Chapter 3: A Scientific Revolutionary: Einstein’s Four Papers of 1905

Chapter 3: A Scientific Revolutionary: Einstein’s Four Papers of 1905

chapter 3: A SCIENTIFIC REVOLUTIONARY: EINSTEIN’S FOUR PAPERS OF 1905

ISAAC NEWTON BECAME A scientific celebrity in the annus mirabilis —the “wonderful year” —of 1665–1666. During that year, he developed the basic ideas of both differential and integral calculus and made the startling empirical discovery that white light is actually made up of colored rays. Indeed, Newton even provided a list of those “colors of the rainbow” —red, orange, yellow, green, blue, indigo, and violet. Yet this discovery was only the beginning of a remarkable career. Just over twenty years later, in 1687, Newton published the work widely known as his Principia, in which he set out his three laws of motion, the modern concepts of force and mass, and the new and deeply counterintuitive concept of universal gravitation.[39]

The acclamation of Newton as a genius was partly the result of a resurgent Britain wishing to impress its intellectual authority on the emerging world of science. Yet Newton’s reputation did not rest entirely on nationalist grounds. His genius was held to lie in his capacity to penetrate beyond the world of experience to a deeper reality that lay behind it. The frontispiece to the 1729 English translation of Newton’s Principia (originally written in Latin, which was just beginning to fall out of favor as the international language of scholarship) showed Newton sitting on the clouds of heaven, being personally instructed by the Muse of mathematics. Newton was a genius who could see beyond our world of appearances and discern a deeper structure, reflecting the mind of God. As the British astronomer royal Edmund Halley put it in a eulogy for Newton, his “sublime Intellect has allowed us to penetrate the dwellings of the Gods and to scale the heights of Heaven.”[40]

Halley’s comments help us grasp what was seen as special about Newton in particular and perhaps why there is such cultural reverence for the idea of a scientific genius in general. The genius is seen as standing above politics and other vested interests, possessing an almost religious authority on account of the quality of their vision of reality. Thomas Jefferson, the principal author of the Declaration of Independence and the third president of the United States, expressed the hope that a “natural aristocracy” based on “worth and genius” would emerge to replace the “artificial aristocracy” of wealth and power.[41]

It’s not difficult to see why the concept of a genius was so attractive to many after the First World War, which ended in November 1918. There was an urgent need for rebuilding nations and putting things right after the catastrophe of a global war. Traditional sources of wisdom were seen to have failed. The world had emerged from a hitherto unimaginable trauma of destruction and devastation. Who could trust their political and social leaders after such an event? Perhaps a genius might show the world a better way. But who would this be?

Introducing Einstein

In 1905, Albert Einstein was working as a clerk in the Swiss patent office —or, to use its official name, the “Federal Office for Intellectual Property” —in the Swiss capital, Bern. He held no academic position in any prestigious research institute or university. His job was to assess patent applications. One of the most famous photographs of Einstein shows him standing at a lectern in room 86 on the third floor of the Federal Office for Intellectual Property, scrutinizing paperwork submitted by eager inventors hoping to secure a patent. The accounts of his time at the Swiss patent office suggest that he was diligent in his duties, and in 1906, after four years of service, he was promoted from technical expert (class III) to technical expert (class II).

His position at the Swiss patent office was intellectually undemanding, and Einstein found that he had time to work at the projects that really mattered to him —solving the riddles of physics that remained unsolved at the opening of the twentieth century.[42] As he later recalled, the patent office became his worldly cloister in which he “hatched [his] most beautiful ideas,” often in discussion with fellow physicist Michele Besso, who worked in the same building. Although Einstein went on to gain worldwide fame after the end of the Great War for his general theory of relativity, and a Nobel Prize in 1921 for his explanation of the photoelectric effect, the roots of that later fame lay in a series of four groundbreaking articles he published in the leading scientific journal Annalen der Physik (“Annals of Physics”) in 1905. We shall consider each of these articles in this chapter. But first, we need to tell the remarkable story of Einstein’s rise to fame.[43]

Einstein was born to nonobservant Jewish parents at Ulm, in the kingdom of Württemberg, on March 14, 1879. Württemberg had recently become part of a unified Germany after the Franco-Prussian War in 1871. The summer after he was born, the family moved to Munich, the capital city of Bavaria, where Einstein began his education at the Luitpold Gymnasium. Later, following the failure of their electrical business, Einstein’s parents moved to northern Italy while he continued his education in Munich.

Einstein’s goal was to settle in Switzerland and train as a teacher in physics and mathematics at the Swiss Federal Polytechnic School (now known as the Swiss Federal Institute of Technology) in Zürich. His grades were not outstanding, and it was clear to Einstein that there was little likelihood he would go on to secure an academic position in Switzerland. Between May 1901 and January 1902, he taught at academies in Winterthur and Schaffhausen before moving to Bern, where he gave private lessons in mathematics and physics to make ends meet. The reasons for this move are not clear, although some suggest that it reflected Einstein’s desire to avoid compulsory military service. Einstein had been stateless, having renounced his German citizenship in January 1896, but he acquired Swiss citizenship in 1901. In 1902, he found a relatively well-paid job as a technical assistant in the Swiss patent office. In January 1903, he married the Serbian mathematician Mileva Marić, who was a fellow student during his time at the Zürich Polytechnic. The couple had two children: Hans Albert, born 1904, and Eduard, born 1910.

