Einstein, Albert
Albert Einstein. Wikimedia Commons (Public Domain)


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Einstein, Albert


(b. Ulm, Germany, 14 March 1879;

d. Princeton, New Jersey, 18 April 1955)

physics. For the original article on Einstein see DSB, vol. 4.

This essay extends and corrects the original entries by Martin J. Klein and Nandor L. Balazs, drawing on recent work in a variety of areas: experimental tests of general relativity and the role of the cosmological constant; new topics based on recently available information, such as the Einstein family business and its influence on young Einstein; his love affairs, first and second marriages, and other women in his life; black hole physics; and inadequate discussions of the nature of Einstein’s light quantum hypothesis; the reasons for his discontent with quantum mechanics; the origins of special relativity and the role of local time; the development of general relativity and the role of metric, affine connection, and Riemann tensor in the theory; his views on the significance of general relativity and the relation between physics and geometry; and his hopes for a unified field theory.

Einstein Family Business . The Einstein brothers’ Munich electrical engineering firm built and installed dynamos, power plants, and electric lighting systems, largely invented and patented by Albert’s uncle Jakob (1850– 1912), an engineer. The new, enlarged factory, started in 1885 with financial help from his mother Pauline’s (1858–1920) wealthy father, was managed by his father Hermann (1847–1902), a businessman. The dynamo division alone employed some fifty people. The firm was initially rather successful, and total employment at its height has been estimated at 150–200 (for the family business in Munich, see Hettler, 1996). But after an acrimonious dispute with its larger German rivals, the firm lost the lighting contract for the city of Munich in 1893.

The brothers decided to move to Northern Italy, where they had already installed several power plants, and in 1895 they built a large factory in Pavia. Their efforts to secure a contract to supply the city with electrical power failed due to various local intrigues, and they again had to liquidate their firm in 1896, losing almost everything in the process (for the Italian firm, see Winteler-Einstein, 1924). Uncle Jakob went to work for another firm but, despite Albert’s warnings, his father opened a small electrical firm in Milan. Albert helped out from time to time during school vacations, but was able to finish his education only with financial help from his mother’s wealthy family.

Prematurely aged by his financial troubles, Hermann died in 1902 deeply in debt to Rudolf Einstein (1843–1928), his cousin and brother-in-law. Young Albert had just started work at the Swiss Patent Office and was unable to support his mother or sister Maja (1881–1951). He had originally been destined to take over the family business and, as an adolescent, demonstrated considerable technical aptitude in electrotechnology, which later stood him in good stead at the Patent Office (1902–1909). But his father’s business failures and the attendant stress on the family contributed to an aversion to commercial activities for profit that ultimately led to his critique of capitalism and espousal of socialism (for Albert’s early development, see The Collected Papers, vol. 1, passim; and John Stachel, New Introduction” to Einstein, 2005). “I was also originally supposed to be a technical worker. But the thought of having to expend my inventive power on things, which would only make workaday life more complicated with the goal of dreary oppression by capital, was unbearable to me” (translation from Stachel, 2005, “New Introduction,” p. xxxiii; see Einstein, 1949, for his later condemnation of the profit system).

Einstein’s Love Affairs . The plaster saint image of Einstein, carefully cultivated by his executors, has been shaken by the disclosure of his many love affairs before, during, and after his two marriages. There is now a danger that the myth of the white-haired saint will be replaced by that of a devil incarnate (“father of the atom bomb,” “plagiarist,” “thief of his wife’s ideas”), but what is starting to emerge is something much more interesting than saint or devil: the rounded portrait of a human being (for a discussion of some common myths, see Brian, 2005).

While a student at the Aargau Kantonsschule (a Realschule, not a Gymnasium) in Aarau (1895–1896), Einstein boarded with the family of Jost (“Papa,” 1846–1929) Winteler, a teacher at the school and his wife Pauline (“Momma,” 1845–1906), with whom he developed close and lasting relationships. His sister later married Paul (1882–1952), one of the Winteler sons, and he had a brief love affair with their daughter Marie (1877–1957), which she later described as “innig [deep]” but “durchaus ideal [completely ideal].” It ended when he moved to Zurich in 1896 to attend the Zurich Poly (1896–1900), where he met Mileva Marić (1875–1948), the only other physics student to enter the program for teachers of mathematics and physics. The two began to study physics together and became intensely involved emotionally during their last years at the Poly. His letters to her from this period (see Einstein, 1992) are the major contemporary source of information on his scientific interests before his first published paper (1901). There is no evidence in his letters or in hers to support claims that she played more than a supporting role in his early research activities (for discussions of their relationship, see Stachel, 2002c; Stachel, 1996; and Martinez, 2005); she was the first of a series of “sounding boards” that he needed in order to help put the fruits of his research, carried out alone and with the aid of non-verbal symbolic systems, into a form that could be communicated to others (for further discussion, including an account of his mode of thought, see the “Introduction to the Centenary Edition” of Einstein, 2005).

After he graduated (she failed the final examinations twice due to poor grades in mathematics), they had a daughter out of wedlock, Lieserl (b. 1902), whose fate is unknown. But they lived apart until his job at the Swiss Patent Office (1902–1909) enabled their marriage in 1903. During these years Einstein did much of his research during working hours, and later stated, “The work on the final formulation of technical patents was a true blessing … and also provided important inspiration for physical ideas” (Einstein, 1956, p. 12). His first biographer reports: “He recognizes a definite connection between the knowledge acquired at the patent office and the theoretical results which, at that same time, emerged as examples of the acuteness of his thinking” (Moszkowski, 1921, p. 22).

In 1909 Einstein obtained his first academic post in theoretical physics at the University of Zurich, and his career slowly began to prosper, with successive posts in Prague and the Zurich Poly. He drifted away from Marić, later attributing his alienation to her taciturnity, jealousy, and depressive personality. By 1912 he was having an affair with Elsa Löwenthal (1876–1936), his cousin and childhood friend. She was a divorcee living in Berlin with her parents—her father Rudolf had been his father’s chief creditor. Albert’s move to Berlin in 1914 as a newly-elected member of Prussian Academy of Sciences precipitated a crisis in the marriage and Mileva returned to Zurich with their two sons, where she remained for the rest of her life.

After Albert’s divorce from Mileva and marriage to Elsa in 1919, he continued to have numerous affairs. In Berlin, the women included Betty Neumann, his secretary; Tony Mendel; and Margarete Lebach; after his move to Princeton in 1933 they included Margarita Konenkova, a Russian citizen living in the United States who has been accused of being a spy (see Pogrebin, 1998, for excerpts from his letters to Konenkova after her return to Russia in 1945; and Schneir, 1998, for contradictions in the spy story). His last close companion was Princeton librarian Johanna Fantova, an old friend from Europe (see Calaprice, 2005 for Fantova’s diary of her conversations with Einstein).

Einstein’s Light Quantum Hypothesis . In 1905 Einstein characterized only one of his papers as “very revolutionary,” the one that “deals with radiation and the energetic properties of light.” Klein comments: “Einstein leaped to the conclusion that the radiation … must consist of independent particle of energy” (p. 315), but a reading of the 1905 light quantum paper shows that he did not. He characterizes his demonstration that, in a certain limit, black body radiation behaves as if it were composed of energy quanta, as “a heuristic viewpoint”; and in 1909 warned against just this misunderstanding: “In fact, I am not at all of the opinion that light can be thought of as composed of quanta that are independent of each other and localized in relatively small spaces. This would indeed be the most convenient explanation of the Wien region of the radiation spectrum. But just the division of a light ray at the surface of a refracting medium completely forbids this outlook. A light ray divides itself, but a light quantum cannot divide without a change of frequency” (Einstein to H. A. Lorentz, 23 May 1909, Collected Papers, vol. 5, p. 193). It was only in 1915 that other considerations led him to attribute momentum to a light quantum (see p. 317), and only a decade later, after Bose’s work (see pp. 317–318) had shown that elementary particles need not be statistically independent, did he describe them as particles (see Stachel, 2000).

Speaking of Einstein’s first paper on mass-energy equivalence, Balazs writes: “[Einstein] observed that the exchange of radiation between bodies should involve an exchange of mass; light quanta have mass exactly as do ordinary molecules” (p. 323). But in his derivation of this result, Einstein speaks about a “light complex,” an entirely classical concept, rather than about a light quantum. In his early works, Einstein never mixed concepts from his quantum papers with those from his relativity papers. And when, after Bose’s work, he did attribute corpuscular properties to light quanta, he distinguished clearly between photons (a word he did not use), zero rest mass bosons (another word introduced later) whose number need not be conserved; and massive bosons, whose number must be conserved. His prediction of a condensed state for massive bosons (see Einstein, 1925), now called a Bose-Einstein condensate, offered the first theoretical explanation of a transition between two phases of a system. The prediction was spectacularly confirmed some seventy years later, winning its discoverers the 2001 Nobel prize in physics.

Discontent [Unbehagen] with Quantum Mechanics . Speaking of Einstein’s “Discontent with Quantum Mechanics,” Klein cites (p. 318) its basically statistical nature and presumed incompleteness as the reasons. Actually, Einstein believed that, if one adopted the statistical ensemble interpretation of quantum mechanics (which he referred to as the Born interpretation, but had actually adumbrated; see Stachel, 1986, Sections 5 and 7), there was no problem with the theory. For him, the problem came when the theory was applied to an individual system: it was here that the issue arose of completeness of the quantum mechanical description. A careful reading of his comments on this topic (see Stachel, 1986) shows that the issue of non-separability was the most fundamental cause of his “Unbehagen.” As Wolfgang Pauli explained: “Einstein does not consider the concept of ‘determinism’ to be as fundamental as it is frequently held to be. … he disputes that he uses as a criterion for the admissibility of a theory the question ‘Is it rigorously deterministic?’” (Pauli to Max Born, 31 March 1954, quoted from Stachel, 1991, p. 411). Once they interact, two quantum systems remain entangled, no matter how far apart in time and space they may have traveled. To Einstein, this seemed to contradict his expectation, based on the role of space-time in his relativity theories, that two systems, sufficiently separated in space-time, should not exert any physical influence on each other.

Does it make sense to say that two parts A and B of a system do exist independently of each other if they are (in ordinary language) located in different parts of space at a certain time, if there are no considerable interactions between those parts … at the considered time? … I mean by “independent of each other” that an action on A has no immediate influence on the part B. In this sense I express a principle a) independent existence of the spatially separated. This has to be considered with the other thesis b) the ψ-function is the complete description of the individual physical situation. My thesis is that a) and b) cannot be true together .… The majority of quantum theorists discard a) tacitly to be able to conserve b). I, however, have strong confidence in a), so I feel compelled to relinquish b). (Einstein to Leon Cooper, 31 October 1949, quoted from Stachel, 1986, p. 375)

Since then the formulation of Bell’s inequality and its experimental testing by Clauser, Horne, and Shimony, and by Aspect, have convinced most physicists that quantum entanglement is not the result of an incompleteness due to neglected statistical correlations, as Einstein suggested. Whatever the ultimate fate of contemporary quantum mechanics, entanglement seems destined to remain a fundamental feature of any future physical theory (for a review of this topic, with references to the original literature, see Shimony, 2006).

Origin of Special Relativity . Balazs points out: “By [Einstein's] own testimony the failure of the ether-drift experiments did not play a determinative role in his thinking but merely provided additional evidence in favor of his belief that inasmuch as the phenomena of electrodynamics were ‘relativistic,’ the theory would have to be reconstructed accordingly” (p. 320). In fact, the phenomena of the optics of moving bodies also played a major role in the development of his ideas. In 1952 he wrote: “My direct path to the special theory of relativity was mainly determined by the conviction that the electromotive force induced in a conductor moving in a magnetic field is nothing other than an electric field. But the result of Fizeau’s experiment and the phenomenon of aberration also guided me” (quoted from Stachel, 1989, p. 262).

As Balazs explains (p. 320), the conductor-magnet example suggested to Einstein that the relativity principle must be extended from mechanics to electromagnetic theory. He then attempted to reconcile the relativity principle with well-known optical phenomena, in particular the

constancy of the velocity of light. Two main alternatives presented themselves: (1) The velocity of light is independent of that of its source, constant relative to the ether; or (2) The velocity of light is constant relative to its source (ballistic theory of light—light behaves like a bullet).

Lorentz’s version of Maxwell’s theory, based on the first alternative, was able to explain the result of Fizeau’s experiment and the phenomenon of aberration, but did not seem to be compatible with the relativity principle— the ether frame of reference is special. So Einstein explored the second alternative, where the situation was just the reverse: The relativity principle presented no problem if one assumed that a moving medium dragged the ether along within it. But Fizeau’s experiment on the velocity of light in moving water, interpreted within the framework of an ether theory, seemed to preclude the idea that ether was totally dragged along by matter. Rather, it confirmed Fresnel’s formula, which had been developed to account for aberration and predicted a partial dragging of the ether (see Stachel, 2005a).

Attempts to explain Fizeau’s experiment using the second alternative led to more and more complications, so Einstein returned to the first, but with a crucial difference: he dropped the ether. He realized that the relativity principle then requires the velocity of light to be a universal constant, the same in all inertial frames of reference. But how is this possible? He pondered this question for several years. Finally in 1905 came the insight that removed the puzzle. It is possible if one gives up the Galileian law of addition of relative velocities! A reanalysis of the concept of time showed that the proof of this law depended on the existence of an absolute time, which implies that one can always say whether two events are simultaneous, however far apart. But careful analysis of the concept of simultaneity showed that one must define when two events occurring at some distance from each other are simultaneous. He showed that one could adopt definition that made the velocity of light the same in all inertial frames—but this definition gives a different answer in each inertial frame and results in a new law for addition of relative velocities.

Einstein’s new definition of frame-dependent time is closely related to Lorentz’s concept of local time, as Balazs points out “Although Lorentz appears to have viewed local time as a mathematical artifice, it represented in embryo a concept of time that Einstein would later justify adopting for the whole of physics” (p. 321). In 1900 Poincaré had given a physical interpretation of the local time within the ether-theoretical framework: It is the time that clocks in a moving frame of reference would read (compared with clocks at rest in the ether, which read the true, absolute time) if they were synchronized using light signals, but without correcting for the effects of motion through the ether on the propagation of light. Einstein may well have been familiar with Poincaré’s work, but his crucial idea was to drop all reference to the ether and accept the local time of each inertial frame as just as good as that of any other.

Development of General Relativity . Einstein divided his work on general relativity into three key steps (for the first two steps, see Stachel, 2002b; for the third step, see Janssen et al., 2007, vol. 2.).

The first step, in 1907, was his “basic idea for the general theory of relativity” (Stachel, 2002b, p. 261). He was referring to his formulation of the equivalence principle—the inability to uniquely separate gravitation and inertia. Balazs states: “Einstein published two remarkable memoirs in 1912 which were efforts to construct a complete theory of gravitation incorporating the equivalence principle” (p. 326). Actually, they were an attempt to construct equations only for a static field, as well as the equations of motion of a test particle in such a field. His recognition that the latter equations describe the geodesics of a non-flat space-time was a major clue that led to the second step, in 1912: his “recognition of the non-Euclidean nature of the metric and of its physical determination by gravitation” (Stachel, 2002b, p. 261). He was referring to the adoption of the metric tensor as the representation of the gravitational potentials.

