“For the invisible things of Him
from the creation of the world are clearly seen.”
The Holy Bible, Romans (56 A.D.)1
Michael Faraday, a Devout Sandemanian
Michael Faraday was born on September 22, 1791, into an impoverished London family where there was barely enough to eat. He was withdrawn from school at 14 years of age, when he became an apprentice to a book-binder and bookseller. That turned out to be a blessing in disguise, for Faraday educated himself by reading the books that were being bound.
At the age of 20, and the end of his apprenticeship, Faraday was given a ticket to lectures by the eminent chemist Humphry Davy at the Royal Institution in London. Faraday sent a bound copy of the lecture notes he had taken to Davy asking for a job, and about a year later he was hired as an assistant in chemical experiments that were carried out in the basement of the Royal Institution. Davy and Faraday discovered that the chemical properties of substances are associated with their electrical powers, and that they are held together by positive and negative charges of electricity.
In 1821, Faraday married Sarah Barnard, after a two-year courtship and many love letters. They moved into modest rooms above the Royal Institution, where Faraday continued with his basement experiments. Michael and Sarah met at the Sandeman Church in London, an offshoot of the Church of Scotland, which provided them with spiritual sustenance throughout their lives.
The Sandemanian’s worked hard, lived simply, and spoke plainly. They had no clergy, leader or social hierarchy and sought guidance from mutual knowledge, friendship, and God’s word in the Bible. Ambition, pride, and the quest for worldly wealth were not, they thought, relevant to the true Christian who sought the eternal spiritual world rather than temporary and mundane involvement in politics, commerce or fashion. They insisted on the spiritual equality of each member irrespective of wealth, age, sex, or accomplishments.2
The Sandemanians took their commitments very seriously. Faraday, for example, was briefly excluded from their fellowship for missing a weekly service, which brought him shame and poor health and spirit. He was just barely excused after explaining that he was following the Queen’s command to dine at Windsor Castle.
To Faraday, scientists had an obligation to share their understandings with everyone. He therefore gave yearly public Christmas lectures at the Royal Institution on topics such as chemistry, electricity and attractive forces. The chemical history of the candle is still a favorite. In another well-known lecture on Mental Education he mentioned in 1854 that: “The book of Nature, which we have to read, is written by the finger of God.”3
In these widely appreciated lectures, Faraday conveyed the wonder, joy and excitement in the contemplation of Nature. He ignited the flame of curiosity in all kinds of people, from common laborers to Prince Albert, and opened the wide eyes of youth even further then normal.
Faraday viewed rewards, patronage and politics as undermining the purity of science. He thought that they were inconsistent with scientific objectives and the pursuit of truth. He twice refused the Presidency of the Royal Society when it was offered because it might require the political intrigue that he deplored. He also turned down a knighthood because he thought the English honors system was corrupt. To his dying days, he was exceptionally humble and preferred to remain plain Michael Faraday.
Faraday’s Unseen Fields of Force
Faraday dismissed both mathematics and theoretical hypothesis as methods of understanding the physical world. To him, mathematical theories were no more than dishonest confessions of our ignorance. The only route to understanding Nature was through experimentally determined facts.
His experiments in electricity and magnetism were stimulated by the investigations of the Danish scientist Hans Christian Ørsted, who showed that electric and magnetic forces are interrelated. He noticed that the magnetic needle of a compass moved when direct current flowed through a nearby wire.4 The magnetic needle also turned in opposite directions when placed above or below the current-carrying wire.
On reading of Ørsted’s results, Michael Faraday and Humphry Davy immediately repeated and extended his experiments. They wanted to learn more about the invisible forces that reached out through empty space to connect the wire and compass needle, as if they were touching each other.
They confirmed that electricity can generate magnetic forces that pass through space unseen, and about ten years later Faraday discovered that a moving magnet can produce invisible electrical forces.5 These two interactions are now used to make electric moters and to generate electricity.
Michael Faraday proposed that every electrically charged body is surrounded by an unseen electric field of force, and that every magnet is enveloped by an invisble magnetic force field. Both the electric and magnetic field of force could be viewed as a manifestations of a single unseen field of force, termed the electromagnetic field.
These invisible fields were supposed to permeate all of space, and their unseen lines of force were believed to stretch through all that exists. For Faraday, and Einstein after him, fields are a force underlying all discernable things. The material things we notice around us are just a limited perception of an unseen reality described by these fields. The points where these fields meet and focus are the points where we perceive matter to exist. The entire Universe is crisscrossed by the invisible lines of force, but the closer you are to the source of a field, the greater its power and hidden ability to act.
