Einstein

by Philipp Frank

  III

  BEGINNING OF A NEW ERA IN PHYSICS

  1. Life in Bern

  When Einstein took up his position at the patent office in Bern, it was in two respects a turning-point in his life. He became engaged in a practical occupation that made him financially independent and filled his time with an obligatory activity, and he founded a family. For most people these two circumstances provide the most important and often the only content of their lives. This was true only to a very slight degree for Einstein, to whom neither professional activity nor a family had a great significance. At times these activities gave him a certain relaxation, but they never really satisfied him.

  Throughout his life Einstein has been in a certain sense a very lonesome man. He sought the harmony of the universe in music as well as in mathematical physics and he has been engaged in these two fields during his entire life. Everything else was significant for him only in so far as it affected his progress toward this goal. He sought friends with whom he could play music or discuss ideas about the universe; yet he did not like to become so intimate with his friends that they could in any way interfere with his freedom. His attractive, frank, and witty personality easily made many friends, but his predilection for isolation and his concentration on his artistic and scientific life disappointed many people and estranged some who had been, or at least had believed themselves to be, his friends. We find repeatedly that throughout his life this contrast has determined his relations to his environment.

  Much later (1930) he himself described this character trait very precisely and strikingly:

  “My passionate interest in social justice and social responsibility has always stood in curious contrast to a marked lack of desire for direct association with men and women. I am a horse for single harness, not cut out for tandem or teamwork. I have never belonged wholeheartedly to any country or state, to my circle of friends, or even to my own family. These ties have always been accompanied by a vague aloofness, and the wish to withdraw into myself increases with the years. Such isolation is sometimes bitter, but I do not regret being cut off from the understanding and sympathy of other men. I lose something by it, to be sure, but I am compensated for it in being rendered independent of the customs, opinions, and prejudices of others, and am not tempted to rest my peace of mind upon such shifting foundations.”

  Although Einstein did not seek much stimulation from others, yet he did not like to develop his ideas in solitude without any contact with other people. Frequently he has liked the presence of a companion in order to be able to speak his mind freely. Even during the early period in his career he liked to try out his ideas on others to see how they reacted to them.

  At Bern his chief companion in this respect was an Italian engineer named Besso. He was somewhat older than Einstein, and a man of critical mind and a highly nervous temperament. He was often able to offer pertinent critical remarks on Einstein’s formulations, and also responded vigorously to those ideas of Einstein’s which were new and astonishing. He frequently remarked about new ideas: “If they are roses, they will bloom.” Around Einstein and Besso there gathered a small group of people interested in science and philosophy, who often met to discuss such questions.

  2. Interest in Philosophy

  Since Einstein was chiefly interested in the general laws of physics or, more precisely, in deriving logically the immeasurable field of our experiences from a few principles, he soon came into contact with a set of problems that are usually dealt with in philosophical works. Unlike the average specialist, he did not stop to inquire whether a problem belonged to his field or whether its solution could be left to the philosophers.

  Einstein read philosophical works from two points of view, which were sometimes mutually exclusive. He read some authors because he was actually able to learn from them something about the nature of general scientific statements, particularly about their logical connection with the laws through which we express direct observations. These philosophers were chiefly David Hume, Ernst Mach, Henri Poincaré, and, to a certain degree, Immanuel Kant. Kant, however, brings us to the second point of view. Einstein liked to read some philosophers because they made more or less superficial and obscure statements in beautiful language about all sorts of things, statements that often aroused an emotion like beautiful music and gave rise to reveries and meditations on the world. Schopenhauer was pre-eminently a writer of this kind, and Einstein liked to read him without in any way taking his views seriously. In the same category he also included philosophers like Nietzsche. Einstein read these men, as he sometimes put it, for “edification,” just as other people listen to sermons.

  Einstein and his graduating class at the Cantonal School, Aarau, Switzerland, 1896 (Illustration Credit 3.1)

  Einstein and Mileva, his first wife (Illustration Credit 3.2)

  Einstein in 1905, the year during which he propounded the theory of relativity and the hypothesis of photons (light quanta) (Illustration Credit 3.3)

  The philosopher whose views Einstein felt helped him most was David Hume, who is usually characterized as the “representative of the English Enlightenment.” What Einstein liked most about Hume was the unsurpassable clarity of his presentation and his avoidance of any ambiguities intended to give an impression of profundity. Hume showed that there are only two methods available for science: experience and mathematical-logical derivations. He was the father of the logical-empirical approach, and he rejected all metaphysical auxiliary concepts if they could not be established by experience and logical derivation. The most famous examples are Hume’s criticism of the ordinary conception of the relation between cause and effect, and of induction — the method of deriving a general law from a few particular instances.

