quite close to the truths that constitute the subject of the special theory of relativity.” Einstein replied to this: “Yes, that is true, but with respect to the general theory of relativity the matter stands otherwise. I doubt whether it would be known now.”

The general theory of relativity grew out of the special theory. Wishing to give a survey of the historical development of the theory of relativity over the last 50 years, we must devote somewhat more time to the general theory of relativity than to the special theory, since about the latter it is difficult to say anything that every theoretical physicist, and possibly also every experimentalist, would not know. On the other hand, the general theory of relativity is less widely known; one can do physics without knowing it. Some physicists try to discredit the general theory of relativity by presenting it as a formal theory, only slightly connected with experiment. The three known confirmations of the general theory of relativity are, in the opinion of some physicists, doubtful, while the facts connected with it are not interesting!

I am one of those physicists who regard such judgments as untenable, who believe that the general theory of relativity solves the problem of gravitation, that it is a remarkable example of a nonlinear field theory, and that its influence on other areas of physics will continually grow. I do not think, however, that on the basis of this theory it has been possible to understand the structure of elementary particles.

After these preliminary remarks I shall allow myself to begin my brief survey of the historical development of the theory of relativity. This survey will be neither complete nor objective. The subject itself does not permit objectivity, and the time allotted to me for the lecture does not permit completeness.

In the seventeenth volume of the journal Annalen der Physik, published in 1905, Einstein’s article “On the Electrodynamics of Moving Bodies” occupies 30 pages. The title of the article is very modest; however, on reading it we at once notice that this work differs from other analogous works. It contains no references to the literature, no authorities are cited, and the individual footnotes are merely explanatory in character. The work is written in simple language, and a large part of it can be understood without profound knowledge of the subject. One can only wonder that this work, which differed so sharply in its form from ordinary scientific papers, was passed over by the referee (if such a person existed at all). This is all the more astonishing because a complete understanding of this article requires such depth of thought as is more valuable and rarer than pedantic knowledge. The method of exposition and the very style of the work have preserved their freshness even today. It still remains the best aid for the study of the theory of relativity. The author of this work did not belong to scientific circles; he was not even a teacher at an institution of higher learning. At that time, 50 years ago, being young

doctor of philosophy; at the age of 26 he was serving in the Swiss Patent Office in Bern.

In the second section of this work it is stated:

1. “The laws according to which the states of physical systems change do not depend on to which of two coordinate systems, situated with respect to one another in uniform translational motion, these changes of state are referred.

2. Every ray of light moves in a ‘stationary’ system of coordinates with a definite velocity \(c\), independently of whether this ray of light is emitted by a body at rest or by a moving body.”

From these two postulates—the principle of relativity of Galileo and the principle of the constancy of the velocity of light, as is known, the Lorentz transformations follow. They are the foundation on which the special theory of relativity was erected. They are those assumptions which led to a radical revision of our concepts of space and time.

In the next volume of the journal Annalen der Physik there appeared a small paper by Einstein entitled “Does the inertia of a body depend on the quantity of energy contained in it?” If I were to characterize the ideas expressed in this work as world-shaking, it would be no exaggeration. Indeed, in this work we find for the first time a theoretical indication of the possibility of a new phenomenon, which opened boundless prospects before science and technology. In this brief article it is asserted: the application of atomic energy is possible in principle. Forty years later it was proved that the application of atomic energy for military purposes was possible. This proof was as manifest as the destruction of Hiroshima and Nagasaki, as the sudden death of two hundred thousand people. About fifty years later the possibility of using atomic energy for the benefit of mankind was also proved. The bitter irony lies in the fact that the seed of both possible applications of atomic energy was sown by the most peace-loving man in the world, a lonely man who hated violence and despised brute force. The bitter irony lies in the fact that 10 years before the creation of the first small atomic power station in the Soviet Union, the destructive power of atomic energy annihilated two cities and a multitude of human lives. At the end of Einstein’s short article we find the following lines:

“The mass of a body is a measure of the energy content in this body; if the energy changes by an amount \(L\), then the mass changes in the same direction by the amount

\[ \frac{L}{9 \cdot 10^{20}}, \]

where the energy is measured in ergs, and the mass—in grams.