Faraday believed that God placed the invisible fields into the physical world at the time of its Creation, and that we can determine the laws by which their unseen powers act. These divinely ordained laws were supposed to govern the physical Universe, and the entire substantive world was believed to be at play in the fields of the Lord.
Ray Vibrations
In the early 1840s Faraday suffered an extended illness and a nervous break-down. He felt sure that his days of discovering the hidden secrets of Nature were over. He was wrong. One of his most prophetic insights was made on April 3, 1846 during one of the Royal Institution’s Friday Evening Discourses.
The chosen speaker, the distinguished Charles Wheatstone, panicked and left just before he was to speak. Faraday filled in by making some private and unpublished “Thoughts about Ray-vibrations.” He attributed radiation and radiant phenomena to vibrations in the electromagnetic fields of force. When disturbed, they would vibrate laterally and send waves of energy along their lengths. Light, he suggested, was a manifestation of these field vibrations. He stressed that they were vibrations of the fields of force themselves, and not of any hypothetical luminiferous aether that some thought necessary for light to propagate in.
Although these were speculative thoughts, just vague impressions of Faraday’s mind that appeared “only as the shadow of a speculation,”6 the concept of invisible vibrations served as a guide to James Clerk Maxwell, whose equations described Faraday’s results and tell us how light moves.
James Clerk Maxwell, by God’s Grace
Maxwell was born in Edinburgh on June 13, 1831 as a member of the Clerk family that had been prominent in Scotland for two centuries. His father, John Clerk Maxwell, added the name Maxwell to that of Clerk as a condition for inheriting a 1500-acre estate on which he built the family house, named Glenlair. James spent his infancy and early boyhood there, but in his ninth year his mother died of abdominal cancer and he was sent to the Edinburgh Academy.
He spent six years at the Academy, which were followed by three years at the University of Edinburgh. Maxwell then proceeded in 1850 to the University of Cambridge, where he became a Fellow at Trinity College. While at Cambridge, Maxwell became seriously ill and was cared for by the Reverend C. B. Taylor and his family. The experience gave him a new perception of the love of God. When subsequently writing to Taylor, on July 8, 1853, Maxwell commented on his own sins and God’s grace and guidance, and stated:
“All the evil influences that I can trace have been internal and not external, you know what I mean — that I have the capacity of being more wicked than any example that man could set me, and that if I escape, it is only by God’s grace helping me to get rid of myself…. by committing myself to God as an instrument of his will.”7
Maxwell’s belief in God played an important role in both his personal life and his work as a scientist. Shortly before his marriage to Katherine Mary Dewar in 1856, the devout Maxwell wrote to her about his strong belief in God, including: “Let us bless God even now for what He has made us capable of, and try not to shut out His spirit from working freely.”8
Maxwell ceased to be a Fellow of Trinity College, whose fellowship excluded married men and all women. He was appointed Professor of Natural Philosophy at the Marischal College, Aberdeen. But he also lost his Professorship a few years later when Marischal was joined with another college into one university; the number of professors was reduced, and it was noticed that Maxwell was an unsuccessful teacher with a disconnected, rambling lecture style. [Astronomers and other scientists were known as natural philosophers until the late 19th and early 20th century when the term scientist was coined and came into use.]
There was no need for Maxwell to be concerned. He was soon appointed to a similar Professorship at the Kings College in London where he stayed from 1860 to 1865. During this time he explained the way we see colors, described physical lines of force, and delineated the kinetic theory of gases. In 1865 he also published his dynamical theory of the electromagnetic field, which predicted the existence of electric and magnetic waves of energy that travel through space unseen. These waves, he supposed, are produced by the changing fields of force that had been carefully studied by Michael Faraday. This explanation also indicated that visible light amounts to only a small band of the possible electromagnetic waves in space, all traveling at the same speed but with different wavelengths.
In 1865 Maxwell retired to Glenlair, but he was called out of retirement six years later to take a new Professorship of Heat, Electricity and Magnetism at the University of Cambridge. He became the first Director of the Cavendish Laboratory, which opened in 1874 and continues today as a place where scientific experiments and measurements are carried out. Upon becoming its Director, Maxwell stated that: “Those aspirations after accuracy in measurement, truth in statement, and justice in action are ours because they are essential constituents of the image of Him who in the beginning created not only the Heaven and the Earth but the materials of which Heaven and Earth consist.”9
Maxwell died on November 5, 1879, at the age of forty-nine, of the same abdominal cancer that had killed his mother at about the same age. And near the end of his life, he told a friend that: “What is done by what I call myself is, I feel, done by something greater than myself in me.”10
Maxwell’s Equations and the Discovery of Radio Waves
Like Faraday, Maxwell believed that God made the Universe; that the laws that describe Nature are God’s laws, and that every discovery further reveals God’s great design. As a devout Christian, Maxwell also believed that God’s word could be found in the Bible.
