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Einstein's dreams.

ALBERT EINSTEIN WAS DIFFERENT. He was aloof; in the popular image, he was the definition of a dweller in the Ivory Tower. He was socially and politically concerned, but only occasionally became involved. He was not a seeker of companions, personal or scientific, yet his writings show deep insights into the psychology of other people; his technical communications, both papers and personal letters, were voluminous. There might be room for a reasonable person to disagree with his social and political opinions, but they cannot be dismissed as naive or shallow.

Einstein's physics was different, too. It may not always seem so because his work is woven into just about all of modern physics, but there is a thread of the truly different running through his many and varied technical contributions. Einstein never followed the crowd, and the crowd, even while incorporating many of his results directly into the main stream, never really followed him.

This paper explores one of the reasons for the unique quality of Einstein's contributions to physics. I will try to show that he had a unique take on fundamental problems, and that this unique approach resulted in answers that, time and again, were so profound as to be the final word on the topic, at least for the last 100 years or so. Einstein had an ability to focus on problems that were sometimes simple but always profound. He could identify and hold to elementary governing principles that, when applied, drove the answers to contain an uncommon degree of universality.

Albert Einstein approached many of his key problems as if he had seen the underlying situation in a dream, with all of a dream's vibrant reality and stark simplicity. I do not maintain that he always had such dreams but rather that the dream metaphor is a useful way of describing this element of his unique approach to physics. What I will discuss are particularly vibrant examples of Einstein's gedankenexperiments, or thought-experiments, a technique that permeated much of his work. Most of Einstein's thought-experiments were emphatically not dreamlike; these were always intricate and usually required long and hard effort to devise. Many of his attempts at formulating counter-examples to quantum mechanics were in this category. (1) Although the two images I will focus on are certainly examples of gedankenexperiments Einstein reported them both to have arisen as dreams, or at least as daydreams.

In each of these dreams of Albert Einstein, some central part of the problem was depicted in a simple and elegant way. These images made it profoundly obvious that there were assertions that must be true for any solution to the problem. In the cases I will describe, Einstein held to his dream throughout the process of finding the answer, bringing the dream image into reality as a piece of physical theory while maintaining the truth of the associated assertions.

My two shining examples of Einstein's dreams concern the Special Theory of Relativity, completed in 1905, and the General Theory of Relativity, which reached final form in 1915. I will also discuss his search for a unified theory of the gravitational and electromagnetic fields, a search that is notable for its lack of a keynote dream, and one in which he was unsuccessful.

I

Special Relativity and Einstein's Annus Mirabilis. Einstein's physics career had a rocky start. He completed his formal training in 1900, but in spite of great academic accomplishment, he left a universally bad impression on his professors. For that reason, Einstein was unable to obtain the references and other support needed to obtain an entry-level university appointment. He made do with temporary work and freelance tutoring until he obtained a position in the Swiss patent office in 1902. He began his physics research in this period, focusing on statistical mechanics and publishing several papers.

His independent researches intensified once he had settled in at the patent office. In 1904, he published several papers on statistical mechanics that were substantial but not groundbreaking. In 1905, he produced the four papers that define his annus mirabilis. In three of the four papers, he used reasoning based on statistical mechanics to examine different physical systems. One paper contained his explanation of Brownian motion, now regarded as the first definitive proof of the existence and size-scale of atoms. In a second, he took a similar approach to the mixing of particles of different sizes. This work was accepted as his Ph.D thesis; the content has wide applicability to practical problems and is Einstein's single most frequently referenced paper. The third of these papers combined statistical mechanics with Planck's 1900 explanation of blackbody radiation, the origin of the quantum principle. In this paper, Einstein introduced the claim that light travelling in the vacuum really exists only in discrete units, later called photons. One of the proofs offered was an explanation of the photoelectric effect, later cited as the basis for his Nobel Prize in 1921. A fourth of his 1905 papers, "Zur Elektrodynamik bewegter Korpe" (2) (On the Electrodynamics of Moving Bodies) had nothing to do with statistical mechanics or the quantum principle. It was based, he would later say, on an imagined scene, perhaps a daydream or even a night dream, and embodied his theory of Special Relativity.

What might the content of such a dream be? Although he clearly described the importance of these dreams, Einstein's descriptions of them were limited to only the barest physical elements. Here is an example composed to evoke the same thoughts that he described, but with added detail:

Example dream: a view from a moving train. A clothesline hangs loosely across a yard. You unfasten one end and hold it. You give the end a vigorous snap, lifting it up and then pulling it back down as fast as possible. The result is a pulse, a kink in the rope that travels away from you towards the far end. Later, you entrust the creation of the wave to an assistant, and run along the rope trying to catch up with the pulse. You succeed in running at the speed of the wave; looking sideways, you perceive that the rope is moving up and down beside you, but the wave does not appear to be going anywhere.

Now you find yourself still running, but you realize that the wave is light and not a kink in a rope. You know that light travels at a very great speed, so you give up running and use a train, the fastest thing there is here in 1895. Somehow you can directly perceive the electric and magnetic fields that make up the light. You know you should see electric and magnetic fields growing and shrinking in place next to you; since you are moving at the speed of light, the waves should not be moving sideways at all. You are looking hard but cannot really see what is happening.

