HPS 2534 General Relativity and Gravitation Fall 2007
| Topic | Comment | Source |
| A. The general theory of relativity | ||
| 0. What is general relativity? | The insultingly simple, no-math guide | John D. Norton, Einstein
for Everyone: A Web*Book See especially 10. General Relativity, 11. Relativistic Cosmology, 12. Black Holes |
| 1. History | How Einstein got from special to general relativity | A. Einstein, "Principle of Relativity and Gravitation," Part V in
"On the Principle of Relativity and the Conclusions Drawn from it,"
Jahrbuch der Radioaktivitaet und Elektronik, 4 (1907), pp.
411-462.
A. Einstein, "On the Influence of Gravitation on the Propagation of Light," Annalen der Physik, 35 (1911). Reprinted in Principle of Relativity, Dover. A. Einstein, "The Foundation of the General Theory of Relativity," Annalen der Physik, 49 (1916). Reprinted in Principle of Relativity, Dover. John D. Norton "A Conjecture on Einstein, the Independent Reality of Spacetime Coordinate Systems and the Disaster of 1913," pp. 67-102 in A. J. Kox and J. Einsenstaedt, eds., The Universe of General Relativity. Einstein Studies Volume 11. Boston: Birkhaeuser, 2005. 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, "'Nature in the Realization of the Simplest Conceivable Mathematical Ideas¹: Einstein and the Canon of Mathematical Simplicity," Studies in the History and Philosophy of Modern Physics, 31 (2000), pp.135-170. |
| 2. The Principles | a) principle of equivalence b) principle of generalized relativity c) principle of no absolute objects d) Mach’s principle |
A. Einstein, Relativity: The Special and the General Theory.
A. Einstein, "The Foundation of the General Theory of Relativity," Annalen der Physik, 49 (1916). Reprinted in Principle of Relativity, Dover. A. Einstein, "Prinzipielles zur allgemeinen Relativitaetstheorie," Annalen der Physik, 55 (1918), 240-44. John D. Norton, "Did Einstein Stumble: The Debate over General Covariance," Erkenntnis, 42 , 1995, pp.223-245; volume reprinted as Reflections on Spacetime: Foundations, Philosophy, History. U. Maier and H,-J Schmidt (eds.), Dordrecht: Kluwer, 1995. John D. Norton, "General Covariance and the Foundations of General Relativity: Eight Decades of Dispute," Reports on Progress in Physics, 56 , pp.791-858. John D. Norton, "Mach's Principle before Einstein." in J. Barbour and H. Pfister, eds., Mach's Principle: From Newton's Bucket to Quantum Gravity: Einstein Studies, Vol. 6. Boston: Birkhäuser, 1995, pp.9-57. John D. Norton, "What was Einstein's Principle of Equivalence?" Studies in History and Philosophy of Science, 16 , pp. 203-246; reprinted in D. Howard and J. Stachel (eds.), Einstein and the History of General Relativity: Einstein Studies Vol. I, Boston: Birkhauser, 1989, pp.5-47. |
| 3. Mathematical background for GR | a) differentiable manifolds and tensor fields b) connections and parallel transport c) the metric d) the field equations of GTR e) the cosmological constant; standard GR vs. unimodular gravity |
Malament, “Classical Relativity Theory,” in Butterfield
and Earman (eds), Handbook of the Philosophy of Science. Vol. 2:
Philosophy of Physics. Malament, “GR Notes,” pre-print. Earman, “The cosmological constant, the fate of the universe, unimodular gravity, and all that,” Studies in the History and Philosophy of Modern Physics 34 (2003): 559-577. |
| 4. Geometrized formulation of Newtonian gravity | Here is Newtonian theory developed using the same mathematical apparatus as general relativity. | Misner, Thorne and Wheeler, Gravitation
Jon Bain, “Theories of Newtonian gravity and empirical indistinguishability,” Studies in History and Philosophy of Modern Physics 35 (2004): 345-376. Malament, “Is Newtonian Gravitation Really Inconsistent?” Philosophy of Science 62 (1995): 489-510. Norton, “The Force of Newtonian Cosmology: Acceleration is Relative,” Philosophy of Science 62 (1995): 511-522. 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. |
| 5. Physical Relativity | Harvey Brown's recent efforts to think different about relativity theory. | Harvey Brown: Physical Relativity: Space-time Structure from a Dynamical Perspective |
| 6. Causal structure of relativistic spacetimes | a) hierarchy of causality conditions
b) recovering global geometric structure from causal structure (Malament’s 1977 result) c) locally any spacetime is past and future distinguishing; thus
by b), locally the causal structure determines the conformal
structure d) what can and can’t we infer from observations about the
structure of spacetime? e) chronology protection, time machines, etc. [Can view this as a subproblem of cosmic censorship.] |
Malament, “The class of continuous timelike curves determines
the topology of spacetime,” Journal of Mathematical
Physics 18 (1977): 1399-1404.
