The Nature of Space and Time
by: Stephen Hawking and Roger Penrose, read in 2006
8 Hawking: "The strongest and physically most important condition [on the causal structure] is that of global hyperbolicity."
8 The conditions for global hyperbolicity.
10 The sentence seems to be wrong to me; it seems 'maximum' should be 'minimum'.
15 Hawking: Definition of singularity: "A spacetime is singular if it is timelike or null geodesically incomplete but cannot be embedded in a larger spacetime."
15 The Penrose-Hawking Theorems
20 Hawking: "almost everyone now beleives that the universe, and time itself, had a beginning at the big bang."
20 Penrose's 'Cosmic Censorship': Singularities occur only in places hidden from external observers. "Nature abhors a naked singularity."
39 No Hair Theorem
44 Schwarzchild Metric
50 Laws of black holes and thermodynamics. Topologies for the spacetime manifold, periodic imaginary time, Euclidean-Schwarzchild Metric
51 This discussion is vaguely reminiscent of my oscillating "transfer of omniscience." May explain info lost in a black hole.
59 Hawking: "microscopic, virtual black holes appear because of quantum fluctuations of the metric."
62 Penrose sees information loss in black holes as complementary to uncertainty of QT.
62 Penrose: "One could say that the missing information is lost when it falls through the horizon of the black hole, but I prefer to regard it as lost when it meets the singularity." I'd say the former from the human perspective, the latter from PC's, if it is indeed lost to PC which I don't think it is.
64 Penrose: "Liouville's theorem...says that volumes in phase space remain constant."
64 Penrose: "violation of Liouville's theorem would ...correspond to a nonunitary evolution [in Hilbert space]"
64 Penrose: "a black hole spacetime violates this conservation. However, in my picture, this loss of phase-space volume is balanced by a process of "spontaneous" quantum measurement in which information is gained and phase-space volumes increase." And the information is gained by whom? PC would complete this picture.
64 Penrose: "One may say that past singularities carry little information whereas future singularities carry lots. This is what underlies the second law of thermodynamics."
89 Hawking: "If the rate of expansion one second after the big bang had been less by one part in 10^10, the universe would have collapsed after a few million years. If it had been greater byt one part in 10^10, the universe would have been essentially empty after a few million years."
92 Hawking: Three kinds of spherical harmonics: "Tensor harmonics -- Gravitational waves, Vector harmonics -- Gauge, Scalar harmonics -- Density perturbations."
96 Hawking: "Thus it seems we don't need string theory even for the beginning of the universe."
96 Hawking: Humans as "little inhomogeneities"
97 Decoherence explained by our inability to observe all of the past universe.
98 Hawking: "I would suggest that the reason we observe classical behavior is that we can see only part of the universe."
107 Penrose: "QFT requires a splitting of the field quantities into positive and negative frequency parts. The former propagate forward in time, the latter backward."
122 Hawking:"To get a better-behaved path integral one does a Wick rotation to Euclidean space by introducing the imaginary time coordinate t = -it."
128 Penrose: "It seems to me that in order to explain how we perceive the world to be, within the framework of QM, we shall need to have one (or both) of the following:
(A) A theory of experience.
(B) A theory of real physical behavior.
129 Penrose: "I believe that (A) is a dangerous view to adopt, which leads into all sorts of troubles."
129 Penrose: "Wick rotation...replaces t by it by means of a rotation of the time axis. This translates Minkowski space into Euclidean space."
132 Penrose: "I believe in gravitational collapse, but not in the collapse of the wave function."
134 Penrose: "Einstein argued that there should exist something like a real world, not necessarily represented by a wave function, whereas Bohr stressed that the wave function doesn't describe a "real" microworld but only "knowledge" that is useful for making predictions. Bohr was perceived to have won the argument."
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