The Janus Point

A New Theory of Time


By Julian Barbour

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In a universe filled by chaos and disorder, one physicist makes the radical argument that the growth of order drives the passage of time — and shapes the destiny of the universe.
Time is among the universe's greatest mysteries. Why, when most laws of physics allow for it to flow forward and backward, does it only go forward? Physicists have long appealed to the second law of thermodynamics, held to predict the increase of disorder in the universe, to explain this. In The Janus Point, physicist Julian Barbour argues that the second law has been misapplied and that the growth of order determines how we experience time. In his view, the big bang becomes the "Janus point," a moment of minimal order from which time could flow, and order increase, in two directions. The Janus Point has remarkable implications: while most physicists predict that the universe will become mired in disorder, Barbour sees the possibility that order — the stuff of life — can grow without bound.
A major new work of physics, The Janus Point will transform our understanding of the nature of existence.



THIS BOOK’S ORIGINAL SUBTITLE was A New Theory of Time’s Arrows and the Big Bang. That is what its substance remains, but I was happy to accept the suggestion of TJ Kelleher, my editor of the US edition, and adopt its present shorter form. I think there is warrant for it. The big bang not only gave birth to time but also stamped on it the eternal aspect of an arrow’s flight. Thus the two together do amount to a new theory of time. Please note the indefinite article in the subtitle. Nothing in science is definitive. Hypotheses are proposed and tested. Science progresses when, through precise experiment and good observation, predictions are either confirmed or refuted. I believe the proposed explanation of time’s arrows is as secure as is the long-established expansion of the universe, but some radical ideas about the big bang, which matured late in the writing of the book, are definitely speculative. I have nevertheless decided to include them because they do represent what seems to me, now that they have been recognised, to be an almost inevitable bringing together of everything else.

This is a very personal book in which I have tried to combine established science of the cosmos with new ideas, but I also include here and there my own reactions to existence in the universe and wonder at its nature. How is it that time has not only created the physical world of atoms and galaxies but also poets, painters, and composers? The works of Shakespeare have been a great joy in my life. You will find him quoted explicitly in a dozen or so places, but for buffs of the Bard I have also, now and then and unattributed, smuggled in from his plays and sonnets a half line or even a single word. I hope you will get a little pleasure if you spot these purloined feathers. The final chapter is not quite an epilogue because it brings in discussion of the arrow we experience most directly, that of the passage of time. I think this is intimately related to the greatest mystery of all—the gift of consciousness. Don’t expect any answer to the mystery, but perhaps I can offer illumination of one of its aspects. Otherwise the chapter is an attempt to identify what it is in the mathematics of the universe that is manifested in art. It must be there since all great art has a unique structure, and structure is the very essence of mathematics.

As regards mathematics itself, inclusion of some in the book is inevitable, if only to avoid endless circumlocution. It is the concepts that count. Formulas are given for three concepts; that’s all there are. Their names then make many appearances. The mere repetition may help. The renowned mathematician John von Neumann is reputed to have said, “Young man, you do not understand mathematics, you get used to it”. There is a lot of truth in that. I think all my readers know perfectly well what the circumference of a circle is. With luck you will come to a similar intuition for the single most important concept in the book. I call it complexity. As I do here, I have used italics in the book almost exclusively to flag the first appearance of an important concept.

At the end of the book there is a list of the figures—there are twenty-six—and the page on which you will find them. Also at the end of the book, together with some additional material, I have compiled some technical notes for readers with at least some background in physics and mathematics, roughly from first-year university students to advanced researchers who want to see the evidence for statements in the body of the book and perhaps follow them up. There is also a bibliography restricted to books and technical papers that have a more or less direct relation to this one. It includes my own The End of Time, published in 1999. I mention it here because some of the readers of this book will have read it and may wonder how my second venture into the genre of books for general readers differs from it. All I will say here is that the two books cover the same theme—time’s arrows and their origin—but from a point of view that is somewhat different. When appropriate, I draw attention to specific differences in footnotes. There is, of course, an index.

