Einstein

by Philipp Frank

  Einstein noticed, however, that there is one type of “real” force that imparts the same acceleration to all bodies. This is the force of gravity. Since the time of Galileo we have known that, apart from the effects of air friction, all bodies fall at the same rate no matter what their masses are. Newton did not regard this as in any way inconsistent with his own law of motion. He simply assumed in his law of universal gravitation that the force of gravity acting on a body is proportional to its mass. The force of gravity acting on any body on the surface of the earth is its weight in the usual terminology. If we denote this by the symbol W, then Newton’s assumption can be expressed mathematically as W = Mg, where M is the mass of the object and g is a constant at a certain point on the earth. Now, Newton’s law of force states that this force Mg is equal to the rate of change of the momentum, which is simply the mass times the acceleration Ma. Thus Mg = Ma, and consequently the mass cancels out and we have simply a = g. The acceleration due to gravity is independent of the mass and has the same value (g) for all bodies which is, again, Galileo’s result.

  Einstein realized that this special character of the force of gravity made it impossible to determine the acceleration with which a laboratory moves relative to an inertial system. When we observe in a laboratory a cart executing an accelerated motion, we have no way of deciding whether this is due to the acceleration of the laboratory system as a whole or to a gravitational attraction caused by bodies whose presence may be unknown to us. Into this gap Einstein penetrated with his keen logical analysis, and laid the foundations for a reconstruction of mechanics. As in his earlier paper of 1905, he again related the motion of bodies to the propagation of light, and in 1911 he published a paper entitled “Über den Einfluss der Schwerkraft auf die Ausbreitung des Lichtes” (“The Influence of Gravity on the Propagation of Light”).

  Einstein started out from the following consideration: In a laboratory L that, like an elevator, can move vertically up or down, experiments are performed to observe the motion of objects relative to it. If the laboratory is held by some means such as a cable so that it is at rest with respect to the earth, any object B falls downward with the acceleration of gravity, no matter what its mass is or what it is made of. If, however, the laboratory itself is allowed to fall freely owing to the action of gravity, then no object B will have any acceleration relative to the laboratory. Everything would occur as if there were no force of gravity. By observing motions with respect to L one is not able to decide whether L is an inertial system with a field of gravity or whether there is no force of gravity but the laboratory is falling freely. To express the result more generally: it is not possible to distinguish by means of mechanical experiments carried out in a laboratory the accelerations that arise from inertial forces and those that arise from gravitational forces.

  To Einstein this conclusion was analogous to Newton’s statement that in no case can the speed of rectilinear uniform motion of a laboratory with respect to an inertial system be determined from mechanical experiments within the laboratory. In 1905 Einstein had extended this principle to include optical experiments. In a similar manner he now extended the properties of accelerated motions of objects to include optical phenomena. Thus Einstein advanced the hypothesis that it is impossible, even by means of observations on the rays of light, to determine whether a laboratory is an accelerated system or whether it is at rest or in uniform motion and subjected to a gravitational field. Einstein called this “the principle of equivalence of gravitational forces and inertial forces,” or, in short, the equivalence principle.

  With this principle Einstein was able to predict new optical phenomena that could be observed and hence give an experimental check on the validity of this theory. According to ordinary Newtonian physics, gravity has no effect on the path of a light ray, but according to the equivalence principle, gravitational forces can be replaced by an accelerated motion. The latter, however, as mentioned in the previous section, certainly has an effect on a beam of light. A ray parallel to the floor of a non-accelerated laboratory is no longer parallel when the system is accelerated. Hence Einstein concluded that the path of a light ray is deflected in a gravitational field. The amount of deflection turned out to be very minute because of the enormous velocity of light and no terrestrial experiment is feasible, but Einstein suggested that the effect might be observable for the light that comes to us from the fixed stars and passes near the surface of the sun. In this case the force of gravity is not uniform with the same strength and direction everywhere, but emanates from the center of the sun with a force that decreases in strength as the distance from the surface increases. But Einstein concluded that there would be a deflection in a direction that bends the light ray toward the sun. Since no stars are visible near the sun under ordinary conditions, however, owing to the blinding sunlight, Einstein pointed out in his paper that:

  “Since the fixed stars in the parts of the sky near the sun become visible during a total eclipse, it is possible to check this theoretical conclusion by experiment.”

  By assuming that the force of gravity has the value accepted by Newton, Einstein showed by a very simple calculation based on his equivalence principle that a ray of light coming from a fixed star and just grazing the border of the sun will be deflected from its straight path by 0.83 seconds of an arc. Consequently, if one photographs the fixed stars near the sun during a total solar eclipse and compares their positions with those where the sun is not near them, differences between their positions are to be expected. Since the light rays are bent toward the sun, the stars must appear shifted away from it, the magnitude depending on the proximity of the rays to the sun as they pass by it. Einstein concluded his paper with these words:

  “It would be extremely desirable if astronomers would look into the problem presented here, even though the consideration developed above may appear insufficiently founded or even bizarre.”

