1905 PORTRAIT of'Einstein was made in the year of his greatest productivity. While he worked as a clerk in the Swiss patent office, he made his great contribu-

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tion to the quantum theory and published a paper en­

titled "On the Electrodynamics of Moving Bodies." It

was this that set forth the special theory of relativity.

© 1949 SCIENTIFIC AMERICAN, INC

THE INFLUENCE

OF ALBERT EINSTEIN This nlonth he js 70. It is an appropriate tinle

to reflect on his achievenlents and to consider

the present state of the work he began in 1905

ALBERT EINSTEIN, whose 70th ft birthday this month is being noted

throughout the civilized world, oc­cupies a position unique among scien­tists. He has become a legend in his own lifetime. The public adulation of him is so great that he dare not list his tele­phone number in the directory. \Vhen he delivers one of his rare lectures at the Institute for Advanced Study in Prince­ton, no nohce of it may be posted on a bulletin board; the news must be passed around among his colleagues by word of mouth, lest it leak out and the lecture hall be overrun by reporters and curios­ity seekers.

It is relativity, of course, that has made Einstein's name a household word, and there can be no question that this one revolutionary achievement has been and will continue to be the distinction that sets him apart. The theory of relativity has a monumental quality that places its author among the truly great scientists of all time, in the select company of Isaac Newton and Archimedes. With its fascinating paradoxes and spectacular successes it fired the imagination of the public-and until recently all but ob­scured Einstein's many other contribu­tions to science.

In the perspective of half a century, these contributions have grown in im­portance. Considering recent develop­ments in physics, any estimate of his influence must recognize not only his quality as a great independent innovator but also his activities in advancing the fruitful progress of physical theory:

Einstein has lived in an era of un­precedented scientific change, much of which was generated by his own dis­coveries. Yet science was ripe for great upheavals even before his arrival. The seeds of scientific unrest that led to the theory of relativity had already been planted when Einstein was a boy. And the fundamental tenets of physical sci­ence were destined to be disrupted even more dramatically by the quantum theo­ry, which had its birth in 1900. To the quantum theory Einstein himself made

by Banesh Hoffmann

vital contributions. Indeed, the Nobel prize was awarded to him in 1921 not specifically for his controversial theory of relativity but "for his merits on behalf of theoretical physiCS, and in particular for his discovery of the law of the photo­electric effect."

Although Einstein is commonly thought of as an ivory-tower scholar, he has always had a happy knack for in­fluencing the course of events, and a remarkable instinct for detecting the needle of truth in a haystack of specula­tion. This is perhaps best shown in his quantum work of 1905. He was then an unknown scientist, not even associated with a university. Five years earlier Max Planck had suggested that matter must absorb and give off energy not in a con­tinuous Row but in minute bundles, or quanta. Nowadays, with the quantum so firmly established, even a professional physicist finds difficulty in recapturing the sense of outrage that such an idea must have provoked at the time. The idea was outright heresy. It was as if a scientist had said, in all seriousness, that something could be in two places at once. (Indeed, the development of the theory ultimately did imply that.)

PLANCK himself viewed his idea with misgiving, and at first it made no

headway. The young Einstein, however, dared to take it seriously. With cogent arguments he showed that the energy that was given off in bundles must some­how continue to exist in bundles-bun­dles of light, which we now call photons. Since centuries of research, culminating in the electromagnetic equations of J ames Clerk Maxwell, had pointed in­disputably to the fact that light was a wave, this idea of bundles or. particles of light was surely nonsense. Yet some­how it had to be sensible, for Einstein showed that it was able to explain phe­nomena that the wave theory could not encompass, notably the photoelectric effect, in which the energy of electrons knocked out of a metallic surface by light shining on it depended not on the inten-

sity but on the wavelength of the light. Einstein's idea of particles of light

marked a turning point in the ·history of the quantum. Though fundamentally simple, it was the product of extraor­dinary boldness and scientific insight. For the idea of particles of light was be­set by enormous difficulties. Perhaps Jigh t did consist of particles, as Einstein said. But it certainly consisted of waves, as he was acutely aware. This paradox plagued scientists for many a year be­fore it was resolved by \Verner Heisen­berg and Niels Bohr in terms of the mod­ern quantum theory.

In the early 1920s the French theoret­ical phYSicist Louis de Broglie put for­ward the weird idea that electrons and other particles of matter were accom­panied by curious sorts of waves. For years he developed his ideas without awakening any echo of response from other scientists. The French physicist P. Langevin was the first to see that they might have merit. And one day Einstein happened to come across them. Struck by their boldness, and by an inner plausi­bility beneath their outward appearance of fantasy, he espoused them in the sci­entific press. The response was spectacu­lar. Einstein's recommendations brought the ideas of de Broglie to the attention of the brilliant Aush'ian physicist Erwin Schr6dinger. Schr6dinger forthwith transformed them into the successful quantum theory of wave mechanics, which now forms a central part of mod­ern atomic physics and which proved to be substantially the same as the appar­ently different theory by which Heisen­berg and Bohr resolved the particle­wave dilemma.

