''Cycles of Time: An Extraordinary New View of the Universe'' is a science book by

mathematical physicist Mathematical physics refers to the development of mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developmen ...

Roger Penrose published by

The Bodley Head The Bodley Head is an English publishing house, founded in 1887 and existing as an independent entity until the 1970s. The name was used as an imprint of Random House Children's Books from 1987 to 2008. In April 2008, it was revived as an adul ...

in 2010. The book outlines Penrose's

Conformal Cyclic Cosmology Conformal cyclic cosmology (CCC) is a cosmological model in the framework of general relativity and proposed by theoretical physicist Roger Penrose. In CCC, the universe iterates through infinite cycles, with the future timelike infinity (i.e. the ...

(CCC) model, which is an extension of

general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...

but opposed to the widely supported multidimensional string theories and

cosmological inflation In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from seconds after the conjectured Big Bang singularit ...

following the Big Bang.

Synopsis

Penrose examines implications of the Second Law of Thermodynamics and its inevitable march toward a maximum

entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...

state of the

universe The universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development of the universe. ...

. Penrose illustrates entropy in terms of information state phase space (with 1 dimension for every

degree of freedom Degrees of freedom (often abbreviated df or DOF) refers to the number of independent variables or parameters of a thermodynamic system. In various scientific fields, the word "freedom" is used to describe the limits to which physical movement or ...

) where particles end up moving through ever larger grains of this phase space from smaller grains over time due to random motion. He disagrees with Stephen Hawking's back-track over whether information is destroyed when matter enters black holes. Such information loss would non-trivially lower total entropy in the universe as the black holes wither away due to

Hawking radiation Hawking radiation is theoretical black body radiation that is theorized to be released outside a black hole's event horizon because of relativistic quantum effects. It is named after the physicist Stephen Hawking, who developed a theoretical a ...

, resulting in a loss in phase space degrees of freedom. Penrose goes on further to state that over enormous scales of time (beyond 10¹⁰⁰ years), distance ceases to be meaningful as all

mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different eleme ...

breaks down into extremely red-shifted

photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they a ...

energy, whereupon time has no influence, and the universe continues to expand without event . This period from Big Bang to infinite expansion Penrose defines as an

aeon The word aeon , also spelled eon (in American and Australian English), originally meant "life", "vital force" or "being", "generation" or "a period of time", though it tended to be translated as "age" in the sense of "ages", "forever", "timele ...

. The smooth "hairless"

infinite Infinite may refer to: Mathematics * Infinite set, a set that is not a finite set *Infinity, an abstract concept describing something without any limit Music *Infinite (group), a South Korean boy band *''Infinite'' (EP), debut EP of American m ...

oblivion of the previous aeon becomes the low-entropy Big Bang state of the next aeon cycle.

Conformal geometry In mathematics, conformal geometry is the study of the set of angle-preserving ( conformal) transformations on a space. In a real two dimensional space, conformal geometry is precisely the geometry of Riemann surfaces. In space higher than two di ...

preserves the angles but not the distances of the previous aeon, allowing the new aeon universe to appear quite small at its inception as its phase space starts anew. Penrose cites concentric rings found in the

WMAP The Wilkinson Microwave Anisotropy Probe (WMAP), originally known as the Microwave Anisotropy Probe (MAP and Explorer 80), was a NASA spacecraft operating from 2001 to 2010 which measured temperature differences across the sky in the cosmic mic ...

cosmic microwave background In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...

survey as preliminary evidence for his model, as he predicted black hole collisions from the previous aeon would leave such structures due to ripples of

gravitational waves Gravitational waves are waves of the intensity of gravity generated by the accelerated masses of an orbital binary system that propagate as waves outward from their source at the speed of light. They were first proposed by Oliver Heaviside in 1 ...

Reception

Most nonexpert critics (nonscientists) have found the book a challenge to fully comprehend; a few such as '' Kirkus Reviews'' and Doug Johnstone for ''

The Scotsman ''The Scotsman'' is a Scottish compact newspaper and daily news website headquartered in Edinburgh. First established as a radical political paper in 1817, it began daily publication in 1855 and remained a broadsheet until August 2004. Its pare ...

'' appreciate the against the grain innovative ideas Penrose puts forth.

Manjit Kumar Manjit Kumar (born 1963) wrote the popular science book '' Quantum'' which was shortlisted for the BBC Samuel Johnson Prize for Non-Fiction, 2009. and was also co-author of the book ''Science and the Retreat from Reason''. He has degrees in physi ...

reviewing for ''

The Guardian ''The Guardian'' is a British daily newspaper. It was founded in 1821 as ''The Manchester Guardian'', and changed its name in 1959. Along with its sister papers ''The Observer'' and ''The Guardian Weekly'', ''The Guardian'' is part of the Gu ...

'' admires the Russian doll geometry play of the CCC concept, framing it as an idea of which

M. C. Escher Maurits Cornelis Escher (; 17 June 1898 – 27 March 1972) was a Dutch graphic artist who made mathematically inspired woodcuts, lithographs, and mezzotints. Despite wide popular interest, Escher was for most of his life neglected in t ...

"would have approved". Graham Storrs for the ''New York Journal of Books'' concedes that this is not the book that an unambitious lay person should plunge into. The American fiction writer

Anthony Doerr Anthony Doerr (born October 27, 1973) is an American author of novels and short stories. He gained widespread recognition for his 2014 novel ''All the Light We Cannot See'', which won the Pulitzer Prize for Fiction. Early life and education Rais ...

in ''

The Boston Globe ''The Boston Globe'' is an American daily newspaper founded and based in Boston, Massachusetts. The newspaper has won a total of 27 Pulitzer Prizes, and has a total circulation of close to 300,000 print and digital subscribers. ''The Boston Glob ...

'' writes "Penrose has never shied away from including mathematics in his texts, and kudos to his publisher for honoring that wish. That said, the second half of ''Cycles of Time'' offers some seriously hard sledding"; "If you'll forgive a skiing metaphor, ''Cycles of Time'' is a black diamond of a book."

References

{{DEFAULTSORT:Cycles of Time (book) 2010 non-fiction books Cosmology books Information theory Popular physics books The Bodley Head books Works by Roger Penrose