In 1865, Maxwell discovered how Faraday’s invisible electric and magnetic fields work.11 Every time a magnet moves, or an electric current varies, a wave of energy moves outward at the speed of light. Moreover, a timechanging electric field generates a magnetic one, and a time-varying magnetic field makes an electric one. This pumping cycle, from one kind of field to another, sends electromagnetic waves spreading through space.
To our delight, we now know that Maxwell’s description also includes invisible electromagnetic waves that had never been imagined before. But no one realized these implications in Maxwell’s time, and in fact there didn’t seem to be anyone who understood his equations. Even Faraday wrote him to ask that he change his mathematical hieroglyphics to something he might grasp.
An exception was a self-taught Englishman, Oliver Heaviside, who slowly worked his way through Maxwell’s complex mathematics, grasped their meaning, and simplified his maze of currents, displacements, inductions, symbols, potentials and forces to just four equations that describe the rates of change of the electric and magnetic field in space and time.12 These are the four famous “Maxwell’s equations” that every physics students learns.
A quarter of a century later, the experimental physicist Heinrich Hertz verified these equations by producing and detecting what we would now call radio waves in his laboratory at the Technische Hochschule in Karlsruhe, Germany.13 He used a high-voltage, oscillating spark to generate the unseen waves that were detected with a loop of wire on the other side of the room. The waves had a wavelength of about one meter and moved at the speed of light, or about 299.79 million meters per second.
A young Italian entrepreneur, Guglielmo Marconi, read of Hertz’s work, and realized that the Hertzian waves might be used to communicate across vast distances without the aid of connecting wires. In 1895, at the relatively young age of 21 years, he used a Hertz oscillator, or spark producer, to send wireless signals over a few kilometers at his father’s country estate near Bologna, Italy. He established communication across the English Channel between England and France four years later and between England and Newfoundland two years after that.14 In ensuing years, Marconi had a grand time sending communications from his yacht Electra while cruising in the Atlantic and Mediterranean and then from the Vatican City to the Pope’s summer residence at Castel Gandolfo. He also enjoyed hunting, cycling, motoring and was twice married to women with aristocratic pedigrees.
Marconi became an international hero, established the American Marconi Company, which later evolved into the Radio Corporation of America, abbreviated RCA, and in 1909 received the Nobel Prize in Physics, jointly with the German physicist Karl Ferdinand Braun for their development of wireless telegraphy.
The pioneering investigations of Maxwell, Hertz, and Marconi provided a foundation for the exploration of the invisible Universe, which can be observed at wavelengths that are longer or shorter than those of visible light (Fig. 4.1). The long ones that Hertz and Marconi investigated are radio waves that can pass through clouds on a stormy day. Like ghosts, they even move through the walls of your house. Invisible x-rays have much shorter wavelengths than light. They can penetrate skin and muscle to reveal your bones.
Figure 4.1 Electromagnetic spectrum Cosmic radiation only penetrates to the Earth’s surface as the light we see with our eyes and as radio waves, respectively represented by the narrow and broad white areas. Radiation at other wavelengths has to be observed from above the atmosphere in Earth-orbiting satellites.
The use of invisible electromagnetic waves has changed our daily lives, from cell phones and global positioning systems to microwave ovens, radios, televisions, radar, and satellite weather images. Every star and galaxy in the Universe is also now emitting a host of these invisible electromagnetic waves, which all move at the speed of light.
The Speed of Light
It was not until the 17th century that astronomers discovered that light does not move instantaneously through space. The Danish astronomer Ole Rømer and Giovanni Domenico Cassini, Director of the Royal Observatory in Paris, noticed a varying time between eclipses of Jupiter’s large inner moon Io, of up to 22 minutes variation in an orbital period of about 42 hours.15 Both astronomers concluded that it was not the orbit of Io around Jupiter that changed, but the time it took light to travel from Io to the Earth, which depended on the Earth’s position in its orbit around the Sun. When the Earth was on the side of its orbit that is closest to Jupiter, the observed eclipse period for Io was shortest, and when the Earth was on the opposite side of its annual orbit around the Sun, Io’s apparent eclipse period was longest.
