The Formative Years of Relativity

The Formative Years of Relativity: The History and Meaning of Einstein's Princeton Lectures

Copyright Date: 2017
DOI: 10.2307/j.ctt1vxm7ts
Pages: 432
  • Cite this Item
  • Book Info
    The Formative Years of Relativity
    Book Description:

    First published in 1922 and based on lectures delivered in May 1921, Albert Einstein'sThe Meaning of Relativityoffered an overview and explanation of the then new and controversial theory of relativity. The work would go on to become a monumental classic, printed in numerous editions and translations worldwide. Now,The Formative Years of Relativityintroduces Einstein's masterpiece to new audiences. This beautiful volume contains Einstein's insightful text, accompanied by important historical materials and commentary looking at the origins and development of general relativity. Hanoch Gutfreund and Jürgen Renn provide fresh, original perspectives, placing Einstein's achievements into a broader context for all readers.

    In this book, Gutfreund and Renn tell the rich story behind the early reception, spread, and consequences of Einstein's ideas during the formative years of general relativity in the late 1910s and 1920s. They show that relativity's meaning changed radically throughout the nascent years of its development, and they describe in detail the transformation of Einstein's work from the esoteric pursuit of one individual communicating with a handful of colleagues into the preoccupation of a growing community of physicists, astronomers, mathematicians, and philosophers.

    This handsome edition quotes extensively from Einstein's correspondence and reproduces historical documents such as newspaper articles and letters. Inserts are featured in the main text giving concise explanations of basic concepts, and short biographical notes and photographs of some of Einstein's contemporaries are included. The first-ever English translations of two of Einstein's popular Princeton lectures are featured at the book's end.

    eISBN: 978-1-4008-8868-9
    Subjects: Physics, General Science, History of Science & Technology

Table of Contents

  1. Front Matter
    (pp. i-vi)
    DOI: 10.2307/j.ctt1vxm7ts.1
  2. Table of Contents
    (pp. vii-viii)
    DOI: 10.2307/j.ctt1vxm7ts.2
    (pp. ix-xii)
    Diana Kormos Buchwald
    DOI: 10.2307/j.ctt1vxm7ts.3

    Almost a century has elapsed since Albert Einstein visited the United States for the first time in the spring of 1921, six years after having published a remarkable series of papers that signaled the completion of his general theory of relativity, the most significant development in theoretical physics since Isaac Newton’sPrincipiamore than two centuries earlier.

    Einstein extemporaneously delivered five lectures at Princeton University during the first week of May 1921;1 six hundred invitations were sent out for these Stafford Little Lectures.2 A large number of guests, among them close to three hundred visiting scientists, came to town, and...

    (pp. xiii-xiv)
    DOI: 10.2307/j.ctt1vxm7ts.4
  5. Part I. Preliminaries

      (pp. 3-10)
      DOI: 10.2307/j.ctt1vxm7ts.5

      The Meaning of Relativity, also known asFour Lectures on Relativity, is Einstein’s definitive exposition of his special and general theories of relativity. It was written in the early 1920s, a few years after he had elaborated his general theory of relativity. Neither before nor afterward did he offer a similarly comprehensive exposition that included not only the theory’s technical apparatus but also detailed explanations making his achievement accessible to readers with a certain mathematical knowledge but no prior familiarity with relativity theory. In 1916, he published a review paper that provided the first condensed overview of the theory but...

      (pp. 11-16)
      DOI: 10.2307/j.ctt1vxm7ts.6

      Einstein became famous after the confirmation of his prediction of the bendingof light from distant stars by the gravitational field of the sun. He subsequently received several invitations to lecture at American universities. In October 1920, Luther Eisenhart, a professor of mathematics at Princeton University, inquired on behalf of John Hibben, the president of the university and a professor of logic, if Einstein would agree to accept a special lectureship in the winter.1 Einstein responded directly to Hibben, accepting the invitation with gratitude and stating that he would be able come to Princeton only in September 1921.2 Following the...