The moving train explained. In his later autobiographical writings, Einstein described imagining this last situation at age 16, in 1895. Well, almost: in his dream, Einstein trusted to his legs; I have added the train to increase the period feeling. In his last autobiographical note, Einstein wrote: "During that year in Aarau [1895-1896], the question came to me: If one runs after a light wave with light velocity, then one would encounter a time-independent wavefield...." (3) The "time-independent" part is not a very precise choice of words. Elsewhere, he wrote "I should observe an electromagnetic field at rest, although spatially oscillating." (4) Einstein's clear meaning is that there would be electric and magnetic fields present beside him, not moving ahead or falling behind, but nonetheless vigorously oscillating up and down.

The kink in the rope is a kind of wave; any physicist would understand if you described it as a "string wave." Such waves, both real and imagined, play a big role in the teaching of physics. Light is a wave, too; in the 1890s light waves and string waves were thought to have a lot in common.

II

A Question of Ether. If light is really a wave, then what is waving? For the string wave on the clothesline, it is the rope itself that carries the waves. The same is true for the strings of a musical instrument. Ocean waves are vertical movements of the surface of the seawater. Sound waves are a displacement of the air or water in which they travel. If light is a wave, it follows logically that there is something doing the waving; some substance, normally at rest, is moving periodically and carrying the light energy from place to place.

By the early 1900s, it was thought that there must be a luminiferous ether that carries light. Such an ether had to be present throughout all of space because light travels to Earth across the vast gulf between the stars. On the other hand, the ether must also permeate matter and not just transparent matter: infrared and radio waves were known to be the same as light and to travel through many types of opaque matter.

In fact, postulating that the propagation of light is supported by a material ether leads to a contradiction, as I will describe. The truth about the luminiferous ether and the basis for Einstein's special relativity can be arrived at by either of two rather different paths: I will call them the experimental and the theoretical paths. Both paths lead to the same answers. The experimental path is by far the more traveled, both by popularizers and by teachers of undergraduate physics. This approach focuses on the existence and properties of the ether. The theoretical approach proceeds so directly to its answers that the existence of an ether barely occurs.

The three steps on the experimental path are all measurements of how light travels, each with a consequent implication for the properties of the ether. Young, in 1803, and later Fresnel, in 1821, showed that all known behaviors of light were explicable in terms of waves. A key testable point was the difference between the speed of light in vacuum and in matter. The indisputable facts of refraction (Snell's Law) led Newton's older particle theory to predict that light speeds up on entering glass or water; a wave theory predicts that light slows down. In 1849, Fizeau did the experiment, a remarkable achievement for a man using nothing but gears, shafts, and belts without electrical or electronic devices. He demonstrated that light travels more slowly in water than in vacuum. Extending his technique, Fizeau later also showed that light was dragged when travelling in a column of moving water. Thus, when traveling in matter, light sets its motion relative to the matter.

The second key constraint on the ether emerged from observations of the positions of stars in the sky. By 1725, the accuracy of astronomical measurements had advanced to where it was observed that stars moved slightly depending on the time of year. Called stellar aberration, this effect is tens of times larger than the better-known phenomenon of stellar parallax, which gives a clue to distances. Stellar aberration was explained by James Bradley, Astronomer Royal, in 1729. The movement of the stars, he explained, was due to the relationship between the telescope tube and the velocity of the Earth in its motion around the Sun. When the Earth is moving toward or away from a star, the telescope is pointed in the same direction as the motion and nothing unusual happens. On the other hand, when the Earth's motion is at right angles to the star, the telescope has to lead the star to offset the sideways motion of the telescope tube during the time it takes for the light to traverse it. The known speeds of light and of the Earth in its orbit accounted exactly for stellar aberration.

Stellar aberration and its explanation have substantial implications for the properties of the ether: if stellar aberration exists, then the telescope and the earth it is attached to must move with respect to the ether. If the local ether were somehow dragged along with the earth, then the light would be carried sideways while it travelled in the telescope tube and there would be no stellar aberration.

Finally, a measurement of the speed of light relative to the motion of the earth was carried out by Michelson in 1881 (5) and in improved form by Michelson and Morley in 1887. (6) They used very sensitive optical techniques to measure directly the difference between the speed of light beams travelling in different directions inside their instrument. The paths were at ninety degrees to each other, so that there was a significant difference in their individual relationships to the velocity of the Earth in its orbit.

If ether supports the light wave, and if the earth moves relative to the ether, as implied by stellar aberration, then just like Fizeau's moving water, the speed of light in Michelson and Morley's apparatus should appear faster when moving against the Earth, be unchanged when moving at right angles, and slower when moving with it. The answer, however, was that there was no difference, or more precisely stated: the maximum possible difference was much smaller than the Earth's known velocity. This experiment's chief implication was that the ether must be dragged along with the Earth, in direct contravention of the stellar aberration result. This contradiction did not go unnoticed before 1905, but attempts to deal with it did not rise to the level of generality of Einstein's.

At its conclusion the experimental path demonstrated that there is no luminiferous ether; light in a vacuum moves at a constant speed regardless of the motion of its source or observer.