This meant that light does moves at a definite speed. Rømer and Cassini neglected to specify that speed, which would have been equal to the diameter of the Earth’s orbit divided by the time difference between the longest and shortest observed Io periods. However, the distance between the Earth and the Sun was not then accurately known. Using today’s estimates for this distance, their measurements would correspond to a light speed of about 227,000 kilometers per second.
The American physicist Albert Abraham Michelson became the recognized expert in designing and refining instruments for use in precise determinations of the velocity of light, as well as other astronomical measurements. Michelson was born on December 19, 1852 in Strzelno, Prussia (now Poland) and traveled to northern California with his family while still a child. He grew up in the rough gold-mining settlement of Murphy’s Camp, where arguments were usually settled with fists, knives or bullets. When Albert reached the age of 12, his parents sent him for high school in San Francisco, and they moved to a silver-prospecting center in Virginia City, Nevada.
After graduation from high school, Albert took a competitive examination to enter the United States Naval Academy in Annapolis, Maryland, and eventually received an appointment there by President Ulysses S. Grant, graduating in 1873 with just less than a third of the entering class. Following graduation, Ensign Michelson began a four-year term as instructor in physics and chemistry at Annapolis, where he started two decades of precision measurements of the speed of light. The transmission of light between mountain tops in 1926, led to his final figure of 299,796 ± 4 kilometers per second, quite close to today’s accepted value of c = 299,792.458.16
The study of light inspired a “pleasure, satisfaction, almost a reverence” in Michelson. He was fascinated by the rainbow of color produced by prismatic raindrops, at the beauties of coloring found on beetles, butterflies and hummingbirds, and at “the intricate wonders of symmetrical forms and combinations of forms, which are encountered at every turn.” When trying to explain it all to his daughter, he said “it doesn’t matter if you don’t understand it now as long as you realize the wonder of it.”17
Michelson resigned from the Navy in 1881, and the next year began teaching at the Case School of Applied Science in Cleveland, when he became intrigued by the possible motion of the Earth through the stationary aether, and devised a way to measure this movement. It was then thought that light waves must propagate in something, named the aether, just as sound waves are carried in air. Many scientists, from Newton to Maxwell, had firmly believed in such a light-carrying aether for nearly two centuries.18
Michelson’s plan was to project a beam of light in the direction in which the Earth is traveling in its orbit, and one at right angles to this. The first beam, he thought, would naturally be retarded by the flow of aether passing the Earth. The second beam, crossing this current at right angles, should arrive ahead of the first by a length of time determined by the velocity of the Earth through the aether.
In the instrument that Michelson designed to make the measurements, a beam of light is split into two parts moving at right angles to one another; when reflected back and recombined, they produce an interference pattern, in which the light wave crests either added together or cancelled — hence the instrument’s name interference-meter that is abbreviated interferometer. Such an interferometer can be used to accurately measure any changes in the speed or path lengths of the two beams.
Michelson’s idea was to use the interferometer to see if light travels with the same velocity in all directions. That might measure how the speed of light depends on the Earth’s motion through the stationary aether. If there is an aether, then the speed of light would vary when moving into the aether or against it, like a boat sailing with or against the wind or a swimmer moving downstream or struggling upstream.
Michelson’s first attempt at using his interferometer to measure the relative velocity of the Earth and the aether, in 1881, indicated to him that there was no such motion and that “the hypothesis of a stationary aether is thus shown to be incorrect.”19 It was not until 1886 and 1887 that Michelson and his friend, the chemist Edward W. Morley of neighboring Western Reserve University, repeated this experiment with greater care and refinement. They were both dedicated to accuracy and precision in measurements, and their precise determination of the speed of light suggested that the aether does not even exist.
Their interferometer was set up in a basement laboratory and mounted on a massive sandstone slab that floated on a pool of mercury to remove unwanted vibrations. Light beams were then sent through the interferometer into the supposed aether wind, in the direction of the Earth’s motion, and at right angles to this path. After a brief interruption by Michelson’s nervous breakdown, the experiment resulted in an unexpected result. Michelson and Morley found that there was no detectable difference in the interference pattern produced when a beam of light was sent into the aether wind in the direction of the Earth’s motion or directed at right angles to it.20 Moreover, there was no difference in the measured speed of light when the Earth was traveling toward the Sun and away from it half a year later.