The third step came with his “1915 field equations of gravitation. Explanation of the perihelion motion of Mercury” (Stachel 2002b, p. 261). Einstein was referring to the final form of the field equations, which he announced on 25 November 1915. This corrects the erroneous date of 25 March given in the table on p. 324 and on p. 327. The correct date, when combined with Balazs’ statement: “[O]n 20 November, David Hilbert, in Göttingen, independently found the same field equations” (p. 327). might suggest that Hilbert actually had priority, a claim that is still maintained by some scholars in the face of new evidence to the contrary (for a review of Hilbert’s role in the development of general relativity, see Renn and Stachel, 2007).

Role of the Affine Connection . A fourth key step may be added: Recognition of the affine connection and parallel displacement as the correct mathematical representation of the inerto-gravitational field (for a discussion of the role of the affine connection in the development of gravitation theory, see Stachel, 2007). This step was first taken by Tullio Levi-Civita in 1917, but Einstein came to recognize its crucial importance:

It is the essential achievement of the general theory of relativity that it freed physics from the necessity of introducing the “inertial system” (or inertial systems). (The Meaning of Relativity, p. 139)

The development … of the mathematical theories essential for the setting up of general relativity had the result that at first the Riemannian metric was considered the fundamental concept on which the general theory of relativity and thus the avoidance of the inertial system were based. Later, however, Levi-Civita rightly pointed out that the element of the theory that makes it possible to avoid the inertial system is rather the infinitesimal [parallel] displacement field Γlik.. The metric or the symmetric tensor field gik which defines it is only indirectly connected with the avoidance of the inertial system in so far as it determines a displacement field. (The Meaning of Relativity, p. 141)

The mathematical formulation of the equivalence principle is that “the displacement field,” also called the affine connection, represents a single inertio-gravitational field.

In all previous physical theories, including the special theory, the space-time structures, metric and connection, had been fixed, background fields, determining the kinematics of space-time: the stage, on which the drama of matter and dynamical fields takes place. With the dynamization of these space-time structures, the stage now became part of the play; moreover a new kind of physics was born, now called background-independent to contrast it with all theories based on fixed background space-time.

Balazs writes: “Gravitation is a universal manifestation because it is a property of space-time, and hence everything that is in space-time (which is, literally, everything) must experience it” (p. 331). But Einstein opposed such a “container” or absolute concept of space-time and forcefully advocated a relational approach to space-time (see, for example, Einstein, 1954), preferring to say that space-time is a property of the gravitational field:

[A]ccording to the special theory of relativity, space (space-time) has an existence independent of matter or field. In order to be able to describe at all that which fills up space …, space-time or the inertial system with its metrical properties must be thought of at once as existing, for otherwise the description of “that which fills up space” would have no meaning. On the basis of the general theory of relativity, on the other hand, space as opposed to “what fills space” … has no separate existence. … If we imagine the gravitational field, i.e., the functions gik to be removed, there does not remain a space of the type (1) [Minkowski space-time], but absolutely nothing, and also no “topological space”. … There is no such thing as an empty space, i.e., a space without field. Space-time does not claim existence on its own, but only as a structural quality of the field. (Einstein, 1952, p. 155).

Balazs writes: “In this way Einstein showed that gravitational fields influence the motion of clocks” (p. 325). Presumably, Balazs meant the rate of clocks, but even that statement would be inaccurate. General relativity is built precisely on the assumption that (ideal) clocks and measuring rods are not affected by the presence of an inertio-gravitational field. However, the rates of two clocks at different places in a gravitational field cannot be directly compared. (If the two clocks are brought to the same place for direct comparison, according to general relativity they will always agree!) Some signal must pass between them. It is the difference between the frequency with which a signal is emitted by one clock and the frequency with which the signal is detected at the position of the other clock that is responsible for gravitational effects on time measurements, such as the gravitational red shift.

Balazs writes “In particular [Einstein] assumed that … the history of a body will be a geodesic … the curve in space-time for which ∫ds is a minimum, δ∫ ds= 0” (p. 227). While this integral is always an extremal of the space-time interval for geodesic curves, for time-like paths it is a maximum. This is the basis of the twin paradox: The stay-at-home, non-accelerating twin will be much older than his adventurous, accelerating sibling when the two meet again.

Balazs writes “Θμν; contains the material sources of the field … In any given physical situation, the Θ μν; may be assumed known” (p. 227). In fact, the expression for Θμν;, the stress-energy-momentum tensor (later in the article symbolized by Tμν;), almost always contains the metric tensor, so the gravitational field equations cannot be solved separately. Rather, one must solve the coupled sets of equations for the source fields and for the metric field.

Curvature Tensors and Field Equations . Balazs writes “[T]he gravitational field can be characterized by Riemann’s curvature tensor Gµν .… [Einstein] wrote the gravitational field equations as Gµν = K(Tµν - 1/2 gµνTT), where T is the scalar of the material energy tensor Tµν and K is a gravitational constant. … The curvature of space-time at a point is determined by the amount of matter and electromagnetic field and their motion at that point” (p. 328). There are several errors here. First, Balazs’ Gµν is the Ricci tensor, not the Riemann curvature tensor. The Riemann tensor is a four-index tensor Rκµλν, the trace of which is equal to the Ricci tensor: Rκµκν,= Gµν, in Balazs’ notation. The Ricci tensor is more commonly denoted by Rµν, whereas Gµν is used to denote the Einstein tensor Rµν - 1/2 gµν R, where R is the trace of the Ricci tensor. The gravitational field equations are now more commonly written in the form: Rµν - 1/2 gµνR = KTµν, which is equivalent to Einstein’s original form.

Second, according to Einstein, it is the affine connection that defines the inertio-gravitational field, not the Riemann tensor:

What characterizes the existence of a gravitational field from the empirical standpoint is the non-vanishing of the Γlik [components of the affine connection], not the non-vanishing of the Riklm [the components of the Riemann tensor]. If one does not think in such intuitive ways, one cannot comprehend why something like curvature should have anything at all to do with gravitation. (Einstein to Max von Laue 1950; English translation from Stachel, 1989, p. 326)

The affine connection is not a tensor between systems of such particles. The Riemann tensor is built from its components and their first derivatives. The affine connection enters the geodesic equation—it would actually be better to say the equation for autoparallel or straightest lines—describing the motion of freely falling sructureless particles, while the Riemann tensor enters the equation of geodesic deviation, which characterizes the tidal gravitational forces between such particles.

A metric affine connection, as in general relativity, is built from the components of the metric and their first derivatives. In this case, the autoparallel lines are also metric geodesics. It follows that a metric Riemann tensor depends on the metric tensor and its first and second derivatives. In spite of Einstein’s comments cited above, general relativity is still often presented entirely in terms of the metric tensor and its derivatives, without proper emphasis on the role of the connection.

The third error is that the curvature at a point of space-time is not “determined by the amount of matter and electromagnetic field and their motion at that point.” The Riemann tensor determined by a metric has twenty independent components at each point, and only the ten components of the Ricci tensor are so determined. It is the additional ten components that enable the propagation of gravitational waves, even in “empty” regions of space-time, that is, regions in which the Ricci tensor vanishes.

Tests of the General Theory . The theory has survived much more precise observations of the three classic predictions: the anomalous precession of Mercury’s orbit, the gravitational red shift, and the apparent bending of light beams in strong gravitational fields. Indeed, the relativistic effects are now so well confirmed that they are routinely used in many new applications (for surveys, see Damour, 2006 and Will, 2005).

The gravitational bending effect is the basis of the phenomenon known as gravitational lensing, originally predicted by Einstein around 1912, but not published by him until 1936 (for Einstein’s role, see Renn, Sauer, and Stachel, 1997). It is now a major tool in observational cosmology, particularly the study of the effects of “dark matter” in galaxies and clusters on light propagation (for gravitational lensing, see Schneider, Ehlers, and Falco, 1992). On a more everyday level, the ubiquitous Global Positioning System (GPS) could not operate without taking into account both special and general relativistic effects (see Ashby, 2005).

The major outstanding project is the direct detection of gravitational waves. Indirect confirmation of the emission of quadrupole gravitational radiation by the binary pulsar PSR 1913+16 through measurement of the resulting modification of the presumed back reaction on their orbits has been extremely successful, winning its observers the Nobel Prize for Physics in 1993 (see Will, 2005). But instruments designed to detect the radiation itself, notably the Laser Interferometer Gravitational-Wave Observatory (LIGO), did not attain sufficient sensitivity to “see” the extremely weak radiation predicted from astrophysical sources (see Saulson, 2005), or the even weaker background cosmological gravitational radiation predicted by some models of the early universe.

The Cosmological Constant . As Balazs points out, Einstein originally introduced the cosmological constant Λ in 1916 order to implement what he called Mach’s principle: On a cosmological scale, the metric tensor field should be completely determined by matter. Einstein took it for granted that, on the average, the universe was static, so he developed such a static cosmological model, for which he needed Λ. When Alexander Friedmann first showed that there are non-static cosmological models with and without the cosmological constant, Einstein thought he had found an error in Friedmann’s work. He quickly withdrew that claim, but regarded the expanding universe solutions as mere mathematical curiosities until the observations of Hubble around 1930 showed their importance for cosmology. By this time Einstein had abandoned Mach’s principle in favor of the reverse, unified field viewpoint: The properties of matter should be completely determined by solutions to some set of unified field equations. Thus, the cosmological constant was no longer needed for its original purpose and there were expanding cosmological models without it, so Einstein abandoned the concept. Others, such as Eddington, kept Λ for other reasons, and it maintained a precarious foothold in cosmological speculations.

In the latter third of the twentieth century, the situation in cosmology began to change dramatically. Theoretical cosmology became more and more closely associated with elementary particle theory, and observational cosmology began to accumulate more and more data limiting the possibilities for and influencing the construction of cosmological models. The cosmological constant has had a dramatic rebirth with the accumulating observation evidence that, rather than slowing down as current theories had predicted, the expansion of the universe is actually accelerating with cosmic time. By an appropriate choice of sign and value for Λ, cosmological models with this property are easily constructed. The problem is to give a physical explanation for such a choice of Λ. One favored explanation as of 2007 is that the Λ-term in the field equations is actually the stress-energy-momentum tensor for “dark energy,” a hitherto unobserved component pervading the entire universe. If this explanation stands the test of time, it may also turn out that the “cosmological constant” is not constant, but varies with cosmological time! (For a review of developments in cosmology, see Padmanabhan, 2005.)

Black Hole Physics . Since the original edition of the DSB, an entire industry has grown up within theoretical physics and observational astronomy known as “black hole physics” (for reviews, see Carter, 2006, and Price, 2005). It is based theoretically on the existence of two solutions to the homogeneous Einstein field equations: the static, spherically symmetric Schwarzschild solution, dating from 1916, and the stationary, axially symmetric Kerr solution, dating from 1963. (For reviews of these and other exact solutions to the Einstein equations, see Bičak, 2000.) Astrophysics predicts that sufficiently massive astrophysical objects ultimately undergo gravitational collapse as gravitation overwhelms the pressures and stresses that keep them from collapsing. If they are massive enough, this process will not be halted by the formation of a neutron star, but will continue until the system passes through an event horizon and forms a black hole, which ultimately ends in a singularity, signaling the breakdown of classical general relativity. This is the upshot of the famous Penrose-Hawking singularity theorems. The external gravitational field outside the horizon must ultimately take the form of either the Schwarzschild field if the system has no net angular momentum, or the Kerr solution if it does. This result was picturesquely stated as “black holes have no hair” by John Wheeler, who coined the term “black hole.” Classically, except for their gravitational fields, such black holes have no influence on their exterior, but Stephen Hawking showed that a semi-classical treatment of quantum-mechanical effects predicts the formation of a radiation field outside the black hole that behaves like black-body radiation at a temperature dependent on the mass of the black hole. Much theoretical work is being done in the early 2000s in the attempt to find an exact quantum-gravitational treatment of black holes, and much observational work on the search for black holes in the cosmos.

Relation Between Geometry and Physics . Balazs asserts: “Minkowski recast the special theory of relativity in a form which had a decisive influence in the geometrization of physics. … This very strong geometrical point of view … led to Einstein’s belief that all laws of nature should be geometrical propositions concerning space-time” (p. 323). Einstein’s supposed “views on the geometrization of physics” are repeated: “He felt that not only the gravitational but also electromagnetic effects should be manifestations of the geometry of space-time” (p. 325). Although many people continue to hold this view of Einstein’s accomplishment and attribute it to him, Einstein explicitly rejected it. In 1928 he wrote: “I cannot agree that the assertion relativity reduces physics to geometry has a clear meaning. One can more correctly say that it follows from the theory of relativity that (metric) geometry has lost its independent existence with respect to the laws usually classified as physical. … That this metric tensor is designated as ‘geometrical’ is simply connected with the fact that the formal structures concerned first appeared in the science called ‘geometry.’ But this is not at all sufficient to justify applying the name ‘geometry’ to every science in which this formal structure plays a role, even when for purposes of visualization [Veranschaulichung] representations are used, to which geometry has habituated us. …” He explicitly rejected the idea that the search for a unified field theory was an attempt to geometrize the electromagnetic field: “The essential thing in Weyl’s and Eddington’s theoretical representations of the electromagnetic field does not lie in their having embedded the field in geometry, but that they have shown a possible way to represent gravitation and electromagnetism from a unified point of view” (Einstein, 1928; translated from the German manuscript, The Einstein Archives Online, Call Nr. [1-68.00]). Peter Bergmann has suggested that “physicalization of geometry” would be a more appropriate phrase (see Bergmann, 1979; the phrase had been used in Zubirini, 1934).

Balazs asserts: “[T]he geometrization of gravitation led eventually to the general theory of relativity; the additional geometrization of the electromagnetic fields of force led to the invention of the unified field theories.” Apart from the use of geometrization language, criticized above, the statement may be misleading. The most successful “geometrization of the electromagnetic fields of force” has been achieved as part of the modern gauge theory of Yang-Mills fields. This has served to unify the electromagnetic and weak nuclear forces, and to a lesser extent, in the theory of quantum chromodynamics, the strong nuclear forces, in the so-called Standard Model. The formulation and quantization of these theories is based on the mathematics of gauge natural fiber bundles, while the standard formulation of general relativity only requires natural bundles. While classical gravitation theory also can be formulated as a gauge natural bundle theory, as of 2007 no successful quantization based on this approach has been accomplished—let alone a unified quantum theory including gravitation (for natural and/or gauge natural theories see Fatibene and Francaviglia, 2003).