This book could never have appeared or taken the form it does without critical input during the last eight years from my current collaborators Tim Koslowski, Flavio Mercati, and David Sloan. Some of the most important ideas come from them. It has been a great pleasure to work with them—Tim since we first met at the Perimeter Institute in Canada in 2008, Flavio since 2011, and Dave since 2015. Flavio also generated all but one of the book’s figures and found online the one he did not create—the fine double-headed Janus on a Roman coin in Fig. 3. The figures are a very important part of the book and I am most grateful to Flavio for them.

To continue with acknowledgements: What we call shape dynamics—it’s a representation of the dynamical essence of the theories of both Newton and Einstein—forms the mathematical core of this book; recent developments of it owe much to Tim, Flavio, and Dave. The notes include references to people who either directly or indirectly contributed to its earlier development, but I should mention here Bruno Bertotti (with whom I collaborated closely from the mid-1970s until 1982 and whom I was able to see in September 2018, just a month before he died), Niall Ó Murchadha, Bryan Kelleher, Brendan Foster, Edward Anderson, Sean Gryb (whom I also met at the Perimeter Institute through my friend Lee Smolin, who was his PhD supervisor there), and Henrique Gomes. Numerous visits to the Perimeter Institute, which hosted three workshops on shape dynamics, were much appreciated, as were, at the invitation of Viqar Husain, two visits (one for a workshop) at the University of New Brunswick in Fredericton. Sean Gryb also organised a valuable shape dynamics workshop at Nijmegen in the Netherlands and, with Karim Thébault, two at the University of Bristol. Two other friends of long standing with whom I have had many valuable and informative discussions are Karel Kuchař, of the University of Utah in Salt Lake City, and Christopher Isham, of Imperial College in London.

Although they are not involved in shape dynamics, I must here also thank very warmly Alain Chenciner and Alain Albouy, of the Institut de Mécanique Céleste et de Calcul des Éphémérides at the Observatory of Paris. Through the kind introduction of Richard Montgomery, of the Department of Mathematics at the University of California, Santa Cruz, I have been interacting with them on and off for twenty years. With their help I have learned much about the oldest and still in many ways the most important problem in mathematical physics; it goes right back to Isaac Newton and concerns the behaviour of point particles that interact in accordance with Newton’s laws of motion and universal gravitation. It turned out that some of the most beautiful results gleaned in its study, literally over centuries, are almost tailor-made to be the foundation of much of this book. It would not be what it is without their help. To combine visits to Paris with discussion at the venerable Observatory has been a rare pleasure.

Closer to my home, Harvey Brown, working in the philosophy of science at the University of Oxford, has been a good friend and sounding board for ideas in discussions over many years; I have also had useful discussions with his colleagues Simon Saunders and Oliver Pooley. Pedro Ferreira, another professor at Oxford, in the Department of Astrophysics, has, almost inadvertently but through welcome interest in shape dynamics, played a critical role in determining the present content of my book. About five years ago he set Tim and me a challenge to see if, in the framework of Newtonian gravity represented in shape-dynamic form, we could find an alternative to what is called inflation in cosmology and is the basis of the current theory of large-scale structure formation in the universe. Pedro was also a great help in introducing us to the cosmologist Michael Joyce, who is also in Paris, though not at the Observatory. I am not going to claim we have met Pedro’s challenge, but through it some entirely unexpected possibilities have come to light and figure prominently in the book. They relate to the nature of the big bang and, presented in Chapters 16 through 18, are the radical ideas mentioned above. Because they may be controversial, this is where, as the author, I must stick my colours to the mast. Hypotheses, especially if they have some plausibility, are, I think, acceptable; outright errors are quite another thing. In this book I am, especially in the ideas about the big bang and the final state of the universe, going out on something of a limb. If it breaks or I fall, any and all mistakes in the book are entirely my responsibility.