At this time, Michelson experienced a lot of personal difficulties. In 1887, a maid charged him with assault and battery; a court found him innocent of these charges. About a decade later, his wife of more than twenty years divorced him, and he seems to have remained a lonely person despite taking a former student as a second wife. Albert always possessed an astonishing indifference to family life and to people in general, confided in no one including either his wife or his children, and was rarely moved by the human attributes of ambition, envy, fate, and love.21
In 1889, Michelson left Case for Clark University of Massachusetts, and in 1893 moved to the University of Chicago, where he headed the Physics Department until 1929. During his tenure at Chicago, Michelson was awarded the 1907 Nobel Prize in Physics “for his optical precision instruments and the spectroscopic and metrological investigations carried out with their aid,” the first American to receive the award.
The Michelson-Morley experiment indicated that the velocity of light is constant, exactly the same in all directions and at all seasons, and independent of the motion of the observer. Light was no longer viewed as luminous ripples in the mysterious aether, and radiation was supposed to always propagate with a definite, unchanging speed in empty space.
This discovery played an important role in Einstein’s famous 1905 account of moving bodies whose physical properties are relative and can change in high-speed motion.22 He assumed that the velocity of light in empty space is independent of the motion of its emitting source and the motion of any observer, which means that light’s speed is the same for any star or galaxy and for all observers, wherever they might be. Moreover, in his theory light has a special, limiting speed, the fastest that any material object can travel.
Nothing in our material world outruns light; it is the fastest thing around. That is because an object’s mass increases without bound when it approaches the speed of light, and there is nothing that can propel such a massive object so fast. It would take an infinite amount of energy to accelerate any material object to the speed of light.
Einstein was later taken to task for omitting any mention of Michelson and Morley in his influential Special Relativity paper, or for that matter related publications of Lorentz, FitzGerald and Poincaré. Not until 1931 did Einstein publicly honor Michelson for his experiment, addressing him in person with: “It was you who led physicists into new paths, and through your marvelous experimental work paved the way for the development of the theory of relativity. You uncovered an insidious defect in the aether theory of light as it then existed, and stimulated the ideas of H. A. Lorentz and FitzGerald out of which the Special Theory of Relativity developed.”23
To astronomers, the important implication of the Michelson-Morley experiment is that starlight is always in motion in empty space at the definite and precise speed of light. Moreover, all electromagnetic waves, regardless of wavelength, move though the vacuum of space at the same constant speed of light. They can persist forever in empty space, never speeding up and never slowing down or coming to a rest. Once emitted, radiation from any star or galaxy might therefore travel for all time in vacuous space, bringing its message forward to the end of the Universe. When some of that radiation is intercepted at the Earth, it tells astronomers about the cosmic object back when it emitted its radiation, as it was then and not as it is now.
Sunlight requires about 8 minutes to travel from the Sun to the Earth, and it takes just a little more than 4 years for starlight to reach us from the nearest star other than the Sun. Moving at the speed of light, it takes 2.3 million years for light to travel from the nearest spiral galaxy, Andromeda, to the Earth, and the light observed from very distant galaxies was emitted about 13 billion years ago. In effect astronomers watch cosmic history race at us at the speed of light, and trace out changes over millions and billions of years.
We can even witness the youth of distant stars that existed before the Sun and Earth were formed, about 4.6 billion years ago. Some of the most distant galaxies may no longer exist, and they may have been embryonic galaxies when the light now reaching the Earth began its journey. These galaxies could have perished over time, but their light can survive without change.
Nevertheless, once radiation encounters matter, it no longer behaves like a wave. Max Planck showed that light then acts like a particle containing little packets of light energy.
Planck’s Uncomfortable Life and Resolute Search
Max Karl Ernst Ludwig Planck, or Max Planck for short, was born on April 23, 1858 at Kiel, Germany within an academic family. Both his grandfather and great-grandfather were Professors of Theology in Göttingen; his father was a distinguished Jurist and Professor of Law at the University of Kiel.
When Max was nine years old, his father received an appointment at the University of Munich, and Planck attended the city’s renowned Maximilians Gymnasium. After graduation in 1874, at age 17, he entered the University of Munich, and in 1877 spent a year of study with Hermann von Helmholtz and Gustav Kirchhoff at the University of Berlin. To Planck, their lectures were boring, monotonous and uninspiring. Returning to Munich, he received the doctoral degree in July 1879, at the unusually young age of 21. The following year, Planck completed his Habilitationsshrift (qualifying dissertation) on the equilibrium states of bodies at different temperatures, and became an unpaid Privatdozent (lecturer) while awaiting an academic position.
In 1885, with the help of his father’s professional connections, he was appointed an Associate Professor at the University of Kiel. In 1889, after the death of Kirchhoff, Planck received an appointment at the University of Berlin, where he had a close personal and professional relationship with Helmholtz. In 1892, Planck was promoted to Full Professor, and he eventually became Dean at the University, which enabled him to establish a new Professorship there for Albert Einstein in 1914. Planck remained in Berlin for the rest of his active life, and died in Göttingen in 1947 at the age of 89.
