Cycles of Time: An Extraordinary New View of the Universe
This groundbreaking book presents a new perspective on three of cosmology’s essential questions: What came before the Big Bang? What is the source of order in our universe? And what cosmic future awaits us?
Penrose shows how the expected fate of our ever-accelerating and expanding universe—heat death or ultimate entropy—can actually be reinterpreted as the conditions that will begin a new “Big Bang.” He details the basic principles beneath our universe, explaining various standard and non-standard cosmological models, the fundamental role of the cosmic microwave background, the paramount significance of black holes, and other basic building blocks of contemporary physics. Intellectually thrilling and widely accessible, Cycles of Time is a welcome new contribution to our understanding of the universe from one of our greatest mathematicians and thinkers.
in §3.2 (end) and §3.3. Whatever value this type of argument may have in other contexts, it is next to useless here. Again there is the very dubious aspect of such reasoning that we do not have a great deal more understanding of the physical requirements for life than we do for consciousness. But even apart from this, and even assuming that natural selection is indeed an essential prerequisite for life, and that it does require the Second Law, this still provides no explanation for the fact that
assumed to be smooth), rather than C diverging wildly, and this statement might be taken to be sufficient for what is required. Fig. 2.49 Schematic conformal diagram of Paul Tod’s proposal for a form of ‘Weyl curvature hypothesis’; asserting that the Big Bang provides a smooth boundary to the space-time . To make this condition mathematically clearer, it is convenient to assert it in the form that the space-time can be continued smoothly, as a conformal manifold, a little way prior to the
material of the black dwarf might eventually collapse into a black hole via such processes, there would be likely to be many ‘rogue’ massive particles that had, in some form, escaped from the clusters of galaxies to which they had originally been attached. My concern is particularly with electrons—and also with their anti-particles, the positrons—because they are the least massive electrically charged particles. It is not a particularly unconventional view that protons, and other charged
flat Minkowski space . When we come to consider the cosmological temperature of de Sitter space , we would expect, by the same token, that it would be an accelerating observer who should feel this temperature, not one who is in free fall (i.e. in geodesic motion; see end of §2.3). An observer moving freely in a de Sitter background would be unaccelerated in these terms, and, so it seems, should not experience the temperature TΛ. The main argument for cosmological entropy seems to be an elegant
Wheeler and others, even the ordinary closely flat space-time of our experiences, if it were to be examined at the minute Planck scale, would be found to have a turbulent chaotic character, or perhaps a discrete granular one—or have some other kind of unfamiliar structure better described in some other way. Wheeler presented the case for quantum effects of gravity causing the space-time at the Planck level to curl up into topological complications that he viewed as a kind of ‘quantum foam’ of