The theoretical path also starts with experiments, but with the nineteenth-century electrical and magnetic experiments of Henry, Ampere, Oersted, and Faraday. These laid the foundation for all things electrical. In the early 1860s a professor of Physics at Cambridge, James Clerk Maxwell, sought to codify the extensive and rather disparate body of electrical and magnetic knowledge that had accumulated in the previous half-century. His synthesis was completed in 1865 and remains one of the masterworks in all of science. Maxwell's Equations govern the behavior of electricity and magnetism under all conditions. However, Maxwell found that his equations could be used to derive a wave equation: an equation governing (or predicting) that electric and magnetic fields could cooperate to create a self-sustaining action that would move through space at a speed given by an expression involving only various fundamental properties of electricity already measured in the lab. The numerical value of the constant matched the well-known speed of light. This led Maxwell to interpret his wave equation as governing light and to declare that light itself was a fundamentally electromagnetic phenomenon.

There is only one more step on the theoretical path, but it takes some explanation. The general equation for fluid motion, the Navier-Stokes equation, is similar to Maxwell's equations and can be used to derive a wave equation for sound that parallels the wave equation for light. However, the sound wave equation is more complicated, and its speed for sound explicitly includes the motion of the medium carrying the sound. The situation is the same for wave equations governing string or sea-surface waves. However, Maxwell's wave equation does not have a place for the medium; the speed of light sits by itself with no place to add or subtract a velocity for the luminiferous ether. The theoretical path to the basis for special relativity, then, is the assertion that Maxwell's Equations describe light, and that they make no allowance for the motion of sources or observers relative to some luminiferous ether.

The theoretical path ends in the same place as the experimental: light in a vacuum moves at a universal speed without reference to the speed of its source or the motion of an observer. This is not a behavior consistent with a wave moving in a medium; there is, in effect no place for the ether.

III

Does It Look Different If You Go Fast? When Einstein came seriously to this problem in 1904, the contradiction between the stellar aberration and the Michelson/Morley result was evident, but the impossibility of a luminiferous ether was not seen as inevitable, not even by Michelson. Lorentz and Fitzgerald in 1901-04 had independently derived the transformations of space required to reconcile the two results, but their results were presented more as parlor tricks than as evidence demanding the redefinition of time and space.

The fundamental question, as captured in Einstein's dream, is: what do you see when you move relative to a speeding wave? For sound, and for other wave phenomena, each wave moves relative to its own medium; you see it moving relative to you, slower or faster depending on the details of your motion. This effect for sound is summed up in the Doppler shift, the subject of a famous nineteenth-century demonstration in Holland by F. Bailout. The apparatus used included a locomotive and flatcar, a train station platform, and two groups of bandsmen. It demonstrated that the perception of a sound wave changed with the motion of the source or the observer relative to the air through which the sound moved. Although Bailout's experiment did not directly address Einstein's dream, it was suggestive and very dramatic.

A very young Albert Einstein certainly knew about this experiment when he had that first earth-shattering dream. His dream of catching a light wave can be seen as central to the discovery of special relativity. So what did Einstein do in 1905 with this image that he had held in mind for eight years or so? The answer is a great deal and, at the same time, not very much. Since 1895 he had changed from a wide-eyed admirer of knowledge to a master of one of its most demanding disciplines. He was fully aware of all of the steps along the experimental path and of the contradictions to be found in positing a luminiferous ether. He had an exceptional grasp of electromagnetism and of Maxwell's Equations; therefore, he was also aware that the structure of the wave equation for light just about forbade the existence of the ether. He knew that catching a light wave, in a dream or for real, meant that Maxwell and his equations were wrong.

Here, then, is the link between Einstein's dream and special relativity: he knew he could catch a sound wave; what was his reaction to catching a light wave? That reaction is contained in the next line from the first quote above: "If one runs after a light wave with light velocity, then one would encounter a time-independent wavefield. However, something like that does not seem to exist!" (7) While you can catch a string wave and watch the rope move up and down, this cannot happen for light because Maxwell's Equations do not allow an oscillating but nonmoving electromagnetic field to exist. He asserted, then, that light waves cannot be caught; the formal statement of this is the same one that emerges from the stellar aberration-Michelson/Morley result: light waves must appear to travel at the speed of light relative to any observer, no matter how fast that observer is moving.

There was one more idea that he brought to the table in 1904, one that almost uniquely defines Einstein's viewpoint on physics: He postulated that the laws of physics should be exactly the same for any observer. This profound idea was not so much brand new as the recognition of something that had been implicit in all physics since at least Galileo. Stated simply, the idea is that when it comes to the laws of nature, everyone should be able to see themselves as the center of their own universe. If so, then everyone should discover exactly the same physical laws; there should be no differences rooted in where the observer is located or how fast he moves. Of course, the outcome of any particular application of those laws might differ among observers, but only in ways that relate to very real differences among them, differences that all would perceive.

