HPS 2534         General Relativity and Gravitation         Fall 2007


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Week Date Topic/Reading Presented by
1 Aug. 30 Introduction Earman and Norton
2 Sept. 6 Einstein's pathway from special to general relativity

Einstein, Albert, Section V. "Principle of Relativity and Gravitation" in "On the Principle of Relativity and the Conclusions Drawn from it," Jahrbuch der Radioaktivitaet und Elektronik, 4(1907), pp. 411-462.

Norton, Notes on Section V. "Principle of Relativity and Gravitation"

Einstein, Albert, "I. Physical Part" of A. Einstein and M. Grossmann, "Outline of a Generalized Theory of Relativity and a Theory of Gravitation," Teubner, Leipzig, 1913. ("Entwurf" paper) (plus one bit from Grossmann's mathematical part).

Norton, Notes on "1. Physical Part" of Entwurf paper.

Einstein's Zurich Notebook

(120 min)
3 Sept. 13 Newtonian gravity as a spacetime theory
1. The formalism

Jon Bain, “Theories of Newtonian gravity and empirical indistinguishability,” Studies in History and Philosophy of Modern Physics 35 (2004): 345-376.

Background reading: Malament, David (1986) "Newtonian Gravity, Limits, and the Geometry of Space," pp. 181-201 in From Quarks to Quasars: Philosophical Problems of Modern Physics. ed., R. G. Colodny,. University of Pittsburgh Press.

Earman, John Notes on "Covariant Newtonian Gravity"

(60 min)
2. Paradox of Newtonian cosmology

John D. Norton, “The Force of Newtonian Cosmology: Acceleration is Relative,” Philosophy of Science 62 (1995): 511-522.

John D. Norton, Notes on the Paradox of Newtonian Cosmology

John D. Norton, "The Cosmological Woes of Newtonian Gravitation Theory," in H. Goenner, J. Renn, J. Ritter and T. Sauer, eds., The Expanding Worlds of General Relativity: Einstein Studies, volume 7, Boston: Birkhäuser, pp. 271-322.
David Malament, “Is Newtonian Gravitation Really Inconsistent?” Philosophy of Science 62 (1995): 489-510.
John D. Norton, "The n-Stein Family" A. Ashtekar et al. (eds.) Revisiting the Foundations of Relativistic Physics: Festschrift in Honor of John Stachel. Kluwer. Kluwer, 2003. pp. 55-67.

(60 min)
4 Sept. 20 Causal structure of spacetime
1. Causality conditions

Wald, Robert "Causal Structure," Ch. 8 in General Relativity. Chicago: University of Chicago Press.

Earman, John, Notes on Causal Structure of General Relativistic Spacetimes

(60 min)
2. Goedel Spacetime

Malament, David "'Time Travel' in the Goedel universe," PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 1984, Volume Two (1984), pp. 91-100.

Background reading: Goedel, Kurt "A Remark about the Relationship between Relativity Theory and Idealistic Philosophy" pp. 556-62 in P. A. Schilpp, ed., Albert Einstein: Philosopher-Scientist. New York: Tudor, 1949; 2nd ed. 1951.

(20 min)
3. Observationally indistinguishable spacetimes

David Malament, “Observationally Indistinguishable Spacetimes,” in Earman, Glymour, and Stachel (eds), Foundations of Spacetime Theories. Minnesota Studies in the Philosophy of Science, Vol. 8.

(40 min)
5 Sept. 27 3. Observationally indistinguishable spacetimes (continued) (30 min remains)
Chronology Protection and Time Machines

Hawking, Stephen W. "The Chronology Protection Conjecture" pp. 3-13 in H. Sato and T. Nakamura, eds., The Sixth Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories. Part A. World Scientific.

Background: Hawking, S. W. "Chronology Protection Conjecture," Physical Review, 46 (1992), pp. 603-611.

(30-45 min)
2. J. Earman, C. Smeenk, C. Wuethrich, "Do the Laws of Physics Forbid the Operation of Time Machines" (manuscript)

John Earman, Notes on Time Travel and Time Machines

(to end of day)
6 Oct. 4 The Hole Argument
1. The History of the Hole Argument

SECTION 5 ONLY of John D. Norton, "How Einstein Found His Field Equations: 1912-1915," Historical Studies in the Physical Sciences, 14 (1984), pp. 253-315. Reprinted in D. Howard and J. Stachel (eds.), Einstein and the History of General Relativity: Einstein Studies Vol. I, Boston: Birkhauser, pp101-159.

John D. Norton, Notes on Einstein's Arguments Against General Covariance

John D. Norton, Draft of new version of "The Hole Argument" Stanford Encyclopedia of Philosophy. See especially supplement "Active and Passive Covariance."

(50 min)
2. Constraints and gauges: how do we identify gauge freedom?

John Earman, Notes on Constraints and Gauge

(50 min)
7 Oct. 11 Background independence

Gordon Belot, "Background Independence" ms

Friedman, Michael, Space-Time Theories," Ch. II in Foundations of Space-Time Theories.

(guest speaker)
Oct. 11- 14 &HPS1: Conference in Integrated History and Philosophy of Science
8 Oct. 18 Physical Relativity
1. Harvey Brown: Physical Relativity: Space-time Structure from a Dynamical Perspective Oxford U. P., 2005. Preface, Ch. 1, 2, 8.

