Time in Powers of Ten: Natural Phenomena and their Timescales, by Gerard ’t Hooft and Stefan Vandoren

Considering different timescales is a fun way to digest serious science, finds Graham Farmelo

July 24, 2014

I doubt any undergraduate lectures have proved more influential than Nobel prizewinner Richard Feynman’s physics course at the California Institute of Technology in the early 1960s. Although the lectures were reputedly not wholly successful in holding the attention of the majority of the students, the three-volume edition of his talks published a few years later became a classic and sold millions of copies around the world. Given this resounding success, it is disappointing that so few world-class scientists have given us their interpretation of the basics of their subject.

So it is pleasing that Gerard ’t Hooft, a theoretical physicist as distinguished as Feynman in my view, has recently been turning his hand to popularisation. In Time in Powers of Ten, he has collaborated with a Utrecht University colleague, the string theorist Stefan Vandoren, to produce this pleasingly accessible volume that will give pleasure to academics, students, connoisseurs of coffee-table books and even the people who compile questions for Trivial Pursuit.

The idea of the book is to compare natural phenomena on different timescales, beginning with the second (usually abbreviated simply to s), and going up and down in factors of 10. The idea is not new. It was apparently conceived by the Dutch teacher Kees Boeke, whose 1957 book Cosmic View: The Universe in 40 Jumps was the precursor to Charles and Ray Eames’ famous educational film Powers of Ten, which focused on scales of distance. Here, ’t Hooft and Vandoren focus on scales of time, from 10⁹⁰s, when the universe will have practically ceased to exist, right down to 10^-44s, the shortest time interval imaginable in our current understanding of the universe.

Cosmologists now know the age of the universe to a higher accuracy than most people know their own weight
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At these extremes, any description of the natural world is necessarily speculative but, as the distinguished physicist Steven Weinberg writes in the foreword, we now have theories and experiments sufficiently reliable that we have predictive understanding of the behaviour of nature on timescales ranging from the age of the universe to the half-life of the shortest-lived fundamental particle: 42 powers of 10. Cosmologists now know the age of the universe to a higher accuracy than most people know their own weight. When Weinberg describes this collective scientific achievement as “amazing”, he is not exaggerating.

The journey begins with the second, derived from the Latin for “next step”, the authors note. This is the time that a metre-long pendulum takes to swing from one side to another and the average duration of a human heartbeat (exact times are not important anywhere in the book, only the nearest order of magnitude, ie, power of 10). These and other examples each furnish the authors with opportunities to illuminate the underlying science, giving us a feel for how the world works on this timescale. Then, as we move up in successive powers of 10 – 10s, 100s, 1,000s, and so on – we gradually acquire a feel for nature on different timescales and how its behaviour is explained by the underlying scientific principles.

In their account of the everyday world, ’t Hooft and Vandoren give us examples from the fields of astronomy, geology, chemistry and even music (one soon sees the artificiality of these labels). Ten seconds, for example, is roughly the world record for the men’s 100m sprint and half the minimum rotation period of a white dwarf star; 100 seconds is close to the world men’s 1,500m record for speed skating on ice, the half-life of radium, and the time it takes to play Chopin’s Minute Waltz.

Human history is included, too – the Cuban Missile Crisis lasted for about a million seconds, three orders of magnitude shorter than the Thirty Years War (1618-48). I was amused to see the authors’ slight and forgivable bias towards Dutch heritage manifest by their inclusion of the little-known war between the Netherlands and the Isles of Scilly. The conflict lasted for about 10 billion seconds and ended officially only in 1986.

By the time we reach 10¹⁷s (3.17 billion years), we have left behind earthly geology and evolution but are still less than a quarter of the way to the age of the universe. Even when we arrive at that point, the journey is not over – several events and processes will take much longer than that, including the minimum foreseeable age of our universe (10¹⁸s) and the maximum lifetime of a red dwarf star, a sextillion seconds. (Sextillion, one of the many abbreviations we learn in the book, is the name scientists give to the multiple 10²¹.)

The authors end their outward trip in what they call “the dark eternities”. These are intimately connected with very short timescales associated with the possible decay of the nuclear particle known as the proton, they note. So it is therefore entirely natural for the second part of their book, a journey home to the second, beginning with the smallest imaginable time interval.

The only hope of scientifically describing reality in this fleeting domain is to use ideas from quantum gravity, a theory that is still currently in an embryonic state. It is nonetheless fascinating to see how knowledge of the behaviour of fundamental particles is informing our picture of the birth of the universe. When we reach a tenth of a billionth of a billionth of a billionth of a second after the beginning of time, “we are slowly but surely reaching timescales that we are able to conceptualise”, as the authors tell us when they begin to consider the timescale of 10^-19s, the time it takes light to traverse an atom.

Yet we are still some way from a millionth of a second, probably the shortest timescale that most people can relate to (it is accessible to the fastest stroboscopes). Soon, however, we are on terra firma, with the average duration of lightning (10^-5 second) and the millisecond workings of nerve cells. Having read in the book about the brief half-lives of subatomic particles, the comparatively huge timescales on which we live is relatively easy to grasp.

Time in Powers of Ten can be enjoyed as a source of scientific stories and images, as an unusual perspective on history, as a popular account of modern physics, and so on. Underneath them all is a wealth of serious science that will give readers insights into abstract fundamental ideas via concrete realities. The illustrations are good, although they would have been even better if they had been animated – the book cries out to be presented as a film or, even better, as an app.

Every science teacher would benefit from reading Time in Powers of Ten, but I hope it will have an even wider reach. Last year Caltech made Feynman’s lectures on physics available free online, a splendidly public-spirited move that I hope ’t Hooft and Vandoren will one day follow after they have made a respectable profit from the book. Their gem of science popularisation deserves nothing less.

