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The Amazing Story of Quantum Mechanics.
To Thomas, Laura, and David,
who truly make the future
Our citizens and our future citizens cannot share
properly in shaping the future unless we understand the
present, for the raw material of events to come is the
knowledge of the present and what we make it.
LIEUTENANT GENERAL LESLIE R. GROVES.
(WHO OVERSAW CONSTRUCTION OF THE PENTAGON AND WAS.
CHIEF MILITARY LEADER OF THE MANHATTAN PROJECT).
FROM THE FOREWORD TO Learn How Dagwood Splits the Atom
WRITTEN BY JOHN DUNNING AND LOUIS HEIL AND DRAWN BY JOE MUSIAL.
(KING FEATURES SYNDICATE, 1949).
Quantum Physics? You're Soaking in It!
Perhaps you share my frustration that, well into the twenty-first century, we still await flying cars, jet packs, domed underwater cities, and robot personal a.s.sistants. From the 1930s on, science fiction pulp magazines and comic books promised us that by the year 2000 we would be living in a gleaming utopia where the everyday drudgery of menial tasks and the tyranny of gravity would be overcome. Comparing these predictions from more than fifty years ago to the reality of today, one might conclude that, well, we've been lied to.
And yet . . . and yet. In 2010 we are able to communicate with those on the other side of the globe, instantly and wirelessly. We have more computing power in our laptops than in the room-size computers that were envisioned in the science fiction pulps. We can peer inside a person, without the slice of a knife, performing medical diagnoses using magnetic resonance imaging. Touch-activated computer screens, from the local ATM to the iPhone, are everywhere. And the number of automated devices we deal with in a given day is surprisingly high-though none of them look like Robby the Robot.
What did the all those rosy predictions miss? Simply put, they expected a revolution in energy, but what we got was a revolution in information. Implicit in the promise of jet packs and death rays is the availability of lightweight power supplies capable of storing large amounts of energy. But the ability of batteries to act as reservoirs of electrical energy is limited by the chemical and electrical properties of atoms. Scientists and engineers are extremely clever in developing novel energy-storage systems, but ultimately we can't change the nature of the atoms. Information, however, requires only a medium to preserve ideas and intelligence to interpret them.
Moreover, information can endure for thousands of years-consider the long-term data storage accomplished by the Sumerians, whose cuneiform writing on clay tablets enables us to learn about their accounting systems and read the epic tale of Gilgamesh from four thousand years ago. These dried clay tablets, currently held in modern-day Iraq, are fairly bulky, and to share information from them the ancient Sumerians had to transport the actual tablets. But today you don't have to go to Iraq to read the Sumerian tablets-you can view them on the Internet, or someone could send images of them to you instantly via a cell phone camera.
These advances in content storage and transmission were made possible by the development of semiconductor devices, such as the transistor and the diode. Back when the science fiction pulp magazines were first published, data manipulation proceeded via bulky vacuum tubes; the first computers employed thousands of such tubes, along with relay switches consisting of gla.s.s tubes filled with liquid mercury. The replacement of these tubes and mercury switches with semiconductor devices enabled an exponential increase in computing power accompanied by a similar decrease in the size of the computer. In 1965 Gordon Moore noted that approximately every two years the number of transistors that could be incorporated onto an integrated circuit doubled. This trend has held up for the past forty years and underlies the technological innovations that define our modern life: from book-size radios in the 1950s to an MP3 player no larger than a stick of gum in 2005; from a cell phone the size of a brick in the 1970s to one smaller than a deck of cards today. These advances in miniaturization have come with continued improvements in the ability to preserve and manipulate information. (If energy storage also obeyed Moore's law, experiencing a doubling in capacity every two years, then a battery that could hold its charge for only a single hour in 1970 would, in 2010, last for more than a century.) With no transistors, computers would still require bulky vacuum tubes, each one generating a significant amount of heat as it regulated electrical currents. A modest laptop computer currently employs approximately more than a hundred million solid-state transistors for data storage and processing. If all of these transistors were replaced with vacuum tubes, each one a few inches long and at least an inch wide, their physical dimensions, and the need to s.p.a.ce them apart to avoid overheating, would yield a vacuum tube computer larger than the White House. Obviously, few inst.i.tutions aside from the federal government and the largest corporations could afford such a ma.s.sive computing device. We would consequently live in a relatively computer-free world. With computers rare, there would be no need to link them together, and no need to develop the World Wide Web. Commerce, journalism, entertainment, and politics would exist under the same constraints they did in the 1930s. If we'd had a revolution in energy storage (like the pulps predicted) rather than information storage, we could zip to work with jet packs, but once we got there we'd find no cell phones, no DVD or personal video recorders, no laser printers, and no personal computers.