I must also warmly thank my agent, Max Brockman, of Brockman Inc in New York, and his parents, John Brockman and Katinka Matson, who handled my book The End of Time. I also want to very especially thank my two editors: TJ Kelleher for Basic Books in the United States (he tells me TJ is the invariable moniker by which he is known, both to family and to colleagues) and Will Hammond of Bodley Head in the UK. Having been involved with few books dealing with science for general readers, Will was glad to leave editing to TJ. Work with him has been most stimulating. He has been just what an editor should be: supportive throughout but clear about what must go or be changed.1

One major excision I will mention. I began work on this book three and a half years ago thinking I needed not only to study the history of thermodynamics, the discovery and development of which first brought to the fore the mystery of time’s arrows, but also to include in the book a lot of the history, which has certainly given me a strong sense of its importance. As TJ pointed out, the first draft contained far too much; all that now remains explicitly is the minimum needed to set the scene and introduce some of the concepts and issues that feature in the heart of the book. However, there remains an arc of history that still informs the structure of the book. Moreover, several friends and colleagues were gratifyingly positive about the history and said it should see the light of day. I have therefore taken the chapters that were written but have been removed and put them as a PDF on my website,; I hope to be able in the not too distant future to tidy them up as a book on the history of thermodynamics. You get that only in a very condensed form in this book; I hope anyone interested in the history will visit my website and perhaps download the PDF.

That brings me to one more thing: the great value of the internet and especially Wikipedia. When I next see an appeal to support Wikipedia, I do intend to make a contribution. I also recommend you check out Google Images for images of the various scientists I mention and look at Wikipedia for their biographies. It is all so easy nowadays; I think you will find it well worth the minor effort of a click.

Mention of modern digital technology brings me to thank Melissa Veronesi of Basic Books for her help with final checking of the text as it came to me from the copy editor, Sue Warga, who has done a great job. It has been an eye-opener to see in how many ways text can be made to flow better. I am also very grateful to my son, Boris, for help with digital issues and preparation of the text.

Boris is not the only member of my family I want to thank. My wife, Verena, succumbed to Alzheimer’s just after I submitted the proposal for this book to my agent in June 2016; she had remained wonderfully cheerful to the end. But in the midst of the writing of this book, eighteen months after her mother’s death, I lost my daughter Jessica. Her two sisters, Naomi and Dorcas, together with Boris, have been a great comfort, as have eight grandchildren, including Jessica’s two daughters. You will see that the book is dedicated to the memory of Verena and Jessica. Both very greatly enriched my life.


1 TJ also suggested I indicate, with extra space between paragraphs, changes of topic within a chapter greater than what you normally find between paragraphs. I liked the idea and the larger spaces are there; they mark places where you can pause, for example, for a tea or coffee break.



The Universe is made of stories, not of atoms.


TIME FLOWS FORWARD. EVERYONE HAS THE FEELING. IT IS MORE THAN MERE feeling; it has a real counterpart in observable phenomena. Processes near and far in space and time all unfold in the same direction. All animals, us humans included, get older in the same direction. We never meet anyone getting younger. Astronomers have observed millions of stars and understand very well how they age—all in the same direction as us. On seashores around the world, waves build and break—they never ‘unbreak’.

We remember the past, not the future. There are arrows of time. A film run backwards confounds cause and effect: instead of divers making a splash on entering the water, they emerge from it while the splash disappears. Myriad arrows permeate our existence. They are the stuff of birth, life, and death. In their totality, they define for us the direction of time.

Three arrows are particularly important because they can be treated with a good degree of mathematical precision.

The first, with which we will be much concerned, is the common process of equilibration. To see an example and its end result, put a tumbler of water on a table and disturb its surface by stirring the water vigorously with your finger. Remove your finger. Very soon the disturbance subsides and the surface becomes flat. You have witnessed an irreversible process. You can watch the surface for hours on end and it will never become disturbed spontaneously. The observationally unchanging state reached through equilibration corresponds to equilibrium. This is an example you can see. More important for the subject of this book is one you can feel—the equalisation of temperature. Go from a warm room to a cold room and you immediately feel the difference because your body is losing heat to the air around it. Many similar examples could be given: hot coffee in a mug, if not drunk, cools to the ambient temperature of the room.