Ellis, Nel, and Maartens, “Ideal observational cosmology,” Physics Reports 124 (1985): 315-417. Malament, “Observationally Indistinguishable Spacetimes,” in Earman, Glymour, and Stachel (eds), Foundations of Spacetime Theories. Minnesota Studies in the Philosophy of Science, Vol. 8. Hawking, S. W. , “The chronology protection conjecture,” in H. Sato and T. Nakamura (eds), The Sixth Marcel Grossmann Meeting, pp. 3-13. Singapore: World Scientific, 1992. Earman, Smeenk, and Wuethrich, “Do the Laws of Physics Forbid the Operation of Time Machines?” preprint |
| 7. The initial value problem, the “hole argument,” and the status of general covariance | a) review of the ivp. Two things to note: (i) the up to diffeo
clause—hole argument; maximal development for which the is
surface is a Cauchy surface—is it maximal simpliciter? The
problem of naked singularities and cosmic censorship.
b) Einstein’s hole argument. History is interesting, but don’t spend that much time on it—it is a recognition of (i). Our focus is on what the implications of (i). Standard view in physics: shows that the diffeo. invariance of GTR is a gauge symmetry. What does this imply about a) the “observables” of the theory? b) the status of general covariance? c) Relation to “background independence” |
Norton, “The Hole Argument,” Stanford Encyclopedia
of Philosophy http://plato.stanford.edu/entries/spacetime-holearg/
Norton, “A Conjecture on Einstein, the Independent Reality of Spacetime Coordinate Systems and the Disaster of 1913,” in A. J. Kox and J. Einsenstaedt (eds.), The Universe of General Relativity. Einstein Studies, Volume 11, pp. 67-102. Boston: Birkhäuser, 2005. (Preprint at http://www.pitt.edu/~jdnorton/homepage/cv.html#Conjecture_HGR6) Norton, “General Covariance and the Foundations of General Relativity: Eight Decades of Dispute,” Reports on Progress in Physics 56 (1993): 791-858. Earman, “Two Challenges to the Requirement of Substantive General Covariance,” Synthese 148 (2006): 443-468. Belot, “Background Independence,” pre-print. |
| 8. Spacetime singularities | a) struggle to understand the nature of singularities in GTR; theorems about the existence of singularities. | Eisenstaedt, “The Early Interpretation of the Schwarzschild
Solution,” in D. Howard and J. Stachel (eds), Einstein and
the History of General Relativity: Einstein Studies, Vol. 1, pp.
213-234. Boston: Birkhauser, 1989.
Earman, “The Penrose-Hawking Singularity Theorems,” in H. Goenner, J. Renn, and T. Sauer (eds), The Expanding Worlds of General Relativity: Einstein Studies, Vol. 7, pp. 235-267. Boston: Birkhauser, 1999. |
| b) Does the fact that singularities are a generic feature of the solutions of GTR show that the theory contains the seeds of its own destruction? Why, if they don’t wreck determinism. Penrose’s cosmic censorship hypothesis. | Earman, Bangs, Whimpers, and Shrieks, Ch. 3 (“Cosmic
Censorship”). Oxford University Press, 1995.
Penrose, “The Question of Cosmic Censorship,” in R. Wald (ed), Black Holes and Relativistic Stars, pp. 103-122. Chicago, IL: University of Chicago Press, 1998. Wald, “Gravitational Collapse and Cosmic Censorship," in Vishveshwara, C. V., Iyer, B. R., and Bhawal, B. (eds), Black Holes, Gravitational Radiation, & the Universe. Dordrecht: Kluwer Academic Publishers, 1998. gr-qc/9710068 |
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| 9. Experimental tests; the PPN formalism | Does the observational and experimental evidence support GR? How well does it separate GR from similar, competing theories? | Clifford Will, Theory and Experimental in Gravitational
Physics.