Einstein and Unified Field Theory . Balazs states: “Between 1907 and 1911 … [Einstein] came to understand that the solution to the dualism [of fields and particles] problem was to write physics in terms of continuous field quantities and nonlinear partial differential equations that would yield singularity-free particle solutions” (pp. 325–326). Similarly, Klein states “[Einstein] never lost his hope that a field theory of the right kind might eventually reach this goal” (pp. 318–319). Actually, as early as 1916, Einstein was presenting arguments suggesting that the continuum was too rich a structure for the treatment of quantum phenomena (for the evolution of his ideas between 1902 and 1954, see Stachel, 1993). While he continued to work on the topic, his hopes for a satisfactory unified field theory grew weaker in his later years, as Balazs himself suggests: “In 1953 Einstein said to the author that … it is doubtful that a unified field theory of the type he was seeking could exist” (p. 330).

Here is Einstein’s last published comment on the subject, written shortly before he died:

One can give good reasons why reality cannot at all be represented by a continuous field. From the quantum phenomena it appears to follow with certainty that a finite system of finite energy can be completely described by a finite set of numbers (quantum numbers). This does not seem to be in accordance with a continuum theory, and must lead to an attempt to find a purely algebraic theory for the description of reality. But nobody knows how to obtain the basis of such a theory. (“Appendix II” to The Meaning of Relativity, 5th ed. Princeton, 1955, p. 166)

Much recent work on quantum gravity has been based on attempts to set up just such a “purely algebraic theory.” For reviews of some attempts, see Gambini and Pullin, 2005; Dowker, 2005; and Ambjorn, Jurkiewicz, and Loll, 2006.


For the Einstein Archives in the Hebrew University of Jerusalem, consult http://www.albert-einstein.org For the Einstein Papers Project, consult http://www.einstein.caltech.edu For updated reviews of most topics in general relativity, consult http://relativity.livingreviews.org.


“Quantentheorie des einatomigen idealen Gases. Zweite Abhandlung.” Preussische Akademie der Wissenschaften(Berlin) Physikalisch-mathematische Klasse. Sitzunsberichte (1925): 3–14.

“A propos de la déduction relativiste de M. Emile Meyerson.” Revue Philosophique 105 (1928): 161–166.

“Lens-Like Action of a Star by the Deviation of Light in a Gravitational Field.” Science84 (1936): 506–507.

“Why Socialism.” Monthly Review (May 1949). Reprinted in Ideas and Opinions. New York: Crown Publishers, 1954, 151–158.

“Relativity and the Problem of Space.” In Relativity: The Special and the General Theory. 15th ed. New York: Crown, 1952. Reprinted in Ideas and Opinions. New York: Crown Publishers, 1954.

“Foreword.” In Concepts of Space, by Max Jammer . Cambridge, MA: Harvard University Press, 1954.

“Autobiographische Skizze.” In Helle Zeit- Dunkle Zeit In Memoriam Albert Einstein, edited by Carl Seelig. Zürich: Europa, 1956.

The Collected Papers of Albert Einstein. Translated by Anna Beck. Princeton, NJ: Princeton University Press, 1987–2004. Vol. 1: The Early Years, 1879–1902. Vol. 2: The Swiss Years: Writings, 1900–1909. Vol. 3: The Swiss Years: Writings, 1909–1911. Vol. 4: The Swiss Years: Writings, 1912–1914. Vol. 5: The Swiss Years: Correspondence, 1902–1914. Vol. 6: The Berlin Years: Writings, 1914–1917. Vol. 7: The Berlin Years: Writings, 1918–1921. Vol. 8: The Berlin Years: Correspondence, 1914–1918. Vol. 9: The Berlin Years: Correspondence, January 1919–April 1920. Vol. 10: The Berlin Years: Correspondence, May-December 1920, and Supplementary Correspondence, 1909–1920. Cited as Collected Papers. These volumes are making available a wealth of new material about his personal life, his scientific work, and his political-social activities. Each volume has an English translation supplement.

Albert Einstein, Mileva Maric: The Love Letters, edited by Jürgen Renn and Robert Schulmann, translated by Shawn Smith. Princeton, NJ: Princeton University Press, 1992.

Einstein’s Miraculous Year: Five Papers that Changed the Face of Physics. New introduction by John Stachel; foreword by Roger Penrose. 2nd ed. Princeton, NJ: Princeton University Press, 2005. Translations of all the 1905 papers, with commentary and notes.

The New Quotable Einstein. Edited by Alice Calaprice; foreword by Freeman Dyson. Princeton, NJ: Princeton University Press, 2005.

The Political Einstein. Edited and translated by David Rowe and Robert Schulmann. Princeton, NJ: Princeton University Press, 2007.


Ambjorn, Jan, J. Jurkiewicz, and Renate Loll. “Quantum Gravity, or the Art of Building Spacetime.” In Approaches to Quantum Gravity, edited by Danielle Oriti Cambridge, U.K.: Cambridge University Press, 2007.

Ashby, Niel. “Relativity in the Global Positioning System.” In 100 Years of Relativity Space-Time Structure, edited by Abhay Ashtekar. Hackensack, NJ: World Scientific, 2005.

Ashtekar, Abhay, ed. 100 Years of Relativity Space-Time Structure: Einstein and Beyond. Hackensack, NJ: World Scientific, 2005.

Bergmann, Peter G. “Unitary Field Theory, Geometrization of Physics or Physicalization of Geometry?” In Einstein Symposion, Berlin: aus Anlaβ der 100. Wiederkehr seines Geburtstages 25. bis 30. März 1979, edited by Horst Nelkowski, A. Hermann, and H. Poser. Lecture Notes in Physics, vol. 100. Berlin and New York: Springer, 1979.

Bičak, Jiri. “Selected Solutions of Einstein’s Field Equations: Their Role in General Relativity and Astrophysics.” Lecture Notes in Physics540 (2000): 1–126.

Brian, Denis. The Unexpected Einstein: The Real Man behind the Icon. Hoboken, NJ: Wiley, 2005.

Carter, Brandon. “Half Century of Black-Hole Theory: From Physicists’ Purgatory to Mathematicians’ Paradise.” In A Century of Relativity Physics, edited by Lysiane Mornas and Joaquin Diaz Alonso. Melville, NY: American Institute of Physics, 2006.

Damour, Thibault. “100 Years of Relativity: Was Einstein 100% Right?” In A Century of Relativity Physics, edited by Lysiane Mornas and Joaquin Diaz Alonso. Melville, NY: American Institute of Physics, 2006.

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Fölsing, Albrecht. Albert Einstein: A Biography. New York and London: Viking, 1997. Good on biographical information, weak on science.

Gambini, Rodolfo, and Jorge Pullin. “Consistent Discrete Space-Time.” In 100 Years of Relativity Space-Time Structure, edited by Abhay Ashtekar. Hackensack, NJ: World Scientific, 2005.

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Hettler, Nicolaus. “Die Elektrotechnische Firma J. Einstein u. Cie in München—1876–1894.” PhD diss. Stuttgart University, 1996.

Highfield, Roger, and Paul Carter. The Private Lives of Albert Einstein. London: Faber, 1993; Boston: St, Martin's, 1994.

Janssen, Michel, John D. Norton, Jürgen Renn, et al. The Genesis of General Relativity, vol. 1: Einstein’s Zurich Notebook: Introduction and Source, vol. 2: Einstein’s Zurich Notebook: Commentary and Essays. Dordrecht, Netherlands: Springer, 2007.

Martinez, Alberto. “Handling Evidence in History: The Case of Einstein’s Wife.” Science School Review 86 (2005): 51–52.

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Pais, Abraham. ‘Subtle is the Lord …’ The Science and the Life of Albert Einstein. New York: Oxford University Press, 1982. The best overall analysis of Einstein’s scientific work.

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John Stachel

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Einstein, Albert

Einstein, Albert

(b. Ulm, Germany, 14 March 1879; d. Princeton, New Jersey, 18 April 1955)


Albert Einstein was the only son of Hermann and Pauline (Koch) Einstein. He grew up in Munich, where his father and his uncle ran a small electrochemical plant. Einstein was a slow child and disliked the regimentation of school. His scientific interests were awakened early and at home—by the mysterious compass his father gave him when he was about four; by the algebra he learned from his uncle; and by the books he read, mostly popular scientific works of the day. A geometry text which he devoured at the age of twelve made a particularly strong impression.

When his family moved to Milan after a business failure, leaving the fifteen-year-old boy behind in Munich to continue his studies, Einstein quit the school he disliked and spent most of a year enjoying life in Italy. Persuaded that he would have to acquire a profession to support himself, he finished the Gymnasium in Aarau, Switzerland, and then studied physics and mathematics at the Eidgenössische Technische Hochschule (the Polytechnic) in Zurich, with a view toward teaching.

After graduation Einstein was unable to obtain a regular position for two years and did occasional tutoring and substitute teaching, until he was appointed an examiner in the Swiss Patent Office at Berne. The seven years Einstein spent at this job, with only evenings and Sundays free for his own scientific work, were years in which he laid the foundations of large parts of twentieth-century physics. They were probably also the happiest years of his life. He liked the fact that his job was quite separate from his thoughts about physics, so that he could pursue these freely and independently, and he often recommended such an arrangement to others later on. In 1903 Einstein married Mileva Marić, a Serbian girl who had been a fellow student in Zurich. Their two sons were born in Switzerland.

Einstein received his doctorate in 1905 from the University of Zurich for a dissertation entitled, “Eineneue Bestimmung der Moleküldimensionen” (“A New Determination of Molecular Dimensions”), a work closely related to his studies of Brownian motion, discussed below. It took only a few years until he received academic recognition for his work, and then he had a wide choice of positions. His first appointment, in 1909, was as associate professor (extraordinarius) of physics at the University of Zurich. This was followed quickly by professorships at the German University in Prague, in 1911, and at the Polytechnic in Zurich, in 1912. Then, in the spring of 1914, Einstein moved to Berlin as a member of the Prussian Academy of Sciences and director of the Kaiser Wilhelm Institute for Physics, free to lecture at the university or not as he chose. He had mixed feelings about accepting this appointment, partly because he disliked Prussian rigidity and partly because he was unhappy about the implied obligation to produce one successful theory after another. As it turned out he found the scientific atmosphere in Berlin very stimulating, and he greatly enjoyed having colleagues like Max Planck, Walther Nernst, and, later, Erwin Schrödinger and Max von Laue.

During World War I, Einstein’s scientific work reached a culmination in the general theory of relativity, but in most other ways his life did not go well. He would not join in the widespread support given to the German cause by German intellectuals and did what he could to preserve a rational, international spirit and to urge the immediate end of the war. His feeling of isolation was deepened by the end of his marriage. Mileva Einstein and their two sons spent the war years in Switzerland and the Einsteins were divorced soon after the end of the war. Einstein then married his cousin Elsa, a widow with two daughters. Einstein’s health suffered, too. One of his few consolations was his continued correspondence and occasional visits with his friends in the Netherlands—Paul Ehrenfest and H. A. Lorentz, especially the latter, whom Einstein described as having “meant more to me personally than anybody else I have met in my lifetime” 1. and as “greatest and noblest man of our times,” 2.

Einstein became suddenly famous to the world at large when the deviation of light passing near the sun, as predicted by his general theory of relativity, was observed during the solar eclipse of 1919. His name and the term relativity became household words. The publicity, even notoriety, that ensued changed the pattern of Einstein’s life. He was now able to put the weight of his name behind causes that he believed in, and he did this, always bravely but taking care not to misuse the influence his scientific fame had given him. The two movements he backed most forcefully in the 1920’s were pacifism and Zionism, particularly the creation of the Hebrew University in Jerusalem. He also took an active part for a few years in the work of the Committee on Intellectual Cooperation of the League of Nations.

Soon after the end of the war, Einstein and relativity became targets of the anti-Semitic extreme right wing. He was viciously attacked in speeches and articles, and his life was threatened. Despite this treatment Einstein stayed in Berlin, declining many offers to go elsewhere. He did accept an appointment as special professor at Leiden and went there regularly for periods of a week or two to lecture and to discuss current problems in physics. In 1933 Einstein was considering an arrangement that would have allowed him to divide his year between Berlin and the new Institute for Advanced Study at Princeton. But when Hitler came to power in Germany, he promptly resigned his position at the Prussian Academy and joined the Institute. Princeton became his home for the remaining twenty-two years of his life. He became an American citizen in 1940.

During the 1930’s Einstein renounced his former pacifist stand, since he was now convinced that the menace to civilization embodied in Hitler’s regime could be put down only by force. In 1939, at the request of Leo Szilard, Edward Teller, and Eugene Wigner, he wrote a letter to President Franklin D. Roosevelt pointing out the dangerous military potentialities offered by nuclear fission and warning him of the possibility that Germany might be developing these potentialities. This letter helped to initiate the American efforts that eventually produced the nuclear reactor and the fission bomb, but Einstein neither participated in nor knew anything about these efforts. After the bomb was used and the war had ended, Einstein devoted his energies to the attempt to achieve a world government and to abolish war once and for all. He also spoke out against repression, urging that intellectuals must be prepared to risk everything to preserve freedom of expression.

Einstein received a variety of honors in his lifetime—from the 1921 Nobel Prize in physics to an offer (which he did not accept) of the presidency of Israel after Chaim Weizmann’s death in 1952.

One of Einstein’s last acts was his signing of a plea, initiated by Bertrand Russell, for the renunciation of nuclear weapons and the abolition of war. He was drafting a speech on the current tensions between Israel and Egypt when he suffered an attack due to an aortic aneurysm; he died a few days later. But despite his concern with world problems and his willingness to do whatever he could to alleviate them, his ultimate loyalty was to his science. As he said once with a sigh to an assistant during a discussion of political activities: “Yes, time has to be divided this way between politics and our equations. But our equations are much more important to me, because politics is for the present, but an equation like that is something for eternity.”3.

Early Scientific Interests. Albert Einstein started his scientific work at the beginning of the twentieth century. It was a time of startling experimental discoveries, but the problems that drew his attention and forced him to produce the boldly original ideas of a new physics had developed gradually and involved the very foundations of the subject. The closing decades of the nineteenth century were the period when the long-established goal of physical theory—the explanation of all natural phenomena in terms of mechanics—came under serious scrutiny and was directly challenged. Mechanical explanation had had great successes, particularly in the theory of heat and in various aspects of optics and electromagnetism; but even the successful mechanical theory of heat had its serious failures and unresolved paradoxes, and physicists had not been able to provide a really satisfactory mechanical foundation for electromagnetic theory. Many were questioning the whole program of mechanism, and alternatives ranging from the energetics of Wilhelm Ostwald to the electromagnetic world view of Wilhelm Wien were widely considered and vigorously debated.

To a young man who looked to science for nothing less than an insight into the “great eternal riddle”4. of the universe, these basic questions were the most challenging and also the most fascinating. Einstein was impressed by both the successes and the failures of mechanical physics and was attracted to what he later called the “revolutionary” ideas of James Clerk Maxwell’s field theory of electromagnetism. His study of the writings of the nineteenth-century masters received a new direction when he read Ernst Mach’s Science of Mechanics. This concern with general principles required something else to make it fruitful, however, and Einstein himself described what it was. He realized that each of the separate fields of physics “could devour a short working life without having satisfied the hunger for deeper knowledge,” but he had an unmatched ability “to scent out the paths that led to the depths, and to disregard everything else, all the many things that clutter up the mind and divert it from the essential.”5. This ability to grasp precisely the particular simple physical situation that could throw light on obscure questions of general principle characterized much of Einstein’s thinking.