The field of solid-state physics, which enabled the development of these and other practical devices, is in turn made possible through quantum mechanics. While science fiction writers were imagining what the future would look like, scientists at industrial laboratories and research universities were busy using the new understanding of the quantum world to create the transistor and the laser. These basic devices form the foundation of our modern lifestyle and have transformed not just consumer electronics, but chemistry, biology, and medicine as well. All of our lives would be profoundly different if not for the efforts in the first quarter of the twentieth century of a handful of physicists trying to understand how atoms interact with light. These pioneers of quantum mechanics recognized that they were changing the face of physics, but they almost certainly did not antic.i.p.ate that they would also change the future.
In this book I will explain the key concepts underlying quantum mechanics and show how these ideas account for the properties of metals, insulators, and semiconductors, the study of which forms the field of solid-state physics. I'll describe how the magnetic properties of atomic nuclei and atoms, an intrinsically quantum mechanical phenomena, allow us to see inside the human body using magnetic resonance imaging and store vast libraries of information on computer hard drives. The wonders enabled by quantum mechanics are almost too many to name: devices such as lasers, light-emitting diodes, and key-chain memory sticks; strange phenomena including superconductivity and Bose-Einstein condensation; and even brighter brights and whiter whites!1 And we'll see how the same quantum phenomena that changed the very nature of technology in the last fifty years will similarly influence the growing field of nanotechnology in the next fifty years.
For a field of physics that has sp.a.w.ned applications that have had such a wide-ranging impact on our lives, it is unfortunate that quantum mechanics has such a reputation for "weirdness" and incomprehensibility. OK, maybe it is weird, but it's certainly not impossible to understand. While the mathematics required to perform calculations in quantum physics is fairly sophisticated, its central principles can be described and understood without resorting to differential equations or matrix algebra.
The cover of the book promised a "math-free" discussion, but I must confess that there will be a little bit of math involved in this presentation of quantum physics. (I hope you are reading this at home and not standing up in the aisle at the bookstore, trying to decide whether or not to purchase this book.) Compared to the rigorous mathematics that underlies the foundations of quantum mechanics, the simple equations employed here practically qualify as "math-free." I will make use of algebraic equations no more complex than those relating distance traveled to speed and time. That is, if I told you that I drove at a speed of 50 miles per hour for 2 hours, you would know that I had traveled 100 miles. By arriving at that conclusion, you have intuitively used the simple equation distance = speed time. None of the math that I will use here will be more complicated than this.
While it may not be incomprehensible, quantum mechanics does have a well-deserved reputation for being confusing. I do not mean that the mathematics employed in a quantum description of nature is obscure or complex-all math is hard if you do not know how to use it, just as every language is opaque if you cannot speak it. Rather, I mean that fundamental questions, such as what happens to a quantum system when a measurement of its properties is performed, are still being argued over by physicists, nearly eighty years after first being posed. One of the most amazing aspects of quantum mechanics is that one can use it correctly and productively-even if one is confused by it.
In this book I invoke a "working man's" view of quantum mechanics that has the advantage of requiring only three suspensions of disbelief, not unlike the "miracle exception from the laws of nature" that science fiction stories or superhero comic books often implicitly employ. Some of my professorial colleagues should note-in the interest of clarity I will sidestep some of the finer points of the theory. This book is intended for non-experts interested in learning how quantum mechanics underlies many of the devices that characterize our modern lifestyle. Meditations on the interpretations of quantum theory and the "measurement problem" are fascinating, to be sure, but philosophical discussions alone do not invent the transistor.
