Space has three dimensions, and if you do not want to stay at your destination, you can buy a return ticket. Time has but a single dimension, and only one-way travel is allowed: we remember a definite, youthful past but can only imagine possible futures where we grow old and decay. Even though the fundamental laws acting on individual atoms appear to care naught for the direction of time’s axis, macroscopic phenomena most definitely do.

To resolve this conundrum, any physicist will refer you to the second law of thermodynamics, and the concept of increasing entropy. The familiar progression from order to disorder is explained as a consequence of statistics: a game of chance becomes effective certainty when more than a few particles are involved. But is it really that simple? Are all the issues resolved?

The final answers to these questions almost certainly lie in the future, as the subtitle to Sean Carroll’s book From Eternity to Here: The Quest for the Ultimate Theory of Time suggests. However, discussing them in the present can still be an interesting exercise. The ideas that Carroll, a physicist at the California Institute of Technology, puts into play are fascinating in their extent, scope and description. They cover areas as diverse as time in special and general relativity (including the question of time travel), entropy and the arrow of macroscopic time, the psychology of time; and the nature of the beginning and end of time.

Carroll’s main theme is the meaning of time’s arrow as embodied in the second law, and its relationship with cosmology and the origin of the universe. He pays particular attention to the conundrum of time as a one-way trip – an oddity that is all the more perplexing because, Carroll believes, the fundamental laws at a microscopic level are time-reversible. But while this may be true, there are nonetheless hints of time asymmetry in the behaviour of certain fundamental particles. We also inhabit a universe where, apparently, there is a gross asymmetry between matter and antimatter. Until we understand the origin of the matter/antimatter asymmetry – which is critical for our existence – I would hesitate to draw conclusions about the extent of other possible asymmetries.

These are deep waters, but Carroll navigates them successfully, thanks in part to extensive and effective footnotes that enable him to separate more technical remarks from the flow of a readable main text. This is a technique that works well. Were it used more widely in the genre, it could enable physics books to reach a wider readership, by allowing those who want to explore deep ideas to do so without at the same time frightening off more general readers. It did, however, provide me with one of the book’s few minor irritants. Occasionally a footnote was used for some more trite remark, as if the author was embarrassed to have put something meaty in the main text and wanted a jokey aside to sweeten the pill. The comparison between the public’s perceptions of Einstein and Paris Hilton was, I felt, particularly grating.

My other minor quibble concerns physics. Throughout much of the text, entropy is described as if it is a pure number. Yet in the notes and in at least one appearance in the main body, it is described in terms of Boltzmann’s constant, and hence carries dimensions of energy per degree. There was sometimes confusion as to whether entropy or log(W) was being discussed, and to what extent, if any, this mattered. If this was explained, I missed it.

Whatever the precise definition of entropy, if it should turn out that time’s arrow for macroscopic objects is tied to entropic increase, there is an unresolved enigma: why was entropy so small at the Big Bang? This forms one of the more powerful themes in Carroll’s book.

The issue of creation is itself an enigma, though not in the way creationists have argued. Some have claimed – erroneously – that the appearance of life requires a decrease in entropy, and thus implies a violation of the second law. Carroll neatly dismantles such claims by pointing out that if they were true, then refrigerators could not exist. The difference between closed and open systems is critical here, as in so many cases.

This much is well known. What I found intriguing was that Carroll then goes on to examine the entropy problem in a quantitative fashion. The sky, he writes, contains a hot Sun in a cold background – the very epitome of a non-equilibrium situation. For every high-energy photon that arrives here from the Sun, the Earth radiates 20 lower-energy photons into space. This increase in entropy exceeds the local decrease produced by the collective efforts of the biosphere. Nevertheless, if the micro-states of the planet started from utter disorder, the entire biomass could still be converted into a state of high order by such processes. And how long would this require? As far as the second law is concerned, Carroll claims, a year would be enough. Ironically, it seems that the creationists have aimed at the wrong target: physics, far from being inconsistent with biblical accounts of human existence, would allow the entire biomass to emerge within a single year, and certainly within 6000. Over to the biologists as to why it actually took billions!

The real creation of our observable universe, 13.6 billion years ago, suggests an even bigger conundrum: how did the universe’s initial state of low entropy arise? One possibility is that in an infinite and everlasting universe, entropy fluctuates. It is therefore conceivable that we could be in a 14 billion year period in which entropy has increased following a long-ago downward fluctuation, the end of which we perceive to be the start of “time”. Carroll examines this thesis, and points out its flaw: a random fluctuation capable of producing human beings would be remarkable enough (although had it not happened we would not be here to ask the question), so it seems too much to accept an entropic fluctuation that produced the order encoded in galaxies of stars – and much else that, so far as we can tell, is unnecessary for our existence.

Carroll does not discuss whether it might be “easier” to fluctuate billions of galaxies into existence than to produce sentient life. After all, if thermodynamics alone could produce a biosphere in a year, biology must introduce lots of “friction” into evolution. Billions of galaxies courtesy of fluctuation, combined with the chance that there is an Earth-like environment somewhere, might be a more efficient route to a winning lottery ticket. Can we rule that out so easily? Although it is hugely unlikely, is it any less likely than the chance that out of the effectively infinite possible combinations of DNA, it was the ones that made me and you that burst into life, enabling us to know that there is a universe?

Possibly it is. You might disagree with Carroll; you might disagree with me; but a book that makes you think is worth reading. Whether the future will show Carroll’s ideas are forever or just the latest in a never-ending debate, only time will tell.