Einstein (20 page)

On another occasion Kepler and Tycho again discussed the arguments favoring or opposing either the Copernican or the Tychonian system, and this time they paid more attention than before to the observable facts and the logical conclusions that could be drawn upon for such proof. Brod describes the attitudes of the two men as follows:

Tycho “began to despair, finding no sign of decision on either side. Kepler, on the other hand, seemed to drink in a copious draught of pleasure and strength from this very uncertainty. The more obscure and the more difficult the decision, the more did he find himself in the humor for jesting, this man who was ordinarily so dry. When confronted by ‘Nature,’ this riddle of the Sphinx, his whole being expanded, he seized without difficulty upon the object, jovially assailing it upon every side, as it were, and firmly rooted himself in it. His voice even took on an unfamiliar, joyously consequential bass-note when he cried in reply to a caustic remark of Tycho’s: ‘Well, perhaps the laws of nature agree only fortuitously.’ ”

Another discussion develops between Tycho and Kepler over the question whether scientists in espousing a hypothesis must consider the beliefs and opinions of rulers and rich men.

“Tycho raised himself, breathing heavily. ‘Now at least the system of Copernicus remains unproved, and as it runs counter to the Bible and as I may not needlessly affront the Catholic Majesty of my Emperor, I have no reason for espousing it.’

“ ‘That is going too far,’ observed Kepler, still smiling. ‘Catholic or not, the hypothesis alone is being considered here, not the Emperor’s favor.’ …

“Tycho answered hotly, feeling that a fundamental principle of his life was being assailed: ‘But without the favor of princes and of the rich we could construct no expensive apparatus, and truth would remain uninvestigated.… Thus the princes help us and the truth; so it is for us in our turn to respect them and to defer to their pleasure.’

“ ‘It is just this that I contest,’ cried Kepler excitedly; ‘we must defer to truth alone and to no one else.…’

“ ‘Why to no one else? … When I have already put it before you that one can serve the truth only if one serves princes. It is quite true that it is more comfortable and simpler to follow your practice, my dear Kepler. You pay regard to nothing in going your own holy way, turning neither to right nor to left. But does it seem less holy to you to belie oneself for truth’s sake? “Be cunning as serpents and harmless as doves”; so did our Lord Jesus Himself speak to His disciples. You are no serpent, you never belie or constrain yourself. Thus you really serve, not truth, but only yourself; that is to say, your own purity and inviolateness. But I see not only myself, I see also my
relations with those among whom I must live in the determination to serve truth with the aid of adroitness and every shrewd device.… And I think it is a better imitation of Christ to work among men, even though subject to the protection of princely favor, than merely to dream away one’s life in ecstasy and thus to forget all labor and vexations.’ ”

Has Einstein always been a good teacher? Did he like the profession? Very different opinions on these points can be obtained by asking people who have been his students or colleagues.

He had two chief characteristics that made him a good teacher. The first was his desire to be useful and friendly to as many as possible of his fellow beings, especially those in his environment. The second was his artistic sense, which impelled him not only to think out a scientific train of thought clearly and logically, but also to formulate it in a way that gave him, and everyone who listened to him, an æsthetic pleasure. This meant that he liked to communicate his ideas to others.

On the other hand, tending to inhibit these qualities, was the trait that has always been so characteristic of Einstein. I have already mentioned his aversion to entering into very intimate personal relations with other people, a trait that has always left Einstein a lonely person among his students, his colleagues, his friends, and his family. To this was added an absence of ordinary academic vanity. For many professors the reflection of their own personality in so many young people, all of whom repeat what the teacher says, offers a kind of multiplication of their personality. This human characteristic, which may appear as a weakness to some people, is also an asset in the teaching profession. It often leads to a devotion on the part of the pedagogue to his job of teaching that appears selfless and even self-sacrificing. Even though in the last analysis it is a desire for self-expression, the teacher must surrender much of his personality. He must spend a good deal of his own life in serving his students. Einstein did not have this vanity, nor did his personality require multiplication, and consequently he was not ready to sacrifice so much for it. For this reason, too, his relation to his students was likewise ambivalent, but in a very peculiar way.

This way is very obvious from his manner of lecturing. When Einstein had thought through a problem, he always found it necessary to formulate this subject in as many different ways as possible and to present it so that it would be comprehensible to people accustomed to different modes of thought and with different educational preparations. He liked to formulate his ideas for mathematicians, for experimental physicists, for philosophers, and even for people without much scientific training if they were at all inclined to think independently. He even liked to speak about subjects in physics that did not directly concern his discoveries, if he had thought up a method of making these topics comprehensible.

In view of this trait, one might think that Einstein was bound to be a very good lecturer and teacher. Indeed, he frequently was. When he was interested in a subject for scientific, historical, or methodological reasons, he could lecture so that his listeners were enthralled. The charm of his lectures was due to his unusual naturalness, the avoidance of every rhetorical effect and of all exaggeration, formality, and affectation. He tried to reduce every subject to its simplest logical form and then to present this simplest form artistically and psychologically so that it would lose every semblance of pedantry, and to render it plastic by means of appropriate, striking pictures. To these qualities were added a certain sense of humor, a few good-natured jokes that hurt no one, and a certain happy mood mixed with astonishment such as a child feels over its newly received Christmas gifts.