The possibility is not excluded that a verification of the theory may be achieved for bodies whose energy content is variable to the highest degree (for example, for radium salts).”

What influence, then, did these two papers have? At first—almost none. In our time important papers are recognized more quickly, and papers that bring about a revolution in science often call forth a whole stream of investigations in the same field. True, the history of the science of our century also knows examples to the contrary, such as, for instance, the two-year lull after de Broglie’s first papers. Einstein’s works were met in a similar way. A whole stream of works on the theory of relativity appeared only after approximately four years, i.e., by 1909. This, undoubtedly, was a long time, which physicists needed in order to grasp one of the most important articles ever published.

And yet, as I know, some physicists even during this period read Einstein’s paper very carefully and saw in it the birth of an infinitely far-sighted idea. My friend, Professor Loria in Poland, told me how his teacher, Professor Witkowski of Cracow, an exceedingly educated physicist with refined taste, remarked to him enthusiastically after reading Einstein’s papers: “Read Einstein’s papers! A new Copernicus has been born!”

Only in 1909 did a larger number of physicists turn their attention to the results obtained by Einstein. A broader acquaintance with the theory of relativity was promoted, in particular, by Minkowski’s report “Space and Time,” delivered by him in 1908 at the eightieth congress of the Society of German Natural Scientists and Physicians. This famous report of Minkowski was probably his last public appearance, since soon afterward, unfortunately very early, he passed away. Minkowski began his report with words that proved to be a prophetic prediction of the profound influence that Einstein’s ideas were destined to exert on modern thought:

“Gentlemen! The views on space and time which I intend to develop before you have arisen on an experimental-physical basis. Therein lies their strength. Their tendency is radical. Henceforth space by itself and time by itself must turn into fiction, and only a certain kind of union of the two must still preserve independence.”

Minkowski’s mathematical genius clothed Einstein’s ideas in a new geometric form, which in finished form revealed all their beauty and simplicity. Since the publication of Minkowski’s works we know that all the laws of nature can be represented in vector or tensor form, with vectors and tensors being certain formations in the four-dimensional space-time manifold. Later it became necessary to add spinors to vectors and tensors as well. From a historical point of view, the further development of the special theory of relativity is connected with the development of the general theory of relativity. Since, however, we do not intend in the present exposition to consider both

...theories together, I would like to say just a few more words about the special theory of relativity, so as then to be able to proceed directly to the general theory.

The further development of the special theory of relativity was a triumphal march of our knowledge. In this connection I should like to point to only three phenomena that constitute a brilliant confirmation of the special theory of relativity, namely: the dependence of mass on velocity; Ives’s elegant experiments on the change in the rate of moving clocks; and the dependence of the lifetime of the meson on its velocity. These experiments, like many others, confirm the special theory of relativity; at the same time there is not a single experiment that would contradict it.

The two greatest triumphs of our century in the prediction of definite phenomena of nature are closely connected with the history of the development of the special theory of relativity. I have in mind de Broglie waves and the theory of the positron. There is an internal connection between the prediction of the existence of de Broglie waves and the Lorentz transformations, between the theory of the positron and the relativistic form of Dirac’s equation for the electron.

I should like to mention here one more phenomenon, which in all probability is unknown to you, since the work on this question has not yet been fully published. One of the young Polish physicists, Werle, has shown that, with the aid of the relativistic equations of motion of the nucleon, the mutual deflection of nucleons as they approach one another to a very small distance can be explained, provided only that the meson field is regarded not as vectorial, but as scalar or pseudoscalar. Here we are dealing with a purely relativistic effect. The proposal of Jastrow and Levy may, consequently, be derived from the equations of the meson field.

Let us now leave the special theory of relativity and proceed to the general theory.

From the age of fifteen or sixteen Einstein, as he repeatedly told me, pondered the following two questions:

1. What will happen if someone runs after a light ray and tries to catch it?
2. What will happen if someone finds himself in a freely falling elevator?

From the answer to the first question grew the special theory of relativity; from the answer to the second—the general theory.

The ideas of the special theory of relativity were in the air. The contradictions it removed were well known to physicists. Poincaré almost arrived in 1904 at the formulation of the special theory of relativity. Many wounds on the body of physics were visible. The situation was otherwise, however, with the general theory of relativity.