  When we observe that a stone A strikes a stone B and sets it in motion, we usually express this occurrence as follows: Stone A has caused stone B to move. By experience we can only confirm the fact that whenever A strikes B, B is set in motion. Before Hume it was usually said that this connection is a necessary one. In physics, however, the word “necessary” can have no meaning other than “regularly connected.” If in addition to this we wish to introduce the word “necessary” as “cause” in another, higher sense, we are asserting something that cannot be proved by any observation. Every observation shows only whether or not the motion of B regularly follows when it is struck by A, but never anything that can be expressed by the statement: “Motion of B necessarily follows from collision with A.”

  According to Hume, then, to explain a phenomenon causally means only to state the conditions under which it occurs. This conclusion of Hume’s that science knows only the regularity of natural phenomena and processes, but nothing about any “causation” that goes beyond this, was of the greatest significance for Einstein’s scientific thought. Many of the polemics later directed against Einstein were fundamentally polemics against Hume. We shall see that his adherence to the “philosophy of the English Enlightenment” was later used by German nationalists to discredit him. It was used to tie up Einstein’s theories with the political philosophy of liberalism, and consequently to condemn them.

  Some of Hume’s ideas also appear in the writings of Ernst Mach, the leader of central European positivism. Next to Hume, Mach was the philosopher who exerted the greatest influence on Einstein. Of particular significance was Mach’s criticism of the remains of medieval physics in Newtonian mechanics, which have already been discussed in Section 8 of the last chapter. Mach’s criticism that such expressions as “absolute space,” “absolute time,” and “absolute motion” could not be connected in any way with physical observations was one of the points from which Einstein set out to replace Newton’s theory of motion by his own. “Mach’s postulate” has in many instances been a useful point of departure for new theories. According to this “postulate,” for every physical phenomenon the conditions of its occurrence must be sought among other observable phenomena. Later “Mach’s postulate” led Einstein to advance his new theor
y of gravitation.

  On the other hand, Einstein was not particularly sympathetic to what he called the “Machian philosophy,” by which he meant Mach’s doctrine that the general laws of physics are only summaries of experimental results. Einstein believed that this conception did not give sufficient credit to the fact that general laws cannot be inferred from experience. In Einstein’s opinion they are to be tested by experience, but owe their origin to the inventive faculty of the human mind.

  It was this very point that Einstein esteemed so highly in Kant’s work. Kant’s principal point was that the general laws of science contain not only the result of experience, but also an element provided by human reason. On the other hand, Einstein did not share Kant’s belief that human reason by itself can yield important natural laws, and that consequently there are laws that are eternally valid. Einstein liked to read Kant because through him he became acquainted with many of Hume’s ideas. The views of Einstein and Kant are similar in their emphasis on the role of the human mind but this similarity is rather emotional than logical.

  3. The Fundamental Hypotheses of the Theory of Relativity

  The blind alley into which the ether theory of light had been led by Michelson’s experiment has already been mentioned in Section 5 of the previous chapter. Michelson had tried to measure the velocity of the earth as it moves through the ether, but had obtained the value zero for this velocity.

  The main idea of this experiment can be explained in this way: We know that a swimmer takes longer to swim upstream than downstream between two points in the bank. In fact, by measuring the two rates of travel, we can easily calculate the velocity of both the swimmer and the stream. According to the mechanistic view, light should travel through the ether in exactly the same way as the swimmer in the stream, and experiments on light propagated through the “stream of ether” relative to the moving earth should be comparable to observations on the swimmer made from the bank of the stream. Thus the measurements of the velocities of light when traveling with the ether stream and against it should enable us to calculate the velocity of the earth through the ether. The execution of this fundamental idea in this simple form, however, is not practicable, since the velocity of light is so very great — 186,000 miles per second — but Michelson devised a means whereby the velocities of light that has traveled along two well-defined paths could be compared. His idea was to measure the difference in time taken by one beam, which travels from a certain point (S) to a mirror (M) in a direction along the motion of the earth through the ether and then back to S against the motion, and another beam which goes from S to another mirror (N) situated the same distance from S as M, but in a direction perpendicular to the motion and back to S. If the mechanistic view is correct, the first beam should take a slightly longer time than the second, and with the sensitive apparatus that Michelson had, the result should have been observable, even if the velocity of the earth through the ether were only a small fraction of the velocity of the earth around the sun. There was no observable difference in the two times, however.

  If we refuse to assume that the earth always remains at rest in the ether, which would contradict other observations, the only possible conclusion that we can draw from Michelson’s experiment is that the hypothesis on which the result was predicted must be false. This hypothesis, however, was the mechanistic theory of light itself.

  Einstein drew a radical conclusion and suggested abandoning entirely the assumption that light is a process in a medium known as the ether. Instead of asking what are the results of the interaction of light and motion according to the ether theory of light, he asked what are the chief characteristics of the interaction of light and motion that are known from actual observations. He condensed these features into a few simple laws and then inquired what could follow from such laws if developed along logical and mathematical chains.