      (pp. 17-22)
      DOI: 10.2307/j.ctt1vxm7ts.7

      It has already been mentioned that this book is not a systematic page-by-page, or even chapter-by-chapter, commentary on Einstein’s text. Thus, it may be useful to provide at the outset a brief summary ofThe Meaning of Relativityand of the appendixes added to later editions. This chapter is intended mainly to show the flow of ideas in the order of their presentation and to emphasize the new ways of their formulation, as influenced by Einstein’s interaction with his colleagues and by his own rethinking of some of the basic concepts. Many of the points and topics mentioned in this...

  6. Part II. The Emerging World of General Relativity

      (pp. 25-33)
      DOI: 10.2307/j.ctt1vxm7ts.8

      The first chapter ofThe Meaning of Relativitybegins with epistemologicalremarks about space and time. Einstein developed his views on geometry in close relation with his formulation of relativity theory. Indeed, the first sentence of the book reads: “The theory of relativity is intimately connected with the theory of space and time.” It is common knowledge that the two theories of relativity have fundamentally changed our notion of space and time. In January 1921, Einstein delivered a lecture to the Prussian Academy of Sciences entitled “Geometry and Experience,” which has become the canonical text reflecting the main points of...

      (pp. 34-45)
      DOI: 10.2307/j.ctt1vxm7ts.9

      What did Einstein want to achieve when he embarked on his intellectualjourney toward a theory of general relativity, and what did he actually achieve? He clearly wanted to generalize the principle of relativity to apply to any type of motion. In his popular account of the special and general theories of relativity, Einstein stated:

      Since the introduction of the special principle of relativity has been justified, every intellect which strives after generalization must feel the temptation to venture the step towards the general principle of relativity.1

      In the seminal review article “The Foundation of the General Theory of Relativity,”...

      (pp. 46-51)
      DOI: 10.2307/j.ctt1vxm7ts.10

      When Einstein published the final form of the field equations on 25 November 1915, only an approximate solution was known. He had first developed an approximation scheme in the framework of theEntwurftheory, then adapted it to the final version and used it to successfully calculate the perihelion motion of Mercury. Given the complicated nonlinear character of the field equations, he did not expect that exact solutions could easily be found. He was all the more surprised when the astronomer Karl Schwarzschild presented him with just such an exact solution. On 9 January 1916, Einstein wrote to him:


      (pp. 52-68)
      DOI: 10.2307/j.ctt1vxm7ts.11

      After completing general relativity, Einstein shared his joy and satisfactionwith friends and colleagues. He was particularly pleased that the theory could, with great accuracy, account for the advance of Mercury’s perihelion as observed in 1859 by the French astronomer Urbain Jean-Joseph Le Verrier (see box below). Einstein wrote to Arnold Sommerfeld:

      The result of the perihelion motion of Mercury gives me great satisfaction. How helpful to us here is astronomy’s pedantic accuracy, which I often used to ridicule secretly!1

      Evidently, Einstein only gradually came to appreciate the merits of astronomy, just as it had taken him some time to...

      (pp. 69-93)
      DOI: 10.2307/j.ctt1vxm7ts.12

      After completing his general theory of relativity, Einstein immediately realizedits relevance to a description of the universe as a whole. Although none of the modern observations existed, the theory had some definitive implications for understanding the structure of the universe. Einstein’s discussion of this subject, his debates with colleagues, and, particularly, his 1917 cosmology paper (see section B below) may be viewed as the genesis of modern cosmology. Until the creation of general relativity, the question of the geometrical properties of space at large and the question of how the structure of the universe is determined by gravity were...

      (pp. 94-105)
      DOI: 10.2307/j.ctt1vxm7ts.13

      With the completion of Einstein’s formulation of the theory of general relativity, the action-at-a-distance interaction between material bodies in Newton’s theory had been replaced by an interaction propagated by the gravitational field. Questions about the nature of this propagation and its velocity already naturally led to a discussion of gravitational waves. Such questions did in fact arise in connection with theEntwurftheory (see chapter 2, p. 42) after Einstein presented it in 1913 in Vienna.1 In the discussion period Max Born asked:

      how fast does the effect of gravitation propagate according to your theory[?] It is not obvious to...