Even keeping it simple, questions regarding the fundamental nature of matter are inescapable when considering quantum mechanics. I discuss fantastical situations such as when two electrons or atoms are so close to each other that they become "entangled" and it is actually impossible to tell them apart. I encourage you to put fear out of your mind and not s.h.i.+rk any necessary heavy lifting, and I'll try to hold up my end by using easily understood a.n.a.logies and examples.
There are many excellent books that describe the historical development of quantum mechanics, some of which are listed in the "Recommended Reading" section. As I am not a historian of science, I will not retrace the steps of the pioneering physicists that led the quantum revolution, but will rather focus on explicating the physical principles they discovered and their applications in solid-state physics.
TALES TO ASTONISH.
Figure 1: Cover of the August 1928 issue of the science fiction pulp magazine Amazing Stories, which featured the debut of "Buck" Rogers.
Quantum Mechanics in Three Easy Steps.
The future began twice: in December 1900, and in August 1928. On the first date, at the German Physical Society, Max Planck presented a resolution to something that would come to be called the ultraviolet catastrophe. Planck suggested that atoms can lose energy only in discrete jumps, and this new idea would tip over the first domino in a chain that by the mid-1920s would lead to the development of a new field of physics termed "quantum mechanics." On the later date, at the end of the summer of 1928, Buck Rogers first appeared in the science fiction pulp Amazing Stories.
With its premier issue published in 1926, Amazing Stories was the first magazine devoted exclusively to science fiction stories, or what publisher Hugo Gernsback called "scientifiction." The magazine's motto was "Extravagant Fiction Today . . . Cold Fact Tomorrow." Planck's breakthrough marked the dawn of a new field of science and is the province of nerds, while the appearance of Buck Rogers began the future as reckoned by geeks. (I should note that as a physics professor who is also an avid fan of science fiction and comic books, I am simultaneously a nerd and a geek.)2 Given the amazing pace of scientific progress at the end of the nineteenth century-the invention of the telegraph, telephone, and automobile had radically altered notions of distance and time, such that, not for the last time, technology had made the world a somewhat smaller place-it is perhaps not surprising that readers of Amazing Stories in 1928 would expect the eventual development of personal flying harnesses and disintegrator rays.
Buck Rogers's first adventure was described in Philip Francis Nowlan's novella Armageddon 2419 A.D., published in that famous issue of Amazing Stories. Anthony Rogers-he would not gain the nickname "Buck" until his appearance in a syndicated newspaper comic strip one year later-was a citizen of both the twentieth and twenty-fifth centuries. Exposure to a gas leak in an abandoned mine near Scranton induced a former army air corps officer to lapse into a form of suspended animation. Upon awakening in the future, he rapidly adjusted to the new age. Nowlan's hero, catapulted into the future, was just as resourceful as Twain's Yankee thrust back into King Arthur's court.
Rogers, armed with the weaponry of tomorrow and a military ac.u.men acquired during his service in World War I, joins a team of rebels fighting against the evil "Hans" invaders from Asia who had conquered America in the early twenty-second century. In fact, many of the stories published in the science fiction pulps of the 1930s and 1940s are distinguished by optimism that in the future there would be continued scientific progress coupled with pessimism that there would be absolutely no improvement whatsoever in international (or interplanetary) relations.
This confidence in scientific advancement, history shows, was justified, as was the expectation of continued global strife. In the pause in hostilities among European nations between the Great War and the next Great War, a revolution in physics occurred that would lay the foundation for technological innovations that would seem outlandish in the pages of Startling Stories. The first half of the Roaring Twenties would see the development of what would eventually be known as quantum mechanics, where the tentative guesses and first steps of Planck, Niels Bohr, Albert Einstein, and others would inspire Erwin Schrodinger and Werner Heisenberg to separately and independently create a formal, rigorous theory of the properties of atoms and their interactions with light. Their scientific papers appeared in print the same year that Hugo Gernsback began publis.h.i.+ng Amazing Stories. While quantum mechanics is not, to be sure, the last word in our understanding of nature, it did turn out to be the key missing ingredient that would enable physicists to develop the field of solid-state physics. When combined with the electromagnetic theory of the nineteenth century, quantum mechanics provides the blueprint for our current wireless world of information and communication. Scientists today, working on twenty-first-century nanotechnology, are still dining off the efforts of the quantum physicists of the 1920s.
