INDEX- CV- PUBLS.- PICT.ESSAYS- ABSTRACTS- INDEX・LAPLACE- OL.ESSAYS-CRS.MATERIALS
SPACETIME: Opened, Dec. 21, 1998; last update, August 10, 2001
This seminar is finished; but many materials will be used again in my new lecture on the philosophy of space and time, Fall 2001; anyone who wishes to attend this lecture should read these materials.
For Supplementary materials by Uchii, refer to the links! And for the assignments (2000), see the bottom of this page! See also Space and Time Index.
Lawrence Sklar, Space, Time, and Spacetime, University of California Press, 1974, 1976.
Ch. I. INTRODUCTION
Ch. II. THE EPISTEMOLOGY OF GEOMETRY
Euclidean differential geometry
Cosmological Term Revised, Apr. 3
Notes on Poincare
Gruenbaum on the Duhemian Thesis and Einstein's Philosophy of Geometry New
Reichenbach on Helmholtz Revised
Gruenbaum on Reichenbach's "Universal Forces"New
Gruenbaum on Eddington's Criticism of Poincare Revised
Riemann and Helmholtz New
Gruenbaum's reply to Malament and Friedman appeared→ PhilSci Archive, "David Malament and the Conventionality of Simultaneity: A reply" New
Malament's Theorem and Allen Janis's Construction New, Mar. 14
Ch. III. ABSOLUTE MOTION AND SUBSTANTIVAL SPACETIME
Mach's Principle Revised
Absoluteness and Relationism
A Comparison, Newtonian, Neo-Newtonian, and Minkowskian space-and-time Revised, Mar. 23
General Principle of Relativity Revised, March 23
Galilean Relativity and Galilean Transformation
Galilean Relativity [Japanese] Revised, Mar.13
The Aristotelian Universe and Space Revised, Mar. 15
General Relativity and Absolute Space
Perihelion of Mercury
Eddington on 1919 Expeditions Revised
The Parable of the Apple New
Ch. IV. CAUSAL ORDER AND TEMPORAL ORDER
Causal Theory of Time
Michelson-Morley Experiment Revised
Einstein on Fizeau's Experiment
The Genesis of General Relativity (1)
The Genesis of General Relativity (2)
The Genesis of General Relativity (3)
The Genesis of General Relativity (4)
Interlude: Einstein in Japan (1922); Einstein with European Physicists
The Genesis of General Relativity (5) Revised (4 Sept)
The Genesis of General Relativity (6)
The Genesis of General Relativity (7)
The Genesis of General Relativity (8) the series completed
For Conventionality of Simulataneity, see Allen Janis' Paper (Norton's discussion is also good: Norton, John D., "Philosophy of Space and Time", in Introduction to the Philosophy of Science (Salmon et al.), Prentice-Hall, 1992.)
Wormholes in General Relativity
Conventionality of Topology
Comments on the 2nd Assignment
Sklar on the Causal Theory of Time New
Ch. V. THE DIRECTION OF TIME
A "Flow" of Time?
McTaggart on the Unreality of Time
Ch. VI. EPILOGUE
The whole structure of Sklar's book is described by the author briefly as follows:
Chapter II is concerned with the spistemology of geometry. Given that mathematics provides us with more than one consistent description of possible spaces oor spacetimes, and given that some physical theories utilize these possibilities to characterize worlds with quite different geometric structures, to what extent can we empirically determine just what geometric structure of the space or spacetime of the world is? Is this an "empirical " matter? Can we, instead, fix upon a structure for the world independently of any observation or experiment? Or is the situation more appropriately described as one in which the geometric structure of the world we posit is one we can choose to please ourselves, "as a matter of convention"?
Chapter III is concerned with a closely related issue. When we deal with the spatiotemporal structure of the world, must we view ourselves as attempting to discover the nature of an entity of the world, space or spacetime itself, or should we instead view ourselves as attempting merely to determine certain general truths about the structure of a set of relations holding among concrete material happenings?