From a young age, Planck was not only gifted in science but also in music. He had absolute pitch, took singing lessons, was a member of the singing club at the University of Munich, composed songs and operas, and was an excellent pianist. In later years he found pleasure in daily playing the piano, which may have provided calm distraction from the tensions of his unlucky personal life.
After a little more than a decade of marriage, Planck’s first wife died in 1909, probably of tuberculosis. They had four children, two sons and twin daughters. In the First World War, his eldest son was killed and the French imprisoned the other son. During World War II, the Gestapo executed his youngest son for his part in an attempt to assassinate Hitler. One daughter died giving birth. The surviving twin fell in love with her sister’s husband. They married and two years later she died in childbirth. And when he was 85 years of age, an Allied bomb destroyed Planck’s house and everything in it, except Planck who was elsewhere. With stoic strength, he continued with his work, sustained by his faith in God.
Max Planck reasoned that both religion and science require a belief in God for their activities, and argued that the truth of their compatibility is the historic fact that the very greatest natural scientists of all times — men such as Kepler, Newton, Leibniz — were permeated by a profound religious attitude.
“Inner peace of mind and soul,” he wrote, “is secured by a firm [and universal] link to God and by an unconditionally trusting faith in his omnipotence and benevolence.” Our scientific understanding “similarly demands that we admit the existence of a real world independent from us, a world which we can never recognize directly, but only indirectly by our measurements.”23
Planck noticed that definite laws govern the physical world of Nature, and he identified that world order with the God of religion. He believed that there are “everywhere active and mysterious forces” in Nature, and that a search for the laws that describe them is comparable to seeking the Divine. In other words, the goal of a scientist’s quest is to approach God and His world order. In Planck’s own words:
“Religion and natural science are fighting a joint battle in an incessant, never relaxing crusade against skepticism and against dogmatism, against disbelief and against superstition, and the rallying cry in this crusade has always been, and always will be: On to God.”24
Planck Invents Light Quanta
Planck’s predecessor at the University of Berlin, Professor Gustav Kirchhoff, found in 1860 that the heat radiation of a black body, which absorbs and emits all radiation that falls on it, has an energy that depends only on the radiation wavelength and the temperature.25 This became known as Kirchhoff’s law. The black body radiation does not depend on the volume or shape of the source, or on the material it is made out of. This meant that the radiation is disconnected, a thing on its own, and when in space radiation is a reality independent of material bodies. This universality fascinated Planck, and he spent years trying to find a deeper, absolute explanation of it.
Planck was not alone in seeking the general properties of black body radiation. In 1879, the Austrian Joseph Stefan, at the University of Vienna, used experiments to show that the total power emitted from a heated body is proportional to the fourth power of the temperature.26 And when size is taken into account, the power also varies as the square of the radius. This explains why giant stars are more luminous than the Sun. With his relation, Stefan also used observations of the Sun to determine the temperature of its visible disk, at about 5700 degrees kelvin.
In 1886, the American astronomer Samuel Pierpont Langley reported laboratory spectral measurements of the radiation from heated copper using the bolometer, an instrument he invented for detecting infrared radiation.27 His observations displayed temperature-dependent intensity maxima and rapid drops in intensity with both increasing and decreasing wavelength (Fig. 4.2). As the temperature increases, more intense radiation is emitted at all wavelengths. Moreover, the wavelength of the most intense radiation shifts toward the shorter wavelengths when the temperature rises.
Figure 4.2 Hot emission The intensity of radiation from copper that has been heated to different temperatures and measured at infrared wavelengths in units of micrometers or 10−6 meters. [Adapted from S. P. Langley’s article published in the Philosophical Magazine 21, 394–409 (1886).]
By the 1890s several investigators, both experimentalists and theorists, were trying to determine and describe the spectral distribution of black body radiation. Precise measurements of the radiation at various wavelengths were also being performed at the Physikalisch-Technische Reichsanstalt in Berlin, where Wilhelm Wien found that the radiation is most intense at a wavelength that is inversely proportional to the temperature.28 He received the 1911 Nobel Prize for Physics “for his discoveries regarding the laws governing the radiation of heat.”
Over a period of five years, Max Planck sought a way of rigorously deriving Wien’s law and tried to find a more comprehensive explanation for the intensity of black body radiation as a function of its wavelength or frequency. The German physicist Heinrich Hertz had discovered waves of invisible radiation in the previous decade, and this led to speculation that numerous “Hertzian oscillators” produce the heat radiation emitted by black bodies. Planck supposed that such microscopic oscillators might resonate at all possible wavelengths, and looked at ways their radiation might be distributed in energy amongst them.