  Michelson’s experiment and similar ones performed by others showed that optical phenomena cannot be regarded as mechanical phenomena in the ether, but that they do have a very general observable feature in common with mechanical phenomena. This feature which is common to the motion of material bodies and the propagation of light Einstein found in the principle of relativity.

  As we have seen in Section 4 of the last chapter, Newtonian mechanics contained a relativity principle, which stated that the future motion of any object with respect to an inertial system can be predicted from its initial position and velocity with respect to this system, without any knowledge of the motion of the inertial system itself.

  Now, if we disregard the existence of the ether, the null result of Michelson’s experiment means exactly that the result can be predicted from the experimental arrangement in the laboratory without any knowledge of its speed with respect to the celestial bodies. Since similar statements could be made for other optical phenomena, Einstein proposed to extend the relativity principle of Newtonian mechanics to include optical phenomena in the following form: “The future course of optical phenomena may be predicted from the conditions of the experiment relative to the laboratory in which it is carried out, without knowing the velocity of the laboratory in the universe.” Thus, according to Einstein, the connection between mechanical and optical laws is not based on a reduction of optics to mechanics, but rather on the fact that one and the same general law holds for both.

  Besides this “principle of relativity,” Einstein needed a second principle dealing with the interaction of light and motion. He investigated the influence of the motion of the source of light on the velocity of the light emitted by it. From the standpoint of the ether theory, it is self-evident that it makes no difference whether or not the source of light moves; light considered as mechanical vibration in the ether is propagated with a constant velocity with respect to the ether. This velocity depends only on the elasticity and density of the ether.

  Dropping the ether theory of light, Einstein had to reformulate this law into a statement about observable facts. There is one system of reference, F (the fundamental system), with respect to which light is propagated with a specific speed, c. No matter with what velocity the light source moves with respect to the fundamental system (F), the light emitted is propagated with the same specific velocity (c) relative to F. This statement is usually called the “principal of the constancy of the speed of light.”

  The constancy of the speed of light has been confirmed empirically from the observation in double stars. They are stars of approximately equal masses, which are close together and revolve about each other, and are well known to astronomers. If the velocity of light depended on the velocity of the source, then as the stars revolve, the time taken for light to reach the earth from the member of the pair that is approaching the earth will be shorter than the corresponding time of the light from the receding member. Analysis of the two beams of light has shown that there is no observable effect from the velocity of the source.

  4. Consequences of Einstein’s Two Hypotheses

  It was a characteristic feature of Einstein’s mode of work to deduce from his fundamental principles all the logical consequences to the limit. He showed that from these hypotheses, which appeared quite harmless and plausible, a rigorous deduction led to results that seemed very novel and in part even “incredible.” From these results he went on to others, which not only seemed incredible but were even pronounced “paradoxical,” “absurd,” and “incompatible with sound logic and psychology.”

  There are at present thousands of papers in which attempts are made to explain Einstein’s theory to the lay public. It is not the purpose of this book to go into all the details of his theories, but to give a description of Einstein’s personality and his relation to his environment. It is necessary, however, to go into his scientific work to a certain extent in order to give the reader some idea of the manner in which he attacked scientific problems in comparison with that of other scientists. In particular we should try to understand how it happened that his theories not only were of interest to phys
icists, but also stimulated and excited philosophers, thus indirectly stirring up a public that had only slight interest in scientific questions but that participated in the general intellectual life of our period.

  From the two basic assumptions Einstein was able to conclude not only that the mechanistic theory of light was erroneous, but that even the Newtonian mechanics of material objects could not be generally valid. This result can be fairly easily understood if we trace it back to the way Einstein speculated on the properties of light as early as at the age of sixteen.

  While still a student, Einstein had pictured to himself the remarkable things that would occur if a body could travel with the speed of light — at the rate of 186,000 miles per second. Let us consider the fundamental system (F) and a laboratory (L) for optical experiments which moves with constant velocity (v) with respect to F. Let there be a source of light (R) at rest in F, from which a beam of light is propagated with velocity c in the same direction as the laboratory (L) is moving. Now, if the velocity (v) of the laboratory (L) is equal to the velocity of light (c) then, according to Newtonian mechanics, the ray of light will be stationary with respect to the laboratory. No vibration is registered in L. Since light does not move with respect to L, there are no rays in L, and the usual experiments of reflection and refraction cannot be performed (fig. 1).

  It is, of course, imaginable that in such a rapidly moving system (L) there would no longer be any optical phenomena in the ordinary sense. This occurrence, however, would be inconsistent with Einstein’s principle of relativity in optics. For according to this principle, all optical experiments should give the same result whatever the speed (v) of the laboratory may be.