Causality, quantum theory and cosmology (Q2906646)

Most what one finds in this article Penrose had already described more elaborately in his former papers and books. However, in this very well readable review text using only a minimum of mathematical formulae, it becomes particularly clear that, in the author's mind, there is an internal connection between such different topics as quantum theory, twistor theory, thermodynamics, general relativity, singular general-relativistic cosmological model, singularity theorems, conformal space-time geometry etc. In the decades of his creative activity, when he delivered fundamental contributions to many of these themes, this conviction took a form that one can call Penrose's physical worldview. This worldview has a great degree of plausibility if one is ready to accept the presuppositions made by Penrose. His major assumption consists in that the development of local physics (in the sense of laboratory physics and astrophysics) should essentially be directed by cosmological and black hole considerations and speculations.NEWLINENEWLINE After some introduction to general relativity and quantum mechanics, the author turns to the relation between general relativity and quantum theory and explains why space-time must take on some quantum-mechanic features such that quantum and general relativity theories must be unified. He stresses that it is his strong opinion that the result of this unification has to differ fundamentally from standard quantum field theory, mainly because he sees some paradoxes in the application of strict quantum rules if they are applied indiscriminately at all levels. He expects ``changes in quantum theory at stages where principles of general relativity and observational aspects of the Universe (via thermodynamics) begin to have serious relevance''. As to the generally accepted reason for founding a theory of quantum gravity saying that one could avoid the singularities this way, he states (and gives later specific arguments in favor of his opinion) that it is most unlikely that such a straightforward-looking picture is likely to hold true. In particular, he does not believe that the Big Bang and black hole singularities are of the same nature. In the following text the fact that the Big Bang has a particular structure is shown to be quite fundamental.NEWLINENEWLINE In the next paragraphs, suggestions are discussed that have been put forward in order to find another approach (differing from the straightforward-looking picture of quantum gravity) to describe the discrete nature of space-time at smallest scales. In this context, Penrose discusses also his own theories, namely the theory of spin-networks (and its influence in the development of the loop-variable approach to quantum gravity) and the twistor theory. In a further section, thermodynamic considerations are introduced to win further information on the initial state of the universe. In particular, it is argued that the spatial isotropy and homogeneity of the universe indicate that the gravitational degrees of freedom were not excited at the beginning of the Universe and certainly not thermalized, with the consequence of an extreme lowness of the Big Bang entropy. Only the formation of black holes (their formation and evaporation is one of assumptions that Penrose's world scenario needs!) represents a vast increase of entropy.NEWLINENEWLINE The main part of the paper is introduced by a very informative section on conformal geometry, especially on boundaries to space-time that enable one to describe the conformal (causal) structure of the Big Bang and the remote (infinite) future. To be able to apply the exact mathematics of conformal space-time geometry for cosmology, then Penrose develops a very speculative cosmic scenario containing assumptions on galaxies' masses consumed by galactic black holes, on material (`rogue' black holes) escaping the galaxies and on collisions of black holes forming larger black holes. As a consequence, after a long time it should be left mainly electromagnetic radiation (``emitted by Big Bang, by stars, by evaporating black holes and by other thermal sources'') and gravitational radiation. Therefore, in the remote future the major constituents of the universe may well be conformally invariant radiation (photons).NEWLINENEWLINEMoreover, by defining an appropriate tensor (up to its behavior under conformal transformations, it equals the Weyl tensor) Penrose reaches that gravitons are eventually effectively described in a conform-invariant way. Now, two `tricks' (he calls them himself so) allow him to found conformal cyclic cosmology (CCC). He writes: ``One of these [tricks] provides a formulation of the Weyl curvature hypothesis (WCH) by postulating that the conformal spacetime geometry extends smoothly to before the Big Bang across a conformally smooth hypersurface B to a hypothetical `pre-Big-Bang' phase. The other provides us with a geometrical framework for describing the asymptotic future of the Universe in an elegant way, by allowing the conformal spacetime geometry of the Universe to extend smoothly to beyond the future infinity across a conformally smooth hypersurface T. ... But here is where CCC comes in. It demands that both extended regions are now to be taken seriously as real universe regions!'' It is argued that the critical issue, according to which in the vicinity of the Big Bang the effect of the gravitational interaction increases at higher and higher energies and densities what would speak against this scenario, is resolved in CCC. Finally, one finds the situation that the infinite future can somehow be equated to an initial state with the seemingly opposite characteristics of infinite compression, infinite density and infinite temperature. Geometrically, this result is reached because not the metric but the conform (causal) geometry of the two regions is mached. In several passages, Penrose gives arguments in favor of this conformal approach which excludes to introduce notions like a clock at a metric level.NEWLINENEWLINE To oppose the suspicion that `as the author admits to be a natural view' such a fantastical scheme ``would lie in the province of philosophy or, perhaps, science fiction'', in the end of the paper, some observational implications of CCC are considered. They mainly refer to those effects which in standard cosmology are explained by an early inflationary phase of the cosmological evolution. It is stated that, despite the successes of the inflationary model in explaining certain observations on the microwave background radiation, it seems probable that CCC can be equally be accounted for within CCC. Furthermore, it is argued that CCC provides deeper insights in the Second Law of thermodynamics and that CCC, in contrast to inflation, does not need to assume quantum fluctuations taking place in the early universe as source of density fluctuations being the starting point of cosmic structure formation. The objection against such fluctuations is related to the above-mentioned critical attitude of Penrose to the ordinary view on quantum theory and, in particular, against quantum gravity. At least, as far as the `quantum foam' is concerned (it is expected according to quantum gravity considerations), for Penrose ``the evidence seems to point, instead, to a highly ordered structure at the Big Bang''.NEWLINENEWLINE Finally, the author mentions that there are numerous constraints and consistency checks from both theory and observation for the stronger version of CCC. This version assumes that each aeon is basically similar to the one preceding it, and `one reads' that ``this stronger version of CCC will stand or fall in accordance with them [these checks]''.NEWLINENEWLINEFor the entire collection see [Zbl 1238.83004].