Einstein's achievements in that single year of 1905 are breathtaking. While busy earning his living in the Swiss pat­ent office, he found time not only for his epoch-making work on the quantum but also for important contributions to the theory of the Brownian movement-the incessant agitation of microscopic parti­cles caused by molecular bombardment. In the same year he published a paper,

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© 1949 SCIENTIFIC AMERICAN, INC

bearing the unprepossessing title "On the Electrodynamics of Moving Bodies," in which he set forth the special theory of relativity. And, to cap it all, in a sec­ond paper on relativity in that same year he made his celebrated deduction of the equivalence of mass and energy: E = mc�.

If the quantum idea required bold­ness, what shall we say of the theory of relativity? ''''here the idea of particles of light challenged a mere theory, relativity challenged a universal and ingrained conception of time. We see nothing out of the way in the statement that Joe DiMaggio hit a home run in one base­ball game at the same moment that Johnny Mize hit one in another. It does not occur to us that this implies that the phrase "the same moment" has meaning. It seems ridiculous to raise the question.

Yet Einstein successfully challenged this attitude. Reasoning from precise experimental data, including the cele­brated experiment of Michelson and Morley on the speed of light through the "ether," he showed that we must give up. at whatever emotional cost, our be­lief that "the same moment" has a defi­nite meaning. Events at different places that occur at the same moment for one observer definitely do not occur at the same moment for another observer mov­ing relative to the first. Simultaneity is not absolute. It depends on the observer. Time is relative.

E JNSTEIN went on to prove that

space, too, must be relative, that no object can move faster than light, that mass increases with speed and, in brief, that all of theoretical physics, based as it was on erroneous ideas of space and time, must be reconstructed.

Newton's theory of gravitation, which had reigned unchallenged for more than 200 years, clearly did not fit the stringent requirements of relativity. Yet the prob­lem of replacing it was so difficult that Einstein took 10 years to find the solu­tion. And to do so he had to construct a general theory of relativity, beside which the special theory of 1905 appeared al­most an incident.

The German mathematician Herman Minkowski had discovered in 1908 a striking relationship between equations of the special theory of relativity and equations used by geometers of multi­dimensional spaces. From this relation­ship he deduced that space and time are fused together into a single four-dimen­sional entity: space-time.

The space-time that Minkowski found .in the special theory of relativity was flat. Einstein, guided by speculations on such simple situations as the operation of gravity with relation to a moving ele­vator, concluded that gravitation must be equivalent to a curvature of space­time, the idea of a force of gravitation being irrelevant. If gravitation was asso­ciated with a curvature of space-time,

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that alone was a reason why bodies under the influence of gravitational "at­traction" followed curved paths.

The general theory of relativity is more than an imposing intellectual structure. It has a grandeur that is also esthetic. From the idea of curved space­time the equations governing gravitation flowed with such inevitability and logical economy as to make the general theory a masterpiece of art as well as science.

Only a deep faith could have sus­tained Einstein's courage through the years of lonely effort before experiment showed his labors had not been in vain. He once made a remark to me that throws a revealing light on his methods. When estimating the value of a possible physical idea, he said, he asked himself whether it seemed so natural that he would have made the universe that way had he been God. If the idea did not possess this esthetic quality, he mis­trusted it.

In the general theory of relativity, gravitation was envisaged as only a minor puckering or roughness in an otherwise smooth space-time. In 1917 Einstein found reasons for supposing that the four-dimensional universe taken as a whole might be roughly cylindrical in shape. Not even Einstein could visual­ize a four-dimensional cylinder, but it could be conceived in mathematical terms. With this idea he inaugurated the subject of relativistic cosmology.

The Dutch astronomer W. de Sitter then suggested a different shape that goes by the name of pseudo-spherical. His theory predicted that distant bodies would appear to recede from us, a pre­diction tentatively borne out by the sketchy astronomical data then avail­able. Thus prompted, the' astronomers made further measurements, and found that the most distant nebulae did indeed appear to be receding at altogether stag­gering rates. Unfortunately de Sitter's model applied only to a theoretically empty universe. Einstein's model, on the other hand, did pertain to a universe in­habited by matter and radiation, but it predicted no· recession of bodies of mat­ter from one another.

To obtain a recession in a universe that was not empty, the Belgian cosmolo­gist Abbe Lemaitre in 1927 developed his theory of the expanding universe, which supposes that the universe ex­ploded long ago and that its fragments are still Hying apart-a theory which has recently been applied by George Gamow and R. A. Alpher to account for the ori­gin of elements and their relative abun­dances in the universe (SCIENTIFIC AMERICAI\', July, 1948).