Einstein, then, started with these two ideas: a light-speed postulate based on either or both the experimental and theoretical paths, and the invariance postulate as described in the previous paragraph. From these two postulates emerges the obvious question: how can it be that light does not appear to move away more slowly if you chase it? Or approach more rapidly if you run toward it? Lorentz and Fitzgerald had already worked out an answer: when you start trying to chase the light wave, the reality of space begins to change in ways that keep you from ever catching or even keeping pace with it. As great physicists as Lorentz and Fitzgerald are acknowledged to be, theirs was merely the algebra of the answer, the solution to a physics homework problem. By coupling Lorentz/Fitzgerald contraction with his invariance postulate, Einstein showed that his two assumptions led to a new interpretation of the world in which the measurement of time and space are not absolute in the sense introduced by Newton. More importantly, it led to a world in which both Maxwell's Equations and the experimental results are true, and in which the laws of nature are invariant, which is to say the same, for all observers.

But why does the title of his seminal paper translate into English as "The Electrodynamics of Moving Bodies"? The answer is that a large part of Einstein's original paper is concerned with the demonstration that Maxwell's Equations are consistent with the theory of special relativity. He showed that Maxwell's Equations make no allowance for a luminiferous ether because they are, in their original 1865 form, already fully consistent with special relativity. Thus, although he never knew it, James Clerk Maxwell himself predicted that the train could never catch the light wave. Because of this focus on Maxwell's Equations, and because the original paper does not even mention the Michelson and Morley result, it appears that Albert Einstein gave most weight to the theoretical path in arriving at special relativity.

As would later be the case for general relativity, however, Einstein was not alone in his quest; others, such as Lorentz, Fitzgerald, and Poincare were searching for the same answers at the same time. In spite of this, Einstein had no rivals for precedence in the discovery of special relativity, not only because he published it first, but because when others were describing the trees, he saw not only the forest but the entire continent on which it rested.

So, at the start of Einstein's life-long quest to describe the physical world in the simplest possible terms consistent with known truth, he assembled two postulates and worked out the astonishing but profound consequences. The postulates were the validity of Maxwell's Equations, that is, the insistence that light moves at constant speed relative to any observer, and the declaration that the laws of physics should be the same for any observer. His dream of catching a light wave can be seen as an impetus--"what happens?"--and guide--"you can't do it!"--to his research. These assumptions were, on balance, so simple that they placed almost no qualifications on the answers that he found. As a result, his theory of special relativity was essentially complete as first set out.

In later years, Einstein was appalled at the arguments for moral and cultural relativism that claimed to be based on the redefinitions of time and space within special relativity. His theory shows that different observers' perception of time and space may disagree, with no one version naturally preferred. However, it prescribes rigorous transformations from one such set of perceptions to another, based on the various observers' states of motion. Equally important in special relativity is the invariance principle: those different sets of perceptions are the consequence of a common set of physical laws, applicable to all. Einstein mused that this philosophical confusion might have been avoided if he had based his naming on this later observation and entitled his works the Special and General Theories of Invariance.

IV

General Relativity. In deriving special relativity, Einstein had limited the scope over which he made the invariance assumption. Specifically, his derivation only demanded that physical laws remain the same for observers moving at constant speed relative to each other. Just as natural as constant speeds, however, is the case of observers who are changing speed, or accelerating, relative to each other. What then? Einstein probably began thinking about the implications of the invariance of natural law as applied to accelerating observers almost as soon as he started work on the special theory; it comes naturally to a physicist to attack such a problem in stages, with the case of constant velocity and no acceleration being treated first because it must be simpler.

Einstein was correct in that assumption; a straightforward application of the results of the special theory to accelerating observers shows that the form of physical laws is not preserved. As early as 1905, Einstein knew that more work was needed. He began working on an extension to the more general case in 1907.

Special relativity had added new chapters to the book of Newtonian dynamics; that is, Newton's laws of momentum, force, and acceleration remained in place for small speeds, but the transformation of space and time when relative speeds approach that of light changed the answers for those cases. However, Newton had postulated another central piece of physics: the universal law of gravitation. Over two centuries or so, the law of gravity had been enormously successful; it had predicted the behavior of asteroids, comets, moons, and planets in the sky. It had also been subjected to measurement in the laboratory, most notably by Cavendish, with results that were consistent with the astronomical observations.

But in a world governed by Newton's dynamics as extended by the special theory, gravity cannot work according to Newton's Law of Gravitation. The most obvious problem is Newton's implicit assertion of action-at-a-distance. For Newton, there is a pull on an object (say the earth) located here due to another object (say, the sun) located over there. Newtonian gravity affects two objects separated in space with no gravitational effect anywhere in between; strictly speaking, a change in one object (for instance, if it moves) is instantaneously felt by the other as a change in the size or direction of the gravitational force. This is referred to as action-at-a-distance. On a philosophical level, the idea had bothered physicists, including Newton, since its introduction. Relativity offered a possible way out through an analogy between gravitational and electromagnetic forces. In electromagnetism, the same kind of action-at-a-distance appears to apply, but Maxwell's Equations show that changes at one charge can only be felt at another after a time-delay corresponding to the time it would take light to move between them. However, trying to fix up gravity in this way is not entirely successful. There is no obvious reason why the speed of light should be the limiting value for gravity. Also, electric and magnetic forces combine to satisfy invariance as the velocity of observers change; Newton's gravity offers no candidate for such a second force. (8)

There is, however, a profound link between gravity and the physics of forces and motions. Newton first postulated that the measure of how much matter is present in a body, its mass, applies identically to both gravity and to dynamics. In other words, the property of matter that makes a ball push back when you try to throw it, called its inertial mass, is exactly the same as the property that gives it weight under the action of gravity, referred to as its gravitational mass. Even in purely classical physics, this unity of the gravitational and inertial mass of all matter was recognized as a fact not demanded by logic or by any known deeper principle; rather, it was recognized as inferred from observation. By 1907 the identity of the two kinds of mass had also been investigated, most notably by Eotvos in 1885, with all investigations resulting in no detectable difference between the two.

