the brightness of the returned pulse of light becomes zero (because it is blocked by the leading edge of the next tooth). Knowing the rotational speed, the dimensions of the wheel, and the distance to the reflecting mirror, the speed of light can be calculated. Fizeau's result was 313,300 km/s.


Fizeau's method is effectively a time-of-flight technique similar to the one employed by Galileo. Here, the rotating toothed wheel is equivalent to observer A's lantern being repeatedly uncovered and covered (see Figure 2), the mirror is equivalent to observer B uncovering his lantern, and the width of the gap between the teeth together with the rotational speed of the wheel is equivalent to a clock.


Leon Foucault

Leon Foucault (1819 – 1868) modified Fizeau's apparatus by replacing the rotating toothed wheel with a rotating mirror, as shown in Figure 9. A collimated beam of light from a fixed source reflects from the mirror rotating in a clockwise direction at t = 0 (at this instant, the mirror is vertical) and moves towards a stationary mirror a distance D away. It is positioned in such a way that the incoming beam is normal to its surface. After the reflection, the light moves back towards the rotating mirror and reflects off of it at t = τ. Since the mirror rotated through an angle θ during the time interval τ, the reflected beam is not moving back to the source. Instead, it moves in the direction 2θ away. If the mirror rotates with an angular velocity ω, then the deflection angle 2θ is equal to 4ωD/c. By measuring the deflection angle and given ω and D, c can be calculated. Foucault's value for c was 298,000 km/s.



Figure 9. Simplified apparatus used by Foucault to measure the speed of light in 1862.


Albert Michelson

Albert Michelson (1852 – 1931) improved on Foucault's design (see Figure 10 below) using a sixteen-faced rotating mirror (the hexagonal mirror depicted in the figure would break apart before reaching the required rate of rotation). He performed a measurement of the speed of light at Mount Wilson Station between 1922 and 1928. The experiment produced the most accurate value to date of 299,796 km/s, which differs by only 4 km/s from the exact value.



Figure 10. The sketch of the experimental setup used by Albert Michelson to measure the speed of light at Mount Wilson Station in 1922 – 1928. The central piece of the apparatus is a sixteen-faced rotating mirror. The figure is adapted from "Michelson and The Speed of Light" by Jaffe.


Michelson also attempted to measure the change in the speed of light due to Earth's motion through the hypothetical luminiferous ether. In the picture where ether supports propagation of light, the speed of light is constant with respect to the stationary ether. It could, however, be higher or lower with respect to an observer moving with respect to the ether. Due to Earth's motion around the Sun, the Earth moves with respect to ether; therefore the speed of light measured by an earthbound observer should be affected by the planet's motion. To find this change, he and his collaborator, Edward Morley (1838 – 1923), built an interferometer, which would detect small changes in the speed of light as an interference pattern. The idea of the experiment is that light from some source, e.g., the Sun, is split into two perpendicular arms, each with a mirror at the end. After reflecting from the mirrors, the light from both arms is made to interfere. In the coordinate system of the Earth, ether moves with respect to the Earth with the speed equal to the Earth's orbital speed. The arms of the interferometer can be arranged so that one beam of light moves in the direction that is perpendicular to ether's motion and the other, parallel. Such motions would produce a phase shift between the two rays resulting in an interference pattern that could be observed. The pattern would depend on the orientation of the apparatus with respect to Earth's direction of motion.


The experiment yielded a null result. There is no ether. The measured value of the speed of light is the same regardless of the observer's motion or the motion of the light's source. The latter is contrary to Galilean's transformation, a component of Newton's laws of mechanics. The constancy of the speed of light becomes one of the two axioms of Albert Einstein's (1879 – 1955) theory of Special Relativity, which redefines the concepts of space and time. The speed of light is an absolute invariant, a constant of nature.


Given that the speed of light is an invariant, the Michelson-Morley interferometer can be used to determine this speed by directly measuring the wavelength of monochromatic light of known frequency. Figure 11 shows the simplified and modern concept of the method.



Figure 11. Simplified and modern version of an experimental setup to measure the speed of light using an interferometry approach.


Refer to panel (a). A monochromatic and polarized light of known frequency ƒ from a frequency-stabilized laser is split into two beams by a beam splitter. One of the two beams travels to a moveable mirror M1 (vertical leg) and the other to a stationary mirror M2 (horizontal leg). After reflecting from the mirrors, the beams are made to interfere. The location of M1 can be adjusted so that a constructive interference results, as shown in panel (a). By moving M1, the path difference of the two beams changes, and when it is λ/2 (which corresponds to moving M1 by λ/4), a destructive interference occurs, as shown in panel (b). If λ can be measured by monitoring the movement of M1, the speed of light can be calculated from Equation 3:



This technique is distinct from those discussed above because it does not involve measuring time, directly or indirectly. The setup is compact, fitting easily on a lab bench. It relies on interference, thus, it is known as an interferometric technique.


This article's review of key experiments to measure the speed of light ends here, although many more were performed after the work of Michelson. Most of them are refined versions of the techniques described above. Although the speed of light has been established, new questions about the exact nature of light arose.


Albert Einstein

When light illuminates the surface of a metal, the surface may emit electrons. This is the photoelectric effect, first observed by Heinrich Hertz in 1887. Classical electromagnetism, summarized in Maxwell's equations, predicts that the kinetic energy of the emitted electrons depends on the intensity of the incident illumination. However, no such dependence is observed. Instead, the kinetic energy depends on the frequency of the incident light. In 1905, Albert Einstein used Max Planck's (1858 – 1947) hypothesis that electromagnetic radiation is quantized: that is, light consists of discrete quanta of energy — now referred to as photons — each with energy E = , where h is Planck's constant and ν is the frequency of light. In this picture, an electron absorbs a photon and gains energy equal to . If the gain is greater than the surface barrier energy (referred to as work function), the electron may escape. Einstein's explanation agrees with all of the empirical characteristics of the photoelectric effect, earning him the 1921 Nobel Prize in Physics.


Apart from the photoelectric effect, there are other phenomena, e.g., Compton scattering, formation of atomic spectra, or black body radiation, that are successfully described using the particle nature of light. Although there is no simple answer to the question "What is a photon?" it is incorrect to associate a photon with Newton's corpuscle. Awaiting a further theoretical clarification of the nature of light and matter, wave-particle duality is a useful approach as stated by Einstein: "It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do."


What is light? We still do not know.


 

 

Go to top