His earliest papers—“my two worthless beginner’s works,”6. as he referred to them a few years later— were an attempt to learn something from experimental materials about intermolecular forces with a view toward their possible relationship with longrange gravitational force, a problem going back to Newton’s time. This work led nowhere, and Einstein’s next series of three articles, published during the years 1902 to 1904, dealt with quite another set of ideas and was clearly the work of a mature scientist. In these articles Einstein rederived by his own methods the basic results of statistical mechanics: the canonical distribution of energy for a system in contact with a heat bath, the equipartition theorem, and the physical interpretations of entropy and temperature. He also emphasized that the probabilities that appear in the theory are to be understood as having a very definite physical meaning. The probability of a macroscopically identifiable state of a system is the fraction of any sufficiently long time interval that the system spends in this state. Equilibrium is dynamic, with the system passing through all its possible states in an irregular sequence. Ludwig Boltzmann had introduced this point of view years before, but Einstein made it very much his own.

It was in the last of this early series of papers, however, that Einstein introduced a new theme. There is one fundamental constant in statistical mechanics, the constant now known as Boltzmann’s constant, k. It appears in the typical exponential factor of the distribution law, exp (–E/kT), Where E is the energy of the system and T is its absolute temperature. It appears too in the relation between the entropy S and the probability W of a state

Einstein asked for the physical significance of this constant K. It was already well-known from the theory of the ideal gas that K was simply related to the gas constant R and to Avogadro’s number, N0, the number of molecules in a gram-molecular weight of any substance,

Einstein showed that K entered into still another basic equation of the statistical theory, the expression for the mean square fluctuation 〈δ2〉 of the4 energy E about its average value〈E〉:

This meant that k defines the scale of fluctuation phenomena or, as Einstein put it, that it determines the thermal stability of a system. This result shows that fluctuations are normally negligibly small so that the average or thermodynamic value of the energy is a very good measure of this quantity, but Einstein was more interested in its other implications. If one could actually measure the energy fluctuations of any system, then k could be determined and with it Avogadro’s number and the mass of an individual atom. None of these quantities was known with any precision, and previous determinations involved very indirect theoretical arguments. Einstein could not refer to any measurements of fluctuations, but he did give a very plausible analysis of the energy fluctuations in black-body radiation showing how k was related to the constant in Wien’s displacement law.

This 1904 paper made little if any impression on Einstein’s contemporaries, but it contained the seeds of much of his later work. No one before Einstein had taken seriously the fluctuation phenomena predicted by statistical mechanics, but he saw that the existence of such fluctuations could be used to demonstrate the correctness of the whole molecular theory of heat. The problem was to find a situation in which fluctuations could be observed, and Einstein found a solution to this problem in 1905, in his paper “Die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen” (“On the Movement of Small Particles Suspended in a Stationary Liquid Demanded by the Molecular-Kinetic Theory of Heat”). This predicted motion of colloidal particles was already widely known as Brownian motion, but at the time Einstein wrote this paper he knew virtually nothing about what had been observed and hesitated to identify the two motions. He was not trying to explain an old and puzzling phenomenon, but rather to deduce a result that could be used to test the atomic hypothesis and to determine the basic scale of atomic dimensions.

One essential assumption Einstein made was that a colloidal particle will come into thermodynamic equilibrium with the molecules of the fluid in which it is suspended, so that the average kinetic energy of the particle associated with its motion in any one direction is just the equipartition value, kT/2. The quantity for that Einstein calculated for this random motion of colloidal particles was not the velocity, which is unmeasurable even in principle, but rather the mean square displacement in some particular direction x during the time interval т. For spherical particles of radius α, satisfying the same law of resistance that a macroscopic sphere would obey in this fluid of viscosity η, he obtained the result

The hope Einstein expressed at the end of his paper, that “some enquirer” undertake an experimental test of his predictions, was fulfilled several years later when Jean Perrin’s experiments confirmed the correctness of all features of the Brownian motion equation and provided a new determination of Avogadro’s number. These results helped to convince the remaining skeptics, such as Wilhelm Ostwald, that molecules were real and not just a convenient hypothesis. The theory of Brownian motion was developed further by both Einstein and Maryan von Smoluchowski. Several years later both men worked on the theory of another fluctuation phenomenon—the opalescence exhibited by a fluid in the immediate neighborhood of its critical point. Einstein’s work, published in 1910, was especially notable for its generalization of fluctuation theory in a form independent of the mechanical foundations of the theory, an old idea of his and one that later proved to be of considerable influence.

All the work discussed thus far, significant as it was, does not represent the predominant concern of Albert Einstein throughout his career—the search for a unified foundation for all of physics. Neither the attempts at a mechanical theory of the electromagnetic field nor the recent efforts to base mechanics on electromagnetism had been successful. The disparity between the discrete particles of matter and the continuously distributed electromagnetic field came out most clearly in Lorentz’ electron theory, where matter and field were sharply separated for the first time. This theory strongly influenced Einstein, who often referred to the basic electromagnetic equations as the Maxwell-Lorentz equations. The problems generated by the incompatibility between mechanics and electromagnetic theory at several crucial points claimed Einstein’s attention. His struggles with these problems led to his most important early work—the special theory of relativity and the theory of quanta.

For the sake of clarity and convenience, Einstein’s development of relativity theory is treated in a separate article following the discussion of his contribution to quantum mechanics that occupies the remainder of the present article. It must be pointed out, however, that separating these two main themes in Einstein’s work does an injustice to the unity of his fundamental purpose.

Quantum Theory and Statistical Mechanics. Einstein once described his first paper of 1905, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt” (“On a Heuristic Viewpoint Concerning the Production and Transformation of Light”), as “very revolutionary.” He was not exaggerating. The heuristic viewpoint of the title was nothing less than the suggestion that light be considered a collection of independent particles of energy, which he called light quanta. Einstein had his reasons for advancing such a bold suggestion, one that seemed to dismiss a century of evidence supporting the wave theory of light. First among these reasons was a negative result: The combination of the electromagnetic theory of light with the (statistical) mechanics of particles was incapable of dealing with the problem of black-body radiation. It predicted that radiation in theromodynamic equilibrium within an enclosure would have a frequency distribution corresponding to an infinite amount of energy at the high-frequency end of the spectrum. This was incompatible with the experimental results, but, worse than that, it meant that the theory did not give an acceptable answer to the problem. Einstein was the first to point to this result, known later on as the “ultraviolet catastrophe,” as a fundamental failure of the combined classical theories, although Lord Rayleigh had hinted at this in a paper in 1900.

Although he was convinced that a new unified fundamental theory was needed for an adequate treatment of the radiation problem, Einstein had no such theory to offer. What he did instead was to analyze the implications of the observed radiation spectrum, well-described, except at low frequencies, by Wien’s distribution law. To carry out his analysis, Einstein used the methods of thermodynamics (“the only physical theory of universal content concerning which I am convinced that, within the framework of the applicability of its basic concepts, it will never be overthrown”) and statistical mechanics. What he found was that the entropy of black-body radiation in a given frequency interval depends on the volume of the enclosure in the same way that the entropy of a gas depends on its volume. And because the latter dependence has its origin in the independence of the gas molecules rather than the details of their dynamics, Einstein leaped to the conclusion that the radiation, too, must consist of independent particles of energy. This identification required the energy E of the particles to be proportional to the frequency ν of the radiation,

where the universal proportionality constant h was the product of k and one of the constants in Wien’s distribution law.

Einstein showed that his strange proposal of light quanta could immediately account for several puzzling properties of fluorescence, photoionization, and especially of the photoelectric effect. His quantitative prediction of the relationship between the maximum energy of the photoelectrons and the frequency of the incident light was not verified experimentally for a decade. The light quantum hypothesis itself attracted only one or two adherents; it represented too great a departure from accepted ideas. It went far beyond the work Max Planck had done in 1900, in which the energy of certain material oscillators was treated as a discrete variable, capable only of values that were integral multiples of a natural unit proportional to the frequency. Planck’s quantum hypothesis had been introduced as a way of deriving the complete distribution law for black-body radiation, but in 1905 it was only just starting to receive critical study.

During the years between 1905 and 1913 it was Einstein who took the lead in probing the significance of the new ideas on quanta. He soon decided that Planck’s work was complementary to his own and not in conflict with it, as he had first thought. Einstein then realized that if Planck had been right in restricting the energies of his oscillators to integral multiples of hv, in discussing the interaction of molecular oscillators with black-body radiation, then this same restriction should also apply to all oscillations on the molecular scale. The success of Planck’s work had to be looked upon as demonstrating the need for a quantum theory of matter, even as his own 1905 paper demonstrated the need for a quantum theory of radiation.

In 1907 Einstein pointed out how one could use the quantized energy of the oscillations of atoms in solids to account for departures from the rule of Dulong and Petit. This empirical rule, that the specific heat is the same for one mole of any element in solid form, was understood as a consequence of the theorem of equipartition of energy. Many light elements, however, had specific heats at room temperature that were much smaller than the Dulong-Petit value. Einstein showed how one could easily calculate the specific heat of a solid all of whose atoms vibrated with the same frequency (an assumption he made only as a convenient simplification) and obtain a universal curve for the variation of specific heat with temperature. The only parameter in the theory was the frequency of the quantized vibrations. This specific heat curve approached the Dulong-Petit value at high temperatures; accounted qualitatively for all the departures from the equipartition result, including the absence of electronic contributions to the specific heat; and predicted a new and general law: The specific heats of all solids should approach zero as the absolute temperature approaches zero. Einstein indicated how the vibration frequencies could be determined from infrared absorption measurements in many cases; several years later he suggested another way of determining these frequencies using their relationship to the elastic constants of the solid.

As it turned out, Einstein’s quantum theory of specific heats appeared at a time when the behavior of specific heats at low temperatures had just become of interest for very different reasons. Walther Nernst was planning a program of such measurements to establish his own new heat theorem, later known as the third law of thermodynamics. Nernst’s results matched the predictions of Einstein’s theory in all essential respects and convinced him that there was something really significant in this “odd” and “grotesque” theory,7. as he called it. The success of Einstein’s theory of specific heats in explaining old difficulties, predicting new laws, and establishing unexpected connections among thermal, optical, and elastic properties of crystals was the single most important element in awakening the interest of physicists in the quantum theory.

Wave-Particle Duality. For Einstein, however, the central problem continued to be the nature of radiation. In 1909, speaking in Salzburg at his first major scientific meeting, he argued that the future theory of light which would have to be constructed would be “a kind of fusion of the wave and emission theories.”8. Einstein’s prediction was based on the results of his continued probings into the implications of Planck’s distribution law for black-body radiation. He had calculated the energy fluctuations of the radiation in a small frequency interval with the help of equation (3) and had found that the fluctuations were the sum of two terms, indicating two apparently independent mechanisms for energy fluctuations. One term was readily intelligible as due to interfering waves, the other as due to variations in the number of light quanta present in the subvolume under study. Neither a wave nor a particle theory could account for the presence of both terms. Einstein confirmed this result by a completely independent calculation of the Brownian motion that a mirror would have to undergo if it were suspended in an enclosure containing a gas and black-body radiation in thermodynamic equilibrium. Once again there were wave and particle contributions to the fluctuations in momentum of the suspended mirror.

Einstein saw this wave-particle duality in radiation as concrete evidence for his conviction that physics needed a new, unified foundation. His view of the role of light quanta in this new fundamental theory had evolved since he put forward the heuristic suggestion of a corpuscular approach to radiation in 1905. Einstein now envisaged a field theory, based on appropriate partial differential equations, probably nonlinear, from which quanta would emerge as singular solutions, along the lines of the electric charges in electrostatics. He found some support for this parallel in the fact that Planck’s constant, h, characteristic for light quanta, was dimensionally equivalent to e2/c, where e is the unit electric charge and c is the velocity of light. To Einstein this suggested that the discreteness of energy and the discreteness of charge might be explained together by the new fundamental theory.

There was unfortunately very little to go on in the search for this new theory. It would have to be consistent with the special theory of relativity, but Einstein saw that theory as only a universal formal principle, analogous to the laws of thermodynamics, which gave no clue to the structure of matter or radiation. The fluctuation properties of radiation, which he had established, “presented small foothold for setting up a theory.”9. We know from Einstein’s correspondence as well as from the brief remarks in his papers of this period that he devoted much of his effort to this problem in the years 1908 to 1911, using Lorentz’ theory of electrons as one of his points of departure. His efforts along this line seem to have been comparable in their intensity, although not in their fruitfulness, to his efforts during the following years to create the new gravitational theory—the general theory of relativity.

When in 1911 Einstein put aside his intense work on the problem of developing a theory from which he could “construct” quanta—“because I now know that my brain is incapable of accomplishing such a thing”10.—he did not give up his interest in quanta. He continued to reflect on the questions surrounding the quantum theory. In a paper in 1914, for example, he used familiar thermodynamic arguments to give a new derivation of Planck’s expression for the average energy of an oscillator. This work led him to suggest the identity of physical and chemical changes at the molecular level: “A quantum type of change in the physical state of a molecule seems to be no different in principle from a chemical change.”11.

Relation to Bohr’s Early Work. When Einstein returned to the radiation problem in 1916, the quantum theory had undergone a major change. Niels Bohr’s papers had opened a new and fertile domain for the application of quantum concepts—the explanation of atomic structure and atomic spectra. In addition Bohr’s work and its generalizations by Arnold Sommerfeld and others constituted a fresh approach to the foundations of the quantum theory of matter. Einstein’s new work showed the influence of these ideas. He had found still another derivation of Planck’s black-body radiation law, an “astonishingly simple and general” one which, he thought, might properly be called “the derivation”12. of this important law. It was based on statistical assumptions about the processes of absorption and emission of radiation and on Bohr’s basic quantum hypothesis that atomic systems have a discrete set of possible stationary states. The proof turned on the requirement that absorption and emission of radiation, both spontaneous and stimulated, suffice to keep a gas of atoms in thermodynamic equilibrium. (This paper introduced the concept of stimulated emission into the quantum theory and is therefore often described as the basis of laser physics.) Einstein himself considered the most important contribution of this work to be not the new derivation of the distribution law but rather the arguments he presented for the directional character of energy quanta. Each quantum of frequency v emitted by an atom must carry away momentum hν/c in a definite direction; spherical waves would simply not exist.

Although Einstein put particular emphasis on the directionality of light quanta, there was no direct evidence for it until 1923 when Arthur Compton explained his experiments on the increase in X-ray wavelength after scattering from free electrons. Compton simply treated the process as a collision, obeying the conservation laws, between the electron and a quantum of energy and momentum hν/c in the direction of the incident X-ray beam. Even before this, however, Einstein was trying to devise a crucial experiment to settle the question of the nature of radiation. He held fast to his view that light quanta were indispensable since they described the particle properties really manifested by radiation. Light quanta did not have many other supporters until after the Compton effect, and they were particularly unpopular with Bohr and his co-workers. Bohr saw no good way of reconciling them with the correspondence principle and was willing to give up the exact validity of the conservation laws in order to avoid quanta. Experiments to check Bohr’s proposals early in 1925 vindicated Einstein’s belief in both the conservation laws and the validity of light quanta.