V

Dreaming of a New Problem. Einstein began working in earnest on a theory of dynamics that would apply to mutually accelerating observers in 1907, a general theory as opposed to the constant-relative-speed case of his special theory. He again proceeded by setting out a few fundamental and governing principles and then looking for physical laws that satisfied these principles while remaining consistent with the rest of human knowledge about the physical world.

One principle was the validity of special relativity when the acceleration of the observer was reduced to zero, an analogy to the requirement that special relativity reduce to Newtonian dynamics for speeds small compared to light. Another was the extension of the invariance principle to accelerating observers: the laws of nature themselves should be identical for all observers, regardless of the magnitude or direction of their acceleration.

These two principles are straightforward extensions of his work on special relativity. However, Einstein adopted another principle into his program for a general theory, one that once more elevated a well-known but little contemplated truth to the status of an organizing principle of the universe. This final principle was based on another daydream, also referred to in English as a thought-experiment. Einstein reported that he had this daydream while sitting at his desk in the Swiss Patent Office in 1907. (9) Although Einstein's description of this dream is better known, it is every bit as sparse as that of his light-speed dream. Here is another example with details added to aid understanding:

Example dream: a man in a falling elevator. You find yourself in an elevator. The doors are closed while it moves between floors. Suddenly, the support cables break. The elevator falls, unimpeded by the cables or by its failed brakes. This is, of course, a dream; you find yourself unconcerned by what will happen if the elevator crashes into the bottom of the shaft. What does concern you is the sensation of floating: you are falling toward the earth; the elevator is also falling, and at exactly the same rate. You find that you can suspend yourself off the floor; you can propel yourself from wall to wall and floor to ceiling with almost no effort. You are weightless.

If you are Albert Einstein in 1907 or anybody in the twenty-first century, the question might occur: am I really in a falling elevator? Or have I forgotten how I got here? Could I and the elevator really be floating in distant outer space, in a region without gravity? Most importantly: how could I tell the difference between floating in outer space and plummeting inside an office building?

Leaving the dream, Einstein's answer to the last question, based on the apparent unity of gravitational and inertial mass, is: "You cannot tell the difference." The final principle on which Einstein based his general relativity is called the Equivalence Principle: there is no difference between falling under gravity and floating freely in outer space; at some fundamental level, they are the same thing.

Of course, merely postulating the invariance and equivalence principles was no guarantee that Einstein would succeed in finding those physical laws of acceleration and gravity that were the same for all observers. It was not even a guarantee that physics really worked in that way.

VI

Fallout from a Falling Elevator. Einstein's derivation of special relativity seems the work of an instant; history does not provide many of the details of his efforts during those months when he worked on it in 1904-05. When one considers that in the same period he proved the existence of atoms, made the revolutionary quantum advance that would result in his Nobel, and wrote his Ph.D. thesis on yet another topic, it seems like all of special relativity must have appeared to him in that dream. On the other hand, Einstein's labors on general relativity lasted for eight years, consumed his professional attention for nearly the entirety of that time, and resulted in voluminous reports of intermediate results and false steps.

His struggles were titanic. He was always driven by the dream and the other principles, but progress was neither steady nor always positive. He and his sometime collaborators Marcel Grossman and Michele Besso were able to divine some aspects of the answer; they certainly learned a great deal about the wrong answers. It can be argued that the entirety of general relativity really emerged in a rush in 1915 once Einstein relented and began using a mathematical formalism that was finally complex enough to describe the fullness of the answer. Albert Einstein could not get to a complete theory of general relativity without appealing, first, to higher-dimensional curved space, and at the end, to tensor calculus. Both of these formalisms he accepted and then learned only with reluctance. In the end, Einstein's dream of a falling elevator enabled him to complete his quest for the general laws of motion and gravity that would be perceived by any observer in uniform acceleration.

The results, published in late 1915 (10) during the heart of the First World War, were both simple and highly complex. Special relativity can be derived in a page or two of algebra by anyone with a solid grounding in Newtonian mechanics and Einstein's starting postulates. Merely demonstrating that Einstein's master equation of general relativity satisfies his equivalence and invariance principles takes reams of paper. The impact of the two theories on practical physics is in the inverse proportion. College freshman regularly use special relativity to address homework problems. Pure general relativity investigations seem limited to a small fraternity of theorists.