Nevertheless, it was rather irksome for him to give regular lectures. To do so requires that the material for an entire course shall be so well organized and arranged that it can be presented interestingly throughout the year. It means that the lecturer has to interest himself as much in each individual problem as Einstein did in the problems on which all his energy was concentrated. The lecturer must devote himself completely to the material that he is to discuss, and consequently it is very difficult to find time to devote to one’s own research. All creative activity requires a great deal of reflection and contemplation, which a superficial observer would regard as a useless waste of time.

There are teachers, especially in German universities, who have arranged their time so precisely that they are able to work out their lectures to the most minute detail and still find time for their own research. But as a result their time is so occupied that they have no place for the unforeseen, for an idea not directly connected with science or the teaching profession, for reflection,
or for a conversation with an unexpected visitor. They become dry; any creative and imaginative qualities that they may have are utilized in their scientific research or in teaching students. In daily intercourse they often remind one of squeezed-out lemons and are unable to say anything interesting in company. Such scientists are not infrequent and are found even among the outstanding ones, although they are rare among the truly creative men.

Einstein was always the very opposite of this type. He did not like to grind out information for the students, but preferred to give abundantly of what interested and concerned him. For this reason he put the emphasis on his present field of interest. Also he had too much of an artistic temperament to solve the difficulty of giving a course of lectures in a wide field by the simple method of basing them on a single good book. It was also impossible for him to accumulate enough intellectual energy for his lectures to imbue them all with his spirit. As a result his lectures have been somehow uneven. He has not been a brilliant lecture-room professor, capable of maintaining the same level of interest and excellence in his lectures for an entire year. His single lectures before scientific societies, congresses, and wider audiences, however, were always imbued with a high degree of vitality and left a permanent impression on each listener.

In Zurich and Prague Einstein worked on the solution of questions which were raised by his theory of relativity (Bern 1905). According to the Newtonian principle of relativity, the velocity of a laboratory cannot be determined from observations on the motion of objects within it. Einstein had in 1905 generalized this principle to include optical phenomena, so that observations of neither material bodies nor light rays enable one to determine the velocity of one’s laboratory. All this is true, however, only if the motion occurs along a straight line with constant speed. But it is quite consistent with Einstein’s theory as developed so far to say that one can determine from experiments in a laboratory
L
whether it moves with varying velocity relative to an inertial system
F
. It would thus be possible to learn something about the motion of the laboratory as a whole from the experiment carried out in
L
. While the velocity itself could not
be determined, the changes in speed and direction (acceleration) could be found. Einstein regarded this situation as very unsatisfactory. Ernst Mach had made a suggestion for the correction of this situation by assuming that from the observation in
L
one does not determine the acceleration relative to an imaginary inertial system, but relative to the fixed stars. Then the events in
L
would be influenced by actual physical bodies, the fixed stars. Mach’s suggestion, however, remained only a program. It was never developed into a physical theory that would enable one to calculate in detail what observable consequences result from the influence of the fixed stars on the observable events in
L
. It was Einstein’s aim to close this gap.

He took as his point of departure the following question: What does Newtonian physics assert about the possibility of learning from experiments carried out in a moving laboratory
L
whether this room as a whole experiences a change in velocity relative to an inertial system? We have already seen that when the system
L
is an inertial system, the two Newtonian laws of motion, the law of inertia and the law of force, are valid relative to it. On the basis of daily experience we can likewise see quite easily that these laws
no longer
hold true for
L
if it is accelerated relative to an inertial system.

For instance, let
L
be a moving railroad car. If the law of inertia is valid for
L
, it means that when I am standing in the car, I can remain standing for any length of time at the same spot relative to the car without exerting any force. Experience teaches us, however, that this is only true as long as the car moves along a straight line at a constant velocity. When the car stops suddenly, I shall fall down unless I make a special effort to remain erect. The same thing happens when the car increases its velocity suddenly or rounds a curve. As long as the change in velocity persists, I must make an effort to remain upright. When the velocity becomes constant again, I am able to stand without any effort. This shows that the force that I must exert to remain standing permits me to recognize whether my car
L
is or is not an inertial system. Moreover, even this crudest kind of experience shows me that the more sudden the stoppage of the car, the greater the required force. More generally speaking, the greater the acceleration, the greater the required force.

From these crude reflections, we can easily develop a method of determining the acceleration (
a
) of a laboratory
L
by observing the motion of objects relative to the walls of
L
. Let us consider, for instance, a little cart lying on the floor of
L
and
free to move in any direction. As long as the laboratory moves in a straight line with uniform velocity, the cart will remain at rest in L, but if the laboratory suddenly changes its velocity, the cart will move with respect to the walls of
L
as if it had received a jolt. The acceleration (
aₒ
) of the cart due to this recoil as seen in
L
will be such that its magnitude equals that of
a
but will be in the opposite direction. For the cart, as described with respect to the inertial system
F
(in which
L
has the acceleration
a
), is a free body not acted on by any force; and hence by the law of inertia its motion is in a straight line with constant velocity. On the other hand, the acceleration of the cart as described relative to
F
is also equal to the sum of the acceleration (
aₒ
) of the cart with respect to
L
, and
a
of the laboratory
L
itself with respect to
F
. Since the resulting acceleration must be zero, we have
aₒ
+
a
= 0. And from this follows
aₒ
= —
a
, as stated above. Thus the observation of the acceleration (
aₒ
) of the cart in
L
produced by the motion of
L
enables us to calculate the acceleration (
a
) of the laboratory
L
with respect to the inertial system
F
.