Lorentz, H. A. Theory of Electrons, p. 230.

2. Reviews of Brown, Physical Relativity.

Dorato, Mauro, "Relativity Theory between Structural and Dynamical Explanations," International Studies in the Philosophy of Science, 21 (2007), pp. 95-102.

Martinez, Alberto, "There's no pain in the Fitzgerald contraction is there?" Studies in History and Philosophy of Modern Physics, 38 (2007), pp. 209-15.

Skow, Bradford, Review of Brown, Physical Relativity. Notre Dame Philosophical Reviews. 2006.05.11 http://ndpr.nd.edu/review.cfm?id=6603

9 Oct. 25 Malament-Hogarth Spacetimes

Gyenis, Balazs and Roberts, Bryan, Untitled manuscript on hypercomputation and formalization of physical theories.

Earman, John and Norton, John D., "Forever is a Day: Supertasks in Pitowsky and Malament-Hogarth Spacetimes," Philosophy of Science, 60 (1993), 22-42.

Earman, John, "Pitowsky Spacetimes, Malament-Hogarth Spacetimes, and All That" Notes.

Roberts and Gyenis
10 Nov. 1 Spacetime singularities
(i) What is a singularity?

Geroch, Robert "What is a Singularity in General Relatiivty," Annals of Physics, 48 (1968), pp. 526-540.

(ii) The Schwarzschild solution and black holes

Eisenstaedt, Jean "The Early Interpretation of the Schwarzschild Solution."

Carroll, Sean, "The Schwarzschild Solution," Spacetime and Geometry:An Introduction to General Relativity, Ch. 5.

11 Nov. 8 De Sitter Spacetime
Einstein, Albert "Cosmological Considerations on the General Theory of Relativity." Earman
Its basic geometry: 4d hyperboloid in 5d space

Schroedinger, E. "The De Sitter Universe," Ch. 1 in Expanding Universes. Cambridge U. P., 1957.

De Sitter's spacetime's non-Machian properties

John D. North, De Sitter's World and Mach's Principle in Measure of the Universe.

Einstein, Hilbert, Weyl, Klein on the "singularity" in de Sitter spacetime

Editors of Einstein Papers, "The Einstein-de Sitter-Weyl-Klein Debate" Collected Papers of Albert Einstein, Vol. 8, Part A.

Notes on static de Sitter spacetime.

(iii) Singularity theorems. (Carried over from November 1)

John Earman, "The Penrose-Hawking Singularity Theorems," in Goenner et al. (eds.), The Expanding Worlds of General Relativity

John Earman, Notes on Singularities

12 Nov. 15 Steady State Cosmology
A cosmology grounded in an a priori principle

Bondi, Hermann and Gold, Thomas, "The Steady State Theory of the Expanding Universe."

Hoyle, Fred, "A New Model for the Expanding Universe."

Bondi, Hermann, " The Steady State Theory," Ch. XII in Cosmology

John D. North, "Continual Creation and the Steady State Theories of Bondi, Gold and Hoyle," Ch. 10 in Measure of the Universe.

Its demise

"Big Bang versus Steady State"

Wilson, Robert W. "The Cosmic Microwave Background Radiation," Nobel Prize Lecture

Hoyle, Fred "An Assessment of the Evidence Against the Steady-State Theory."

The horizon problem in big bang cosmology

Ellis, George, "Lost Horizons," American Journal of Physics, 61 (1993), pp. 883-93.

Nov. 15 Term paper topic due
Nov. 19-23 Thanksgiving break
13 Nov. 29 Early Universe Inflationary
The horizon and flatness problems and how inflation solves them

Alan Guth, "Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems," Physical Review D, 23(1981), pp. 347-56.

Alan Guth, "The Inflationary Universe" Ch. 10. in Inflationary Universe: The Quest for a New Theory of Cosmic Origins

Models of Inflation

M. Hobson, G. Efstathiou, A. N. Lasenby, General Relativity: An Introduction for Physicists Cambridge U. P., 2007, Ch. 16.


Stefan Hollands and Robert M. Wald, "An Alternative to Inflation" arXiv:gr-qc/0205058
Stefan Hollands and Robert M. Wald, "Comment on Inflation and Alternative Cosmology" arXiv:hep-th/0210001
Starkman, Glenn D., Schwarz, Dominik J., "Is the Universe OUT OF TUNE?" Scientific American, 00368733, Aug2005, Vol. 293, Issue 2

14 Dec. 6 Late Universe Inflation
Is the expansion of the universe accelerating? If so, why? Lambda? Some new form of matter in dark energy?
Sean Carroll, "Why Is the Universe Accelerating?" astro-ph 0310342 Roberts
Sean Carroll, "The Cosmological Constant," astro-ph 0004075; also "The Cosmological Constant" in http://relativity.livingreviews.org
Rachel Bean, Sean Carroll, Mark Trodden "Insights in Dark Energy: Interplay Between Theory and Observation," astro-ph 0510059 Gyenis
Noon, Friday, Dec. 14 Friday December 21 Term paper due. Two hard copies by noon in 1017CL or e-versions emailed to the two Johns by 5pm.