In the fall of 1900, while waiting for the outcome of his application for Swiss citizenship, Einstein used his spare time to keep up with his scientific reading. He was particularly influenced by the German physicist Ludwig Boltzmann, who explained the observed properties of gases as “discrete particles of definite size which move according to certain conditions.” This “kinetic theory of gases” developed by Boltzmann emphasized that atoms were not some kind of hypothetical theoretical construction but were real objects. This ran counter to the dominant view of that time, which was forcefully expressed in the writings of Ernst Mach. Einstein later criticized Mach and his followers for allowing their scientific ideas to be determined by unacknowledged philosophical presuppositions, arguing that their prejudices against atomic theory were due to “their positivistic philosophical views.”[44]

Boltzmann’s ideas stimulated Einstein to write his first published scientific paper in 1901 on the implications of the well-known “capillary effect” —the ability of a liquid to flow in confined spaces without the assistance of gravity, or even in opposition to gravity. A familiar example of this is the phenomenon of “rising damp,” in which water moves upwards in concrete or masonry, or the rising of sap in trees. But why did it happen in the first place?

Sadly, Einstein’s paper —which was not particularly well written or argued —did not provide any convincing answers to this question.[45] Einstein’s proposal for a correlation between the atomic weight of a liquid and the extent of its capillary action is no longer taken seriously. However, despite the shortcomings of his first scientific paper, Einstein now had the distinct advantage of having a published article to his name, which he circulated to academic institutions in the hope of finding a proper academic position.

In recent years, increased attention has been paid to this early article on account of a suspicion that Einstein might have had some unacknowledged assistance from Mileva Marić. At the time when Einstein was researching and writing this 1901 article, the couple were living together, although from mid-1900 until December 1902, they generally lived in different cities and sometimes even in different countries.

Einstein himself referred to the capillarity article of 1901 as “ours” in a letter to Marić, suggesting that she was somehow involved in its production. This has led some scholars to suggest that Marić was actually Einstein’s collaborator and possibly the source of some of his ideas.[46] This point is important, given the remarkable series of papers that Einstein published in Annalen der Physik in 1905. Surely it would not be possible for one person to achieve such an astonishing feat, given the brilliance and originality of these articles?

This suggestion fits an influential media narrative, which (rightly) notes that male artists and academics of this period were prone to incorporate the ideas of female students or collaborators into their own work without due acknowledgment. A 2003 documentary titled Einstein’s Wife, developed by Australian filmmaker Melsa Films, asserted that Marić was originally credited as a coauthor on several of these 1905 papers before her name was mysteriously removed from the final version of the texts. Was this a plot to disguise that she was actually a coauthor of these papers?

Following extensive scholarly criticism of this film,[47] this suggestion is no longer taken seriously, as it seems to rest on a series of misjudgments, including a mistranslation of some (questionable) comments by the Russian physicist Abram F. Joffe.[48] The evidence is now generally accepted to indicate that Marić did indeed support and encourage Einstein, helping him to track down information and perhaps occasionally checking his mathematics. She played a role similar to Michele Besso, whom Einstein valued as a “sounding board” for his ideas. Yet the core ideas were Einstein’s own, even if he was wise enough to consult others in his quest to present them most effectively.[49]

So what were these four articles? And why did they have such an impact? In the sections that follow, we shall consider each one and explain its scientific importance.

March 1905 —The Photoelectric Effect and the Nature of Light

What is now known as the “photoelectric effect” was first observed in 1887 by the German physicist Heinrich Hertz[50] and investigated more thoroughly later by Hertz’s colleague Philipp Lenard in a series of studies, culminating in a major article of 1902.[51] Under the right circumstances, it was found that if a beam of light was shone on certain metals, the beam was able to eject electrons from the surface of those metals.

Perhaps this was not surprising. Classical physics recognized that every form of electromagnetic radiation transmitted energy, and it is quite easy to think of this energy pushing tiny particles of negative charge (i.e., electrons) off the surface of a metal, especially if these electrons were only loosely attached to that surface. It’s a bit like throwing stones at a wall of rock. Sometimes the stones just bounce back, but sometimes they dislodge small pieces of rock as well. It all depends on how hard they are thrown and how many hit the wall at any one time.

As might be expected, Lenard’s 1902 experiments found that the rate of emission of electrons from the surface of the metal was directly proportional to the intensity of light falling on it. The brighter the light, the more electrons were dislodged from the metal surface. Yet something else was observed that did not seem to fit existing theories.

Lenard also found that the brightness or intensity of the beam of light falling on a metal surface seemed to have no effect on the energy of these emitted electrons. The electrons emitted through exposure to a very bright light turned out to have the same energy as those emitted through exposure to a very dim light. It didn’t really make sense. Common sense suggested that it was the brightness of the light that determined how much energy it transmitted. Furthermore, photoelectrons were emitted only if the frequency of the light exceeded a threshold frequency, which varied from one metal to another. (The frequency of light refers to the number of waves that pass a fixed point in a given period of time —typically one second.)

So why should the color of the light matter? Why did blue light seem more effective than red light? Surely it was the brightness of the light, not its color, that was really important? At that time, nobody thought that the color of light had anything to do with how much energy it transmitted. What really mattered, everyone thought, was its intensity. There was, of course, another explanation —that classical physics had missed something and Lenard’s experiments were pointing towards a new way of thinking about the nature of light. So how could these observations be explained?

The Photoelectric Effect

An electron is emitted from metal when light hits it.

In his first article of 1905, Einstein proposed that according to the evidence, light seemed to be composed of particles (later named photons). He also proposed that each particle’s energy was proportional to the frequency of the electromagnetic radiation of which it was part. In proposing this, Einstein drew on the theories of Max Planck set out in a publication of 1900 developing the hypothesis of the “quantization” of energy.[52] This hypothesis stated that the energy of an oscillator is not infinitely continuous but is made up of “packets” of fixed size. Planck introduced a fundamental constant, h (now known as “Planck’s constant”), to refer to this basic unit of energy. For an oscillator of frequency ν, the energy of the oscillator can be defined as hν.

