This assignment is the first and last chapters of a book written (in 1920) not long after Einstein published his general theory of relativity (in 1915) and just after it had received one of its major tests in observations of stars near the sun during an eclipse (in 1919). The whole book is available on line as a PDF file; the link above should lead you to open or download it. While the chapters that we will be discussing address philosophical issues, much of the book is devoted to an introductory presentation of Einstein’s theory. An exception is ch. VII (pp. 101-111), which provides an account of the test Eddington was involved with; it is relatively independent of the presentation of the theory, so if you are curious, you could read it without reading the earlier chapters.
Prologue (pp. 1-14—assignment for Mon. 11/7)
The prologue is a dialogue between two physicists, a relativist and a classical physicist, with a mathematician occasionally joining in. The main topic is the chief philosophical issue raised by general relativity, the nature of space, and the chief issue raised by special relativity, the relation of space and time.
• Although the first question is raised by the later and more difficult theory, it is probably easier conceptually and it is discussed first (pp. 1-9). The heart of the relativist’s argument is a shift from the Newtonian conception of space outlined on p. 6 to a conception of space as a physical quantity that is tied to measurement procedures.
• This prepares the way for the discussion of the second issue (pp. 9-14), because it is considerations of measurement that are used to question the absoluteness of simultaneity and thus the absolute independence of spatial and temporal separation.
Chapter XII (pp. 165-182—assignment for Wed. 11/9)
After describing the content of general relativity, Eddington returns in this chapter to issues raised in the prologue and offers his view of the significance of the theory of relativity and of mathematical physics generally. His discussion can be divided into four parts, an initial statement of his philosophical position (pp. 165-170), which will be our main focus, a summary (pp. 170-180) of his account of the physics, and some more speculative final words (pp. 180-182) that look forward to the development of quantum theory (whose outlines were set in place about five years after this book was published).
• Eddington uses two key ideas to present his view of mathematical physics. The first is the notion of “synthesis” he discusses on pp. 166-168, and the second is the analogy he presents and applies on pp. 168-170. (The principles Eddington refers to on p. 165 are the fundamental assumptions of special and general relativity, respectively. You can find them stated on pp. 18 and 68.)
• The chief philosophical content of the second part is Eddington’s discussion of the nature of matter, which begins on p. 173.
Eddington displays some of the technical notation of general relativity in the course of his summary of it in this part of the chapter. Don’t suppose that he expects you to understand this notation. He doesn't fully explain it in the main text of the book but instead tries only to give his reader a feel for its significance, and the notes below are intended only to fill in a little of what he might have expected a reader of the earlier chapters to see in the notation after reading them.
• The interval s is the space-time distance between point-events, and the formula
is a generalization of the formula ds2 = dx12 + dx22 for the square of the infinitesimal distance in a plane with Cartesian coordinates. (You can find an explanation of the reasons for the generalization, along with simple examples, on pp. 70f.)
• The “ten g’s” mentioned on p. 172 are the coefficients gi j in the formula displayed above. (You can see the full formula on p. 74.)
• All that’s really important for what Eddington says here about the quantities Bρμνσ and Gμν is that they are derived from the coefficients gi j, so they are aspects of the geometry. (Their actual definitions appear only in a note on p. 185.)
• The second equation on p. 173, which reappears in a different form on p. 180, is the Einstein field equation, which is the central equation of general relativity and has the significance for it that Newton’s laws of motion together with his law of gravitation had in classical pre-relativistic physics.
• The key thing to think about in the last part of ch. XII is the relation between the picture sketched in first full paragraph on p. 180, which summarizes his discussion of matter, and the idea of a “law of atomicity” that is explored on pp. 181-182.