Bose-Einstein Statistics and Wave Mechanics. In 1924 Einstein received a paper from a young Indian physicist, S. N. Bose, setting forth a theory in which radiation was treated as a gas of light quanta. By changing the statistical procedure for counting the states of the gas, Bose had arrived at an equilibrium distribution which was identical with Planck’s radiation law. Einstein was much taken with this extension of his old idea. He not only translated Bose’s paper into German and saw to its publication, but he also applied Bose’s new statistical idea to develop an analogous theory for an ideal gas of material particles. A gas obeying the Bose-Einstein statistics, as the new counting procedure was later called, showed a variety of interesting properties. Even though the particles exerted no forces on each other the gas showed a peculiar “condensation” phenomenon: Below a certain temperature a disproportionately large fraction of the total number of particles are found in the state of lowest energy.

Einstein’s interest in the parallel between the gas of particles and the gas of light quanta deepened when he read Louis de Broglie’s Paris thesis late in 1924. De Broglie, inspired by Einstein’s earlier work on the wave-particle duality, had become convinced that this duality must hold for matter as well as radiation. In his thesis he developed the idea that every material particle has a wave associated with it, the frequency ν and wavelength λ of the wave being related to the energy E and momentum p of the particle by the equations

De Broglie had no experimental evidence to support his idea and deduced no experimentally testable conclusions from it, so it aroused very little interest. Einstein, however, was immediately attracted to the idea of matter waves because he saw its relationship to his new theory of the ideal gas. He found a confirmation of de Broglie’s wave-particle duality for matter in the results of his calculation of the density fluctuations of this ideal gas. These fluctuations showed the same structure as had the energy fluctuations of black-body radiation; only now it was the particle term that would have been the only one present in the classical gas theory. Einstein saw the wave term in the fluctuations as a manifestation of the de Broglie waves, and he was sure he was not dealing with a “mere analogy”. He proposed several kinds of experiments which might detect the diffraction of de Broglie waves.

Einstein’s support for de Broglie’s work brought it the attention it deserved, particularly from Erwin Schrodinger. In describing the origins of his wave mechanics a few years later, Schrodinger wrote: “My theory was stimulated by de Broglie’s thesis and by short but infinitely far-seeing remarks by Einstein.” 13. Those remarks were the ones linking de Broglie’s ideas to the properties of the Bose-Einstein gas.

When the new matrix mechanics appeared, in the papers of Werner Heisenberg, Max Born, and Pascual Jordan, Einstein was interested but not convinced. “An inner voice tells me that it is still not the true Jacob”, 14. he wrote to Born in 1926. He looked more favorably on Schrodinger’s wave mechanics: “I am convinced that you have made a decisive advance with your formulation of the quantum condition, just as I am equally convinced that the Heisenberg-Born route is off the track.”15.

Discontent With Quantum Mechanics. In 1927 the synthesis that constituted the new quantum mechanics was worked out. One of its key features was Born’s statistical interpretation of Schrödinger’s wave function. This meant that a full quantum mechanical description of the state of a system would generally specify only probabilities rather than definite values of the dynamical variables of the system. The new theory was intrinsically statistical and renounced as meaningless in principle any attempt to go beyond the probabilities to arrive at a deterministic theory. Bohr expressed what became the generally accepted viewpoint when he described quantum mechanics as a “rational generalization of classical physics”, the result of “a singularly fruitful cooperation of a whole generation of physicists.”16.

Einstein dissented from this majority opinion. He never accepted the finality of the quantum mechanical renunciation of causality or its limitation of physical theory to the unambiguous description of the outcome of fully defined experiments. From the Solvay Congress of 1927, when the quantum mechanical synthesis was first discussed, to the end of his life, Einstein never stopped raising questions about the new physics to which he had contributed so much. He tried at first to propose conceptual experiments that would prove the logical inconsistency of quantum mechanics, but these arguments were all successfully refuted by Bohr. In 1935 Einstein began to stress another objection to quantum mechanics, arguing that its description of physical reality was essentially incomplete, that there were elements of physical reality which did not have counterparts in the theory. Bohr answered this argument, saying that Einstein’s criterion of physical reality was ambiguous and that from Bohr’s own complementarity standpoint the theory satisfied any reasonable standard of completeness.

Einstein never abandoned his opposition to the prevailing mode of thought despite the enormous success of quantum mechanics. He was convinced that a fundamental theory could not be statistical, “that He does’t play dice”, 17. Even more serious in Einstein’s view was the incompleteness of the theory. He would not give up the idea that there was such a thing as “the real state of a physical system, something that objectively exists independently of observation or measurement, and which can, in principle, be described in physical terms.”s 18. The search for a theory that could provide such a description of reality was Einstein’s program. He never lost his hope that a field theory of the right kind might eventually reach this goal.

That Einstein, without whom twentieth-century physics would be unthinkable, should have chosen to follow a separate path was a source of great regret to his colleagues. In Max Born’s words: “Many of us regard this as a tragedy—for him, as he gropes his way in loneliness, and for us who miss our leader and standard-bearer.”19. But to Einstein himself his choice was inevitable; it was the natural outgrowth of all his years of striving to find a unified foundation for physics. This was what he meant when he ended his scientific autobiography by writing that he had tried to show “how the efforts of a lifetime hang togeather and why they have led to expectations of a definite form.”20.

Martin J. Klein

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Einstein, Albert (1879-1955)

Einstein, Albert (1879-1955)

German-born American physicist

Albert Einstein ranks as one of the most remarkable theoreticians in the history of science. He was also a heartfelt pacifist dedicated to world peace. During a single year, 1905, he produced three papers that are among the most important in twentieth-century physics , and perhaps in all of the recorded history of science, for they revolutionized the way scientists looked at the nature of space , time, and matter. These papers dealt with the nature of particle movement known as Brownian motion, the quantum nature of electromagnetic radiation as demonstrated by the photoelectric effect, and the special theory of relativity. Although Einstein is probably best known for the last of these works, it was for his quantum explanation of the photoelectric effect that he was awarded the 1921 Nobel Prize in physics. In 1915, Einstein extended his special theory of relativity to include certain cases of accelerated motion, resulting in the more general theory of relativity.

Einstein was born in Ulm, Germany, the only son of Hermann and Pauline Koch Einstein. Both sides of his family had long-established roots in southern Germany, and, at the time of Einstein's birth, his father and uncle Jakob owned a small electrical equipment plant. When that business failed around 1880, Hermann Einstein moved his family to Munich to make a new beginning. A year after their arrival in Munich, Einstein's only sister, Maja, was born.

Although his family was Jewish, Einstein was sent to a Catholic elementary school from 1884 to 1889. He was then enrolled at the Luitpold Gymnasium in Munich. During these years, Einstein began to develop some of his earliest interests in science and mathematics, but he gave little outward indication of any special aptitude in these fields. Indeed, he did not begin to talk until the age of three and, by the age of nine, was still not fluent in his native language.

In 1894, Hermann Einstein's business failed again, and the family moved once more, this time to Pavia, near Milan, Italy. Einstein was left behind in Munich to allow him to finish school. Such was not to be the case, however, since he left the gymnasium after only six more months. Einstein's biographer, Philipp Frank, explains that Einstein so thoroughly despised formal schooling that he devised a scheme by which he received a medical excuse from school on the basis of a potential nervous breakdown. He then convinced a mathematics teacher to certify that he was adequately prepared to begin his college studies without a high school diploma. Other biographies, however, say that Einstein was expelled from the gymnasium on the grounds that he was a disruptive influence at the school.

In any case, Einstein then rejoined his family in Italy. One of his first acts upon reaching Pavia was to give up his German citizenship. He was so unhappy with his native land that he wanted to sever all formal connections with it; in addition, by renouncing his citizenship, he could later return to Germany without being arrested as a draft dodger. As a result, Einstein remained without an official citizenship until he became a Swiss citizen at the age of 21. For most of his first year in Italy, Einstein spent his time traveling, relaxing, and teaching himself calculus and higher mathematics. In 1895, he thought himself ready to take the entrance examination for the Eidgenössiche Technische Hochschule (the ETH, Swiss Federal Polytechnic School, or Swiss Federal Institute of Technology), where he planned to major in electrical engineering. When he failed that examination, Einstein enrolled at a Swiss cantonal high school in Aarau. He found the more democratic style of instruction at Aarau much more enjoyable than his experience in Munich and soon began to make rapid progress. He took the entrance examination for the ETH a second time in 1896, passed, and was admitted to the school. (In Einstein, however, Jeremy Bernstein writes that Einstein was admitted without examination on the basis of his diploma from Aarau.)

The program at ETH had nearly as little appeal for Einstein as had his schooling in Munich, however. He apparently hated studying for examinations and was not especially interested in attending classes on a regular basis. He devoted much of this time to reading on his own, specializing in the works of Gustav Kirchhoff, Heinrich Hertz, James Clerk Maxwell , Ernst Mach, and other classical physicists. When Einstein graduated with a teaching degree in 1900, he was unable to find a regular teaching job. Instead, he supported himself as a tutor in a private school in Schaffhausen. In 1901, Einstein also published his first scientific paper, "Consequences of Capillary Phenomena."

In February, 1902, Einstein moved to Bern and applied for a job with the Swiss Patent Office. He was given a probationary appointment to begin in June of that year and was promoted to the position of technical expert, third class, a few months later. The seven years Einstein spent at the Patent Office were the most productive years of his life. The demands of his work were relatively modest and he was able to devote a great deal of time to his own research.

The promise of a steady income at the Patent Office also made it possible for Einstein to marry. Mileva Maric (also given as Maritsch) was a fellow student in physics at ETH, and Einstein had fallen in love with her even though his parents strongly objected to the match. Maric had originally come from Hungary and was of Serbian and Greek Orthodox heritage. The couple married in 1903, and later had two sons, Hans Albert and Edward.

In 1905, Einstein published a series of papers, any one of which would have assured his fame in history. One, "On the Movement of Small Particles Suspended in a Stationary Liquid Demanded by the Molecular-Kinetic Theory of Heat," dealt with a phenomenon first observed by the Scottish botanist Robert Brown in 1827. Brown had reported that tiny particles, such as dust particles, move about with a rapid and random zigzag motion when suspended in a liquid.

Einstein hypothesized that the visible motion of particles was caused by the random movement of molecules that make up the liquid. He derived a mathematical formula that predicted the distance traveled by particles and their relative speed. This formula was confirmed experimentally by the French physicist Jean Baptiste Perrin in 1908. Einstein's work on the Brownian movement is generally regarded as the first direct experimental evidence of the existence of molecules.

A second paper, "On a Heuristic Viewpoint concerning the Production and Transformation of Light," dealt with another puzzle in physics, the photoelectric effect. First observed by Heinrich Hertz in 1888, the photoelectric effect involves the release of electrons from a metal that occurs when light is shined on the metal. The puzzling aspect of the photo-electric effect was that the number of electrons released is not a function of the light's intensity, but of the color (that is, the wavelength) of the light.

To solve this problem, Einstein made use of a concept developed only a few years before, in 1900, by the German physicist Max Planck , the quantum hypothesis. Einstein assumed that light travels in tiny discrete bundles, or "quanta," of energy. The energy of any given light quantum (later renamed the photon), Einstein said, is a function of its wavelength. Thus, when light falls on a metal, electrons in the metal absorb specific quanta of energy, giving them enough energy to escape from the surface of the metal. But the number of electrons released will be determined not by the number of quanta (that is, the intensity) of the light, but by its energy (that is, its wavelength). Einstein's hypothesis was confirmed by several experiments and laid the foundation for the fields of quantitative photoelectric chemistry and quantum mechanics. As recognition for this work, Einstein was awarded the 1921 Nobel Prize in physics.

A third 1905 paper by Einstein, almost certainly the one for which he became best known, details his special theory of relativity. In essence, "On the Electrodynamics of Moving Bodies" discusses the relationship between measurements made by observers in two separate systems moving at constant velocity with respect to each other.

Einstein's work on relativity was by no means the first in the field. The French physicist Jules Henri Poincaré, the Irish physicist George Francis FitzGerald, and the Dutch physicist Hendrik Lorentz had already analyzed in some detail the problem attacked by Einstein in his 1905 paper. Each had developed mathematical formulas that described the effect of motion on various types of measurement. Indeed, the record of pre-Einstein thought on relativity is so extensive that one historian of science once wrote a two-volume work on the subject that devoted only a single sentence to Einstein's work. Still, there is little question that Einstein provided the most complete analysis of this subject. He began by making two assumptions. First, he said that the laws of physics are the same in all frames of reference. Second, he declared that the velocity of light is always the same, regardless of the conditions under which it is measured.

Using only these two assumptions, Einstein proceeded to uncover an unexpectedly extensive description of the properties of bodies that are in uniform motion. For example, he showed that the length and mass of an object are dependent upon their movement relative to an observer. He derived a mathematical relationship between the length of an object and its velocity that had previously been suggested by both FitzGerald and Lorentz. Einstein's theory was revolutionary, for previously scientists had believed that basic quantities of measurement such as time, mass, and length were absolute and unchanging. Einstein's work established the oppositethat these measurements could change, depending on the relative motion of the observer.

In addition to his masterpieces on the photoelectric effect, Brownian movement, and relativity, Einstein wrote two more papers in 1905. One, "Does the Inertia of a Body Depend on Its Energy Content?" dealt with an extension of his earlier work on relativity. He came to the conclusion in this paper that the energy and mass of a body are closely interrelated. Two years later he specifically stated that relationship in a formula, E=mc2 (energy equals mass times the speed of light squared), that is now familiar to both scientists and non-scientists alike. His final paper, the most modest of the five, was "A New De Determination of Molecular Dimensions." It was this paper that Einstein submitted as his doctoral dissertation, for which the University of Zurich awarded him a Ph.D. in 1905.

Fame did not come to Einstein immediately as a result of his five 1905 papers. Indeed, he submitted his paper on relativity to the University of Bern in support of his application to become a privatdozent, or unsalaried instructor, but the paper and application were rejected. His work was too important to be long ignored, however, and a second application three years later was accepted. Einstein spent only a year at Bern, however, before taking a job as professor of physics at the University of Zurich in 1909. He then went on to the German University of Prague for a year and a half before returning to Zurich and a position at ETH in 1912. A year later Einstein was made director of scientific research at the Kaiser Wilhelm Institute for Physics in Berlin, a post he held from 1914 to 1933.

Einstein was increasingly occupied with his career and his wife with managing their household; upon moving to Berlin in 1914, the couple grew distant. With the outbreak of World War I, Einstein's wife and two children returned to Zurich. The two were never reconciled; in 1919, they were formally divorced. With the outbreak of the war, Einstein's pacifist views became public knowledge. When 93 leading German intellectuals signed a manifesto supporting the German war effort, Einstein and three others published an antiwar counter-manifesto. He also helped form a coalition aimed at fighting for a just peace and for a worldwide organization to prevent future wars. Towards the end of the war, Einstein became very ill and was nursed back to health by his cousin Elsa. Not long after Einstein's divorce from Maric, he was married to Elsa, a widow. The two had no children of their own, although Elsa brought two daughters to the marriage.