It is plausible that the lull in global antagonisms in the brief time between the two world wars helped facilitate these advances in physics. The collaborations and interactions among scientists from Germany, France, Italy, Britain, Denmark, the Netherlands, and the United States heralded an unprecedented fertile period, which came to a close with the resumption of hostilities in Europe in 1938. Physics turned out to be in a race against history, and the pace quickened with the discovery of the structure of the atomic nucleus in the 1930s. The realization by German and Austrian physicists that it is possible to split certain large unstable nuclei, and thereby release vast amounts of energy-such that a little over two pounds of uranium would yield the same destructive force as does seventeen thousand tons of TNT-came a year before the German army marched into Poland. The quantum alliance of scientific cooperation would fracture with the formation of a geopolitical axis, and the center of gravity of physics would s.h.i.+ft from Europe to America in the 1940s. The development of solid-state physics would have to await the end of World War II and would be carried out primarily in the United States and Britain. Unfortunately the pulp fiction writers were accurate prognosticators when they described militaristic struggles in the far future or on distant planets, suggesting that human nature evolves at a much slower pace than does technology.
Just as the hotbed of activity in physics would s.h.i.+ft from Europe to America following World War II, the epicenter of science fiction would undergo a similar transition. Hugo Gernsback wrote in "The Rise of Scientification" in the spring 1928 issue of Amazing Stories, "It is a great source of satisfaction to us, and we point to it with pride, that 90 percent of the really good scientifiction authors are Americans, the rest being scattered over the world." In Gernsback's perhaps biased opinion, homegrown talent had eclipsed the seminal contributions to the genre by Jules Verne, H. G. Wells, and other European pioneers of "scientifiction."
Verne in particular is considered by many to be the "father of science fiction." He is lauded for his accurate descriptions of future technology (heavier-than-air transport, long-range submarine travel, lunar travel via rockets) as well as for his impossibly exotic locales (hollow centers of the Earth and mysterious islands). Verne's success at prediction stems from his following the same principles that guide scientific research. Whether uncovering new scientific principles or creating a new genre of speculative fiction, one must head out for uncharted terrain. One will not discover a new continent, after all, if one travels only on paved highways. As Edward O. Wilson once cautioned, for us mere mortals, who are not able to make the dramatic leaps of a Newton or Einstein, care must be taken to not metaphorically sail too far from home, in case the world really is flat. The preferred tack is to make small excursions from the known world, trying always to keep the sh.o.r.e in sight. Verne would frequently make reasonable extrapolations on current scientific developments and imagine a mature technology that could exist, if a few details (and perhaps a miracle exception from the laws of nature) were finessed.
A Jules Verne adventure inevitably takes place in the time period that the novel is published, and a then physically improbable mode of transportation will bring our heroes to an exotic locale. This was the format of Verne's first successful novel, Five Weeks in a Balloon, in which a trio of adventurers in 1863 travel to uncharted Africa, as well as his later novels Journey to the Center of the Earth, 20,000 Leagues Under the Sea, From the Earth to the Moon, The Mysterious Island, and Robur the Conqueror. Yet in the second novel he wrote, though it was the last to be published, Jules Verne considered the most extraordinary voyage of all-to Paris in the Twentieth Century.
This novel marks a radical departure for Verne. Written in 1863, it describes the everyday life and mundane experiences of a young college graduate in Paris in 1960. In contrast to the optimistic view of technological wonders one a.s.sociates with Verne, the novel despairs for a future world where commerce and mechanical engineering are the highest values of society, and cultural pursuits such as literature and music are disdained. So uncommercial did Verne's publisher find this ma.n.u.script decrying the triumph of commerce that he convinced Verne to lock it away in a safe. There it sat, neglected and forgotten, until the 1990s, when the safe, which was believed to be empty and whose key had long been lost, was cut open with a blowtorch, and the tome was discovered.
