Einstein (10 page)

As the first of these critics, we may mention Gustav Kirchhoff, the discoverer of spectral analysis. In 1876 he stated that the task of mechanics was “to describe completely and as simply as possible motions occurring in nature.” This meant that Newtonian mechanics is itself only a convenient scheme for a simple presentation of the phenomena of motion that we observe in daily experience. It does not give us an “understanding” of these occurrences in any other philosophical sense. By thus contravening the general opinion that Newton’s principles of mechanics are self-evident to the human mind, he created something of a sensation among natural scientists and philosophers.

Furthermore, with Kirchhoff’s conception that mechanics is only a description of the phenomena of motion, the mechanical explanations of the phenomena in optics, electricity, heat, etc. — the aim of mechanistic physics — became simply descriptions of these results in terms of a pattern that had been found to be most suitable for mechanics. Why should one describe by this roundabout method of using mechanics instead of trying to find directly the most suitable scheme for the description of various phenomena? Newtonian mechanics was thus deprived of its special philosophical status.

In 1888 Heinrich Hertz discovered the electromagnetic waves,
which form the basis of our modern wireless telegraphy and radio, and he then set out to explain these phenomena in terms of a physical theory. He took as his starting-point Maxwell’s theory of electromagnetic fields. James Clerk Maxwell had derived his fundamental equation from mechanistic physics by assuming that electromagnetic phenomena are actually mechanical oscillations in the ether. Hertz noticed that in doing this Maxwell had been compelled to invent mechanisms that were very difficult to calculate, and found it was simpler to represent electromagnetic phenomena directly by means of Maxwell’s equation between electric and magnetic fields and charges. Since it was also evident to him, however, that these relations could not be derived directly from experience, he was led to a consideration of the logical character of these equations. In 1889 he made a remark that can be regarded as the program for the new approach to physics, a conception that was eventually to replace the mechanistic view. Hertz said:

“But in no way can a direct proof of Maxwell’s equations be deduced from experience. It appears most logical, therefore, to regard them independently of the way in which they had been arrived at, and consider them as hypothetical assumptions and let their plausibility depend upon the very large number of natural laws which they embrace. If we take up this point of view we can dispense with a number of auxiliary ideas which render the understanding of Maxwell’s theory more difficult.”

Thus Hertz consciously abandoned that which during both the organismic and the mechanistic period was described as the “philosophical” foundation of physics. He maintained that it was sufficient to have a knowledge of laws from which phenomena could be calculated and predicted without raising any question of whether these laws were intrinsically evident to the human mind.

The criticisms of the mechanistic philosophy by physicists such as Kirchhoff and Hertz were only occasional and aphoristic. There were others, however, whose criticisms were
based on a very precise conception of nature and of the task of science. The French philosopher Auguste Comte advanced the sociological theory that the “metaphysical” stage in the development of a science is already succeeded by a “positivistic” one. This means that the demand for the use of a specific analogy such as the organismic and mechanistic views is abandoned and after that a theory is judged only as to whether it presents “positive” experience in a simple, logically unobjectionable form.

This approach was most widely and profoundly developed by the Austrian physicist Ernst Mach, who became one of Einstein’s immediate forerunners. Mach carried out a thorough historical, and logical analysis of Newtonian mechanics and showed that it contains no principle that is in any way self-evident to the human mind. All that Newton did was to organize his observations of motion under several simple principles from which movements in individual cases can be predicted. But all these predictions are correct only so long as the experiences upon which Newton based his principles are true.

Mach emphasized, in particular, the demand for simplicity and
economy of thought
in a physical theory: the greatest possible number of observable facts should be organized under the fewest possible principles. Mach compared this requirement to the demand for economy in practical life and spoke of the “economic” nature of scientific theories. Thus Mach, instead of demanding the use of a specified analogy, insisted that science be “economical.”

Furthermore, not only did Mach criticize the attempts of philosophers to make a philosophical system out of Newton’s mechanics, but he also criticized the remains of medieval physics that it still retained. He pointed out that Newton’s theory contained such expressions as “absolute space” and “absolute time,” which cannot be defined in terms of observable quantities or processes. In order to eliminate such expressions from the fundamental laws of mechanics, Mach raised the demand which is now frequently described as the
positivistic criterion
of science: namely, that only those propositions should be employed from which statements regarding observable phenomena can be deduced.

This demand is very aptly elucidated by his criticism of Newton’s law of inertia. If we wish to test this law experimentally, we can never formulate a question such as this: Does a body tend to maintain the direction of its initial velocity relative to absolute space? The question is meaningless since absolute space is
unobservable. If we perform, say, Foucault’s pendulum experiment, which gives an experimental proof of the rotation of the earth, we observe actually that the pendulum maintains its plane of oscillation relative, not to absolute space, but rather to the fixed stars in the sky.

Consequently, according to Mach, all mention of absolute space should be removed from the law of inertia, and it would then be expressed as follows: Every body maintains its velocity, both in magnitude and in direction, relative to the fixed stars as long as no forces act upon it. This means that the fixed stars exert an observable influence on every moving body, an effect that is in addition to and independent of the law of gravitation. For the motion of terrestrial objects this latter influence is hardly observable in practice, since the force of gravity decreases with the square of the distance between the attracting bodies, but the laws of inertia will determine all terrestrial motion if the framework of the fixed stars is declared as an inertial system.

