I have just been trying to make sense of an apparently brilliant new book by the eminent British mathematics professor, Roger Penrose, who is also the author of such earlier popular science bestsellers as The Road to Reality, a Complete Guide to the Laws of the Universe (Random House, New York, 2004) and The Emperor’s New Mind, Concerning Computers, Minds and the Laws of Physics (Oxford University Press, 1989). He also co-authored (with Professor Stephen Hawking) The Nature of Space and Time (Princeton University Press, 1996), which became a popular science best-seller.
Penrose’s latest work is Cycles of Time: An Extraordinary New View of the Universe (Knopf, New York, 2011, 288 pages). As you may have deduced already, a new work by Penrose is an important event in the world of astrophysics and, consequently, “Attention must be paid.” Well, I have to report to you that I paid significant attention to this book, but the experience left me a rather sadder and a barely wiser person. There is no “ah-ha” here, no revelations that make the theories of the expanding universe startlingly clear.
The problem is largely one of high-level mathematics, notably based on conformal geometries and 2-spinor formalism. “Saaay, whaat?” After the usual bromides that all the “real” mathematics is mostly dumped in a series of appendices, Penrose enthusiastically serves up a large dollop of conformal space-time geometries in an attempt to get the readers (or post-graduate doctoral fellows, if you get my drift!) up to speed on Prof. Penrose’s version of the Second Law of Thermodynamics and implications of the Big Bang Theory.
By the way, the book contains more than 30 pages of mathematics dealing with such topics as “conformal rescaling, 2-spinors, Maxwell and Einstein theory.” You may notice that when a math type describes some theoretical operation as “trivial,” it is far from being so. I have refrained from quoting the equations that Prof. Penrose provides mainly because my word processor does not have the appropriate Greek symbols. Trivial they are not!
You may be asking yourself, “So what is this new book about and why should I read it?” Well, in the book, Penrose does much to confirm how “black holes” could be formed and how they can result (in theory, at least) in the Big Bang as we know it.
But Penrose offers the radical extension to the Big Bang theory in which he proposes that the expansion of the galaxies as we know them could, by the mathematical examination with conformal geometries, have a cyclical life—the cycles of time that he proposes in this book. Prof. Penrose offers his theories by examining the thermal radiation in the Cosmic Microwave Background (CMB) that theoretically is expected to appear some 380,000 years after the Big Bang.
Prof. Penrose proposes that the universe could experience another Big Bang as the CMB slows the expanding universe. He calls this the Conformal Cyclic Cosmology (CCC), the “Cycles of Time,” as listed in the title of this book. However, all this is highly theoretical and based on abstruse math that even the best post-docs are unlikely to understand. I suspect that the number of scientists who could argue Penrose’s CCC could be counted on the fingers of one hand. Penrose admits as much himself.
The book has three major sections, plus a lengthy and somewhat curious prologue, a very brief and enigmatic epilogue, and the aforementioned mathematical appendices. The prologue purports to be a conversation between Tom, an apparently scientifically curious schoolboy, and his Aunt Priscilla, an astrophysics professor at the University of Cambridge. It should be noted that Penrose is the Emeritus Rouse Ball Professor of Mathematics at the University of Oxford. There are Rouse Ball Chairs at both Oxford and Cambridge.
As reported in the prologue, Priscilla attempts to give her nephew Tom an impromptu lecture on the Second Law of Thermodynamics. While out for an afternoon stroll, the pair examines an old water-powered mill and Priscilla babbles on about the Big Bang, managing to leave Tom (and this reader) completely in the dark. In my view, this appears to be an important book, but I’m damned if I can tell you why!
Penrose proposes that the expansion of the galaxies as we know them could, by the mathematical examination with conformal geometries, have a cyclical life—the cycles of time that he proposes in this book.