Einstein was the only person who still saw the difficulties and worked to remove them. The general theory of relativity was, as it were, a medicine for a serious illness that no one except Einstein noticed. Even Planck said to Einstein: “Everything is now so well explained; why are you occupying yourself with these other problems?” But Einstein, quite alone, continued to occupy himself with them. Eight years separate the special theory of relativity from the general one—eight years of constant thought, which in the end bore fruit in the form of a new solution to the great problem of gravitation.

The first work in which Einstein undertook the solution of the problem of gravitation appeared in 1911 in the journal Annalen der Physik and bears the title “On the Influence of Gravity on the Propagation of Light.” It is a very interesting work. It contains Einstein’s thoughts that are partly incorrect. It contains half-truths, conjectures, a vague certainty that the true solution of the problem, though near, is nevertheless quite different. This work was the first glimmer of light in the process of overcoming total darkness. At the same time, it shows Einstein’s predilection for thought experiments and his boyish capacity to be astonished by simple things—things that seem so simple and familiar that others do not notice them at all.

Since the time of Galileo, physicists had known that all bodies fall with the same acceleration. In our century no one, with the exception of Einstein, was any longer surprised by this law. Experiment had shown that the law is strictly fulfilled; with this phrase, it was thought, the problem was exhausted.

Our capacity for wonder is suppressed by teaching. Only genius can withstand this. In the last three centuries of the development of science, Einstein was the first to see in the equality of accelerations a certain important hint. For we can imagine a world in which this law does not hold, a world in which elephants fall so slowly that they seem to hover in the air, while infants at the breast rush toward the ground with dangerous acceleration. But in the gravitational field of our planet, both infants at the breast and elephants fall with the same acceleration. What does this important indication of the equality of inertial and gravitational mass mean? Within the framework of classical mechanics this equality seems a pure accident.

I have already mentioned that the image of a man falling in an elevator, which even in his boyhood had been the subject of Einstein’s reflections, led him several years later into the circle of ideas of the general theory of relativity. This image is also contained in the work by Einstein that we are considering; using this example of the falling elevator, the necessity of the deflection of light in a gravitational field was shown! True, the numerical value calculated on this basis...

the value of the deflection of light proved to be too small. Einstein had not yet fully mastered the general theory of relativity. He achieved this only four years later, when, returning to his calculations, he corrected them. The prediction of this effect, however, is already contained in Einstein’s paper published in 1911. He concluded it with the following significant words:

“It would be highly desirable for astronomers to interest themselves in the question posed here, even if the preceding considerations seemed insufficiently substantiated or risky. For, quite apart from any theory, one must ask oneself whether it is possible at all, by modern means, to establish the influence of gravitational fields on the propagation of light.”

Eight years passed before an answer was obtained to the question posed by Einstein. During this time he moved from Prague to Zurich, and then from Zurich to Berlin. Here Einstein was overtaken by the outbreak of the First World War; here, too, he completed his work on the general theory of relativity.

Recognition of the theory of relativity spread slowly from theoretical physicists to experimental physicists, astronomers, mathematicians, and philosophers. It was regarded as an extremely difficult subject. In Cambridge I was told about a lecture on the general theory of relativity delivered during the war by Sir Arthur Eddington. After the lecture one of the physicists remarked to Sir Arthur: “That was an excellent lecture. You are one of the three people in the world who understand and know the general theory of relativity.” When an expression of doubt appeared on Eddington’s face, this physicist observed: “Professor, you need not be embarrassed; you are too modest.” Sir Arthur replied: “I am not embarrassed; I am only wondering who the third is.”

Understanding the general theory of relativity required knowledge of mathematical methods that at that time were not only little known but also insufficiently developed. The general theory of relativity influenced the further development of Riemannian, and later non-Riemannian, geometry. The theory of relativity greatly promoted the growth of these branches of mathematics.

Knowledge of the general theory of relativity spread in England, the Soviet Union, and other countries only after the First World War. In 1919 two English expeditions were organized, one of which went to Sobral (Brazil), and the other to Principe (on the African coast). Their task was to determine, during a solar eclipse, whether light rays emitted by stars are deflected in the gravitational field of the Sun, and whether this effect agrees numerically with the predictions of the general theory of relativity. The results reported at that time seemed brilliantly to confirm Einstein’s predictions. Although later measurements worsened this agreement, today

L. INFELD

nevertheless no one doubts that light rays are indeed deflected by the gravitational field.