The war years also marked the culmination of Einstein's attempt to extend his 1905 theory of relativity to a broader context, specifically to systems with non-zero acceleration. Under the general theory of relativity, motions no longer had to be uniform and relative velocities no longer constant. Einstein was able to write mathematical expressions that describe the relationships between measurements made in any two systems in motion relative to each other, even if the motion is accelerated in one or both. One of the fundamental features of the general theory is the concept of a space-time continuum in which space is curved. That concept means that a body affects the shape of the space that surrounds it so that a second body moving near the first body will travel in a curved path.

Einstein's new theory was too radical to be immediately accepted, for not only were the mathematics behind it extremely complex, it replaced Newton's theory of gravitation that had been accepted for two centuries. So, Einstein offered three proofs for his theory that could be tested: first, that relativity would cause Mercury's perihelion, or point of orbit closest to the sun , to advance slightly more than was predicted by Newton's laws. Second, Einstein predicted that light from a star would be bent as it passes close to a massive body, such as the sun. Last, the physicist suggested that relativity would also affect light by changing its wavelength, a phenomenon known as the redshift effect. Observations of the planet Mercury bore out Einstein's hypothesis and calculations, but astronomers and physicists had yet to test the other two proofs.

Einstein had calculated that the amount of light bent by the sun would amount to 1.7 seconds of an arc, a small but detectable effect. In 1919, during an eclipse of the sun, English astronomer Arthur Eddington measured the deflection of starlight and found it to be 1.61 seconds of an arc, well within experimental error. The publication of this proof made Einstein an instant celebrity and made "relativity" a household word, although it was not until 1924 that Eddington proved the final hypothesis concerning redshift with a spectral analysis of the star Sirius B. Thus, it was proved that light would be shifted to a longer wavelength in the presence of a strong gravitational field.

Einstein's publication of his general theory in 1916, the Foundation of the General Theory of Relativity, essentially brought to a close the revolutionary period of his scientific career. In many ways, Einstein had begun to fall out of phase with the rapid changes taking place in physics during the 1920s. Even though Einstein's own work on the photoelectric effect helped set the stage for the development of quantum theory , he was never able to accept some of its concepts, particularly the uncertainty principle. In one of the most-quoted comments in the history of science, he claimed that quantum mechanics, which could only calculate the probabilities of physical events, could not be correct because "God does not play dice." Instead, Einstein devoted his efforts for the remaining years of his life to the search for a unified field theory, a single theory that would encompass all physical fields, particularly gravitation and electromagnetism.

In early 1933, Einstein made a decision. He was out of Germany when Hitler rose to power, and he decided not to return. In March 1933, he again renounced his German citizenship. His remaining property in German was confiscated and his name appeared on the first Nazi list of those who were stripped of citizenship. He accepted an appointment at the Institute for Advanced Studies in Princeton, New Jersey, where he spent the rest of his life. In addition to his continued work on unified field theory, Einstein was in demand as a speaker and wrote extensively on many topics, especially peace.

The growing fascism and anti-Semitism of Hitler's regime, however, convinced him in 1939 to sign his name to a letter written by American physicists warning President Franklin D. Roosevelt that the Germans were nearing the possibility of an atomic bomb, and that Americans must develop the technology first. This letter led to the formation of the Manhattan Project for the construction of the world's first nuclear weapons. Although Einstein's work on relativity, particularly his formulation of the equation E=mc2, was essential to the development of the atomic bomb, Einstein himself did not participate in the project. He was considered a security risk, although he had renounced his German citizenship and become a U.S. citizen in 1940, while retaining his Swiss citizenship.

In 1944, he contributed to the war effort by hand writing his 1905 paper on special relativity, and putting it up for auction. The manuscript, which raised $6 million, is today the property of the U.S. Library of Congress.

After World War II and the bombing of Japan, Einstein became an ardent supporter of nuclear disarmament. He continued to support the efforts to establish a world government and the Zionist movement to establish a Jewish state. In 1952, after the death of Israel's first president, Chaim Weizmann, Einstein was invited to succeed him as president; he declined the offer.

Among the many other honors given to Einstein were the Barnard Medal of Columbia University in 1920, the Copley Medal of the Royal Society in 1925, the Gold Medal of the Royal Astronomical Society in 1926, the Max Planck Medal of the German Physical Society in 1929, and the Franklin Medal of the Franklin Institute in 1935. He also received honorary doctorates in science, medicine and philosophy from many European and American universities and was elected to memberships in all of the leading scientific academies in the world. In December 1999, Time magazine named Einstein "Person of the Century," stating: "In a hundred years, as we turn to another new centurynay, ten times a hundred years, when we turn to another new millenniumthe name that will prove most enduring from our own amazing era will be that of Albert Einstein: genius, political refugee, humanitarian, locksmith of the mysteries of the atom and the universe."

A week before he died, Einstein agreed to include his name on a manifesto urging all nations to give up nuclear weapons. Einstein died in his sleep at his home in Princeton at the age of 76, after suffering an aortic aneurysm. At the time of his death, he was the world's most widely admired scientist and his name was synonymous with genius. Yet Einstein declined to become enamored of the admiration of others. He wrote in his book The World as I See It : "Let every man be respected as an individual and no man idolized. It is an irony of fate that I myself have been the recipient of excessive admiration and respect from my fellows through no fault, and no merit, of my own. The cause of this may well be the desire, unattainable for many, to understand the one or two ideas to which I have with my feeble powers attained through ceaseless struggle."

See also History of exploration III (Modern era); Relativity theory

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Albert Einstein

Albert Einstein

The German-born American physicist Albert Einstein (1879-1955) revolutionized the science of physics. He is best known for his theory of relativity.

In the history of the exact sciences, only a handful of men—men like Nicolaus Copernicus and Isaac Newton—share the honor that was Albert Einstein's: the initiation of a revolution in scientific thought. His insights into the nature of the physical world made it impossible for physicists and philosophers to view that world as they had before. When describing the achievements of other physicists, the tendency is to enumerate their major discoveries; when describing the achievements of Einstein, it is possible to say, simply, that he revolutionized physics.

Albert Einstein was born on March 14, 1879, in Ulm, but he grew up and obtained his early education in Munich. He was not a child prodigy; in fact, he was unable to speak fluently at age 9. Finding profound joy, liberation, and security in contemplating the laws of nature, already at age 5 he had experienced a deep feeling of wonder when puzzling over the invisible, yet definite, force directing the needle of a compass. Seven years later he experienced a different kind of wonder: the deep emotional stirring that accompanied his discovery of Euclidean geometry, with its lucid and certain proofs. Einstein mastered differential and integral calculus by age 16.

Education in Zurich

Einstein's formal secondary education was abruptly terminated at 16. He found life in school intolerable, and just as he was scheming to find a way to leave without impairing his chances for entering the university, his teacher expelled him for the negative effects his rebellious attitude was having on the morale of his classmates. Einstein tried to enter the Federal Institute of Technology (FIT) in Zurich, Switzerland, but his knowledge of nonmathematical disciplines was not equal to that of mathematics and he failed the entrance examination. On the advice of the principal, he thereupon first obtained his diploma at the Cantonal School in Aarau, and in 1896 he was automatically admitted into the FIT. There he came to realize that his deepest interest and facility lay in physics, both experimental and theoretical, rather than in mathematics.

Einstein passed his diploma examination at the FIT in 1900, but due to the opposition of one of his professors he was unable to subsequently obtain the usual university assistantship. In 1902 he was engaged as a technical expert, third-class, in the patent office in Bern, Switzerland. Six months later he married Mileva Maric, a former classmate in Zurich. They had two sons. It was in Bern, too, that Einstein, at 26, completed the requirements for his doctoral degree and wrote the first of his revolutionary scientific papers.

Academic Career

These papers made Einstein famous, and universities soon began competing for his services. In 1909, after serving as a lecturer at the University of Bern, Einstein was called as an associate professor to the University of Zurich. Two years later he was appointed a full professor at the German University in Prague. Within another year and a half Einstein became a full professor at the FIT. Finally, in 1913 the well-known scientists Max Planck and Walter Nernst traveled to Zurich to persuade Einstein to accept a lucrative research professorship at the University of Berlin, as well as full membership in the Prussian Academy of Science. He accepted their offer in 1914, quipping: "The Germans are gambling on me as they would on a prize hen. I do not really know myself whether I shall ever really lay another egg." When he went to Berlin, his wife remained behind in Zurich with their two sons; after their divorce he married his cousin Elsa in 1917.

In 1920 Einstein was appointed to a lifelong honorary visiting professorship at the University of Leiden. During 1921-1922 Einstein, accompanied by Chaim Weizmann, the future president of the state of Israel, undertook extensive worldwide travels in the cause of Zionism. In Germany the attacks on Einstein began. Philipp Lenard and Johannes Stark, both Nobel Prize-winning physicists, began characterizing Einstein's theory of relativity as "Jewish physics." This callousness and brutality increased until Einstein resigned from the Prussian Academy of Science in 1933. (He was, however, expelled from the Bavarian Academy of Science.)

Career in America

On several occasions Einstein had visited the California Institute of Technology, and on his last trip to the United States Abraham Flexner offered Einstein—on Einstein's terms—a position in the newly conceived and funded Institute for Advanced Studies in Princeton. He went there in 1933.

Einstein played a key role (1939) in mobilizing the resources necessary to construct the atomic bomb by signing a famous letter to President Franklin D. Roosevelt which had been drafted by Leo Szilard and E.P. Wigner. When Einstein's famous equation E □ mc2 was finally demonstrated in the most awesome and terrifying way by using the bomb to destroy Hiroshima in 1945, Einstein, the pacifist and humanitarian, was deeply shocked and distressed; for a long time he could only utter "Horrible, horrible." On April 18, 1955, Einstein died in Princeton.

Theory of Brownian Motion

From numerous references in Einstein's writings it is evident that, of all areas in physics, thermodynamics made the deepest impression on him. During 1902-1904 Einstein reworked the foundations of thermodynamics and statistical mechanics; this work formed the immediate background to his revolutionary papers of 1905, one of which was on Brownian motion.

In Brownian motion (first observed in 1827 by the Scottish botanist Robert Brown), small particles suspended in a viscous liquid such as water undergo a rapid, irregular motion. Einstein, unaware of Brown's earlier observations, concluded from his theoretical studies that such a motion must exist. Guided by the thought that if the liquid in which the particles are suspended consists of atoms or molecules they should collide with the particles and set them into motion, he found that while the particle's motion is irregular, fluctuating back and forth, it will in time nevertheless experience a net forward displacement. Einstein proved that this net forward displacement of the suspended particles is directly related to the number of molecules per gram atomic weight. This point created a good deal of skepticism toward Einstein's theory at the time he developed it (1905-1906), but when it was fully confirmed many of the skeptics were converted. Brownian motion is to this day regarded as one of the most direct proofs of the existence of atoms.

Light Quanta and Wave-Particle Duality

The most common misconceptions concerning Einstein's introduction of his revolutionary light quantum (light particle) hypothesis in 1905 are that he simply applied Planck's quantum hypothesis of 1900 to radiation and that he introduced light quanta to "explain" the photoelectric effect discovered in 1887 by Heinrich Hertz and thoroughly investigated in 1902 by Philipp Lenard. Neither of these assertions is accurate. Einstein's arguments for his light quantum hypothesis—that under certain circumstances radiant energy (light) behaves as if it consists not of waves but of particles of energy proportional to their frequencies— were absolutely fundamental and, as in the case of his theory of Brownian motion, based on his own insights into the foundations of thermodynamics and statistical mechanics. Furthermore, it was only after presenting strong arguments for the necessity of his light quantum hypothesis that Einstein pursued its experimental consequences. One of several such consequences was the photoelectric effect, the experiment in which high-frequency ultraviolet light is used to eject electrons from thin metal plates. In particular, Einstein assumed that a single quantum of light transfers its entire energy to a single electron in the metal plate. The famous equation he derived was fully consistent with Lenard's observation that the energy of the ejected electrons depends only on the frequency of the ultraviolet light and not on its intensity. Einstein was not disturbed by the fact that this apparently contradicts James Clerk Maxwell's classic electromagnetic wave theory of light, because he realized that there were good reasons to doubt the universal validity of Maxwell's theory.

Although Einstein's famous equation for the photoelectric effect—for which he won the Nobel Prize of 1921— appears so natural today, it was an extremely bold prediction in 1905. Not until a decade later did R.A. Millikan finally succeed in experimentally verifying it to everyone's satisfaction. But while Einstein's equation was bold, his light quantum hypothesis was revolutionary: it amounted to reviving Newton's centuries-old idea that light consists of particles.

No one tried harder than Einstein to overcome opposition to this hypothesis. Thus, in 1907 he proved the fruitfulness of the entire quantum hypothesis by showing it could at least qualitatively account for the low-temperature behavior of the specific heats of solids. Two years later he proved that Planck's radiation law of 1900 demands the coexistence of particles and waves in blackbody radiation, a proof that represents the birth of the wave-particle duality. In 1917 Einstein presented a very simple and very important derivation of Planck's radiation law (the modern laser, for example, is based on the concepts Einstein introduced here), and he also proved that light quanta must carry momentum as well as energy.

Meanwhile, Einstein had become involved in another series of researches having a direct bearing on the wave-particle duality. In mid-1924 S.N. Bose produced a very insightful derivation of Planck's radiation law—the origin of Bose-Einstein statistics—which Einstein soon developed into his famous quantum theory of an ideal gas. Shortly thereafter, he became acquainted with Louis de Broglie's revolutionary new idea that ordinary material particles, such as electrons and gas molecules, should under certain circumstances exhibit wave behavior. Einstein saw immediately that De Broglie's idea was intimately related to the Bose-Einstein statistics: both indicate that material particles can at times behave like waves. Einstein told Erwin Schrödinger of De Broglie's work, and in 1926 Schrödinger made the extraordinarily important discovery of wave mechanics. Schrödinger's (as well as C. Eckart) then proved that Schrödinger's wave mechanics and Werner Heisenberg's matrix mechanics are mathematically equivalent: they are now collectively known as quantum mechanics, one of the two most fruitful physical theories of the 20th century. Since Einstein's insights formed much of the background to both Schrödinger's and Heisenberg's discoveries, the debt quantum physicists owe to Einstein can hardly be exaggerated.