Chapter IV is devoted to discussing the relation between the temporal order of the world and its causal order. The first part of the chapter discusses the revolution in our views about time brought about by the adoption of the special theory of relativity and deals with such questions as: the empirical basis fot this conceptual change, the "philosophical" ingredients in the adoption of special relativity, the problem of whether the special-relativistic theory of time is a matter of "convention", etc. The later parts of the chapter examine the claim that temporal relations among events can be "reduced" to causal relations among events in some plausible way----the so-called causal theory of time.
In Chapter V[,] I discuss the philosophical issue sometimes called the question of the direction of time. The primary focus of the chapter is on the question of whether the intuitive notion of the direction of time received any clarification by the study of various physical processes that we might intuitively describe as behaving asymmetrically in time. (pp.2-3)
+ New Material: For the history of the relativity theories, an up-to-date and readable exposition by John Stachel is recommended:
Twentieth Century Physics, vol. l, ed. by Laurie M. Brown, Abraham Pais, and Brian Pippard, Institute of Physics, 1995; Japanese translation 『20世紀の物理学』vol. 1、第4章「相対性理論の歴史」、丸善、1999年
[Sklar's photo by Robert Kalmbach, fron The Research News, Vol. 31, Nos. 1-2,
The University of Michigan, 1980]
2000年度 (In order to update your information, you may also consult Michael Friedman's book: Foundations of Space-Time Theories, Princeton Univ. Press; another, advanced book is John Earman's World enough and Space-Time, MIT, 1989, but since Earman is not kind enough to untrained readers, you need a considerable preparation.)
This year, we will begin from chapter 3, section D "The evolution of physics and the problem of substantival space", page 194. For the newcomers, I will briefly summarize the most important points of Sklar's discussions so far.
Chapter 2 contains basic materials for discussing the epistemology of geometry.
(1) History of geometry
The structure of space has been regarded as clarified by geometry, and that's why Sklar's discussion begins with the epistemology of geometry. You've got to know the Euclidean geometry and its axiomatic structure; you have to know the status of the fifth postulate (the parallel postulate). Non-Euclidean geometry appeared in the 19th century, and roughly speaking, it replaces the fifth postulate in one way or another, producing Lobachevski geometry (many parallel postulate) and Riemann geometry (no parallel).
(2) Some mathematics
Also, you have to know at least basic results of Minkowski spacetime which is indispensable for special relativity, and the Gaussian and Riemannian analytic geometry, or differential geometry, which is indispensable for general relativity.
(3) Some physics
The contemporary spacetime philosophy naturally centers on relativity theories. So that you've got to know at least elementary portion of special relativity and general relativity. The essential difference is that the graviation is treated in the latter. Spacetime in special relativity is flat, spacetime in general relativity is curved, because gravity cannot be treated without curvature. Local spacetime can be approximated by special relativity, but global structure cannot be. Grasp at least the intuitive significance of the Equivalence Principle and the Einstein Equation in general relativity.
(4) Poincare's conventionalism
Poincare's conventionalism (as regards geometry) is also an indispensable topic. He argued that geometrical axioms are neither a priori truths nor empirical truths, and claimed that they are conventions. What did he mean by this? And how did some empiricists argued against this? These questions lead us to the Duhemian problem: how can we check the geometry of the actual world by means of empirical tests conducted in the midst of a whole network of physics, geometry, and many other experimental hypotheses?
Chapter 3 treats a long-standing problems of motion, space and time.
(5) Absolute vs. Relative, Substantivalist vs. Relationist
What is space, what is time? What is the nature of each? Some argue that space is nothing but a bunch of relations among physical objects in the world, and there is no space apart from such relations (relationist). Others argue that there is space independent from physical objects within it, and space is a kind of substance, different in nature from physical objects (substantivalist).
Their controversy center around the notions of absolute motion, relative motion, absolute space, absolute acceleration, etc. Major opponents are Leibniz and Newton. Leibniz argued that only relative motions can be observed, so that any claim unsupported by such observations are meaningless; Newton introduced a new epoch by his argument for absolute space, based on empirical grounds, i.e. forces produced by accelerated motions. Read carefully Newton's Scholium.
Comments on the 2nd Assignment New
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