According to Planck, energy is continuous but is actually made up of very small packets or discrete units. An analogy may be helpful in explaining this idea. It is like looking at a great sand dune in the African desert. From a distance, it seems smooth; on closer examination, you see it is made up of millions of small grains of sand. Or think of quantized energy being like the rungs of a ladder. If you want to climb the ladder, you can go up only in increments of one or more whole rungs. There are no intermediate levels.

Energy may seem to be continuous, but on closer examination, it is made up of tiny packets of energy. A quantum is the smallest bit of electromagnetic radiation that can be emitted —in some ways paralleling the idea of an atom as the smallest unit of matter (although this idea had to be abandoned in the 1930s, when Cockcroft and Walton demonstrated that they had split an atom). We may think that light is a continuous wave of electromagnetic radiation, but it is actually a stream of discrete packets of energy, now known as photons. Einstein considered the photoelectric effect to confirm Planck’s ideas and to further undermine the increasingly beleaguered classical approach to the nature of light.

Einstein argued that the photoelectric effect was best understood in terms of a collision between an incoming particle-like bundle of energy and an electron close to the surface of the metal. The electron could be ejected from the metal only if the incoming photons possessed sufficient energy to dislodge this electron.

Einstein’s theory allowed two of Lenard’s otherwise puzzling observations to be explained:

Einstein’s brilliant theoretical account for the photoelectric effect suggested that electromagnetic radiation had to be considered as behaving as particles under certain conditions. It met with intense opposition, not least because it appeared to involve the abandonment of the prevailing classical understanding of the total exclusivity of waves and particles: something could be one or the other but not both. It was not until 1915 that Einstein’s approach began to achieve acceptance, particularly on account of the meticulous research of the American physicist Robert Millikan.[53]

This article led to Einstein’s being awarded the Nobel Prize in Physics in 1921 “for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect.”

So why is Einstein’s article on the photoelectric effect so significant? What are its wider implications? Historically, Einstein’s article was of critical importance in developing the field of quantum mechanics. Quantum mechanics arose in the aftermath of the collapse of classical approaches to the nature of light as a beam of particles (Newton) or as a wave motion, analogous to sound (James Clerk Maxwell). These two models of light were thought to be incompatible: if one was right, the other must be wrong.

Although Einstein was cautious in the way he stated it, his paper opened the way to thinking of light in terms of “packets of waves,” an idea that could be interpreted as meaning that light could be seen as both a particle and a wave and that Einstein later referred to as the “wave-particle duality of light.” The Danish physicist Niels Bohr, widely regarded as the founder of the “Copenhagen approach” to quantum theory, developed this idea using the idea of complementarity. For Bohr, the classical models of both waves and particles were required to explain the behavior of light and matter. Bohr’s basic argument was that we need to use both particle and wave models of light to cope with the experimental observations, even though these are inconsistent and cannot easily be integrated into a larger picture of the nature of light.

Einstein, then, can be seen as one of the founders of quantum theory. Yet Einstein later did not like the way in which quantum theory developed during the 1920s, especially as it came to place an emphasis on probability. But by then, Einstein was famous for another reason —the theory of general relativity —to which we shall turn in the next chapter.

May 1905 —Are Atoms Real?: Einstein on Brownian Motion

Words have histories, and the word atom is no exception. The word atomos (Greek: “something that cannot be divided”) was introduced in the period of classical Greek philosophy by Democritus to refer to the fundamental components of reality. Atoms were seen as the basic building blocks of our world. Although there was sporadic discussion of the idea at many points in the history of science, it was not until the early nineteenth century that the idea began to solidify and become part of mainstream science.

This growing interest in “atomism” —the idea that the fabric of physical reality was made up of atoms —was largely due to the British chemist John Dalton. In his New System of Chemical Philosophy (1808), Dalton suggested that many of these chemical reactions could be understood in terms of atoms of different chemical elements combining with each other to produce new compounds. Dalton’s atomic theory held that all chemical compounds were composed of combinations of atoms in defined ratios and that chemical reactions could be thought of as a rearrangement of the reacting atoms. Dalton was able to show that one tin atom will combine with either one or two oxygen atoms to form chemicals that we now know as tin oxide and tin dioxide, respectively. On the basis of his study of chemical reactions, Dalton also suggested that carbon dioxide was a compound made up of one carbon and two oxygen atoms. The Austrian physicist and philosopher Ludwig Boltzmann developed the ideas further, holding that gases —such as air —were made up of atoms and molecules.

This, however, proved controversial. Ernst Mach, Boltzmann’s colleague at the University of Vienna, argued that atoms could not be seen or detected empirically; they were simply mental constructions that might be helpful in trying to make sense of our experience of the world. The idea of an atom was “a didactic utility” —a fiction that was nevertheless useful in deriving experimentally observable results. Although there were exceptions, the physics establishment around the year 1900 was generally of the view that atoms did not exist in reality.

All of this changed as a result of Einstein’s second paper of 1905, which dealt with what is generally known as “Brownian motion” —the observation that very small particles of matter, when suspended in a liquid, do not remain stationary but move around randomly. The phenomenon was named after the Scottish botanist Robert Brown (1773–1858), who noticed that pollen behaved in this way when suspended in water and viewed through a microscope. The particles of pollen seemed to vibrate as if they were being shaken, and they moved within the liquid in irregular patterns.