  No matter what one may think of Einstein’s hypothesis, he had brought forward a definite observational check on his theory. Since total solar eclipses are not very frequent and are observable only from a very limited part of the earth, astronomers were stimulated to undertake interesting and adventurous journeys. It took three years, however, until 1914, to find enough support and money to dispatch an expedition equipped to perform this observation. But just as this first expedition left Germany for Russia, World War I broke out, and the members of the expedition became Russian prisoners and were prevented from making the observation.

  9. Departure from Prague

  While he was a professor at Prague, Einstein not only founded his new theory of gravitation but also developed further the quantum theory of light that he had begun while in Bern. His hypothesis that a quantum of violet light possesses much more energy than that of red light seemed to be in agreement with experimental results on the chemical action of light. Every photographer is familiar with the fact that the action of violet light is much stronger than that of red light on a photographic plate. Einstein started with the simple assumption, very closely related to his photon theory of light, that the chemical decomposition of a molecule always takes place with the absorption of only a single light quantum. In his paper published in 1912 under the title “Über die thermodynamische Begründung des photochemischen Äquivalenzgesetzes” (“On the Thermodynamic Foundations of the Photochemical Equivalence Law), he showed that the assumption is also in accord with the general principles of thermodynamics.

  About this time, however, Einstein began to be much troubled over the paradoxes arising from the dual nature of light: the wave character exemplified by the phenomena of interference and diffraction and the particle aspect shown by the photoelectric and chemical actions. His state of mind over this problem can be described by this incident:

  Einstein’s office at the university overlooked a park with beautiful gardens and shady trees. He noticed that there were only women walking about in the morning and men in the afternoon, and that some walked alone sunk in dee
p meditation and others gathered in groups and engaged in vehement discussions. On inquiring what this strange garden was, he learned that it was a park belonging to the insane asylum of the province of Bohemia. The people walking in the garden were inmates of this institution, harmless patients who did not have to be confined. When I first went to Prague, Einstein showed me this view, explained it to me, and said playfully: “Those are the madmen who do not occupy themselves with the quantum theory.”

  Soon after Einstein’s arrival in Prague, he had received an offer of a professorship of theoretical physics at the Polytechnic School in Zurich, the institution from which he had graduated. The Polytechnic belongs to the Swiss Confederation and is a larger and more important institution than the University of Zurich, where Einstein had first taught and which is maintained by the canton of Zurich. Einstein was in doubt whether or not to return to Zurich, but his wife decided the matter. She had never felt at ease in Prague and was attached to Zurich, which had become her ideal home while she was a student there.

  Einstein informed the university at Prague that he would leave it at the end of the summer semester of 1912. But with his usual indifference to all official formalities, he did not send to the administrative authorities the documents that had to be filled out when one resigned from the service of the Austrian state. The Ministry of Education in Vienna did not receive the application that had to be forwarded in such cases. One can well imagine that the official in charge was unhappy at being unable to close Einstein’s record according to regulations. For many years the dossier for the “Einstein case” remained incomplete in a pigeonhole. Some years later, when Einstein went to Vienna for a lecture, a friend told him that the official in the ministry was still unhappy over the gap in the records. Einstein with his good nature did not want to make anybody unhappy. He visited the ministry, made his excuses to the official, and filled out the appropriate form. The pigeonhole lost its blemish.

  Einstein’s sudden departure from Prague gave rise to many rumors. An editorial in the largest German newspaper of Prague asserted that because of his fame and genius Einstein was persecuted by his colleagues and compelled to leave the city. Others maintained that because of his Jewish origin he had been badly treated by the administrative authorities in Vienna and therefore did not want to remain in Prague any longer. Einstein was much astonished by all this talk, as his stay in Prague had been a very pleasant one, and he had been favorably impressed by the Austrian character. Since he did not like to create any unpleasantness for anyone, he wrote a letter to the head of the Austrian university administration in Vienna. Before taking over my position in Prague, I paid a visit to this man. He was a Pole and embraced me according to the Polish custom as if I were a close friend. In the course of the call he told me about Einstein’s letter and said with great enthusiasm: “I received a splendid letter from Mr. Einstein, such as one is not accustomed to receive from a professor of our universities. I recall this letter very often. It gave me a great deal of satisfaction, particularly since so many attacks were directed against our government on account of Einstein.”

  For me Einstein’s departure from Prague is bound up with a rather humorous story, which I wish to relate because it is linked with the checkered history of our time. Like every Austrian professor, Einstein had had to get a uniform. It resembled the uniform of a naval officer and consisted of a three-cornered hat trimmed with feathers, a coat and trousers ornamented with broad gold bands, a very warm overcoat of thick black cloth, and a sword. An Austrian professor was required to put on this uniform only when taking the oath of allegiance before assuming his duties or when he had an audience with the Emperor of Austria. Einstein had worn it only once, on the former occasion. Since the uniform was rather expensive and he had no use for it after his departure, I bought it for half the original price. But before Einstein gave me the uniform, his son, who was then perhaps eight years old, said to him: “Papa, before you give the uniform away, you must put it on and take me for a walk through the streets of Zurich.” Einstein promised to do so, saying: “I don’t mind; at most, people will think I am a Brazilian admiral.”