Clifford M. Will, The Confrontation between General Relativity and Experiment, Living Reviews in Relativity. |
| B. General relativistic cosmology | ||
| 1. Early cosmological models and the triumph of the hot big bang model | Einstein static universe De Sitter solution The discovery of the expanding universe; Friedmann models Rival steady state model Triumph of the hot big bang model |
Ellis, “The Expanding Universe: A History of Cosmology from 1917 to 1960,” in D. Howard and J. Stachel (eds), Einstein and General Relativity. Einstein Studies, Vol. 1, pp. 367-431. Birhkäuser, 1989. |
| 2. Discontents with the hot big bang model: the genesis of inflationary cosmology | Despite success of the hot big bang model, there were discontents with the perceived explanatory adequacy of the standard hot big bang model: the horizon problem and the flatness problem, which inflationary cosmology claimed to explain. Later inflationary cosmology received support from its ability to explain structure formation and the spectrum of density perturbations encoded in the CBR. | |
| Concentrate on 1) formulation of the horizon and flatness problems |
Watson, “An Exposition of Inflationary Cosmology,”
astro-ph/0005003 Guth, ... |
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| 2) horizons in cosmology | Ellis and Rothman, “Lost horizons,” American Journal
of Physics 61 (1993): 883-893
Ellis and Stoeger, “Horizons in inflationary universes,” Classical and Quantum Gravity 5 (1988): 207-220. |
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| 3) Does inflation provide an effective smoothing mechanism?
4) Inflation and scientific explanation. a) Should scientific explanations eschew special initial conditions? b) Does inflation obviate the need for special initial conditions? |
Penrose, Review of G. W. Gibbons, S. W. Hawking, and S. T. C.
Siklos (eds), The very early universe. Cambridge: Cambridge
University Press. Observatory 106 (1986), 20-21.
Hollands and Wald, “An alternative to inflation,” General Relativity and Gravitation 34 (2002): 2043-2055. gr-qc/0205058. Hollands and Wald, “Comment on inflation and alternative cosmology,” hep-th/0210001. Hawking and Page, “How probable is inflation?” Nuclear Physics B 298 (1988): 789- 809 |
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| 3. Accelerating expansion and dark energy | Evidence that the expansion of the universe is accelerating. Alternative explanations for the acceleration | Earman, “Lambda: The Constant That Would Not Die,”
Archive for History of Exact Sciences 55 (2001): 189-220.
Carroll, S, “Why is the universe accelerating?” In W. L. Friedman (ed), Measuring and modeling the universe. Cambridge: Cambridge University Press. astro-ph/0310342 |
| Controversy over whether dark energy required for accelerating expansion. | Kolb, Matarrese, and Riotto, “On cosmic acceleration without
dark energy,” astro-ph/0506534.
Ishibashi and Wald, “Can the Acceleration of Our Universe Be explained by the Effects of Inhomogeneities?” gr-qc/0509108. |
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| Should we be skeptics over the whole edifice of modern cosmology, as Disney suggests, because of its large number of adjustable parameters? Or is a more measured assessment appropriate? | Michael J. Disney, "Modern
Cosmology: Science or Folktale?" Column in American Scientist,
Sept-Oct, 2007.
Rachel Bean, Sean Carroll, and MarkTrodden, "Insightsinto DarkEnergy: InterplayBetweenTheory and Observation" http://arxiv.org/pdf/astro-ph/0510059 |
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| 4. Eternal inflation, the multiverse, and anthropic selection | Some more speculative ideas | Knobe, Olum, and Vilenkin, “Philosophical Implications of
Inflationary Cosmology,” British Journal for the Philosophy
of Science 57 (2006), 47-67.
Aguirre, “On making predictions in a multiverse: conundrums, dangers, and coincidences,” astro-ph/0506519. White, “Fine-Tuning and Multiple Universes,” Noûs 34 (2000): 260-276. Smolin, “Scientific alternatives to the anthropic principle,” hep-th/0407213. |
| 5. The beginning and end of time | (a) If spacetime a manifold without boundary, then no beginning in
sense of a first instant. But there can be a beginning in sense that
time is finite in the past. Problems in unpacking this notion in the
setting of relativistic spacetimes.
(b) Hawking-Penrose singularity theorems indicate that there is a singularity in the past. The results require energy conditions that are violated in inflationary eras. So can we have eternal inflation in the past? Attempted no-go results. |
Borde and Vilenkin, “Eternal Inflation and the Initial
Singularity,” Physical Review Letters 72 (1994):
3305-3308.
Borde and Vilenkin, “Violation of the weak energy condition in inflating spacetimes,” Physical Review D 56 (1997): 717-723. Borde, Guth, and Vilenkin, “Inflationary spacetimes are not past-complete,” gr-qc/0110012 v2. Ellis and Maartens, “Eternal inflation without quantum gravity,” gr-qc/0211082. Ellis and Maartens, “The emergent universe: inflationary cosmology with no singularity,” Classical and Quantum Gravity 21 (2004): 223-232. |
| (c) Other ways to avoid the initial singularity (i) quantum gravity effect. Senses in which LQG does and does not avoid the initial singularity. (b) M-theory | ||
| 6. GTR and quantum physics—black hole evaporation |