With dogged perseverance, Planck continued in his search, despite several mistakes and setbacks when new experimental data were found inconsistent with his latest results. In what he described as “an act of desperation” and “a fortunate guess,” he assumed that the total energy of all the black body oscillators in the cavity walls was distributed into finite portions of energy, each proportional to the oscillator frequency. Planck called the constant of proportionality the quantum of action, and it is now known as Planck’s constant. Radiation at shorter wavelengths, or higher frequencies, has larger quantum energy and vice versa.
Using this approach Planck found, at the turn of the 20th century, an equation that described the spectral distribution of the energy emitted from a black body at any given temperature, which agreed with all the observations.29 This spectral distribution for the black body radiation intensity peaks at a wavelength that is inversely proportional to the temperature, drops precipitously at shorter wavelengths, and falls off gradually at longer ones (Fig. 4.3).
The entire spectrum increases in intensity and shifts toward shorter wavelengths as the temperature increases. That’s the reason that very hot, million-degree objects emit most of their radiation at short x-ray wavelengths, while cold interstellar space is most luminous at long radio wavelengths.
The Sun’s radiation spectrum closely matches this distribution at a temperature of 5780 degrees kelvin (Fig. 4.4). This spectrum is most intense at visible wavelengths, which explains why the Sun illuminates the world we see. It is also the reason that we notice other stars, of comparable temperatures, when looking up at the dark night sky.
Planck’s spectral distribution formula supposed that black body radiation does not interact with matter in a continuous stream at all possible energies, but instead in discrete bundles of energy, which Planck called quanta. That is, the radiation was not being expelled in a steady flow like water from a hose, but instead like microscopic bullets from a machine gun. The 1918 Nobel Prize in Physics was awarded to Max Planck for “his discovery of energy quanta.”
Figure 4.3 Black body radiation Intensity of black body radiation plotted as a function of wavelength in meters. At higher temperatures the wavelength of peak emission shifts to shorter wavelengths.
Figure 4.4 Solar radiation spectrum The Sun’s radiation at the top of the Earth’s atmosphere (gray) and below the atmosphere at sea level (dark). The maximum intensity occurs at visible wavelengths, and a black body at a temperature of 5780 degrees kelvin describes its spectral distribution. Oxygen, water vapor, and carbon dioxide molecules in the air absorb the sunlight. The solar irradiance is given in units of watts per square meter per nanometer, and the wavelength is in micrometers, or 10−6 meters.
How Radiation Interacts with Matter
In the meantime, back in 1905, Albert Einstein had interpreted the photoelectric effect in terms of the quantum interpretation of the interaction of light with matter.30 When you shine ultraviolet light on a metal surface, some electrons will come out of the metal’s atoms, which is known as the photoelectric effect (Fig. 4.5). It was found in the laboratory that the energy of these liberated electrons is unrelated to the intensity of the light, but simply related to its frequency, and that the total energy an electron absorbs from the light is exactly one quantum of energy. The product of the radiation wavelength and frequency is equal to the speed of light.
The energy transfer from one light quantum to a single electron is independent of the presence of other light quanta. Moreover, an atom only ejects an electron when the radiation frequency is above a threshold-frequency. Einstein received the 1921 Nobel Prize in Physics, “especially for his discovery of the law of the photoelectric effect.”
The indestructible and indivisible light quanta are now known as photons, a term that was coined by the American chemist Gilbert N. Lewis in 1926.31 Photons are created whenever a material object emits radiation, and the photons are consumed when matter absorbs radiation. The interaction of each photon with matter depends on its energy, which is exactly the energy of Planck’s quanta — the product of Planck’s constant and the radiation frequency. This is the reason why energetic, high frequency x-rays pass through your skin and muscles with very little absorption until they reach your bones. Less-energetic ultraviolet sunlight can burn your skin, while visible sunlight, of even lower frequency, just warms your face.
Figure 4.5 Photoelectric effect A metal can emit electrons when ultraviolet light shines on it. These electrons indicate that light behaves as a packet of energy, called a photon, when it interacts with matter.
Figure 4.6 Solar absorption lines The visible portion of the Sun’s radiation displayed as a function of wavelength. When we pass from long wavelengths to shorter ones (left to right, top to bottom), the spectrum ranges from red through orange, yellow, green, blue and violet. Dark gaps in the spectrum are due to absorption by atoms in the outer atmosphere of the Sun. (Courtesy N. A. Sharp, NOAO/NSO/Kitt Peak FTS/AURA/NSF.)