In consequence of the criticisms of Mach and others, it had become clear that the laws of Newtonian mechanics and the understanding of all physical phenomena in terms of it are not demanded by human reason. However, Mach’s assertion that the general laws of physics are only simple economical summaries of observed facts was not satisfactory to many scientists. Particularly for physicists who thought along mathematical lines and had a greater formal imagination, the assertion, for example, that Newton’s law of gravitation is only a simple summary of observation on the positions of the planets did not seem adequate. Between the actual observation of the position of the planets by a telescope and the statement that the gravitational force between two bodies is inversely proportional to the square of the distance there seemed to be a wide gap.

Criticism of nineteenth-century physics in this direction was carried on chiefly by the French mathematician Henri Poincaré. His writings on the logical character of the general laws of nature probably exerted more influence on mathematicians and physicists toward the end of the nineteenth century than any other similar writings. He paved the way for a new, logically
satisfying conception of nature, and his ideas also played an outstanding part in the reception and discussion of Einstein’s theories.

Poincaré’s view is often described as “conventionalism.” According to him, the general propositions of science, such as the theorem about the sum of the angles of a triangle, the law of inertia in mechanics, the law of conservation of energy, and so on, are not statements about reality, but arbitrary stipulations about how words, such as “straight lines,” “force,” “energy,” are to be employed in the propositions of geometry, mechanics, and physics. Consequently one can never say whether one of those propositions is true or false; they are free creations of the human mind and one can only question whether these stipulations or conventions have been expedient or not.

This conception may be elucidated by means of two examples. Let us first consider the geometrical theorem referred to above: namely, that the sum of the angles of a triangle is equal to two right angles. According to nineteenth-century tradition this is an unshakable proposition, which is a product of human reasoning and at the same time a statement concerning what is actually observed in nature. On the one hand, we can derive this proposition from the axioms of geometry, which are “directly evident to the mind”; on the other hand, by measuring the angle of an actual material triangle, we can corroborate this relationship. Poincaré, however, says: if an actual triangle is formed from, say, three iron rods, and the measurement shows that the sum of the angles is
not
exactly equal to two right angles, one of two different conclusions can be drawn: either that the geometrical theorem is not valid, or that the rods forming the triangle are not straight lines. We have the two alternatives, and we can never decide by experiments the validity of geometrical theorems. Consequently we can say that the propositions of geometry are arbitrary stipulations or definitions and not statements about empirical facts. They establish under what circumstances we wish to call a rod a “straight line.” Thus geometrical theorems are not statements about the nature of space, as it is often expressed, but rather definitions of such words as “straight lines.”

According to Poincaré, the laws of mechanics are of somewhat similar character to the propositions of geometry. Let us, therefore, consider the law of inertia as the second example. The possibility of verification of the law rests on our ability to determine whether or not a body moves with uniform velocity in a straight line. As long as we cannot do this, the law of inertia can only
be characterized in some such statement as this: “When a body moves without being influenced by forces, we call this state a uniform motion along a straight line.” It is simply a definition of the expression “uniform motion in a straight line,” or, according to our discussions in sections 3 and 4, a definition of the term “inertial system.”

Thus the general principles, such as the theorem about the sum of the angles of a triangle or the law of inertia, do not describe observable phenomena, but are rather definitions of expressions such as “straight line” or “uniform motion along a straight line.” One has to add definitions by which one recognizes whether a given rod is straight or the motion of a ball is uniform and along a straight line and which have been named “operational definitions” by P. W. Bridgman. These, together with the physical laws (e.g., the law of inertia), constitute a a system of propositions that can be verified by experience.

One of the chief consequences of this conception is that it makes no sense in science to inquire into the philosophical significance or the “nature” of such physical expressions as “force,” “matter,” “electric charge,” “duration of time,” etc. The use of such concepts is always justified if statements permitting experimental verification can be derived from the propositions in which these expressions occur. Apart from this they have no meaning. Because Newtonian mechanics was able to describe very complex phenomena such as the motion of the planets in simple statements with the aid of the words “force” and “mass,” these terms have scientific meaning. There is no need to puzzle one’s brain over whether “force” can be explained from a “mechanistic” standpoint or “matter” from an “organismic” one. “Force” and “matter” are constructions of the human mind.

The idea of Mach that the general laws of science are simple summaries of experimental facts, and the idea of Poincaré that they are free creations of the human mind, appear to be diametrically opposed to each other; but when we consider the intellectual currents of the last quarter of the nineteenth century, we can see that they were only two wings of the same intellectual movement, generally known as the
positivistic movement
. It was directed chiefly against the metaphysical foundations
of science. The proponents of this view asserted that the validity of the general principles of science cannot be proved by showing that they are in agreement with some eternal philosophical truths, and they set out to investigate how the validity can be judged within science itself. They found that two criteria are possible, an empirical and a logical. In the former the observable facts that follow from the general principles must have experimental confirmation, and in the latter the principles and operational definitions must form a practical and consistent system. The emphasis put on the empirical or the logical criterion determined one’s position in one or the other wing of the movement. Mach was on the extreme empirical wing, while Poincaré was on the extreme logical side. There was therefore no conflict between them; it was only that two different aspects of the same scientific method were being emphasized.

The positivistic movement exerted a great influence in central and western Europe during the last quarter of the nineteenth century. The central European positivism, chiefly centered in the Austrian Ernst Mach, was to be found in the universities of Vienna and Prague. It had but little influence and few followers in the universities of the German Reich. At this time Germany was completely under the influence of various versions of Kantian philosophy, whose status was almost that of a state religion. Since German was also the chief language of science in Austria, Central European positivism developed largely as the critic and rival of Kantian philosophy. For this reason it was more militant than French positivism, led by Poincaré.