Initially, Brown thought that the pollen moved because it was alive. After all, pollen was produced by flowers, which were living organisms. Brown eliminated this possibility by showing that the same pattern was observed when he used finely ground rock instead of pollen. “Extremely minute particles of solid matter, whether obtained from organic or inorganic substances, when suspended in pure water, or in some other aqueous fluids, exhibit motions for which I am unable to account.”[54] Nobody else seemed able to make sense of his observations, which were easily reproduced in laboratories.[55]

Brownian Motion

The random motion that occurs when small particles are suspended in liquid.

This phenomenon of a constant erratic zigzag movement of small particles in a liquid was well known by 1905, when Einstein wrote his article. But what did it mean?[56] Einstein took the view that “the suspended particles perform an irregular movement . . . on account of the molecular movement of the liquid.” In other words, the movement of the suspended particles in a liquid —like pollen in water —is due to the movement of the molecules of the liquid itself, which bump into the particles and thus cause them to behave erratically. Einstein was able to show how this random motion would be affected by, among other things, the temperature of the liquid and its viscosity.

Einstein explicitly drew on Boltzmann’s “kinetic theory,” which proposes that the temperature of a liquid is ultimately a measure of the rate of movement of its individual molecules, which could be compared to billiard balls moving around with increasing speed in a closed container. Raising the temperature of a liquid causes the molecules to move more quickly and hence to bump into any suspended particles with greater force.

On the basis of these assumptions, Einstein was able to derive an equation predicting the relationship between the extent of Brownian motion and the temperature of the liquid in which particles were suspended. Broadly speaking, Einstein predicted that the motion of suspended particles increases with the temperature of the liquid, that it decreases with increasing viscosity of that liquid, and that it decreases with an increasing size of the suspended particles. Einstein knew he was taking a risk in proposing such a mathematically precise formulation, which could be verified or falsified by experiment. If his prediction of the amount of this movement was shown to be incorrect, a weighty argument would be provided against the molecular kinetic conception of heat —and the physical existence of atoms.

Several attempts were made in 1906 to confirm Einstein’s approach, although the outcomes were initially confusing.[57] By late 1908, however, a steady stream of experimental results from French physicists emerged, which were strongly supportive of Einstein’s theory.[58] For the French physicist Jean Perrin and others, the empirical verification of Einstein’s mathematical formula implicitly affirmed the core assumption that lay behind it: liquids are made up of real physical molecules.

Einstein’s greatest achievement in this paper was to show that Mach was wrong. It might not be possible to see atoms or molecules, but their real existence could be inferred from precisely the properties of particles suspended in liquid so carefully analyzed by Einstein in 1905. There were, of course, important parallels with Isaac Newton’s proposal of gravity. For Newton, gravity was a legitimate scientific inference from an observable phenomenon to the unobservable entity that best explains it. Similarly, atoms were not observed; their existence was inferred. Yet that process of inference was robust and generated further hypotheses that were open to empirical confirmation.

Following Einstein’s article of 1905, the pace of exploration of the atomic hypothesis quickened. Interestingly, the notion of atoms was initially more readily accepted by chemists than by physicists. However, a number of factors catalyzed the further acceptance of the atomic hypothesis within physics. One of the most important was the discovery of the phenomenon of radioactive decay. This was discovered in 1896 by the French scientist Henri Becquerel, who noticed that chemicals containing uranium blackened photographic plates, as if they had been exposed to light. Further research in England by Ernest Rutherford and Frederick Soddy suggested that radioactive decay could result in the transmutation of one element to another. Radioactive elements, such as uranium and radium, were shown to emit what were initially termed alpha particles, beta particles, and gamma rays. The best explanation of these observations was that they involved change at the atomic level.[59]

We shall return to reflect on the importance of atoms when we consider another of Einstein’s dramatic interventions of 1905, his formulation of perhaps the most iconic equation of the modern period: E = mc2. But we must now turn to consider the next paper of 1905, in which he set out the basic themes of his theory of special relativity.

June 1905 —Riding Beams of Light: Einstein on Special Relativity

Einstein’s third article of 1905 set out his preliminary reflections on what we have come to know as relativity. Put simply, this is the basic idea that the fundamental laws and constants of physics are the same whether you are stationary or moving. Some will find this statement surprising in that they assume relativity is all about relativism —the idea that there are no absolutes and each of us can determine our own ideas. This is not what Einstein meant. In fact, the core assumption of Einstein’s approach to relativity is that the laws of physics are universally true.

In an earlier chapter, we explored some aspects of Newton’s classical mechanics, which set out the basic principles that govern the interaction of physical bodies. The crowning achievement of Newton’s mechanics was a complete explanation of the workings of the solar system so that astronomers were able to predict with great accuracy and complete reliability such events as eclipses or the return of comets that lay decades or even centuries in the future. Yet Newton’s mechanical philosophy dealt with large objects that were moving relatively slowly compared with the speed of light —such as planets orbiting the sun or apples falling to the earth. So what difference does it make if we consider the behavior of very small bodies —such as subatomic particles —moving at very high speeds?

In an autobiographical reflection written a month before he died in April 1955, Einstein recalled an early thought experiment that had intrigued him while he was a student at the cantonal high school in the Swiss city of Aarau: What would it be like to travel so quickly that it was possible to catch up with a beam of light?