Meanwhile Hermann 'Neyl of Ger­many had introduced the idea of a uni­fied field theory. If what was once called gravitational force could be considered as curvature, he argued, why should not electromagnetic forces also have a geo-

metrical basis? Gravitational curvature affects directions: for instance, an air­plane Hying half way round the earth would end up pointing in the direct,ion opposite to the one in which it started. Weyl therefore suggested that electro­magnetic forces might be connected with an analogous effect upon lengths, much as if the airplane ended up not only with [, different direction but also a different size. Because this plausible and ingen­ious idea actually yielded the same equations as those of Maxwell governing the electromagnetic field, it excited con­siderable attention. But Einstein, while greatly admiring it, found it unaccept­able because it violated physical princi­ples; he proved that the Weyl theory implied that atoms would emit light of all frequencies, whereas actually they produce sharp spectral lines indicating radiation only at specific frequencies.

The German mathematician Th. Kalu­za later showed that Einstein's gravita­tional equations could be made to yield Maxwell's electromagnetic equations by expanding them to fit a special five-di­mensional setting. What the fifth climen­sion might be, Kaluza could not say. Despite this, the result was so remark­able that Einstein and many others have since worked on the idea. And in 1930 the American geometer Oswald Veblen discovered that the so-called fifth dimen­sion was not 'a fifth dimension at all but a familiar mathematical quantity used by geometers in studying what they can the projective geometry of four dimensions.

THE EQUATIONS of Maxwell and Einstein were thus successfully

brought together. But the problem of the structure of matter and radiation could not be solved in terms of the equations as they stood. If it was ever to be solved along the lines of a field theory-which was by no means certain-modifications of some sort would have to be intro­duced. Accordingly the search was re­newed with more ambitious aims.

For more than 25 years Einstein has de­voted his main scientific energies to this problem. While the quantum theorists are moving ahead in close touch with the latest details of nuclear experiment, Einstein is attempting to gain an insight into the nature of matter and radiation by abstract reasoning from a few general assumptions. In this he is following the heroic method that proved so successful -in his hands-in the formulation of the theory of relativity. Unfortunately there are many possible approaches, and since each requires a year or more of intensive computation, progress has been heart­breakingly slow.

What was once the broad sh'eam of relativistic research has shrunk to a slen­der rivulet. The quantum theory, so frail in 1905 when Einstein first befriended it. now dominates physics. It has developed a stature comparable to that of the theory

© 1949 SCIENTIFIC AMERICAN, INC

of relativity, and has proved to be even more iconoclastic. It has corroded con­cepts such as determinism and causality that once seemed indispensable to any rational science. It has elevated chance to a commanding position in scientific theory. And it has upset our powers of visualization by replacing the former conception of a particle by a hybrid monstrosity such that when we speak of its precise position we are forbiddet1 to speak of its motion, while when we think of its exact motion we may not regard it as possessing position at all.

While developing his theory of rela­tivity, Einstein continued to contribute valuable ideas to the burgeoning quan­tum theory. He applied it with signal success to the theory of specific heats. He propounded the quantum law of photochemical equivalents that goes by his name. He gave a new deduction of Planck's radiation formula, introducing important concepts regarding the proc­ess of radiation. And he applied de Broglie's ideas to the theory of gases when those ideas were still unproved.

NEVERTHELESS, Einstein is out of

sympathy with the modern form of the quantum theory. Most theoretical physicists, on the other hand, doubt that the problem Einstein has set himself is aimed in the right direction, since it ap­parently avoids the quantum. But it must be remembered that in 1905 most theo­rists were doubting the very idea of the quantum. Einstein's present views may not be fashionable, and the chances of a successful outcome of his work may ap­pear slim. Yet he has always been a lone­ly thinker, and physicists will not easily forget that Einstein is the man who, from abstract considerations of space and time alone, was able to deduce the equiv­alence of mass and energy without need­ing to know the detailed sh'ucture of either. The quantum theorists them­selves are encountering formidable diffi­culties of a fundamental nature. The time seems ripe for a further synthesis through an imaginative stroke of insight by an Einstein.

The importance of Einstein's scientific ideas does not reside merely in their great success. Equally powerful has been their psychological effect. At a crucial epoch in the history of science Einstein demonstrated that long-accepted ideas were not in any way sacred. And it was this more than anything else that freed the imaginations of men like Bohr and de Broglie and inspired their daring tri­umphs in the realm of the quantum. Wherever we look, the physics of the 20th century bears the indelible imprint of Einstein's genius.

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Banesh Hoffman It is associate professol' of mathematics at Queens College and au­thol' of The Strange Story of the Quantum.

IN 1939 Einstein was photographed at home at Princeton, N. J. There h.e

gives an occasional lecture at the Institute for Advanced Study. Today Ills activity is limited by his convalcscense from a recent surgical operation.

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