This short fiction certainly could never be mistaken for a typical Verne adventure tale-the protagonist is a young poet who loses his job at his uncle's bank, fails to find gainful employment, loses contact with his only friends and his young love, and ends the novel wandering aimlessly through the streets of Paris during a bitter winter storm until he pa.s.ses out in the snow in a cemetery containing many famous French authors of the nineteenth century. And yet there are enough accurate descriptions of life in the next century to clearly place it among Verne's body of work. The 1863 novel describes automobiles that drive quietly and efficiently using a form of the internal combustion engine (thirteen years before Nikolaus Otto invented the four-stroke engine and more than forty years prior to the ma.s.s production of automobiles by Henry Ford), and it is suggested that the energy source involves the burning of hydrogen. Elevated trains are propelled by compressed air (while the London Underground opened the year this novel was written, elevated tracks would not see real construction for another five years); the city is illuminated at night by electric lights (Cleveland, Ohio, rather than Paris, would earn the t.i.tle of first city of electric lights five years later); and skysc.r.a.per apartments are accessible by automatic elevators, again five years before the construction of the elevator in the eight-story Equitable Life a.s.surance Building in New York City.
Verne posited that by 1960 global communication would be an established fact and a worldwide web of telegraph wires would bring "Paris, London, Frankfurt, Amsterdam, Turin, Berlin, Vienna, Saint Petersburg, Constantinople, New York, Valparaiso, Calcutta, Sydney, Peking, and Nuku Hiva3" together. Furthermore, he described "photographic telegraphy," to be invented at the end of the nineteenth century, which "permitted transmission of the facsimile of any form of writing or ill.u.s.tration, whether ma.n.u.script or print, and letters of credit or contracts could be signed at a distance of five thousand leagues." This last had to await developments in physics more profound than pneumatic trains-for the modern fax machine is a demonstration of quantum mechanics in action!
Verne also suggested in this novel that mechanical progress would result in a military arms race that would yield such destructive cannons and equally formidable armor s.h.i.+elding that the nations of the world would just throw up their hands and abandon war entirely. Friends of the main character in the novel, bemoaning the loss of the honorable occupation of professional soldier, note "that France, England, Russia and Italy have dismissed their soldiers; during the last century the engines of warfare were perfected to such a degree that the whole thing had become ridiculous." Verne did accurately predict the "mutually a.s.sured destruction" theory of war ushered in by intercontinental ballistic missiles, but he underestimated the capacity of humans to find ways to wage wars nevertheless.
There is a deep similarity between the young physicists who developed quantum theory and the fans of the science fiction pulps of the 1920s and 1930s. Namely, they were both able to make a leap-not of faith but of reason-to accept the impossible as real and to will their disbelief into suspension.
Science fiction fans can entertain the possibility of faster-than-light s.p.a.ce travel, of alien races on other planets, of handheld ray guns capable of shooting beams of pure destruction, and of flying cars and humanoid robots. The physicists at the birth of quantum mechanics, trying to make sense of senseless experimental data, had to embrace even more fantastic ideas, such as the fact that light, which since the second half of the nineteenth century had been conclusively demonstrated both theoretically and experimentally to be a wave, could behave like a particle, while all solid matter has a wavelike aspect to its motion.
It is perhaps small wonder that, faced with such bizarre proposals concerning the inner workings of a universe that had heretofore exhibited clockwork predictability, these scientists sought relaxation not in fantastic science fiction adventures but in the conventionality of dime-store detective novels and American cowboy motion pictures. In fact, the predictability of these western films led Niels Bohr, one of the founders of quantum theory, and his colleagues to construct theories regarding plot development in Westerns, when not grappling with the mysteries of atomic physics. In one partic.i.p.ant's recollection, Bohr proposed a theoretical model for why the hero would always win his six-shooter duel with the villain, despite the fact that the villain always drew first. Having to decide the moment to draw his pistol actually impeded the villain, according to Bohr's theory, while the hero could rely on reflex and simply grab his weapon as soon as he saw the villain move. When some of his students doubted this explanation, they resolved the question as good scientists, via empirical testing using toy pistols on the hallways of the Copenhagen Inst.i.tute (the experimental data confirmed Bohr's hypothesis).
