Matthias Schemmel

An astronomical road to general relativity : the continuity between classical and relativistic cosmology in the work of Karl Schwarzschild

In this article it is argued that a continuity exists between Karl Schwarzschilds work on foundational problems on the borderline of physics and astronomy and his later occupation with general relativity. Based on an analysis of Schwarzschilds published works as well as formerly neglected unpublished notes it is shown that, long before the rise of general relativity, Schwarzschild was concerned with problems that later became associated with that theory. In particular he considered non-Euclidean cosmologies, linked the phenomena of gravitation and inertia to the problem of the precession of Mercurys perihelion, and entertained the possibility of inertial frames rotating with respect to one another. It is argued that these earlier considerations, which reflect his interdisciplinary outlook on the foundations of the exact sciences, enabled Schwarzschild to recognize the significance of general relativity for astronomy, astrophysics, and cosmology earlier than most of his collegues and shaped his contributions to this theory.

The Challenging Images of Artillery

Princely families of old were in the habit of engaging historians who were charged with producing tailor-made histories, in which the achievements of these families received due attention. For a long time this, remarkably, was exactly what natural scientists also expected from their historians. As a matter of fact, from the point of view of developed science, the knowledge of a discipline is simply represented by the natural laws that define its object. It was accordingly a matter of course for its historians to concentrate solely on the question of who had discovered which of these laws when and in what manner. In this sense, the history of science is a biographically oriented, heroic history of the great discoverers and their discoveries (fig. 1).

Theories of Gravitation in the Twilight of Classical Physics

More than is the case for any other theory of modern physics, general relativity is usually seen as the work of one man, Albert Einstein. In taking this point of view, however, one tends to overlook the fact that gravitation has been the subject of controversial discussion since the time of Newton. That Newton’s theory of gravitation assumes action at a distance, i.e., action without an intervening mechanism or medium, was perceived from its earliest days as being problematical. Around the turn of the last century, in the twilight of classical physics, the problems of Newtonian gravitation theory had become more acute, also due to the rise of field theory suggesting alternative perspectives. Consequently, there was a proliferation of alternative theories of gravitation which were quickly forgotten after the triumph of general relativity. Yet in order to understand this triumph, it is necessary to compare general relativity to its contemporary competitors. General relativity owes much to this competition. The proliferation of theories of gravitation provides an exemplary case for studying the role of alternative pathways in the history of science. Thus, from this perspective, the emergence of general relativity constitutes an ideal topic for addressing longstanding questions in the philosophy of science on the basis of detailed historical evidence.

Einstein and the changing worldviews of physics

Mine is one of several talks at this meeting that consider the revival of relativity and its integration into the mainstream of physics beginning in the 1950s. Ted Newman has described the physics problems that created confusion during the slow period 1930–1950, and how eventually a new generation of young physicists pulled the theory out of its mire. Silvio Bergia has emphasized the changes of thinking that were required, and the importance of the physical insight and especially the geometrical perspective that John Wheeler, among others, brought to the subject. I want to focus on the gulf that opened up during the slow period between relativists and the rest of what I will call mainstream theoretical physics. This gulf is important not just because of the negative influence it exerted on the development of relativity. It also has much to teach us about what physicists expect from a theory of physics, and especially about the role of heuristic concepts in physicists’ communication with one another.

The Continuity Between Classical and Relativistic Cosmology in the Work of Karl Schwarzschild

Only a few weeks after Einstein had presented the successful calculation of Mercury’s perihelion advance on the basis of his new theory of general relativity in late 1915, the German astronomer Karl Schwarzschild (1873–1916) published the first non-trivial exact solution of Einstein’s field equations (Schwarzschild 1916a). The solution describes the spherically symmetric gravitational field in a vacuum and holds a central place in gravitation theory, comparable to that of the Coulomb potential in electrodynamics. It was not only an important point of departure for further theoretical research but also, up to recent times, the basis for all empirical tests of general relativity that proved not only the principle of equivalence but also the field equations themselves. Schwarzschild made a further substantial contribution to the theory when he found another exact solution describing the interior gravitational field of a sphere of fluid with uniform energy density (Schwarzschild 1916b). In this communication an important quantity makes its first appearance. It is the quantity that is later known as the Schwarzschild radius , which plays an important role in the theory of black holes many decades later. 1 But even long before the final theory of general relativity was established, Schwarzschild had already occupied himself with possible implications of its predecessors for astronomy; in 1913 he carried out observations of the solar spectrum in order to clarify if the gravitational redshift predicted by Einstein on the basis of the equivalence principle was detectable (Schwarzschild 1914). In view of the fundamental role played by general relativity in astronomy, astrophysics, and cosmology today, it appears quite natural that an astronomer would engage in the study of this theory. Astronomical objects of all scales ranging from supermassive stars via galaxy nuclei and quasars to the universe as a whole are described on its basis. However, at the time when Schwarzschild made his contributions, the situation was quite different. None of the spectacular objects nowadays so successfully described by general relativity were in the focus of research, most of