Theory of Relativity

The second of the two most fruitful physical theories of the 20th century is the theory of relativity, which to scientists and laymen alike is synonymous with the name of Einstein. Once again, there is a common misconception concerning the origin of this theory, namely, that Einstein advanced it in 1905 to "explain" the famous Michelson-Morley experiment (1887), which failed to detect a relative motion of the earth with respect to the ether, the medium through which light was assumed to propagate. In fact, it is not even certain that Einstein was aware of this experiment in 1905; nor was he familiar with H.A. Lorentz's elegant 1904 paper in which Lorentz applied the transformation equations which bear his name to electrodynamic phenomena. Rather, Einstein consciously searched for a general principle of nature that would hold the key to the explanation of a paradox that had occurred to him when he was 16: if, on the one hand, one runs at, say, 4 miles per hour alongside a train moving at 4 miles per hour, the train appears to be at rest; if, on the other hand, it were possible to run alongside a ray of light, neither experiment nor theory suggests that the ray of light—an oscillating electromagnetic wave—would appear to be at rest. Einstein eventually saw that he could postulate that no matter what the velocity of the observer, he must always observe the same velocity c for the velocity of light: roughly 186,000 miles per second. He also saw that this postulate was consistent with a second postulate: if an observer at rest and an observer moving at constant velocity carry out the same kind of experiment, they must get the same result. These are Einstein's two postulates of his special theory of relativity. Also in 1905 Einstein proved that his theory predicted that energy E and mass mare entirely interconvertible according to his famous equation, E□mc2.

For observational confirmation of his general theory of relativity, Einstein boldly predicted the gravitational red shift and the deflection of starlight (an amended value), as well as the quantitative explanation of U. J. J. Leverrier's long-unexplained observation that the perihelion of the planet Mercury precesses about the sun at the rate of 43 seconds of arc per century. In addition, Einstein in 1916 predicted the existence of gravitational waves, which have only recently been detected. Turning to cosmological problems the following year, Einstein found a solution to his field equations consistent with the picture (the Einstein universe) that the universe is static, approximately uniformly filled with a finite amount of matter, and finite but unbounded (in the same sense that the surface area of a smooth globe is finite but has no beginning or end).

The Man and His Philosophy

Fellow physicists were always struck with Einstein's uncanny ability to penetrate to the heart of a complex problem, to instantly see the physical significance of a complex mathematical result. Both in his scientific and in his personal life, he was utterly independent, a trait that manifested itself in his approach to scientific problems, in his unconventional dress, in his relationships with family and friends, and in his aloofness from university and governmental politics (in spite of his intense social consciousness). Einstein loved to discuss scientific problems with friends, but he was, fundamentally a "horse for single harness."

Einstein's belief in strict causality was closely related to his profound belief in the harmony of nature. That nature can be understood rationally, in mathematical terms, never ceased to evoke a deep—one might say, religious—feeling of admiration in him. "The most incomprehensible thing about the world," he once wrote, "is that it is comprehensible." How do we discover the basic laws and concepts of nature? Einstein argued that while we learn certain features of the world from experience, the free inventive capacity of the human mind is required to formulate physical theories. There is no logical link between the world of experience and the world of theory. Once a theory has been formulated, however, it must be "simple" (or, perhaps, "esthetically pleasing") and agree with experiment. One such esthetically pleasing and fully confirmed theory is the special theory of relativity. When Einstein was informed of D.C. Miller's experiments, which seemed to contradict the special theory by demanding the reinstatement of the ether, he expressed his belief in the spuriousness of Miller's results—and therefore in the harmoniousness of nature—with another of his famous aphorisms, "God is subtle, but he is not malicious."

This frequent use of God's name in Einstein's speeches and writings provides us with a feeling for his religious convictions. He once stated explicitly, "I believe in Spinoza's God who reveals himself in the harmony of all being, not in a God who concerns himself with the fate and actions of men." It is not difficult to see that this credo is consistent with his statement that the "less knowledge a scholar possesses, the farther he feels from God. But the greater his knowledge, the nearer is his approach to God." Since Einstein's God manifested Himself in the harmony of the universe, there could be no conflict between religion and science for Einstein.

To enumerate at this point the many honors that were bestowed upon Einstein during his lifetime would be to devote space to the kind of public acclamation that mattered so little to Einstein himself. How, indeed, can other human beings sufficiently honor one of their number who revolutionized their conception of the physical world, and who lived his life in the conviction that "the only life worth living is a life spent in the service of others"? When Einstein lay dying he could truly utter, as he did, "Here on earth I have done my job." It would be difficult to find a more suitable epitaph than the words Einstein himself used in characterizing his life: "God is inexorable in the way He has allotted His gifts. He gave me the stubbornness of a mule and nothing else; really, He also gave me a keen scent."

Further Reading

Numerous biographies of Einstein have been written. Three of the best are Philipp Frank, Einstein: His Life and Times, translated by George Rosen (1947); Carl Seelig, Albert Einstein: A Documentary Biography, translated by Mervyn Savill (1956); and Ronald W. Clark, Einstein: The Life and Times (1971). Einstein's illuminating "Autobiographical Notes" and bibliographies of his scientific and nonscientific writings can be found in P.A. Schilpp, ed., Albert Einstein: Philosopher-Scientist (1949; 2d ed. 1951). See also Max Born, Einstein's Theory of Relativity (trans. 1922; rev. ed. 1962); Leopold Infeld, Albert Einstein: His Work and Its Influence on Our World (1950); and Max Jammer, The Conceptual Development of Quantum Mechanics (1966). □

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Einstein, Albert

Einstein, Albert

Albert Einstein is generally regarded as the greatest theoretical physicist of the twentieth century, if not of all time. Modern physics bears his mark more than any other physicist. His Special Theory of Relativity changed our conceptions of space, time, motion, and matter, and his General Theory of Relativity was the first new theory of gravitation since Isaac Newton's. Yet his work went beyond the boundaries of physics as he engaged himself in the educational, cultural, and philosophical concerns of his generation. Less known is Einstein's interest and personal engagement in religious matters. In specific, he strongly opposed the proposition that science and religion are irreconcilable.

Early life and influences

Albert Einstein, whose ancestors had lived in southern Germany for many generations, was born on March 14, 1879, in Ulm, Germany. The fact that his parents, Hermann Einstein and Pauline Einstein, née Koch, did not call him Abraham after his deceased grandfather, as Jewish tradition required, and that his sister, his only sibling, born 1881, was called Maria, shows that his parents did not observe religious rites although they never renounced their Jewish heritage. In 1889, the Einstein family moved to Munich, where Albert at the age of six was sent to a Catholic elementary school. At home a distant relative introduced him to the principles of Judaism and evoked in him such a fervent religious sentiment, that he observed Jewish religious prescriptions and even chided his parents for eating pork. At age ten he entered the interdenominational Luitpold Gymnasium, where he excelled in mathematics and Latin.

Ironically, his religious enthusiasm ended abruptly as the result of the only religious custom his parents observed, the hosting of a poor Jewish student for a weekly meal. This beneficiary was Max Talmud, a medical student older than Albert by ten years. He gave Albert books on science and philosophy, amongst them Ludwig Büchner's (18241899) materialistic Force and Matter (1874). Albert was particularly impressed by Büchner's survey of theriomorphic and therianthropic religions, in which animals or their combinations with humans were apotheosized. As Einstein, in his autobiographical notes, wrote, "through the reading of these books I reached the conclusion that much in the stories of the Bible could not be true. The consequence was a fanatic freethinking . . . suspension against every kind of authority . . . an attitude which has never again left me, even though later on, because of a better insight into the causal connections, it lost much of its original poignancy" (Schlipp p. 5).

In 1894, Albert's parents, for commercial reasons, moved to Italy. Left alone and hating the authoritarian discipline at the Gymnasium, Albert joined his parents before finishing school. At the Swiss cantonal school in Aarau he obtained the diploma that enabled him to enroll in the Swiss Federal Polytechnic School (ETH) in Zurich, where he studied physics and mathematics and graduated in 1900. Unable to find a regular academic position, he supported himself by tutoring and part-time school teaching until June 1902, when he obtained the appointment of technical expert third class at the patent office in Berne. A year later he married Mileva Maric, a Greek Orthodox Serbian, with whom he had fallen in love when they were classmates at the ETH. Little is known about their daughter Lieserl, who was born in 1902 before their marriage during Mileva's visit to her parents. Albert seems never to have seen her. Their first son, Hans Albert, was born in 1904, and their second son, Eduard, in 1910.

Theories and career

Einstein liked the job at the patent office because it was interesting and also left him time to pursue his own work in theoretical physics. He already had a number of important publications, mostly on thermodynamics, to his credit. But the year 1905 became his annus mirabilis. In March he completed his paper on the light-quantum hypothesis, in May his paper on Brownian motion, and in June his celebrated essay on the special theory of relativity, which was followed in September by his derivation of the famous mass-energy relation E = mc 2, the most famous equation in science.

In 1908 Einstein became Lecturer at the University of Berne, in 1911 full professor in Prague, and a year later he became a professor at the ETH. In April 1914, less than four months before the outbreak of the First World War, he moved to Berlin with his wife and two sons to serve as university professor without teaching obligations and as director of the Kaiser Wilhelm Institute of Physics.

Mileva disliked Berlin and returned with the children to Zurich. In February 1919 Albert and Mileva got divorced. Six months later Einstein married his cousin, the divorced Elsa Löwenthal, mother of two daughters, Ilse and Margot. Einstein detested the military enthusiasm that swept Germany after the declaration of war and courageously refused to sign the manisfesto, in which German intellectuals declared their solidarity with German militarism.

Einstein continued his work on the general theory of relativity, which he had begun in 1907. In November 1915, he derived the exact value of the perihelion precession of the planet Mercury, which for over sixty years had been an unresolved problem, and he predicted how much a ray of light, emitted by a star and grazing the sun, should be deflected by the gravitation of the sun. In 1917 he applied general relativity to the study of the structure of the universe as a whole, raising thereby the status of cosmology, which theretofore had been a jumble of speculations, to that of a respectable scientific discipline. His prediction of the gravitational deflection of light was confirmed in 1919 by two British eclipse expeditions to West Africa and Brazil. When their results were announced in London, Einstein's theory was hailed by the President of the Royal Society as "perhaps the greatest achievement in the history of human thought." From that day on Einstein gained unprecedented international fame. In 1922, he was awarded the Nobel Prize for physics. But when the Nazi terror began in Germany, he, as a Jew and pacifist, and his theory, became the target of brute attacks. At Adolf Hitler's rise to power early in 1933, Einstein was in Belgium and, instead of returning to Germany, accepted a professorship at the Institute for Advanced Study in Princeton, New Jersey, where he remained until his death on April 18, 1955.

Later life and influence

During the twenty-two years in Princeton he resumed his work on quantum theory. Although he was one of its founding fathers, he rejected its generally accepted probabilistic interpretation because, influenced by the philosopher Baruch Spinoza (16321677), whom he had read in his youth, he was utterly convinced of the causal dependence of all phenomena. Nor did he accept the prevailing view that the concept of a physical phenomenon includes irrevocably the specifics of the experimental conditions of its observation. For him "physics is an attempt conceptually to grasp reality as it is thought independently of its being observed" (Schlipp, p. 81). His famous 1935 paper, written in collaboration with physicists Nathan Rosen and Boris Podolsky challenged the completeness of orthodox quantum mechanics and had far-reaching consequences debated still today. But most of his time, until the day of his death, he devoted to the last great project of his life, the search for a unified field theory, which however remained unfinished.

Apart from his scientific work Einstein, using his prestige, engaged himself in promoting the causes of social justice, civil liberty, tolerance, and equity of all citizens before the law. He believed in the ideal of international peace and in the feasibility of establishing a world government, led by the superpowers, to which all nations should commit all their military resources. Although having signed in August 1939 the famous letter to President Franklin Delano Roosevelt proposing the development of an atomic bomb, he later admitted that, had he known that the Germans would not succeed in producing an atomic bomb, he "would not have lifted a finger."

Having been, during his later years in Berlin, a victim of anti-Semitic propaganda, and being aware of the cruel persecutions of Jews by the Nazis, Einstein most actively supported Zionism, which he regarded as a moral, not a political, movement to restore his people's dignity necessary to survive in a hostile world. When once, in this context, he declared: "I am glad to belong to the Jewish people, although I do not regard it as 'chosen'" (Schlipp, p. 81) he obviously referred to his disbelief in the Bible, which he retained from his adolescence. And when he said, as quoted above, that he later recanted his juvenile freethinking "because of a better insight into causal connections," he referred to his realization that science, by revealing a divine harmony in the universe expressed by the laws of nature, imbued him with a feeling of awe and humility that made him believe in a "God who reveals himself in the harmony of all that exists." He defined the relation between science and religion in a much-quoted phrase: "Science without religion is lame, religion without science is blind." But retaining his early uncompromising rejection of anthropomorphisms, he stated that, following Spinoza, he cannot conceive of a God who rewards or punishes his creatures or has a will of the kind humans experience. In his Princeton years, Einstein wrote numerous articles and addresses on what he called his "cosmic religion" and protested strongly against the identification of his belief in an impersonal God with atheism. The philosophy of religion and the quest for religious truth had occupied his mind in those years so much that it has been said "one might suspect he was disguised as a theologian," as the Swiss playwright Friedrich Dürrenmatt once said.

On December 31, 1999, the well-known weekly newsmagazine Time proclaimed Albert Einstein "Person of the Century" on the grounds that he was not only the century's greatest scientist, who altered forever our views on matter, time, space, and motion, but also a humanitarian, who fought for the causes of justice and peace, and "had faith in the beauty of God's handiwork."

See also Grand Unified Theory; Gravitation; Physics, Quantum; Relativity, General Theory of; Relativity, Special Theory of; Space and Time


einstein, albert. the world as i see it. new york: covici-friede, 1934.

einstein, albert. ideas and opinions. new york: crown, 1949.

einstein, albert. out of my later years. new york: philosophical library, 1950.

fölsing, albrecht. albert einstein: a biography, trans. ewald osers. new york: viking, 1997.

holton, gerald, and elkana, yehuda, eds. albert einstein: historical and cultural perspectives. princeton, n.j.: princeton university press, 1982.

jammer, max. einstein and religion. princeton, n.j.: princeton university press, 1999.

pais, abraham. subtle is the lordthe science and life of albert einstein. oxford and new york: oxford university press, 1982.

schilpp, paul arthur, ed. albert einstein: philosopher-scientist. new york: tudor, 1949.

max jammer

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Einstein, Albert

Albert Einstein

Born: March 14, 1879
Ulm, Germany
Died: April 18, 1955
Princeton, Massachusetts

German-born American physicist and scientist

The German-born American physicist (one who studies matter and energy and the relationships between them) Albert Einstein revolutionized the science of physics. He is best known for his theory of relativity, which holds that measurements of space and time vary according to conditions such as the state of motion of the observer.

Early years and education

Albert Einstein was born on March 14, 1879, in Ulm, Germany, but he grew up and obtained his early education in Munich, Germany. He was a poor student, and some of his teachers thought he might be retarded (mentally handicapped); he was unable to speak fluently (with ease and grace) at age nine. Still, he was fascinated by the laws of nature, experiencing a deep feeling of wonder when puzzling over the invisible, yet real, force directing the needle of a compass. He began playing the violin at age six and would continue to play throughout his life. At age twelve he discovered geometry (the study of points, lines, and surfaces) and was taken by its clear and certain proofs. Einstein mastered calculus (a form of higher mathematics used to solve problems in physics and engineering) by age sixteen.