In most discussions of quantum mechanics, at both the popular and technical levels, one typically begins with a recitation of the experimental findings that challenged accepted theories and then proceeds to describe how these data motivated physicists to propose new concepts to account for these observations. Let's not do that. In the spirit of the 1970s television detective show Columbo,4 I'll begin with the solution to the mystery of the atom and only then describe its experimental justification.
There are three impossible things that we must accept in order to understand quantum mechanics: Light is an electromagnetic wave that is actually comprised of discrete packets of energy.
Matter is comprised of discrete particles that exhibit a wavelike nature.
Everything-light and matter-has an "intrinsic angular momentum," or "spin," that can have only discrete values.
It is reasonable at this stage to ask: Why wasn't this brought to our attention sooner? How is it possible to live a careful and wellobserved life and yet never notice the particle nature of light, the wave nature of matter, and the constant spinning of both? It turns out that these are all easy to miss in our day-to-day dealings. While the human eye is physically capable of detecting a single light particle, rarely do we come across them in ones or twos. On a sunny day, the light striking one square centimeter (roughly equivalent to the area of your thumbnail) is comprised of more than a million trillion of these packets of energy every second, so their graininess is not readily apparent.
The second principle discusses the wavelike nature of matter. I show in Chapter 3 that a thrown baseball has a wavelength less than a trillionth the size of an atomic nucleus; it is consequently undetectable. The wavelength of an electron within an atom, in contrast, is about as large as the atom itself, and thus this wavelike property cannot be ignored as we seek to understand how the atomic electrons behave.
Atoms interact with light in minute quant.i.ties, and the wavelike nature of the motion of electrons in the atom turns out to be crucial to determining how it can absorb or lose the energy contained in light. Thus any model of the atom and of light that relies solely on our day-to-day experiences fails to accurately account for observation. The influence of the third principle, concerning the "intrinsic angular momentum," also referred to as "spin," is fairly subtle and comes into play when two different electrons or two atoms are so close to each other that their matter-waves overlap. This effect turns out to be rather important and is the key to understanding solid-state physics, chemistry, and magnetic resonance imaging.
While it is certainly true that these three basic principles of quantum mechanics seem weird, it is important to note that making counterintuitive proposals about nature is not a unique aspect of quantum mechanics. In fact, putting forth a seemingly weird idea to describe some aspect of the physical world, developing the logical consequences of this weird idea, experimentally testing these consequences, and then accepting the reality of the weird idea if it conforms to observations is pretty much what we call "physics."
Weird ideas have been the hallmark of physics for at least the past four hundred years. Sir Isaac Newton argued in the mid-1600s, in his first law of motion, that an object in motion remains in motion unless acted upon by an external force. In my personal experience, when I am driving in a straight line along a highway at a constant speed of 55 miles per hour, I must continue to provide a force in order to maintain this velocity. If I take my foot off the accelerator, I do not remain in uniform straight-line motion (even if my tires are properly aligned) but rather slow down and eventually come to rest. This is, of course, due to the influence of other external forces acting on my automobile, such as air drag and friction between the road and my tires. We do not find the effects of friction strange or mysterious, as we have had a few centuries to accept the concept of dissipative forces. These forces appear "invisible" to us, and it required tremendous insight and abstraction on Newton's part to imagine what an object's motion would be like in their absence. This strange idea of drag and frictional forces, no less counterintuitive than anything quantum theorists have suggested, applies to large objects such as people and apples.
The quantum realm is more mysterious, as most of us, aside from superheroes such as the Atom or the Incredible Shrinking Man, do not regularly visit the interior of an atom. Nevertheless, it took roughly sixteen hundred years for Newton's first law of motion to overturn Aristotle's proposal that objects slowed down and came to rest not due to friction, but owing to the fact that they longed to return to their "natural state" on the ground.