The authors

“I wanted to become a scientist from as young an age as I can recall,” says Gerard ‘t Hooft, professor of theoretical physics at Utrecht University (top left). “I wanted to understand the laws of nature. I wanted to understand everything - although I was never very good in what we call the humanities.”

He was born in Den Helder, although he notes that it “left no trace in my memory. I was one year old when we moved to The Hague, where I spent my childhood. That, and my Dutch nationality, is certainly part of my character.

“The Netherlands is small enough to make one feel an important member of society there, and big enough to make a dent in world history. We have an excellent science tradition, and a rich cultural history.”

‘t Hooft lives in Houten, near Utrecht, “with my wife Betteke. I have two daughters, and now I am the proud grandfather of four”. Although his career has taken him to CERN in Switzerland and to Stanford and Harvard universities in the US, and he was “tempted” to remain in America, he chose “to live in the Netherlands and raise my children here. They later said that they would have been more than happy to grow up in America.” His daughter Ellen is a veterinarian; her sister Saskia translated Time in Powers of Ten from the Dutch.

Although ‘t Hooft’s CV lists countless accolades, all the rest are dwarfed by the one he collected in Stockholm in 1999 with his co-honoree, Martinus J. G. Veltman.

“The Nobel prize is the ultimate recognition one can receive for one’s work, and I found it extremely gratifying,” ‘t Hooft admits. Did it change how his research was seen? “It certainly affected the way people look at me. I do my best not to become too presumptuous about my own work, but you’ll have to ask others if I have failed in that.”

Appropriately for a scholar whose books include Playing With Planets (2008),’t Hooft has had an asteroid named after him, 9491 Thooft. He has written a satirical constitution that includes the prohibition of the use anywhere on 9491 of apostrophes – in recognition of the fact that the asteroid’s name has none, owing to International Astronomical Union conventions – and the requirement for its government officials to apologise “humbly” if anyone is obliged to wait for more than 15 minutes to be seen.

‘t Hooft observes: “The constitution of 9491 is just a persiflage. I could reflect some of my frustrations in it.” What would he would alter in constitutions on Earth were he given the job? “If I could change anything, I would change the act of religious freedom in the constitutions of many countries. Now, they dictate an infinite amount of respect for all the nonsense that many, if not all, religions proclaim. That’s the problem with all religious fanatics and extremists today; people are too afraid to say out loud how ill-conceived their thoughts are. They should be more thoroughly ridiculed.”

In his spare time, ‘t Hooft says, although even “enthusiastic amateur is an overstatement, I do like to play classical piano music. I used to paint, and now I like to produce art with my computer. As a child I built up a large shell collection from any beach I ever walked on, but now it’s rather in disarray.”

‘t Hooft’s “splendid colleague and co-author”, Utrecht professor of theoretical physics Stefan Vandoren (below left), was born and raised “in a small town called Bilzen, close to the Dutch and German border, in the northeastern part of Belgium. I am still attached to my roots, I visit about once a month, and I have definitely carried over some Belgian culture and tradition here into the Netherlands. It’s nice to have two legs in two countries and cultures!”

Vandoren has now lived for almost 15 years “in the centre of Utrecht, and I like it very much. It is a beautiful city with many canals, shops, bars and good restaurants, all in walking distance, or a short bicycle ride from home. Plenty of activities, and only half an hour away from Amsterdam.”

He recalls: “I was a very lazy student as a kid. I always had low marks and was not interested in studying anything at school. But reading popular science books about the universe made me want to study physics at university, despite the negative advice from everybody around me.” He duly applied to, and was accepted at, Belgium’s oldest and most acclaimed institution, Katholieke Universiteit Leuven. There, his cousin “taught me how to study as an undergraduate, and gradually I became ambitious, hard-working and more confident.” He adds: “These days I am interested in pretty much everything, and the passion for physics still keeps me going strong!”

Vandoren worked as a postdoctoral researcher at the University of Wales in Swansea and at the State University of New York, Stony Brook, before joining Utrecht in 2001. “I spent three years in the UK and two in the US. I loved it, and the postdoc years were a fantastic adventure. I once applied for a faculty position in the UK, but just missed out on it. Then came the Utrecht offer, and the rest is history. Sometimes, though, it does cross my mind to think about going to the US again. There’s no urgent need at the moment, although it’s true that the grass seems always greener somewhere else.”

On the question of whether it is harder for physicists to address to address a general readership today than it might have been in 1914 or 1964, Vandoren says, “I think this applies to most of science – think for instance about understanding the complexity of the human brain – but it probably was not that different 50 or 100 years ago. Einstein’s theory of general relativity, written down in 1915, was very hard to understand and explain to the general reader, even to many physicists of that time! It is only when the dust settles many years later, when the basic ideas become transparent and clear, that science can be explained well to a broader public. Yet in the meantime, we must do our utmost best to explain to laymen what we are doing and why.”

Invited to name the most important question about physics that he hopes will be answered in his lifetime, he replies, “That question would be: ‘What are black holes made of?’ We have so many puzzles and paradoxes about black hole physics, that the answers to them will likely lead to a new theory for the fundamental laws of physics.”
If he could magically obtain any skill he lacks, Vandoren would opt for “the talent to ask and formulate good questions that nobody has ever asked before. It leads to new ideas and insights, and eventually to new theories and applications. But this is pretty much the same as asking for the talent to become smarter, I’m afraid.”

Asked for his experience of the rather well-worn jokes about his countrymen that are still current in his adopted land, Vandoren confirms that, yes, “Dutch people do always joke about Belgians being stupid. So I just ask them: ‘So why did you give me a job?’”

Karen Shook