Course Materials

Seminar on Spacetime, 2003 Fall

by Prof. Soshichi Uchii

We will use the following text (should be available at Renais by October):

Julian Barbour, The End of Time, Phoenix, 2000. [This presents an updated Machian point of view, together with a readable exposition of basic physics related with space and time. Other materials, if necessary, will be provided by photocopy.]


  1. There is a widespread prejudice in the contemporary philosophy of space and time. After Einstein's two theories of relativity, most writers assume that "4 dimensional spacetime" is basic. Julian Barbour, taking Dirac's question seriously, is one of the few contemporary physicists who challenge this prejudice. It might be the case that the prejudice is after all correct, or close to be correct; but nothing should be accepted, in philosophy, without close scrutiny, and Barbour's challenge is quite worthwhile.
  2. In relation to theories of relativity, Mach's criticism of Newton is quite frequently discussed; but the significance of Mach has seldom been made clear. Most writers say "Mach's criticisms are sharp, but his idea of relativist mechanics (on the basis of relative distances between particles, without absolute space and time) cannot be realized"; but they never say why this is so. Barbour is one of the few who persistently pursued the Machian line (in mechanics) and obtained substantive results, which suggest that the majority's verdict may well be premature.
  3. In order to discuss the philosophy of space and time, and of physics in general, it is indispensable to get into some detail of physics. This book is useful in that it enables the uninitiated reader to do this. Maybe you have heard of the "crisis" of the contemporary physics, that it is quite hard to unify general relativity and quantum mechanics; but without knowledge of these two fields (in some depth), such second-hand knowledge is of no use. What's quantum gravity? How is time related with it? What's timeless mechanics? You will begin to understand these questions by reading this book.

Part 1 The Big Picture in Simple Terms

Part 2 The Invisible Framework and the Ultimate Arena

Assignment, due November 7 (Fri). See this.

Second Assignment, due Dec. 5 (Fri). See this.

Part 3 The Deep Structure of General Relativity

Part 4 Quantum Mechanics and Quantum Cosmology


Be ready to acquire some knowledge of general relativity. If you want to prepare yourself in advance, read the following books (Warning: reading the preceding text alone is not sufficient for understanding basic physics, let alone general relativity; you are expected to study elementary materials, along with the text).

Taylor, E.F. and Wheeler, J.A., Exploring Black Holes, Addison Wesley Longman, 2000. [Sample chapters can be downloaded at Taylor's site: If you know elementary physics--otherwise learn it during the summer!--, this is the best introduction to general relativity. If you wish to begin from special relativity, read Spacetime Physics, Freeman, 1992 by the same authors. These books are highly recommended.]

アインシュタイン『相対性理論』内山龍雄訳・解説、岩波文庫、1988 [特殊相対性理論のみ]。

Many introductory mateirals by myself are available at:

Last modified April 15, 2006.
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