Since the general theory is much less well known than the special theory, I will briefly describe some key results. The dynamics that result from general relativity can be simply described: objects move through space from point A to point B by the shortest possible path. However, since our three-dimensional space is curved through a fourth dimension, the shortest path is not always the straight line we would guess it to be based on Euclidean geometry. The physics of motion is controlled by the details of that curvature. But where does the curvature come from? The answer is mass. The mass of an object is the source of the curvature of space around it. These two ideas are what brings gravity together with dynamics in a way that makes gravitational and inertial mass not merely numerically equal, but essentially the same thing. The pithiest version of these results is due to John Archibald Wheeler, a noted general relativist and collaborator of both Einstein and Bohr, who wrote: "Mass tells space-time how to curve, and space-time tells mass how to move." (11)

During his long struggles, Einstein gained insights into two key results that he thought might be subject to experimental tests. These were the precession of the orbit of planet Mercury and the effect of gravity on light.

By 1900 the astronomers had established that Mercury's orbit, measured over decades, did not quite follow the predictions of Newton's laws. The problem is not an easy one because of the large size of the Sun compared to its distance from Mercury, but the discrepancy was much too large to be due to minor effects like the influence of the Sun's atmosphere.

Once Einstein realized that mass was linked to the shortest distance between points, he focused on the problem of Mercury's orbit, and was able to recognize that a correct general relativity theory would predict a value for its precession. The values derived from the final theory were a good match to observation.

Einstein also determined by 1913 that the changes in space caused by gravity should affect the path that light travels. Efforts to confirm this prediction using a solar eclipse were dramatically complicated by the First World War. This prediction was eventually confirmed in 1919. The ease with which the effect, if not the cause, could be described in newspapers marked the beginnings of Einstein's fame as a public figure.

In summary, starting in about 1907, Einstein attempted to extend what he had begun with Maxwell's Equations and the equivalence of all moving observers to the general case of accelerating observers. As indicated by his new dream of falling in an elevator, the inclusion of acceleration brought gravity to the table through the equivalence of gravitational and inertial mass. After eight years of effort, he finally succeeded in producing another theory so general that there is literally nothing that it does not affect. (12)

The story of what happened after Albert Einstein finished the general theory is worthy of its own paper. He ended up becoming, in the popular imagination, a symbol of the redemption of science and rationality as a force for peace in the aftermath of the horrors of the First World War. He also became a participant in the reconciliation of the rest of European science with Germany. By about 1920, Einstein was well on his way to becoming the most famous living man and the most famous scientist of all time.

VII

Unified Fields: All Things Are One. In both special and general relativity, Einstein accomplished wonders of physical discovery by starting with a few simple but profound concepts about how the world and its governing laws should work. In both cases, the elevation of these concepts to principles, and the working out of their consequences, led to discoveries that were at once shocking, profound, and simple. In both cases, the theories embodied in his original papers have been elaborated in the century since, but not changed.

A few years later, he tried again. This time, he sought a theory that would bring the two classical fields, electromagnetism and gravity, into a single, physical unity. This time, he would not succeed.

Einstein finalized general relativity in 1915; he focused much of his effort on working out its implications for some years thereafter. The general theory had one huge hole, however: it said nothing about electromagnetism. By about 1920, Einstein began a search for a unified field theory. In such a theory, gravity and electromagnetism would appear as differing aspects of some single, underlying phenomenon.

If a dream or two and the insistence that a few simple principles must hold under all circumstances could lead to such profound and universal discoveries as the special and general theories, might not everything in the physical world be explainable by an even more all-encompassing theory with the same roots? The fact is that Einstein started his search for a unified field theory without a dream as a guide. Through the last thirty years of his life, he found neither the dream nor the theory.

He did have a goal, however: to find a theory that would bring electromagnetism and the general theory into a single framework. He also had his reasons; one was the synthesis of two, apparently independent theoretical constructs into a single whole. This prospect appealed to his sense of simplicity and beauty. Perhaps more important, however, was that a unified theory promised to offer a way out of the conceptual difficulties that Einstein had perceived with the quantum theory since at least 1916.

The quantum, as understood in the 1920s, appeared to be a fundamentally electromagnetic phenomenon. All known quantum effects arose either from charged electrons localized around the charged nucleus of an atom or from interactions between electrons and photons, the quintessentially electromagnetic particles. Einstein expected that within a successful unified theory quantum effects would be seen as a natural and, he hoped, unique aspect of electromagnetism. He also expected that this larger theory would supersede the probabilistic dimension that permeated quantum mechanics and restore to the atom the strict determinism to which he subscribed. His anticipation was that there would be new physics beyond the quantum; in light of that new physics, the puzzles of quantum mechanics would be explained as the consequences of deeper and more intricate, but not puzzling, physical processes.

In his search for a unified field theory, Einstein applied all of the tools, both mathematical and conceptual, that had contributed to or emerged from his special and general theories. But over almost three decades, he never enunciated the same kind of compelling physical insight into a central aspect of the problem that characterized his work on relativity; he never had a dream about the unified theory. Over time, he went back and forth between two approaches to the problem. Without an equivalent of his train or elevator dreams, however, he lacked a compass to point the direction for his efforts. One approach was a curved-space form in which space itself was described in a more intricate way than that used for the general theory. The other involved higher-dimensional space, which added a fifth dimension to the four needed by general relativity.