During this year in Aarau the following question came to me: if you were to chase a light wave with the speed of light, you would have a time independent wave field in front of you. Yet such a thing does not seem to exist! This was the first childish thought experiment that was related to the special theory of relativity.[60]

Einstein’s point here is that if he were able to ride alongside a beam of light, it would appear as a stationary electromagnetic field. Yet surfing such a wave led to an impossible conclusion. How could an electromagnetic wave seem stationary —in effect, to become a frozen wave of light? Einstein knew that James Clerk Maxwell had shown that electromagnetic fields moved and vibrated. It had become clear that light was a good example of an electromagnetic wave. Yet Einstein’s thought experiment suggested that under certain circumstances light stopped moving and vibrating. It didn’t make sense. It was as if light had stopped being light. Something was wrong somewhere. But what? As Einstein remarked, the conflict between his thought experiment and Maxwell’s equations caused him some degree of “psychic tension.”

Einstein’s third article of 1905 develops what was later termed the “theory of special relativity,” which applies to objects that are moving in a straight line at constant speeds relative to each other. (Einstein’s later theory of general relativity, proposed in 1915, applies to any form of motion. We shall consider this in the following chapter.)

Einstein’s argument in this third paper of 1905 is based on two central assumptions: “the principle of relativity” and “the principle of the constancy of the velocity of light in a vacuum.”

The “principle of the constancy of the velocity of light in a vacuum” holds that the speed of light in a vacuum has the same value, c, in all inertial frames of reference. It’s easy to accept —but, as Einstein would show, it leads to some counterintuitive consequences. The “principle of relativity” states that the laws of physics do not change, even for objects moving in inertial frames of reference. In other words, the same laws of physics govern the behavior both of stationary objects and objects that are moving with constant speeds in a straight line.

This point had been established by the great Italian astronomer and physicist Galileo Galilei in the seventeenth century —again, using a thought experiment.[61] In 1632, Galileo set out what we might call a classic version of relativity. Imagine you are standing on a dock, watching a ship sail past you at a constant speed. Now imagine that a sailor perched on the top of the ship’s mast drops a rock. Where would this rock actually land? At the base of the mast? Or perhaps a short distance behind the mast, corresponding to the distance the ship had covered while the rock was falling? From the point of view of the sailor who dropped the rock and watches it as it falls, the rock falls straight downwards. And although common sense suggests that the rock ought to land behind the mast, it will actually land at the base of the mast.

Let’s use a more modern analogy to make sure this point has been understood. Imagine you are on an airplane traveling at constant speed (typically about 500 miles per hour, or 223 meters per second). You drop the book you are reading onto the floor. Common sense suggests it ought to shoot past you towards the back of the plane. After all, the plane is moving forwards at 500 miles per hour. But so is the book.

As we all know from experience, the book falls directly to the floor. The book shares the same forward motion of the aircraft. Or, to use technical language, your book (and Galileo’s sailor’s rock) are both located within inertial frames. Both the book and the rock possess a forward motion as they are dropped on account of the inertial frames of the airplane or boat. This forward motion causes the book to land at your foot and the sailor’s rock to land at the bottom of the mast —not where you might expect them to land on the basis of common sense.

Einstein develops aspects of his theory using thought experiments, which are rather more accessible than abstract mathematical formulation. In his later writings on relativity, Einstein asks us to imagine a real-life situation and think through its consequences. In what follows, I shall paraphrase Einstein at points while retaining as much as possible of the core elements of his approach.[62] So let’s think ourselves into the analogy he uses in developing his theory of special relativity. Read each of the four elements of the analogy carefully, and make sure you are comfortable with the points being made:

Einstein uses this and other analogies to make the point that motion is relative, not absolute. Each observer uses a frame of reference to assess both the direction and the speed of movement so that the same movement will appear to be different from different standpoints.

Now that we feel comfortable with this analogy, it can be developed further. Einstein asks us to replace the idea of a human being moving along the train with that of a beam of light traveling in the same direction.

Special Relativity Illustrated by a Train in Motion

So how can this contradiction be resolved? Is there a problem with either or both of the two basic principles that Einstein presupposes? Or does the problem lie somewhere else? Let’s allow Einstein to make the point himself:

If every ray of light is propagated relative to the embankment with the velocity c, then for this reason it would appear that another law of propagation of light must necessarily hold with respect to the carriage —a result contradictory to the principle of relativity. In view of this dilemma there appears to be nothing else for it than to abandon either the principle of relativity or the simple law of the propagation of light in vacuo.[63]

For Einstein, light travels at the same speed, no matter what the speed of its source of emission. So if the speed of light does not change as it moves through space and time, what other way is there of dealing with this dilemma? Einstein realized the need to rethink the relation of space and time. What the observer might see as changes in the speed of light actually reflect variations in what Einstein came to call “space-time.” The solution had to lie in rethinking classical concepts of space and time. As a result, Einstein concluded that space and time must be seen as interwoven —a single continuum, known as space-time. This is not an easy point to grasp —which perhaps explains why nobody seems to have thought of it before Einstein. The same event can occur at different times for different observers. Time does not pass in the same way for everyone. Perhaps the best-known example of this is the “twin paradox,” which concerns two identical twins, one of whom spends some time in a hypothetical spaceship traveling near the speed of light and returns to discover that his twin has aged much more than he has.[64]

Einstein’s notion of relativity has, of course, been seriously misunderstood. As we noted earlier, the most significant and widespread misreading of Einstein presents him as offering scientific support for the idea of moral and cultural relativism. Some suggest that Einstein’s theory of relativity is the outcome of his own radical political and social views —a symbol of “generational rebellion” against the fixed certainties of the past.[65] It is certainly true that many novelists and philosophers have argued that this is the case. For example, Gilbert Harman used Einstein’s theory of special relativity to argue that “moral right and wrong . . . are always relative to a choice of moral framework.”[66] Yet Einstein did not say that, and he certainly did not think that.