Mental Models as Cognitive Instruments in the Transformation of Knowledge

The chapter is concerned with the epistemic structures of mechanical knowledge in its historical transformations. It describes these structures using the concept of mental models as cognitive instruments, which function as mediators between the realm of practice and experience on the one hand, and conceptual systems on the other. With the help of the concept of mental model, the chapter discusses how mechanical knowledge has emerged from experience in practical contexts and how it was transformed into theoretical and mathematically formalized knowledge systems. Focusing on one particular mental model, which describes the cognitive structure conceptualizing motion as being caused by forces, the chapter then follows its transformations in the long-term history of mechanical thinking. This so-called “motion-implies-force” model is rooted in intuitive, non-written mechanical knowledge. Over the course of history, the model was recruited, complemented, and transformed in the context of the use of mechanical tools and articulated in the work of practitioners dealing with machines, arms, ships, buildings, fortifications, and the like. Eventually, under specific cultural circumstances, this and other mental models were elaborated and integrated into mathematically formalized systems that were used, for example, in the explanation of terrestrial and celestial motions in early modern natural philosophy and the mathematical disciplines of European universities.

Creating Room for Historical Rationality

Ludwik Fleck, a Polish bacteriologist, physician, and historian of science, published Entstehung und Entwicklung einer wissenschaftlichen Tatsache (translated in 1979 as Genesis and Development of a Scientific Fact) in 1935. In providing astonishingly timely insights into the collective nature of human and, in particular, scientific knowledge, the book is still as well placed as ever to offer guidance and direction to our ongoing thinking about these issues. This is what makes it worthwhile to invite the reader to undertake a renewed, critical reception of the book. Ludwik Fleck was born in a Jewish-Polish family on 11 July 1896 in Lemberg/Lwów/Lvív. His father ran a medium-scale painting business. He served in the military during World War I and concluded his medical studies with a nonspecialist medical Ph.D. thesis. With a specific interest in microbiology, he served the typhoid specialist Rudolf Weigl as an assistant. From 1923 onward he worked in a private bacteriological laboratory that he had established himself and also in several hospital departments that specialized in the diagnosis of syphilis, in tuberculosis, and, most of all, in serological problems of a general nature. When World War II broke out Lwów became part of the Soviet Union. Fleck was appointed teacher and departmental director for microbiology at the Ukrainian Medical Institute and director of the Lwów City Institute for Hygiene. In

Natural Conditions of Spatial Cognition

The similar biological constitution of all humans and the fundamental similarities in their physical environments make it plausible to assume that there are structures of spatial cognition that do not vary between different cultures or over history, but constitute the foundation for all cultural manifestations of spatial knowledge. In order to understand the dependence of spatial thinking on culture it is important first to identify these structures. The chapter discusses the sensorimotor schemata that are formed in humans regardless of society and historical age in similar ways as with nonhuman primates. The examples presented are (1) the schema of permanent objects, which allows for successful handling of objects on a mesocosmic scale, and (2) the landmark model of larger-scale space underlying cognitive mapping skills and allowing for successful navigation through various types of environment.

The Decline of an Autonomous Concept of Space

The renewed revolution of the concept of space in twentieth-century physics can be understood as a process of reflective knowledge integration, an integration of disciplinarily highly structured knowledge. The chapter discusses the loss of autonomy of the concept of space that resulted from the demise of the Newtonian concept. The examples presented are (1) the spacetime of special relativity, which emerged from an integration of knowledge from mechanics and electrodynamics and resulted in a close entanglement of the concepts of space and time; and (2) the spacetime of general relativity, which emerged from the additional integration of knowledge on gravitation and resulted in a close entanglement of the concepts of space and matter (or energy).

Culturally Shared Mental Models of Space

The essential difference of human as compared to animal cognition is to be found in the social abilities of human beings. Humans possess unique abilities to share knowledge, a fact that constitutes the basis for the cultural evolution of human spatial cognition, leading to elaborate cultural systems for environmental orientation. The chapter discusses mental models of large scale space that humans share by means of communicative actions, gestures, spoken language, and other kinds of material knowledge representation. Two well-studied examples from recent non-literate societies are presented: (1) the network of spatial designations of the Eipo of West New Guinea, and (2) the absolute-directional system of the expert navigators of the Caroline Islands of Micronesia. It is argued that the cultural practices build upon the elementary structures of spatial knowledge described in the previous chapter, which are, at the same time, modified and partly overridden by them.