In the century preceding the development of quantum theory, physicists such as Michael Faraday and James Clerk Maxwell suggested that the forces felt by electric charges and magnets were due to invisible electric and magnetic fields. Faraday was the first to suggest that electric charges and magnetic materials create "zones of force" (referred to as "fields") that could be observed only indirectly, through their influence on other electrical charges or magnets. Scientists at the time scoffed at such a bizarre idea. To them, even worse than Faraday's theory was his pedigree: He was a self-taught experimentalist who had not attended a proper university such as Oxford or Cambridge. But Maxwell took Faraday's suggestion seriously and was able to theoretically demonstrate that visible light consists of an electromagnetic wave of oscillating electric and magnetic fields.
Changing the frequency of oscillation of the varying electric and magnetic fields yields electromagnetic waves that can range from radio waves, with wavelengths of up to several feet, to X-rays, with a wavelength of less than the diameter of an atom. Each of these forms of light are outside our normal limits of detection but can be detected with appropriate devices. The weird ideas of Faraday and Maxwell are the basis of our understanding of all electromagnetic waves, without which we would lack radio, television, cell phone communication, and Wi-Fi.
If the nature of progress in physics involves the introduction and gradual acceptance of weird ideas, then why does quantum mechanics have a particular reputation for bizarreness? It can be argued that, in part, the weirdness of the ideas underlying quantum mechanics is a consequence of their unfamiliarity. It is no less counterintuitive, in my opinion, to state that electric charges generate fields in s.p.a.ce, and that we are always moving through a sea of invisible electromagnetic waves, even in a darkened room, than to say that light is composed of discrete packets of energy termed "photons." Phrases such as "magnetic fields" and "radio waves" are part of the common vernacular, while "wave functions" and "de Broglie waves" are not-at least not yet. By the time we are done here, such terms will also become part of your everyday conversation.5
Photons at the Beach.
Light is an electromagnetic wave that is actually
comprised of discrete packets of energy.
The cover of the August 1928 issue of Amazing Stories, shown in Figure 1, which contained Buck Rogers's debut, featured a young man flying via a levitation device strapped to his back. While rocket packs would be labeled "Buck Rogers stuff" (and levitating belts would soon be featured in Buck Rogers's newspaper strip adventures), the cover of this issue of Amazing Stories actually ill.u.s.trated E. E. Smith's story "The Skylark of s.p.a.ce." The cover depicts d.i.c.k Seaton, a scientist who is testing out a flying device that employs a newly discovered chemical. When an electrical current is pa.s.sed through this substance, Element X, while it is in contact with copper, the "intra-atomic energy" of the copper is released, providing an energy source for a personal levitation belt, a s.p.a.ces.h.i.+p (the Skylark of the t.i.tle), or a handheld weapon firing "X-plosive bullets."
"The Skylark of s.p.a.ce" leaves vague the exact nature of the "intra-atomic energy" released by the copper when catalyzed by Element X and an electrical current. A rival scientist of Seaton's puts it as follows: "Chemists have known for years that all matter contains enormous stores of intra-atomic energy, but have always considered it 'bound'-that is, incapable of liberation. Seaton has liberated it." As chemists certainly knew, even in 1928, how to release the energy stored in chemical bonds between atoms in molecules such as nitroglycerin or TNT, the vast amounts of intra-atomic energy liberated by Element X may refer to the conversion of ma.s.s into energy through Einstein's relations.h.i.+p E = mc2. This seems likely; when a s.p.a.ces.h.i.+p propelled by Element X is accidently set to full thrust, the resulting acceleration becomes so great that no one on board can move to the control board to decrease their speed and the s.h.i.+p stops its motion only when the copper supplies are exhausted. While ill.u.s.trating Einstein's principle of the interrelation between energy and ma.s.s, this scene contradicts the Special Theory of Relativity when it reveals that this uncontrolled acceleration has resulted in the s.h.i.+p traveling many times the speed of light. When Seaton wonders how this can be reconciled with Einstein's famous work, his companion replies, "That is a theory, this measurement of distance is a fact, as you know from our tests." Like any good scientist, Seaton agrees that observation is the final arbiter of correctness and concludes of Einstein, "That's right. Another good theory gone to pot."
The scientists in "The Skylark of s.p.a.ce" should not be so quick to abandon Einstein, for their X-plosive bullets of intra-atomic energy provide confirmation of another of his theories. This application of Element X, as well as the ray guns wielded by Buck Rogers, Flash Gordon, and other heroes of the science fiction pulps and comic strips, is not too far from the mark, as reflected in the first quantum principle, at the top of this chapter. As proposed by Albert Einstein the same year he developed his Special Theory of Relativity, all light consists of "bullets," that is, discrete packets of energy, termed "photons."