For Einstein, the physical laws underlying relativity are constant and universal. There is no sense in which they can be said to be “relative.” Moral relativism has been around since the pre-Socratic philosophers in classical Greece, so its origins have nothing to do with Einstein. In any case, Einstein explicitly repudiated any connection between his theories and a system of morals or ethics. The great German physicist Arnold Sommerfeld declared that the essence of Einstein’s theory was “not the relativity of space and time but rather the independence of the laws of nature from the viewpoint of the observer.” Sommerfeld, however, felt that the phrase “theory of relativity” was an “unfortunate choice” on Einstein’s part, given the way in which it was being misunderstood as somehow endorsing a “relativity of ethical conceptions.”[67]

Richard Feynman, who won the Nobel Prize in Physics in 1965, was scathing about lazy and careless writers who were more interested in being trendy than in giving accurate accounts of Einstein’s ideas. Feynman ridiculed “cocktail-party philosophers” who reduced Einstein’s ideas to cultural slogans such as “all is relative” or “there are no absolutes.”[68] As the (serious) philosopher Bertrand Russell remarked back in the 1920s, philosophers tended to interpret Einstein in the light of their own ideas and concluded that Einstein showed they were right all along.[69]

Yet Einstein’s concept of relativity is the result of absolute laws, not their denial. Einstein believed he had restored order and coherence to our understanding of the universe, following the observation of anomalies that classic Newtonian mechanics couldn’t explain. As he later pointed out, “Nearly every great advance in science arises from a crisis in the old theory, through an endeavour to find a way out of the difficulties created.”[70] Instead of bending the rules to fit in these awkward observations, Einstein uncovered the deeper rules of our universe that ultimately explained these discrepancies. So let’s get this straight: Einstein’s theory of relativity has nothing to do with moral relativism. Einstein has simply been hijacked here by people who misread his ideas and then used them to justify their own moral and social views. Einstein’s theory resolved an accumulation of scientific riddles that otherwise seemed insoluble. Perhaps his ideas seem to make little difference to our everyday lives —although global positioning devices have to use Einstein’s theory to calculate our location. Einstein’s achievement is to make it possible to develop a coherent understanding of our universe, something that lies at the heart of the scientific quest.

September 1905 —E = mc2: The Equivalence of Matter and Energy

Einstein’s famous equation E = mc2 states that the energy, E, of a physical system is numerically equal to the product of its mass, m, and the speed of light, c, squared. This assertion of “the equivalence of mass and energy” is widely seen as one of the most important principles underlying modern physics and was first set out by Einstein in the last of his articles of 1905, titled “Is the Inertia of a Body Dependent on Its Energy Content?” Although this short paper —a mere three pages long —does not explicitly use the equation E = mc2, the basic idea is clearly formulated.

It was not, however, an original idea. In 1881, the British physicist J. J. Thomson proposed that a charged conductor in motion increases its mass in relation to its energy content. Perhaps more significantly, in 1904 —the year before Einstein’s paper was published —the Austrian physicist Fritz Hasenöhrl published an article in the same journal examining the properties of blackbody radiation in a moving cavity and concluded that the radiation energy has an apparent mass associated with it.[71] While there were some problems with Hasenöhrl’s calculations, the basic idea developed by Einstein the following year is unquestionably present in this earlier article.

But did Einstein prove that the equation E = mc2 was right in 1905? Here, scholars are divided.[72] My own reading of the literature leads me to the conclusion that Einstein conceived the idea of “the equivalence of mass and energy” in the summer of 1905 but never managed to derive his idea from first principles. Like Eugene Hecht, I suspect that the way in which Einstein derives this idea in his 1905 article suggests “he already knew the answer he was looking for before he devised the rather elaborate scheme he used to reveal it.”[73] Einstein returned to this question at least half a dozen times in the next twenty years, offering improved accounts of his basic idea and more rigorous justifications of his argument.[74]

My own view is that the idea of “the equivalence of mass and energy” seems to have been an intuition on Einstein’s part, but an intuition rooted in a deep understanding of the physical world, so clearly displayed in his earlier articles of 1905. The philosopher of science Pierre Duhem wrote of experienced physicists possessing le bon sens, a rational faculty that allows us to intuit the truth of fundamental principles or axioms. Perhaps unkindly, Duhem suggested that German scientists lacked this capacity for intuition, which was better seen among their French counterparts![75]

Einstein hints at the influence of Duhem’s approach on his research in a paper of 1918 celebrating the sixtieth birthday of Max Planck. Noting that the supreme task of the physicist is to search for general elementary laws that can be woven together to give a “picture of the world” (Weltbild), Einstein notes that “there is no logical path to these laws.”[76] Rather, they arise through the “intuition, resting on a sympathetic understanding of experience.” This seems to describe at least something of the strongly imaginative and intuitive process of reflection that lies behind Einstein’s paper. He expressed much the same idea to Max Wertheimer towards the end of his life, remarking that he never thought primarily in the form of logical symbols or mathematical equations but rather in terms of images, feelings, and even music.[77]

In the end, what confirmed Einstein’s formulation of the equivalence of mass and energy was not so much any arguments from first principles but experimental observations of the phenomenon. It is generally agreed that the experiment that confirmed Einstein’s formula E = mc2 was Cockcroft and Walton’s famous “splitting of the atom” in 1932. This experiment, carried out at the Cavendish Laboratory in Cambridge, led to both Cockcroft and Walton being awarded the Nobel Prize in Physics in 1951 for their “pioneer work on the transmutation of atomic nuclei by artificially accelerated atomic particles.”