Albert Einstein did not succeed on this last and longest quest of his life, and neither has anyone since. He did not even come close. There are reasons. As described above, Einstein set as his goal the unification of the electromagnetism of Maxwell's Equations with the dynamics and gravity of general relativity. When he started looking in the 1920s, electromagnetism and gravity accounted for all of the fields and all of the forces known to physics. That is why these two were the elements he set out to unify.

However, by the time that Einstein was ten years into his search, new physics had emerged not from his theories but from the laboratory. The discovery of the neutron in 1932 (13) began a process that led to the realization that beta decay, the process by which electrons are emitted by radioactive nuclei, required a new set of rules. In 1936, Tuve and others demonstrated that protons had mutual affinities that could not possibly be explained by electromagnetic forces. (14) Since it was already understood that proton interactions had nothing to do with beta decay, yet another set of rules was required. By 1938, it was recognized that Einstein's two fundamental forces of nature, gravity and electromagnetism, were supplemented by two more: the strong force and the weak force. There were not two but four forces that required unification. Worse still for Einstein's unification program, quantum effects clearly played as large a role in the new forces as they did for electromagnetism.

Einstein continued on his quest through the 1930s, 1940s, and 1950s. He never attempted to incorporate the new forces. He probably hoped that their very short ranges would allow the long-ranged gravity and electromagnetism to be unified first, with the other forces to be incorporated later. For all of his efforts, when Einstein died in 1955 he was no closer to a unified field theory than he had been in the early 1920s.

VIII

A Missing Answer. There is a dispute among biographers as to whether Einstein's obstinate but failed search for a unified field theory is tragic. Isaacson seems to think so. (15) Pais, a physicist, defends the logic behind the unified field program, while agreeing that the likelihood of its success diminished over the decades. (16) Einstein himself said on occasion that his age and previous success freed him to pursue goals that were ambitious, or even hopeless. A younger man, he said, would be too concerned with success and promotion to work on long-term problems with such dubious prospects. (17) I would suggest that an Albert Einstein who ceased making ground-breaking scientific contributions at age fifty is a man who should be celebrated rather than mourned.

Is there a unified field theory of gravity and electromagnetism? Are there answers that only Einstein's unique insights and genius could have found? Could such a theory restore the narrowest possible determinism to the world? My comments above should make it clear that I don't think so. Einstein was asking the wrong question; or rather, he was asking the right question but in the wrong way. He could not have known in the early 1920s that there were other forces comparable in strength to electromagnetism that are important at the nuclear level. It is certainly unfortunate that he failed to change his approach by the early 1940s when the facts about these new forces became clear. By then, however, he was sixty years old and can hardly be faulted in his choice.

How have researches in this area progressed since Einstein laid down his chalk? Ironically, progress has been in directions completely opposite from his vision. On gravity, people are still discovering the realities hidden by the complexity of the general relativity equations, but there has been no fundamental progress. Theories of gravity beyond general relativity are only notional. As for unifying fields, the standard model of particle physics is a field theory. On the electromagnetic parts of it are based the best predictions of experimental results ever made. In the 1970s, Weinberg and Salaam used techniques radically different from Einstein's to forge a theory that unifies not gravity and electromagnetism, but electromagnetism and the weak nuclear force (18). It would, one suspects, be much to Einstein's dismay that this electro-weak theory is fundamentally quantum mechanical, and that the ongoing effort to extend to it to the strong force follows suit.

Einstein postulated a unified theory of intricate classical fields from which quantum effects would emerge in the electromagnetic corner. In the standard model we have, instead, a theory of profoundly quantized fields that are responsible both for forces and for matter itself. The path from this micro world of subatomic particles to the macro world where gravity reigns is still unknown.

IX

A realm of dreams. In a century of unprecedented advance in theoretical science, how unique were Albert Einstein's dreams? When considered in the light of their relationship to the problems at hand, very unique indeed. Most of the more famous images or dreams reported by scientists are about their answers; the dreams I have discussed were statements about the problem. They were not only statements, but tools that could be used to guide choices and to test possible answers to the questions at hand.

Kekule, the French chemist, famously solved the mystery of benzene rings via a dream while sleeping on a bus. He saw six carbon atoms dancing in a ring while changing the way they were holding hands. This was the first description of the resonance bond. Maxwell's rather fanciful first mechanical analog for electromagnetism (19) might best be described as a mechanical nightmare of rotating rings and little parts that were guided between them. Its action mimicked all that was known about electromagnetism, but had no predictive value. As with Kekule, Maxwell's dream constituted an answer, not an insight into the problem.

The closest dreams to those of Einstein were, perhaps, Michael Faraday's. Faraday was one of the greatest experimentalists who ever lived, but he was almost entirely self-taught and had no formal mathematical training. Faraday had a facility for the visualization required to formulate the most sophisticated and dreamlike images of unseen physical reality. Without access to complex mathematical tools, he had little choice but to exercise that facility. As he contemplated the complex behavior of electric and magnetic fields, many of whose properties he was first to discover, Faraday created the modern idea of a force field: a real but invisible thing present in space, interacting with itself and with matter, whose strength and changes are governed by physical laws. Faraday's images of magnetic fields in space, forming great loops and resisting change by pulling back when stretched, are both compelling and correct. The equations governing magnetism, first written down by his friend Maxwell, show exactly those properties in every detail. Faraday's visions for magnetic fields have, I find, a great deal in common with Einstein's dreams, but they are still closer to the answer than to the question.