The next arrow relates to what are called retarded waves. Don’t worry about the name. You see a beautiful example whenever you throw a stone into a still pond and circular waves spread out from the point of entry. The waves are said to be retarded because they are observed after the impact of the stone—the effect follows the cause. You never see waves that mysteriously start in unison at the bank of the pond, converge on its centre, and eject a stone that then lands in your hand—although the laws of hydrodynamics and mechanics are perfectly compatible with the possibility. It is not only water waves that invariably exhibit retardation; so do the radio and TV signals that reach your home from transmitters.

The third example is in quantum mechanics and is the notorious problem of Schrödinger’s cat. In accordance with the quantum formalism, a certain wave function can describe a cat that is simultaneously both dead and alive. Only when an observation is made to establish the cat’s state is there collapse of the wave function and just one of the two possibilities is realised.

Arthur Eddington, the British astrophysicist who in 1919 made Einstein into a world celebrity overnight with a famous telegramme to the London Times that confirmed a prediction of the general theory of relativity, coined the expression ‘arrow of time’ in the 1920s. Eddington had in mind mainly the arrow associated with equilibration, but people often use it as a portmanteau expression to cover all the arrows, as I will.

BECAUSE THE ARROWS of time are so ubiquitous it’s easy to take them for granted, but since the early 1850s theoreticians have seen in them a major problem. It is easily stated: apart from a tiny temporal asymmetry in one single law that, just after the big bang, was one of the factors that prevented complete mutual annihilation of matter and antimatter but cannot have played any significant role in creating the currently observed huge asymmetry between past and future, all the remaining laws of nature make no distinction between past and future. They work equally well in both time directions. Take a very simple law, the one that governs billiard balls. Unlike divers plunging into water, a film that spans their impact does look the same forwards and backwards. Physicists say laws like that are time-reversal symmetric. By this, they do not mean that time is reversed but that if at some stage all relevant velocities are precisely reversed, the balls will retrace, at the same speeds, the paths previously taken. More complicated is the case of charged particles in a magnetic field; the direction of the field must also be reversed along with the particle velocities if the retracing is to occur. There is an even more subtle case related to electric charges, mirror reflection, and the single fortuitous rule-breaking exception which allowed a minuscule amount of matter to survive after the big bang and we who are made of it to come into existence billions of years later. In all cases, the problem is the same: if the individual laws of nature that count do not distinguish a direction of time, how does it come about that innumerable phenomena do?

This question throws up such basic issues that we cannot hope to answer it unless we identify secure foundations for our theorising. One such foundation is that all meaningful statements in science are about relationships. This applies to the very notion of the direction of time. We recognise one because all around us we have those multitudinous unidirectional arrows. Without their constant presence, a single diver emerging backwards out of turbulent water, leaving it smooth and flat, would not appear to violate the normal course of nature. Also important are the nature and precision of observation. Wearing night-vision spectacles sensitive to infrared light, we would not see the collision of billiard balls as the same backwards and forwards—we would see hot spots appear on both balls after the collision, while the film run backwards would show those spots disappearing. In cricket, infrared imaging cameras are used when umpires are in doubt whether the ball has nicked the bat or pad and, through friction, raised the temperature at a localised spot.

This sensitivity to the means of observation raises a critical question: are the laws of nature truly time-reversal symmetric? The answer almost universally given is that yes, they are at the fundamental level of elementary particles—there is no microscopic arrow of time, only one at the macroscopic level. This was the conclusion that scientists reached in the second half of the nineteenth century. It came about in the first place through one truly remarkable study. Towards the end of the eighteenth century, people started to investigate seriously the properties of heat. A large part of the stimulus for this was to understand the workings of steam engines and how to make them as efficient as possible. In 1824, the young French engineer Sadi Carnot published a book, remarkable for its profundity and brevity, on this problem. Initially it passed unnoticed, but in 1849 a paper by William Thomson (later Lord Kelvin) brought Carnot’s work to the notice of Rudolf Clausius, with dramatic effect: together with Thomson, Clausius played a key role in the creation of an entirely new science, for which Thomson coined the name thermodynamics.