So what did Cockcroft and Walton do? They constructed a piece of equipment that allowed them to accelerate hydrogen nuclei —protons —that had been created in a discharge tube down a long glass tube with a nearly 700,000-volt electrical gradient onto a plate of lithium metal. If a proton was absorbed by a lithium nucleus, it would become unstable and split into two atoms of helium, releasing energy in doing so. We can represent this as follows:

Li3 + H → He2 + He2

In a short letter to the editor of the journal Nature, Cockcroft and Walton explained how they had observed the production of alpha particles —helium nuclei —after bombarding lithium in this way.[78] They had split an atom.

Cockcroft and Walton did not mention Einstein’s equation in their article, nor did they present their experiment as an attempted confirmation of Einstein’s postulation of the equivalence of mass and energy. Nevertheless, this experiment is regularly cited as the first empirical confirmation of Einstein’s equation. Why? The earlier equation I set out is not quite accurate, as it fails to mention that energy was produced in this reaction. When the energy of the two resulting alpha particles was measured, it was calculated that Einstein’s theory predicted the conversion of the mass lost in this reaction to energy with an accuracy of 99.5%. A small amount of mass had been converted into a substantial amount of energy.[79]

So might there be some way to exploit the massive potential of atomic nuclei to release energy in this way? In the year following Cockcroft and Walton’s experiment, Einstein expressed skepticism about such a possibility, rightly noting that an enormous amount of energy needed to be used to accelerate protons to split atoms in this way, releasing a small amount of energy by comparison. Ernest Rutherford, widely considered to be Britain’s leading physicist at this time, agreed, arguing that this “was a very poor and inefficient way of producing energy,” even if the process was “scientifically interesting.”[80] In part, the problem was that Cockcroft and Walton fired protons —positively charged hydrogen nuclei —into atomic nuclei, which were also positively charged. Inevitably, most of the protons were deflected through electrostatic repulsion. A lot of energy was wasted in accelerating protons that would not penetrate an atomic nucleus.

Nuclear Fission: The Splitting of an Atom

So what if neutrons —discovered by James Chadwick in 1932 and which have the same mass as protons but no electrical charge —were to be used instead? Might that make the process less wasteful and increase its potential to generate energy? In 1934, the Italian physicist Enrico Fermi announced that he had been able to create radioactive elements by bombarding atoms with slow neutrons in this way. Fermi’s work with slow neutrons prepared the way for the discovery of nuclear fission, the key to extracting energy from nuclear reactions. Yet the key to the massive release of energy from atomic nuclei was realized to lie in a nuclear chain reaction, in which a neutron enters an atomic nucleus, causing it to split and release energy —and in doing so also release other neutrons, which could kick off the same process in other nuclei. But was this actually possible?

In early 1939 —the year in which the Second World War broke out in Europe —German researchers demonstrated that uranium nuclei that were bombarded with neutrons released substantial amounts of energy in a process of fission, producing two new nuclei, called “fission fragments.” It soon became clear that this process of fission caused neutrons to be emitted and that the neutrons from the fission of one uranium nucleus could thus cause the fission of other nuclei. In short, a nuclear chain reaction could be initiated, which would then sustain itself and release massive amounts of energy, which could be used in a controlled way to generate electrical power —or to create a bomb that could destroy entire cities.

Léo Szilárd, a Hungarian physicist who had emigrated to the United States in 1938, got wind of these developments and grasped their potential implications. Working alongside Enrico Fermi at Columbia University, Szilárd had realized that “secondary” neutrons were released as a result of the fission of uranium, setting in place the chain reaction that was essential for atomic reactors and atomic bombs. Worried that Nazi Germany might be able to establish an unassailable technological lead in these fields, with massive implications for the outcome of a future European war, Szilárd asked to meet Einstein and explain the significance of these developments.[81] They already knew each other from their Berlin days during the 1920s, when they had collaborated on the design of a new type of refrigerator, which failed commercially.

Einstein was alarmed. He agreed to sign a letter to President Franklin Delano Roosevelt, drafted by Szilárd, outlining the threat that the probable development of atomic weapons posed and recommending that the United States should invest in research in the field. The letter, sent to Roosevelt on August 2, 1939, did not recommend, as is sometimes suggested, that America develop its own atomic bomb. America was not then at war with Germany, and there was no expectation that this would happen. That situation changed, of course, in December 1941, following the Japanese attack on Pearl Harbor. Having declared war on Japan and its allies —including Nazi Germany —Roosevelt authorized the Manhattan Project, which led to the creation and use of the world’s first working atomic bombs.

Einstein played no part in the Manhattan Project and seems to have been unaware of its existence or intended outcomes. The FBI regarded Einstein as unreliable politically and recommended that he should not have access to any sensitive information.[82] The use of atomic bombs thus came as a total and very unwelcome surprise to Einstein. He wrote a short piece titled “On My Participation in the Atom Bomb Project” for a Japanese magazine in 1952, making it clear that it was his belief that the Nazis might develop the atomic bomb first that motivated him to write to President Roosevelt, urging him to consider his options.[83]

So is Einstein to blame for the production of atomic weapons and the threat they are now seen to pose to the future of humanity? Time magazine certainly seemed to think so. Its front cover of July 1, 1946, shows Albert Einstein against a backdrop of a dark mushroom cloud, billowing above an atomic explosion. Emblazoned on the top of the mushroom cloud is the equation for which Einstein is best known: E = mc2. Yet this is clearly unfair to Einstein, who had no idea that his postulation of the equivalence of mass and energy would lead others to produce and use viable weapons of mass destruction. Nobody in 1905 could have seen that Einstein’s idea had military implications. Einstein can no more be blamed for nuclear weapons than Newton can be blamed for developing the equations that are now used to determine the trajectory of artillery shells or ballistic missiles.