Now that we have the answers to quantum mechanics-what were the questions that called for these new physical principles? The ultraviolet catastrophe alluded to earlier concerned the brightness of the light emitted by an object as a function of temperature. Certain objects, such as graphite and coal dust, are black, as they absorb nearly all light that s.h.i.+nes on them. In equilibrium, the light energy absorbed is balanced by light given off. The spectrum of light of such blackbodies, that is, how much light is emitted at a given frequency, depends only on how hot it is and is the same for metals, insulators, gases, liquids, or people if they are at the same temperature.
The theory of electromagnetic waves, developed by James Clerk Maxwell in the second half of the nineteenth century, was able to account for the energy emitted by a glowing object at low frequencies, such as infrared light, but at higher frequencies (above visible light) this theory predicted results that were nonsensical. Calculations indicated that the light from any heated object would become infinitely intense at high frequencies, above the ultraviolet portion of the spectrum. Thus, anyone looking at the glowing embers in a fireplace, or the interior of an oven, should be instantly incinerated with a lethal dose of X-rays. If this were true, most people would notice. This so-called ultraviolet catastrophe (which, as indicated, was a catastrophe more for theoreticians making the predictions than for anyone else) disappeared following Planck's suggestion that when the atoms in a glowing object emit light, the atoms lose energy as if they were moving down the steps of a ladder, and that those atoms must always move from rung to rung of the ladder and cannot make any other transitions between rungs. Why this would resolve the ultraviolet catastrophe, we'll explain in Section 4. For now let's focus on this "ladder" of possible energy values.
Figure 2: A plot of the light intensity given off from a "blackbody" object as a function of the frequency of light. The measured curve (solid line) shows that the total amount of light emitted is finite, while the pre-quantum mechanics calculated curve (dashed line) continues to rise as the frequency of light increases. That is, before quantum mechanics, physics predicted that even objects at room temperature would give off an infinite amount of light energy in the ultraviolet portion of the spectrum-a clearly ridiculous result.
Planck firmly believed that light was a continuous electromagnetic wave, like ripples on the surface of a lake,6 as theoretical considerations and extensive experimental evidence indicated. His proposal of discreteness in atomic energy loss was fairly modest (or as modest as a revolution in scientific thought can be). It turns out that while Planck justly receives credit for letting the quantum genie out of the bottle, there were other experimental conundrums waiting in the wings regarding how atoms interacted with light that would require far bolder steps than Planck was willing to take. At the same time that scientists were measuring the light given off by hot objects, giving rise to the ultraviolet catastrophe, Philipp Lenard was studying the electrons emitted by metals exposed to ultraviolet light. This led to a different catastrophe, both personal and scientific.
In the late 1800s physicists had discovered that certain materials, such as radium and thorium, gave off energy in the form of what would eventually be termed "radiation." Scientific researchers entered a "library phase," cataloging all of the different types of radiation that different substances emitted. Using the Greek alphabet as labels (, , , etc., instead of a, b, c, and so on), they started with "alpha rays," which turned out to be helium nuclei (two protons and two neutrons) ejected from atoms found near the end of the periodic table of the elements,7 then moved on to "beta rays," (high-speed electrons), followed by "gamma rays" (very high-energy electromagnetic radiation).8 When William Roentgen discovered a form of radiation that would fog a photographic plate, pa.s.sing through paper or flesh but not metal or bones, he termed this unknown ra diation "X-rays." Roentgen's discovery came before the Greek nomenclature tradition used for naming rays; he used the letter X, as it is the letter traditionally employed in math problems for the unknown quant.i.ty. (Roentgen's "X-rays" were the forerunner of many science fiction X-based characters, such as the X-Men, Professor X, Planet X, Dimension X, Element X, and X the Unknown). It was later shown that X-rays are simply electromagnetic waves-that is, light-with more energy than visible and ultraviolet light but less energy than gamma rays.