      (pp. 106-121)
      DOI: 10.2307/j.ctt1vxm7ts.14

      Since his student days, Einstein had developed a deep concern for issues of thephilosophy and history of science. He read Mach’s philosophical-historical critique of classical mechanics as well as his book on the principles of thermodynamics. He was also familiar with Eugen Dühring’s history of mechanics and with Ferdinand Rosenberger’s book on Newton. He was fascinated by Arthur Schopenhauer and, as a student at the Polytechnic School in Zurich, had attended a course on Kant. Throughout his life, Kant remained a figure with whom Einstein took issue, as the historians Thomas Ryckmann and Michael Friedman have shown.1 Later, together...

      (pp. 122-139)
      DOI: 10.2307/j.ctt1vxm7ts.15

      With the completion of the general theory of relativity there were twodistinct dynamical field theories on the physical arena, which Einstein attempted to unify.1

      In the nineteenth century, James Maxwell had created the first successful field theory. Maxwell’s equations tell us how the electric and magnetic components of the electromagnetic field change in space and time, how they are generated by electrical charges and currents, and how electromagnetic waves propagate. The motion of charged particles is determined by the field that they produce. The three components of the electric field vector and the magnetic field vector are derived from...

      (pp. 140-154)
      DOI: 10.2307/j.ctt1vxm7ts.16

      In the previous chapters, we discussed various aspects of the process of revision and refinement of the basic ideas underlying the general theory of relativity and the controversial debates about their consequences during the formative period of Einstein’s new theory. This process progressed through articles published in scientific journals and through extensive correspondence between the physicists, mathematicians, astronomers, and philosophers who formed a network of scientists interested in these developments. This process was also accompanied by public and university lectures and by the publication of a series of monographs and textbooks that contributed to the dissemination and acceptance of Einstein’s...

      (pp. 155-158)
      DOI: 10.2307/j.ctt1vxm7ts.17

      The commentaries in this book cover the early years of general relativity, when its epistemic status was uncertain in many respects: from the understanding of its physical implications via the understanding of its mathematical apparatus, to its philosophical interpretation, which constituted a major issue for many contemporary scientists, as it was for Einstein himself. The correspondence about gravitational waves and approximate solutions between Einstein, Karl Schwarzschild, and Willem de Sitter is one example of how unclear and unexplored the connections between the theory and its physical consequences were in those early days.

      And if Einstein’s quest for the interpretation of...

  7. Part III. Einstein’s Book with the Appendixes

      (pp. 161-183)
      DOI: 10.2307/j.ctt1vxm7ts.18

      THE theory of relativity is intimately connected with the theory of space and time. I shall therefore begin with a brief investigation of the origin of our ideas of space and time, although in doing so I know that I introduce a controversial subject. The object of all science, whether natural science or psychology, is to co-ordinate our experiences and to bring them into a logical system. How are our customary ideas of space and time related to the character of our experiences?

      The experiences of an individual appear to us arranged in a series of events; in this series...

      (pp. 184-214)
      DOI: 10.2307/j.ctt1vxm7ts.19

      THE previous considerations concerning the configuration of rigid bodies have been founded, irrespective of the assumption as to the validity of the Euclidean geometry, upon the hypothesis that all directions in space, or all configurations of Cartesian systems of co-ordinates, are physically equivalent. We may express this as the “principle of relativity with respect to direction,” and it has been shown how equations (laws of nature) may be found, in accord with this principle, by the aid of the calculus of tensors. We now inquire whether there is a relativity with respect to the state of motion of the space...

      (pp. 215-238)
      DOI: 10.2307/j.ctt1vxm7ts.20

      ALL of the previous considerations have been based upon the assumption that all inertial systems are equivalent for the description of physical phenomena, but that they are preferred, for the formulation of the laws of nature, to spaces of reference in a different state of motion. We can think of no cause for this preference for definite states of motion to all others, according to our previous considerations, either in the perceptible bodies or in the concept of motion; on the contrary, it must be regarded as an independent property of the space-time continuum. The principle of inertia, in particular,...