The composition of any material can be inferred from the specific wavelengths at which it absorbs radiation. When the Sun’s light, for example, is examined with sufficiently fine wavelength intervals, numerous dark features are found irregularly distributed within the colors (Fig. 4.6). These dark features are known as spectral lines because they look like a line in the spectral display. They are further designated as dark lines or absorption lines since atoms in a relatively cool tenuous gas produce them when absorbing the radiation of hotter, denser underlying material. When broad wavelength intervals are used, adjacent bright emission obscures the dark places that cannot then be found.
Just seven of the dark gaps of missing colors in the Sun’s light were first noticed in 1802 by William Hyde Wollaston, a London chemist.32 Hundreds of the dark spectral lines were subsequently discovered by the Bavarian glassmaker Joseph Fraunhofer, who had a rather grim early life. He was the eleventh child of an impoverished father, who died when the youngster was just 12 years old. Two years later, the slum building in which he lived collapsed, trapping the young Fraunhofer and killing everyone else inside. When the Bavarian prince, Maximilian Joseph, heard of the ordeal, he rescued Fraunhofer from his misery, giving him enough gold coins to follow an interest in optics, lens making, and the Sun.
By directing incoming sunlight through a slit, and then dispersing it with a prism, Fraunhofer was able to overcome the blurring of colors, and discovered numerous dark features in this spectral display.33 He measured the wavelengths of these dark spectral lines, and catalogued more than 300 of them. Fraunhofer also found that bright stars exhibit spectral lines like those seen in the Sun, as well as some lines that he did not detect in sunlight. Unlike Wollaston, Fraunhofer was convinced that the spectral lines originate in the Sun or the other stars, but he did not know what caused the dark lines to appear in the stellar spectra, or where the missing colors went.
It was the German scientist Gustav Kirchhoff and his chemist colleague Robert Bunsen who showed that every chemical element, when burned and vaporized as a gas, emits brightly colored lines at unique wavelengths. Copper, for example, provides a green color to a flame, and sodium burns a bright yellow. These bright spectral features are known as emission lines because substances heated to incandescence emit them.
One evening, the two men noticed distant buildings that were burning, and detected emission line spectra in the flames. This suggested that they had a way of investigating the Sun’s fires from a distance. By comparing the wavelengths of the Sun’s dark absorption lines with those of emission lines from elements vaporized in their laboratory, Kirchhoff and Bunsen identified several chemical elements in the solar atmosphere.
As Bunsen wrote in 1859:
“At the moment I am occupied by an investigation with Kirchhoff, which does not allow us to sleep. Kirchhoff has made a totally unexpected discovery, inasmuch as he has found out the cause for the dark lines in the solar spectrum and can produce these lines artificially intensified both in the solar spectrum and in the continuous spectrum of a flame, their position being identical with that of Fraunhofer’s lines. Hence the path is opened for the determination of the chemical composition of the Sun and the fixed stars.”34
They had unlocked the chemistry of the Universe! Each chemical element, and only that element, produces a unique set, or pattern, of wavelengths at which the dark lines fall. It is as if every element has its own characteristic signature that can be used to identify it, as a fingerprint or DNA sample might identify a person. Every one of the numerous absorption lines found in the Sun’s spectra have been identified with a specific chemical element or compound.
Some of the Sun’s spectral lines are exceptionally dark, extracting great amounts of energy from sunlight. They are produced by hydrogen, sodium, magnesium, calcium and iron. It was therefore initially supposed that the Sun is made out of the same material as the Earth in similar abundance, but this is only partly true. Many of the visible solar lines were associated with hydrogen, which is by far the most abundant element in the Sun and most other stars but a terrestrially rare element.
Darker absorption lines generally indicate greater absorption and therefore larger amounts of the absorbing element, but the strength of an element’s absorption lines depends only to some extent on an element’s abundance. There are other mitigating circumstances, so unlocking the chemistry of the Universe was not as straightforward as scientists initially supposed.
Atoms, for example, exist in altered physical states at the high temperatures that prevail within stars, and this can result in a change in the intensity of the spectral lines that are observed in stellar atmospheres. Once this was understood, astronomers could estimate the number of atoms or ions responsible for the production of different dark lines within the Sun’s colors. They found that there is a systematic decrease in the abundance of solar elements with increasing atomic number and weight. So the heavier elements are less abundant in the Sun than light ones.
This concludes our discussion of how light moves and interacts with matter, and brings us to the ways the stars move.