Einstein (21 page)

In the above consideration the cart was initially at rest in the laboratory, but this is not necessary, and in fact it would be even simpler to have it move initially in a straight line with constant velocity in
L
. Then when the recoil occurs, the cart will in general be deflected from its straight path and move in a curve. From the observation on the shape of this curve we can determine the acceleration of the laboratory.

Furthermore, the acceleration of the laboratory need not be restricted to increase or decrease in its speed. The laboratory may rotate about a certain axis. Such a case is familiar to everyone in the form of a merry-go-round or a railroad car rounding a curve. Just as a recoil in the opposite direction to the acceleration of
L
occurs in the former case, so in the latter case an impulse directed away from the axis of rotation appears in
L
. This acceleration is known to physicists as “centrifugal acceleration,” and it is entirely analogous to the recoil that occurs when a vehicle begins to move or stop.

In elementary mechanics this situation should be stated as follows: The motion of a body relative to an accelerated or a rotated laboratory cannot be calculated merely from the effect of the gravitation or electric forces acting on it. Accelerations due to recoil and centrifugal forces also occur and must be taken into account. It is often said that these accelerations are due to the appearance of “inertial forces” under such circumstances. They
are so called because they arise from the inertia of masses relative to an inertial system.

With Einstein’s generalization of the Newtonian principle of relativity to include optical phenomena, it should be possible to use light rays instead of a material object (such as a cart) to find out the acceleration of a laboratory. If a beam of light is arranged so that the rays are parallel to the floor of the laboratory while it is not accelerated, then when it is accelerated the rays will no longer be in a straight line parallel to the floor, but will be deflected. Observations on the magnitude of this deflection will enable us to calculate the acceleration of the laboratory.

Thus we see that according to nineteenth-century mechanics and Einstein’s theory of light and motion, advanced in 1905, the acceleration of a laboratory
L
with respect to an inertial system
F
has measurable influence on physical occurrences in
L
, even though it is not possible to state under what observable conditions a system
F
is an inertial system. But then the part played by the inertial system is none other than that of Newton’s “absolute space.”

It was Einstein’s aim to eliminate this “absolute space” from physics. This did not seem to be an easy task, in view of the fact that such clearly perceptible phenomena as recoil and centrifugal force in railroad cars could not be explained except by the effect of absolute space. Einstein’s theory of relativity of 1905 was restricted to motions in a straight line with constant speed and had done nothing in this direction. A new idea leading to even more profound changes had to be introduced into physics. As so often happens, the difficulty was solved by recognizing that it is related to another previously unsolved problem. When one observes the motion of a cart or the deflection of a light ray in a laboratory, the accelerations actually seen may be due to another cause than to the acceleration of the laboratory itself. They may be due to real forces that act on the cart or light ray and, in accordance with Newton’s law of force, impart acceleration. How are we to distinguish the effects that arise from this entirely different cause? For forces delivered directly by human beings or some mechanical device, the distinction can be made in this way: Consider two carts of unequal masses instead of one.
If the same force acts on the two, since Newton’s law of force states that the change in momentum — that is, the change in the product of the mass and the velocity — is equal to the applied force; the lighter cart will experience a bigger acceleration than the heavier one. On the other hand, if the accelerations are due to inertial forces, they will both be the same. Thus there is this difference: Accelerations due to actual forces (like push or pull) depend on the mass of the object moved; while accelerations due to recoil and centrifugal forces are independent of the mass.

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.

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 deep 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.