The phenomenon of the deflection of rays in the gravitational field of the Sun suddenly captivated the entire civilized world. Einstein, this most modest of men, soon after 1920 became a world-famous scientist. It seems to me that Einstein’s sudden and ever-growing fame was due to humanity’s striving for peace. A phenomenon of nature had been discovered, as majestic and mysterious as the star-covered sky itself during a solar eclipse; a phenomenon that led to cooperation between the scientists of two nations which, only two years earlier, had still been at war with one another. A phenomenon of nature had been discovered whose theory had been created by a German professor and whose truth had been confirmed by an English scientist. I also believe that this was what provoked the reactionary struggle against Einstein. Einstein was probably the most famous man in the world. He was admired more than others and ridiculed more than others. To both he remained as indifferent as he was to many other private manifestations of the external world. He himself perhaps realized his sudden fame less than anyone else.

While Einstein was formulating and correcting the general theory of relativity in the pages of the journal Berichte der Preussischen Akademie, its development proceeded comparatively slowly. Penetrating ever more deeply into the problems of gravitation, Einstein was repeatedly forced to return to his works in order to correct various errors. The building of the general theory of relativity was erected by 1916, when, in the pages of Annalen der Physik, in an extensive work entitled “The Foundations of the General Theory of Relativity,” a complete exposition of the theory was given. Later no fundamental changes were introduced into the theory, although many of its propositions underwent further development and many new results were added. Among the consequences that can be obtained from the general theory of relativity, in contrast to classical mechanics, there is one well known—the motion of the perihelion of Mercury. In 1916 it was the first confirmation of the general theory of relativity. The famous astronomer Schwarzschild at that time derived this consequence quite rigorously from Einstein’s equations. This assertion, however, in a certain sense oversimplifies the actual state of affairs. The whole history of the solution of this problem is much more complex. I shall dwell on it briefly.

The general theory of relativity, in the form in which it was formulated in 1916, rested on two pillars. One of them was the field equations, i.e., equations describing changes of the gravitational field or, if one likes, of the geometrical field in space and time. The other pillar was the equations of motion, which determine the motion of a body in such a gravitational field. These equations, i.e., the equations of geodesic...

...lines, replace the former equations of motion of Newton, in which the force of gravity is proportional to acceleration. Now, in the general theory of relativity, the equations of motion, like all laws of nature in general, are valid in any, and not only in an inertial, frame of reference.

Consequently, if we wish, for example, to determine the motion of some planet in the gravitational field of the Sun, then we must first of all determine, with the aid of the field equations of the general theory of relativity, the gravitational field of the Sun. After that we must apply the equation of motion to the field thus found and determine the motion of the planet. This is precisely what Schwarzschild did, with great mathematical brilliance. The results he obtained are valid, however, only for a planet very small in comparison with the Sun. But what is the situation in the case of double stars, in the case of the problem not of one body, but of two bodies? Schwarzschild’s method is not applicable here. The second support of the general theory of relativity gives nothing here!

Although we have at our disposal both the field equations and the equations of motion, the latter have only limited validity. Before 1938 it was not possible to solve the problem of the motion of double stars within the framework of the general theory of relativity, despite the fact that the solution of this problem in classical mechanics is trivial; it is almost as simple as the solution of the one-body problem, i.e., the problem of the motion of a light planet around the Sun.

Einstein had long believed that the equations of motion in the general theory of relativity are unnecessary, that there is no need to postulate these equations, that they can be obtained from the field equations, that we can dispense with equations of motion, and that the sole foundation on which the general theory of relativity rests consists of the field equations alone.

This, as it turned out, was correct, but the proof required much time.