X

Conclusion. Albert Einstein had a unique approach to all of his physics, whether he was addressing the dynamics of the cosmos or refining our understanding of the world on a much more intimate scale. There is no better example of his unique style than the search for his two relativity theories. In both cases, the macro scale of the problems lend themselves to popular description, and his motivating images, or dreams, are easily related to a nontechnical audience.

For Albert Einstein, the ability to see important aspects problems in everyday terms seemed to come naturally. Einstein said early in his career that he avoided the purely mathematical approach in favor of visualization and of frequent appeals to physical intuition, the quintessence of which were his dreams of catching a wave or falling in an elevator. This attitude served him well developing the special theory. The way to the general theory was blocked until he added elaborate mathematical reasoning to his intuitive insights. Some argue that the formal mathematical approach, the savior of the general relativity effort, was a major contributor to the failure of his unified field efforts. I argue that it was his failure to find a compelling insight into what such a unification would look like or how it would work that was the real problem. In the absence of a dream, even Einstein could not sustain his progress revealing the mysteries of the physical world.

Kensington, Maryland

(1) These intricate imaginings include the clock-in-a-box that Einstein devised during the 1927 Solvay Conference to challenge Bohr and Heisenberg. See 446-47 in Abraham Pais, Subtle is the Lord (Oxford: Oxford University Press, 1982) for a description. Although the gedankenexperiment involving the fate of Schrodinger's famous cat was created by Schrodinger, it was based on a similar device using explosives (but no felines) that was due to Einstein. See also Walter Isaacson, Einstein, (New York: Simon and Schuster, 2007), 455-56.

(2) Albert Einstein, "Zur Elektrodynamik bewegter Korpe, " Annalen der Physik 17 (1905): 891.

(3) Helle Zeit, Dunkle Zeit: In Memoriam Albert Einstein, ed. C. Seelig (Zurich: Europa-Verlag, 1956), quoted in Pais, Subtle is the Lord, 131.

(4) Albert Einstein in Albert Einstein: Philosopher-Scientist, ed. P. A. Schilpp (New York: Tudor, 1949), 49.

(5) Albert A. Michelson, "The Relative Motion of the Earth and the Luminiferous Ether," American Journal of Science 22 (1881): 120-29.

(6) Albert A. Michelson and Edward W. Morley, "On the relative motion of the Earth and the luminferous ether," American Journal of Science 34 (1887): 333-45.

(7) Quoted in Pais, Subtle Is the Lord, 131; my emphasis.

(8) Additional gravitational forces that serve the same relativistic purpose as magnetism actually do emerge in general relativity. These have never been given a separate name, but their effects are most commonly referred to as "gravitational frame dragging."

(9) Einstein's most succinct description of this experience is found only in his papers: The Collected Papers of Albert Einstein: Volume 7, trans. Alfred Engel (Princeton: Princeton University Press, 2002), 113-50.

(10) The key breakthrough was the formulation of the gravitational field equations, first published in the proceedings for the Prussian Academy: Albert Einstein, "Sitzungsberichte," Preussische Akademie der Wissenschaften (1915): 844.

(11) Charles Misner, Kip Thorne, and John. A. Wheeler, Gravitation, (San Francisco: Freeman, 1973), 5. Wheeler was also responsible for originating the term "black hole" for the unique collapsed state of matter predicted by general relativity.

(12) Of course, for both the special and general theories, the practical effect on life at the surface of the earth is nil; here, Newton rules. You need to travel at ten percent of the speed of light before special relativity effects become measureable in everyday terms. You need to be in gravitational fields many thousands of times stronger than we can ever encounter, or even survive, before the general theory departs noticeably from Newton's gravity.

(13) James Chadwick, "Possible Existence of a Neutron," Nature 129 (1932): 312.

(14) Merle A. Tuve, Norman P. Heydenburg, and Lawrence. R. Hafstad. "The Scattering of Protons by Protons." Physical Review 50, no. 9 (1936): 806.

(15) Isaacson, Einstein, ch. 23, especially the discussion on 512.

(16) Pais, Subtle Is the Lord, ch. 26, especially section 26c.

(17) Gerald J. Whitrow, Einstein: The Man and His Achievement (London: BBC, 1967), xii.

(18) It is difficult to represent this development by reference to a single original paper. A popular summary is found in: Steven Weinberg, "Unified Theories of Elementary-Particle Interaction." Scientific American 231, no. 1 (1974): 50-59.

(19) James Clerk Maxwell, "XXV. On Physical Lines of Force," The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 21, no. 139 (1861): 161-75.

Correspondence to: John H. Sweeney, 10604 Drumm Ave, Kensington, MD 20895.
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Publication:The Review of Metaphysics
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Date:Jun 1, 2014
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