  I too wore it only once, when taking the oath of allegiance, and I had it in my trunk for a long time. After six years the Austrian monarchy disappeared and the Czechoslovakian Republic was established at Prague. The oath of allegiance to the Emperor was replaced by that of allegiance to the Republic, and the professors had no uniform any more. The uniform remained only as a memory of Franz Joseph and Einstein. Soon after the Russian Revolution, when a large number of refugees, many of whom were officers, came to Prague, my wife said to me: “Why should such a good coat lie unused when so many are freezing? I know a former commander in chief of the Cossack army who cannot buy a warm winter coat. Einstein’s coat looks almost like the coat of a high-ranking cavalry officer. It will please the general and keep him warm.” We gave him the coat, but he was not interested in its distinguished past. The rest of the uniform, including the sword, remained in the German University. When the Nazis invaded Czechoslovakia in 1939, the university became a bulwark of Nazism in the east and Einstein’s sword probably became booty of a Nazi soldier, a symbol of the final defeat of “international Jewish science” — until 1945, when the Red Army entered Prague.

  V

  EINSTEIN AT BERLIN

  1. The Solvay Congress

  In the fall of 1912 Einstein entered upon his duties as professor at the Polytechnic in Zurich. He was now the pride of the institution where he had once failed to pass the entrance examination, where he had studied and met his wife, and where on graduation he had been unable to obtain even a minor position.

  As early as 1910, when Lampa was considering Einstein’s appointment to Prague and seeking an opinion of his qualifications from a scientist who was generally recognized as an authority, Max Planck, the leading theoretical physicist, had written to the faculty committee at Prague: “If Einstein’s theory should prove to be correct, as I expect it will, he will be considered the Copernicus of the twentieth century.” Einstein was already beginning to be surrounded by an aura of legend. His achievements were characterized as a turning-point in physics comparable to the revolution initiated by Copernicus.

  In 1911, when a conference of a small number of world-famous physicists was to be convened in Brussels to discuss the crisis in modern physics, there was no question that an invitation would be extended to Einstein. The selection of the conferees was suggested by Walter Nernst, a leading investigator in the fields of physics and chemistry, and among others there were Sir Ernest Rutherford of England, Henri Poincaré and Paul Langevin of France, Max Planck and Walter Nernst of Germany, H. A. Lorentz of Holland, and Madame Curie of Poland, who was working in Paris. Einstein represented Austria, together with Friederich Hasenöhrl, the Viennese, whose name after his tragic death was to be linked in a peculiar manner with the fight against Einstein. This conference was Einstein’s first opportunity to meet these scientists whose ideas shaped the physical research of this period.

  The costs of the conference, including the traveling expenses to Brussels and the living expenses there and in addition a remuneration of a thousand francs to each conferee, was defrayed by a rich Belgian named E. Solvay. This man had been successful in the chemical industry, but his hobby was a physical theory of the outmoded mechanistic type. Although it led to many complications and not to the discovery of new laws, he was greatly interested in attracting the attention of physicists to his theory and in learning their opinions about it. The clever chemist Walter Nernst, who was in social contact with him, thought that this rich man’s hobby might be utilized for the benefit of science while at the same time fulfilling Solvay’s desire. He proposed that he call a conference of leading physicists to discuss the present difficulties in their science, to whom he could present his ideas on this occasion. The conference became known as the Solvay Congress. In the opening address Solvay presented a summary of his ideas, and the conferees then discussed the
new developments in physics. Finally in the concluding address Solvay thanked the speakers for their interesting discussions, emphasizing how much pleasure he had derived from them. Nevertheless, all this had not shaken his faith in his own theory. All the speakers had avoided entering upon any criticism of his theory, to prevent any conscientious scruples arising between their feelings of gratitude and courtesy toward their host and their scientific convictions. Solvay was imbued with such sincere interest in the advancement of science that he subsequently convened similar conferences quite often, and at these meetings Einstein always played a leading role. A man like Nernst who has the interests of science at heart and is practical can utilize such opportunities for the benefit of progress in scientific research.

  The world marveled at the great number of new and astonishing ideas and at the thoroughness with which these concepts were developed, presented, and arranged in a larger chain of ideas that Einstein had already produced in 1912 after less than ten years as a physicist. But Einstein himself thought only of the defects and the gaps in his creations. His new theory of gravitation, which he had made public in 1911 at Prague, dealt only with one very special case of the effects of gravity. Only the case where the force of gravity has the same direction and intensity throughout the entire space under consideration was completely clear, and the theory as developed so far was unable to furnish a complete solution to cases where the force of gravity had different directions at different points in space.