All the technical means needed for such a proof were already, by 1916, in the hands of mathematicians and physicists. The field equations were known to them. It was only necessary to show that the equations of motion were already contained in them. All this resembled the search for a deeply buried treasure whose location was known. Einstein repeatedly undertook the solution of this problem. He would then leave it in order to occupy himself with many other questions, and return to it again. When Hitler came to power, Einstein left Berlin and in 1933 became a professor at the Institute for Advanced Studies in Princeton. In 1938 a paper was published in which, for the first time, equations describing the motion of double stars in an approximation representing a step forward in comparison with Newton’s equations were derived from the field equations of the theory of relativity.

I have already said that my report will be neither complete nor objective. For the sake of order, I would only like to list here a few more of the most important topics that I have not touched upon at all. These are: consideration of the third effect, i.e., the red shift; the history of the application of the general theory of relativity to cosmological problems; and the search for a unified field theory, to which Einstein devoted 35 years of his life. The selection of the problems touched upon in my brief survey of the historical development of the theory of relativity was, of course, subjective.

I shall try here to answer one more question—the question of what the world of physicists thinks about the general theory of relativity.

It seems to me that the majority of physicists will agree that it is the only reasonable and elegant theory of the gravitational field. There are, it is true, some other theories; Einstein’s theory, however, surpasses them in beauty, depth, and logical completeness. In some of these theories the motion of the perihelion of Mercury is explained only by a special choice of the constant entering into them. On the contrary, in Einstein’s theory there are no new constants, which is its enormous advantage. Most often, in these other theories of gravitation the inertial frame of reference of the special theory of relativity is used. According to some of them, the center of gravity of double stars moves with acceleration (!), whereas in Einstein’s general theory of relativity this center behaves reasonably, i.e., it moves only with constant velocity. To physicists who adhere to their own theory of gravitation, Einstein’s theory seems too radical. But I think that this is precisely where its strength lies. In fact, Einstein’s theory of gravitation has no serious competitors. The general theory of relativity has existed for 40 years! The Bohr theory of the atom, put forward at the same time as it, became obsolete twelve years later thanks to the new theory of Schrödinger and Heisenberg. It is remarkable that after forty years of existence Einstein’s theory remains a living theory, that important works are appearing in this field, although, to be sure, it is not at the center of physicists’ attention.

There exists, as I have already mentioned, a very small group of physicists who, for various reasons, prefer other theories of gravitation. At the same time there also exists a more numerous group of physicists who accept the mathematical scheme of the general theory of relativity, but reject Einstein’s interpretation of its basic concepts. The two fundamental ideas of the general theory of relativity are as follows:

1. The gravitational and metric fields are identical.
2. The general principle of relativity is valid, i.e., arbitrary transformations are admissible.

Both these ideas are disputed by some physicists. Some of them, while not objecting to Einstein’s field equations, see in them only equations for determining the gravitational field, whereas they regard the metric field as pseudo-Euclidean. Other physicists do not believe in the general principle of relativity. They postulate such coordinate conditions as single out a group of coordinate systems connected by Lorentz transformations. In this case the coordinate conditions are considered together with the field equations.

My report is not a polemic, but I should nevertheless like to note that Einstein believed that the center of gravity of his theory lies in the acceptance of both of the points mentioned, especially in the acceptance of the general principle of relativity. According to Einstein, changing these hypotheses means abandoning the ideas that led to the general theory of relativity.

In concluding my report, I should like to make one more observation.

The results of Einstein’s research already today exert a profound influence on the world; they raise important questions of a political and moral character. The history of the development of atomic energy begins with the equivalence relation between mass and energy. Einstein was one of the first, after the discovery of the fission of uranium nuclei, to realize the tremendous possibilities contained in atomic energy and the danger of its misuse.

For a whole number of years Einstein has been passionately fighting against the misuse of atomic energy for purposes of mass murder, and for the preservation of peace throughout the world. In his postwar message to the American people he wrote:

“On us, the scientists who unleashed this monstrous force, rests a tremendous responsibility to direct atomic energy to the service of the good of mankind, and not to destruction.”

With this message of Einstein’s I should like to conclude my report. It remains for me only to thank you for the invitation to deliver this report in the very city and in the very hall where, a quarter of a century ago, Planck and Einstein spoke. I should like to express to my listeners and to the entire German people my heartfelt wish that in Berlin, in the future capital of a united and democratic Germany, theoretical physics worthy of the traditions created by Kirchhoff, Helmholtz, Planck, and Einstein may flourish.