Einstein’s final article of 1905 raises difficult questions about the human use of scientific developments. We have developed nuclear and pathological weapons capable of wiping out entire populations, and we may quite possibly end up becoming the first species to bring about its own extinction. Einstein was acutely aware of the need for a broader context of discussion of scientific advances that took ethical issues seriously:

By painful experience we have learnt that rational thinking does not suffice to solve the problems of our social life. Penetrating research and keen scientific work have often had tragic implications for mankind, producing, on the one hand, inventions which liberated man from exhausting physical labor . . . but on the other hand . . . creating the means for his own mass destruction.[84]

In later chapters, we shall consider Einstein’s ethical and religious views, which inform his concerns about how science was being used. In particular, we shall consider how he tried to hold together science, religion, and ethics in a meaningful and workable manner. But first, we need to ask what happened to Einstein after his Wunderjahr of 1905.

[39] Iliffe, Priest of Nature. For further reflections on the social context of the idea of “genius” at the time, see Fara, Newton: The Making of Genius.

[40] Albury, “Halley’s Ode on the Principia of Newton,” 27.

[41] Letter to John Adams, dated October 28, 1813.

[42] For an excellent account of these developments, see Rigden, Einstein 1905.

[43] For a full account of Einstein’s life, career, and achievements, see Isaacson, Einstein: His Life and Universe; Pais, “Subtle Is the Lord.”

[44] Brush, “Mach and Atomism.”

[45] Einstein, “Folgerungen aus den Capillaritätserscheinungen.”

[46] See, for example, Krstić, Mileva & Albert Einstein.

[47] For the critical report by the PBS ombudsman into the factual basis of Einstein’s Wife, see http://www.pbs.org/ombudsman/2006/12/einsteins_wife_the_relative_motion_of_facts.html.

[48] The best study of the background to these articles, which deals with these assertions in depth, is Stachel, Einstein’s Miraculous Year. For a good general account, see Isaacson, Einstein, 90–106.

[49] See the careful study of Martinez, “Handling Evidence in History.”

[50] Hertz, “Über den Einfluβ des ultravioletten Lichtes auf die electrische Entladung.”

[51] Lenard, “Über die lichtelektrische Wirkung.”

[52] Nauenberg, “Max Planck and the Birth of the Quantum Hypothesis.”

[53] Millikan, “A Direct Photoelectric Determination of Planck’s ‘h.’”

[54] Brown, “A Brief Account of Microscopical Observations on the Particles Contained in the Pollen of Plants.”

[55] Ford, “Confirming Robert Brown’s Observations of Brownian Movement.”

[56] For what follows, see Maiocchi, “The Case of Brownian Motion.”

[57] For details, see Maiocchi, “The Case of Brownian Motion,” 263–74.

[58] See especially Perrin, “Mouvement brownien et réalité moléculaire.”

[59] Rutherford, “The Scattering of α and β Particles by Matter and the Structure of the Atom.”

[60] Einstein, “Autobiographische Skizze,” 10.

[61] Renn, “Einstein as a Disciple of Galileo.”

[62] I here use material from various sections of Einstein, Relativity, although I have presented it in a different order than Einstein for the sake of clarity. This work is very accessible and is recommended as a starting point for serious exploration of both special and general relativity.

[63] Einstein, Relativity, 17.

[64] Davies, About Time, 59–65.

[65] See, for example, Feuer, “The Social Roots of Einstein’s Theory of Relativity,” 2.

[66] Harman and Thomson, Moral Relativism and Moral Objectivity, 3.

[67] Sommerfeld, “Philosophie und Physik seit 1900,” 99.

[68] Feynman, Six Not-So-Easy Pieces, 73–74.

[69] Russell, “Relativity,” 331.

[70] Einstein and Infeld, The Evolution of Physics, 77.

[71] Boughn, “Fritz Hasenöhrl and E = mc2.”

[72] For the debate, see Ohanian, “Did Einstein Prove E = mc2?”

[73] Hecht, “How Einstein Confirmed E = mc2.”

[74] The best of these, in my view, is his 1935 article “Elementary Derivation of the Equivalence of Mass and Energy.”

[75] See Duhem, La science allemande. This work was written during the First World War, which might help explain its hostility towards German science.

[76] Einstein, Ideas and Opinions, 226.

[77] Wertheimer, Productive Thinking, 213–28. For this remarkable relationship, see Miller, “Albert Einstein and Max Wertheimer.”

[78] Cockcroft and Walton, “Disintegration of Lithium by Swift Protons.”

[79] Cockcroft and Walton noted that the sum of the rest-masses of the original proton and the lithium nucleus was 8.0176 atomic mass units. However, the sum of the rest-masses of the two alpha particles produced by this reaction was 8.0022 atomic mass units. The reaction thus led to a loss of mass of 0.0154 atomic mass units.

[80] Speech given to the British Association for the Advancement of Science, September 11, 1933.

[81] See Lanouette and Silard, Genius in the Shadows. There is a good account of Einstein’s involvement with the development of the atomic bomb in Isaacson, Einstein, 471–86.

[82] Jerome, The Einstein File.

[83] Einstein, “On My Participation in the Atom Bomb Project.”

[84] Einstein, Essays in Humanism, 24–25.

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