Einstein's formal secondary education ended at age sixteen. He disliked school, and just as he was planning to find a way to leave without hurting his chances for entering the university, his teacher expelled him because his bad attitude was affecting his classmates. Einstein tried to enter the Federal Institute of Technology (FIT) in Zurich, Switzerland, but his knowledge of subjects other than mathematics was not up to par, and he failed the entrance examination. On the advice of the principal, he first obtained his diploma at the Cantonal School in Aarau, Switzerland, and in 1896 he was automatically admitted into the FIT. There he came to realize that he was more interested in and better suited for physics than mathematics.

Einstein passed his examination to graduate from the FIT in 1900, but due to the opposition of one of his professors he was unable to go on to obtain the usual university assistantship. In 1902 he was hired as an inspector in the patent office in Bern, Switzerland. Six months later he married Mileva Maric, a former classmate in Zurich. They had two sons. It was in Bern, too, that Einstein, at twenty-six, completed the requirements for his doctoral degree and wrote the first of his revolutionary scientific papers.

Famous papers

Thermodynamics (the study of heat processes) made the deepest impression on Einstein. From 1902 until 1904 he reworked the foundations of thermodynamics and statistical mechanics (the study of forces and their effect on matter); this work formed the immediate background to his revolutionary papers of 1905, one of which was on Brownian motion.

In Brownian motion, first observed in 1827 by the Scottish botanist (scientist who studies plants) Robert Brown (17731858), small particles suspended in a liquid such as water undergo a rapid, irregular motion. Einstein, unaware of Brown's earlier observations, concluded from his studies that such a motion must exist. He was guided by the thought that if the liquid in which the particles are suspended is made up of atoms, they should collide with the particles and set them into motion. He found that the motion of the particles will in time experience a forward movement. Einstein proved that this forward movement is directly related to the number of atoms per gram of atomic weight. Brownian motion is to this day considered one of the most direct proofs of the existence of atoms.

Another of Einstein's ideas in 1905 was that under certain conditions radiant energy (light) behaves as if it is made up not of waves but of particles of energy. He presented an equation for the photoelectric effect, in which electrons (particles in the outer portion of an atom that are said to have a "negative" electrical charge equal to that of protons, particles with a larger mass that are said to have a "positive" electrical charge) are ejected from a metal surface that has been exposed to light. Einstein proved that the electrons are not ejected in a constant stream but like bullets from a gun, in units, or "quanta." Although Einstein's famous equation for the photoelectric effectfor which he won the Nobel Prize in physics in 1921appears obvious today, it was an extremely bold prediction in 1905. Not until years later did R. A. Millikan finally succeed in confirming it to everyone's everyone's satisfaction.

The theory of relativity came from Einstein's search for a general law of nature that would explain a problem that had occurred to him when he was sixteen: if one runs at, say, 4 4 miles per hour (6.4 kilometers per hour) alongside a train that is moving at 4 4 miles per hour, the train appears to be at rest; if, on the other hand, it were possible to run alongside a ray of light, neither experiment nor theory suggests that the ray of light would appear to be at rest. Einstein realized that no matter what speed the observer is moving at, he must always observe the same velocity of light, which is roughly 186,000 miles per second (299,274 kilometers per second). He also saw that this was in agreement with a second assumption: if an observer at rest and an observer moving at constant speed carry out the same kind of experiment, they must get the same result. These two assumptions make up Einstein's special theory of relativity. Also in 1905 Einstein proved that his theory predicted that energy (E) and mass (m) are entirely related according to his famous equation, E=mc 2. This means that the energy in any particle is equal to the particle's mass multiplied by the speed of light squared.

Academic career

These papers made Einstein famous, and universities soon began competing for his services. In 1909, after serving as a lecturer at the University of Bern, Einstein was called as an associate professor to the University of Zurich. Two years later he was appointed a full professor at the German University in Prague, Czechoslovakia. Within another year-and-a-half Einstein became a full professor at the FIT. Finally, in 1913 the well-known scientists Max Planck (18581947) and Walther Nernst (18641941) traveled to Zurich to persuade Einstein to accept a lucrative (profitable) research professorship at the University of Berlin in Germany, as well as full membership in the Prussian Academy of Science. He accepted their offer in 1914, saying, "The Germans are gambling on me as they would on a prize hen. I do not really know myself whether I shall ever really lay another egg." When he went to Berlin, his wife remained behind in Zurich with their two sons; they divorced, and Einstein married his cousin Elsa in 1917.

In 1920 Einstein was appointed to a lifelong honorary visiting professorship at the University of Leiden in Holland. In 1921 and 1922 Einstein, accompanied by Chaim Weizmann (18741952), the future president of the state of Israel, traveled all over the world to win support for the cause of Zionism (the establishing of an independent Jewish state). In Germany, where hatred of Jewish people was growing, the attacks on Einstein began. Philipp Lenard and Johannes Stark, both Nobel Prizewinning physicists, began referring to Einstein's theory of relativity as "Jewish physics." These kinds of attacks increased until Einstein resigned from the Prussian Academy of Science in 1933.

Career in America

On several occasions Einstein had visited the California Institute of Technology, and on his last trip to the United States he was offered a position in the newly established Institute for Advanced Studies in Princeton, Massachusetts. He went there in 1933.

Einstein played a key role (1939) in the construction of the atomic bomb by signing a famous letter to President Franklin D. Roosevelt (18821945). It said that the Germans had made scientific advances and that it was possible that Adolf Hitler (18891945, the German leader whose actions led to World War II [193945]), might become the first to have atomic weapons. This led to an all-out U.S. effort to construct such a bomb. Einstein was deeply shocked and saddened when his famous equation E=mc2 was finally demonstrated in the most awesome and terrifying way by using the bomb to destroy Hiroshima, Japan, in 1945. For a long time he could only utter "Horrible, horrible."

It would be difficult to find a more suitable epitaph (a brief statement summing up a person's person's life) than the words Einstein himself used in describing his life: "God gave me the stubbornness of a mule and nothing else; really He also gave me a keen scent." On April 18, 1955, Einstein died in Princeton.

For More Information

Cwiklik, Robert. Albert Einstein and the Theory of Relativity. New York: Barron's Educational Series, 1987.

Goldberg, Jake. Albert Einstein. New York: Franklin Watts, 1996.

Goldenstern, Joyce. Albert Einstein: Physicist and Genius. Springfield, NJ: Enslow Publishers, 1995.

Hammontree, Marie. Albert Einstein: Young Thinker. New York: Aladdin, 1986.

Ireland, Karin. Albert Einstein. Englewood Cliffs, NJ: Silver Burdett Press, 1989.

McPherson, Stephanie Sammartino. Ordinary Genius: The Story of Albert Einstein. Minneapolis: Carolrhoda Books, 1995.

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Einstein, Albert

Einstein, Albert


For most people asked to name a scientist, "Albert Einstein" is the first name that comes to mind. Einstein's life story, including his difficulties with math in high school, his time spent as a patent clerk in the Swiss Patent Office, his development of the theory of relativity, and his influence on the development of the nuclear bomb, is the stuff of legends. Indeed, many a struggling high school science student has sought refuge in the notion that Einstein did not do well in that capacity either.

Einstein is perhaps best known for his work on relativity, and his simple but elegant equation E = mc 2, which expresses an equivalence between energy and matter. It is this equation that describes the possibility of the transformation of mass into energy, and the phenomenon that is operational in a nuclear power plant or nuclear bomb. Very little matter can become an inordinate amount of energy, as the speed of light is a constant having an inordinately large value.

What is not so well known about Einstein is that he made contributions to the development of modern chemistry, particularly to the area of quantum mechanics. The Nobel Prize Committee awarded Einstein 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." His explanation of the photoelectric effect helped to validate Planck's view of quantized energy, and has become the basis of the quantitative laws of photochemistry.

The photoelectric effect had been observed as early as 1887, when the physicist Heinrich Hertz noted that light shining on metal decreased the amount of energy or voltage needed to eject electrons from the metal's surface. Further studies showed that the kinetic energy of the liberated electrons was independent of the intensity of the light; more light only produced more electrons. This kinetic energy was found to be dependent on wavelength. If the wavelength of the incident light was less than a threshold wavelength, no electrons were observed. Einstein explained the phenomenon in a paper published in the journal Annalen der Physik in 1905, the first of four papers by Einstein (all appearing in 1905) that changed science. In essence, Einstein argued that there is an intrinsic "work function" that is required to remove an electron from a metal, a specific amount of energy that depends only on the identity of the metal. The kinetic energy of the released electron is then the difference between the energy supplied by the incoming electromagnetic radiation (including visible light) and the work function. Subsequent experimental verification of Einstein's argument affirmed the claim that light was quantized.

It is one of the ironies of twentieth century science that, although his work on the photoelectric effect helped to advance quantum mechanics, Einstein came to be its chief critic. It was his antagonism toward the probabilistic and nondeterministic nature of quantum phenomena that prompted Einstein to make the often-quoted remark, "I cannot believe that God would choose to play dice with the universe."

Einstein's explanation of the photoelectric effect was not his only contribution to chemistry. His Ph.D. dissertation, submitted in 1905, was entitled "A New Determination of Molecular Dimensions." His investigation of Brownian motion (the random movement of microscopic particles suspended in liquids or gases) was intended to establish the existence of atoms as being indispensable to an explanation of the molecular-kinetic theory of heat. And the concept of relativity has shed light on the motions of electrons in the core orbitals of heavy elements.

see also Quantum Chemistry.

Todd W. Whitcombe


Pais, Abraham (1982). Subtle Is the Lord: The Science and Life of Albert Einstein. New York: Oxford University Press.

Stachel, John J., ed. (1998). Einstein's Miraculous Year: Five Papers that Changed the Face of Physics. Princeton, NJ: Princeton University Press.

Internet Resources

Friedman, S. Morgan. "Albert Einstein Online." Available from <http://www.westegg.com/einstein/>.

Nobel e-Museum. "Albert EinsteinBiography." Available from <http://www.nobel.se>.

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Einstein, Albert

Einstein, Albert

German-born, Swiss-educated Physicist 1879-1955

Albert Einstein was a scientist who revolutionized physics in the early twentieth century with his theories of relativity. Born in Ulm, Germany, in 1879, Einstein was interested in science from an early age. While he performed well in school, he disliked the academic environment and left at the age of fifteen. He took an entrance exam for the Swiss Federal Institute of Technology (ETH) in Zurich but failed; only after completing secondary school was he able to gain entrance to ETH, where he graduated in 1900. Unable to find a teaching position, Einstein accepted a job in the Swiss patent office in 1902.

During his time as a patent clerk Einstein made some of his most important discoveries. In 1905 he published three papers, which brought him recognition in the scientific community. In one he described the physics of Brownian motion, the random motion of particles in a gas of liquid. In another paper he used the new field of quantum mechanics to explain the photoelectric effect, where metals give off electrons when exposed to certain types of light. Einstein published his third, and arguably most famous, paper in 1905, which outlined what later became known as the special theory of relativity. This theory showed how the laws of physics worked near the speed of light. The paper also included the famous equation E=mc2, explaining how energy was equal to the mass of an object times the speed of light squared.

These papers allowed Einstein to exchange his patent clerk job for university positions in Zurich and Prague before going to Berlin as director of the Kaiser Wilhelm Institute of Physics. Shortly thereafter he published the general theory of relativity, which describes how gravity warps space and time. This theory was confirmed in 1919 when astronomers measured the positions of stars near the Sun during a solar eclipse and found that they had shifted by the amount predicted if the Sun's gravity had warped the light.

The acceptance of Einstein's general theory turned him into an international celebrity. During the 1920s he toured the world, giving lectures. In 1922 he won the Nobel Prize for physics, although it was officially awarded for his work studying the photoelectric effect, not relativity. In 1932 he accepted a part-time position at Princeton University in Princeton, New Jersey, and planned to split his time between Germany and the United States. But when the Nazis took power in Germany one month after he arrived at Princeton, Einstein decided to stay in the United States.

Einstein spent the rest of his scientific career in an unsuccessful pursuit of a theory that would explain all the fundamental forces of nature. He also took a greater role outside of physics. In 1939 he cowrote a letter to President Franklin Roosevelt, urging him to investigate the possibility of developing an atomic bomb and warning him that Germany was likely doing the same. After the war he urged world leaders to give up nuclear weapons to preserve peace. In ill health for several years, he died in Princeton in 1955.

see also Age of the Universe (volume 2); Astronomy, History of (volume 2); Black Holes (volume 2); Cosmic Rays (volume 2); Cosmology (volume 2); Gravity (volume 2); Wormholes (volume 4); Zero-Point Energy (volume 4).

Jeff Foust


Brian, Denis. Einstein: A Life. New York: John Wiley & Sons, 1996.

Clark, Ronald W. Einstein: The Life and Times. New York: Avon Books, 1972.

Internet Resources

"Albert Einstein." University of St. Andrews, School of Mathematics and Physics. <http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Einstein.html>.

Weisstein, Eric. "Einstein, Albert (1879-1955)." <http://www.treasure-troves.com/bios/Einstein.html>.

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Einstein, Albert

Einstein, Albert

American Physicist and Mathematician 18791955

Albert Einstein is perhaps the best-known scientist who ever lived. His contributions include the special and general theories of relativity , the assertion of the equivalence of mass and energy, and the quantum explanation of the behavior of electromagnetic radiation, including light. Einstein was born in Ulm, Germany, in 1879 and died in Princeton, New Jersey, in 1955.

Einstein showed little academic ability before entering the Federal Polytechnic Academy in Zurich, Switzerland, in 1896, where he studied both mathematics and physics. After graduating in 1900, he briefly taught school and then took a position in the patent office. During this time, he wrote articles on theoretical physics in his spare time.

Einstein's ability to apply advanced mathematics in the solution of complex physical problems led to the publication of a group of momentous papers in 1905. A doctorate from the University of Zurich and world fame soon followed.

The subjects of the 1905 publications included special relativity, the equivalence of matter and energy, and the quantum nature of radiation. These revolutionary publications, in combination with the general theory of relativity, which he published in 1915, and the development of quantum mechanics, to which he made significant contributions, transformed science and again demonstrated the indispensability of mathematics in the scientific endeavor.

The atomic age, the space age, and the electronic age owe much to Einstein's contributions to physics, changing human civilization more dramatically in the twentieth century than in previous centuries combined.

J. William Moncrief


Hoffmann, Banesh. Albert Einstein: Creator and Rebel. New York: Viking, 1972.

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Einstein, Albert

Einstein, Albert (1879–1955) US physicist, b. Germany, who devised the famous theories of relativity. Einstein published many important theoretical papers: his explanation of Brownian movement confirmed the reality of atoms, his application of quantum theory to photoelectricity won him the 1921 Nobel Prize in physics. In 1905, he devised the special theory of relativity, which completely revolutionized physics and led, through its equivalence of mass and energy (E = mc2), to the invention of the atomic bomb. In 1916, Einstein produced the general theory of relativity. He also made other fundamental contributions to quantum theory.

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