Cycles of Time: An Extraordinary New View of the Universe

The two key ideas underlying this novel proposal are a penetrating analysis of the Second Law of thermodynamics-according to which the ‘randomness’ of our world is continually increasing-and a thorough examination of the light-cone geometry of space-time. Penrose is able to combine these two central themes to show how the expected ultimate fate of our accelerating, expanding universe can actually be reinterpreted as the ‘big bang’ of a new one.

When I entered Cambridge University as a mathematics graduate student, in the early 1950s, a fascinating cosmological theory was in the ascendant, known as the steady-state model. According to this scheme, the universe had no beginning, and it remained more-or-less the same, overall, for all time. The steady-state universe was able to achieve this, despite its expansion, because the continual depletion of material arising from the universe’s expansion is taken to be compensated by the continual creation of new material, in the form of an extremely diffuse hydrogen gas.

the Second Law of thermodynamics is not an equality, but an inequality, asserting merely that a certain quantity referred to as the entropy of an isolated system-which is a measure of the system’s disorder, or ‘randomness’-is greater (or at least not smaller) at later times than it was at earlier times. Going along with this apparent weakness of statement, we shall find that there is also certain vagueness or subjectivity about the very definition of the entropy of a general system. Moreover, in most formulations, we are led to conclude that there are occasional or exceptional moments at which the entropy must be regarded as actually (though temporarily) reducing with time (in a fluctuation) despite the general trend being that the entropy increases.

What life depends upon is the fact that the Sun is much hotter than the darkness of space, and consequently the photons from the Sun have a considerably higher frequency (namely that of yellow light) than the infra-red photons that Earth returns to space

Thinking of these numbers as being just integers (whole numbers) gives a certain ‘granularity’ to phase space, and this provides the discreteness of the ‘quanta’ of quantum mechanics.

We call it Minkowskian if it is flat and Lorentzian if it is curved.

Photons, and their interactions with charged particles, do need space-time to have a null-cone structure-i.e. a conformal space-time structure in order that their equations can be formulated, but they do not need the scale factor that distinguishes one actual metric from another, consistent with this given null-cone structure.

When the universe enters this apparently final stage-what one might well call the ‘very boring era’-nothing of great interest seems to be left for it to do. The most exciting events prior to this were the final ‘pops’ of the last tiny remnants of black holes, eventually disappearing (it is supposed) after they had very gradually lost all their mass via the painfully slow process of Hawking radiation. One is left with the dreadful thought of a seemingly interminable boredom confronting the final stages of our great universe-a universe which would have once seemed so exciting, teeming with fascinating activity of hugely different kinds— most of this activity occurring within beautiful galaxies, with a wonderful variety of stars and often attendant planets, among which would be those supporting life of some kind, with its exotic plants and animals, some of whom having the capabilities of deep knowledge and understanding, and profound capabilities of artistic creation. Yet all this will eventually die away. The final dregs of excitement will have to be the waiting, and the waiting, and waiting, for maybe 10^100 years or more, for that final pop.