      (pp. 239-268)
      DOI: 10.2307/j.ctt1vxm7ts.21

      WE are now in possession of the mathematical apparatus which is necessary to formulate the laws of the general theory of relativity. No attempt will be made in this presentation at systematic completeness, but single results and possibilities will be developed progressively from what is known and from the results obtained. Such a presentation is most suited to the present provisional state of our knowledge.

      A material particle upon which no force acts moves, according to the principle of inertia, uniformly in a straight line. In the four-dimensional continuum of the special theory of relativity (with real time co-ordinate) this...

      (pp. 269-292)
      DOI: 10.2307/j.ctt1vxm7ts.22

      SINCE the first edition of this little book some advances have been made in the theory of relativity. Some of these we shall mention here only briefly:

      The first step forward is the conclusive demonstration of the existence of the red shift of the spectral lines by the (negative) gravitational potential of the place of origin (see p. 92). This demonstration was made possible by the discovery of so-called “dwarf stars” whose average density exceeds that of water by a factor of the order 10?. For such a star (e.g. the faint companion of Sirius), whose mass and radius can...

    • 6. Appendix II (PUP 4th edition, 1953): GENERALIZATION OF GRAVITATION THEORY
      (pp. 293-325)
      DOI: 10.2307/j.ctt1vxm7ts.23

      THE content of the general theory of relativity presented above is formally expressed by the equation

      (1)Rik? ?gikR=Tik.

      The left-hand side of this equation depends only on the symmetrical tensor,gik, which represents the metric properties of space as well as the gravitational field. The right-hand side of (1) is a phenomenological description of all the sources of the gravitational field.ikrepresents the energy which generates the gravitational field, but is itself of non-gravitational character, as for example the energy of the electromagnetic field, of the density of ponderable matter etc. To represent this tensor,...

    • 7. Appendix II (PUP 5th edition, 1956): RELATIVISTIC THEORY OF THE NON-SYMMETRIC FIELD
      (pp. 326-360)
      DOI: 10.2307/j.ctt1vxm7ts.24

      BEFORE starting with the subject proper I am first going to discuss the “strength” of systems of field equations in general. This discussion is of intrinsic interest quite apart from the particular theory presented here. For a deeper understanding of our problem, however, it is almost indispensable.

      Given certain field variables and a system of field equations for them, the latter will not in general determine the field completely. There still remain certain free data for a solution of the field equations. The smaller the number of free data consistent with the system of field equations, the “stronger” is the...

  8. Part IV. The Popular Lectures

      (pp. 363-365)
      DOI: 10.2307/j.ctt1vxm7ts.25

      The first two lectures, given in Princeton on 9 and 10 May 1921, under thetitle “Generalities on the Theory of Relativity (Without Using Mathematical Symbols),” were attended by a large, nonprofessional audience that almost filled the lecture hall. The first lecture was dedicated to the special theory of relativity, and the second presented the transition to the general theory and discussed the experimental tests of its validity.

      The lectures were delivered in German and a German stenographer took shorthand notes. The typescript of these notes was not edited and is reproduced, in its rudimentary form, in CPAE, vol. 7,...

      (pp. 366-386)
      DOI: 10.2307/j.ctt1vxm7ts.26

      [9 May 1921]

      Ladies and Gentlemen!

      I will arrange my lectures about relativity in this way: today I present first some general ideas, either without any, or with a minimum of formal mathematical support, and in the later lectures I will expand somewhat more explicitly on the question of what the basic idea of the theory of relativity is. The theory of relativity is so named because this whole theory is concerned with the question of the extent to which any motion is merely relative motion. Namely, the point of it is this. When we generally speak of the motion...

    (pp. 387-408)
    DOI: 10.2307/j.ctt1vxm7ts.27
  10. INDEX
    (pp. 409-416)
    DOI: 10.2307/j.ctt1vxm7ts.28