Its first law states that energy can be neither created nor destroyed. Within physics, this formalises the long-held belief reflected in Lear’s warning to Cordelia: “Nothing will come of nothing”. The second law of thermodynamics introduces the fundamental concept of entropy, a great discovery by Clausius, who introduced the name. Entropy is, to say the least, a subtle notion that, since Clausius’s discovery, has been formulated in many different ways. Indeed, a search through the technical literature throws up about twenty different definitions of the second law. Some of them include entropy; others do not. Despite that, entropy is one of those scientific concepts that have entered common parlance along with energy, the big bang, the expansion of the universe, black holes, evolution, DNA, and a few more. In a non-technical simplification that can mislead, entropy is widely described as a measure of disorder. The most common formulation of the second law states that, under controlled conditions that allow proper definition, entropy cannot decrease and generally will increase. In particular, entropy always increases in any process of equilibration in a confined space. Among the various arrows of time, entropy’s growth is the one that the majority of scientists take to be the most fundamental. The second law, often referred to without the addition ‘of thermodynamics’, has acquired an almost inviolable aura. In quite large part this is due to Clausius, who knew how to make sure that, deservedly, his results lodged securely in the mind. The paper of 1865 in which he coined ‘entropy’ ends with the words “Die Entropie der Welt strebt einem Maximum zu” (the entropy of the universe tends to a maximum). This statement had the impact that Clausius intended and was taken to mean that the universe will eventually expire in the heat death of thermal equilibrium. In human terms, there’s a near anticipation of this in the final quatrain of Shakespeare’s Sonnet 73:

In me thou see’st the glowing of such fire,

That on the ashes of his youth doth lie,

As the death-bed whereon it must expire,

Consum’d with that which it was nourish’d by.

Not surprisingly, the second law is grist for the mill of all pessimists. For many scientists, the growth of entropy, and with it disorder, is the ineluctable arrow that puts the direction into time. The mystery then is how the arrow gets into things so profoundly if the laws give no indication that it should.

THE DIFFICULTY RESIDES in the structure of the laws. By themselves they do not tell you what will happen in any given situation. You have to specify an initial condition. In the billiard example, you need to say where the two balls are at an initial time and the velocities they have at that moment. The law will then tell you what subsequently happens. It will give you a solution. The situation is this: Law + Initial ConditionSolution. In the simplest billiard example, the solution is time-reversal symmetric, just like the law that creates it. But the examples of processes with which I began this book most definitely are not. As I indicated then, scientists have not yet been able to resolve the mismatch between the symmetric laws and the asymmetric solutions.

What they have been able to do is at best give a partial solution. To illustrate this, one needs a game with more balls than billiards: snooker. The game begins with the white cue ball striking the triangle of fifteen reds. Successive impacts send the balls flying in all directions. No individual two-ball impact distinguishes a direction of time. But what then happens does. That’s where the law which at the elementary two-ball (microscopic) level describes a phenomenon without an arrow is able to create a many-ball effect with a macroscopic arrow. Theoreticians are universally in agreement that many dynamical ‘agents’ (the balls in snooker, elementary particles in fundamental physics) must be present if a macroscopic arrow is to emerge from time-symmetric microscopic laws.

However, this is at best a necessary condition; by itself it is not sufficient. To understand this, make a film of the initial impact in a game of snooker, its explosive effect, and a few bounces off the table walls. Run it backwards. Each individual impact again satisfies the reversible billiard law. But, in a seeming miracle, reds with apparently random speeds and directions of motion conspire in the midst of their chaos to come to rest in a perfect triangle and eject the white.

Of course, there is no miracle. The game begins with a special initial condition. That singles out a special solution. Only the tiniest fraction of all possible solutions is like that. But the example does at least show that reversible laws are compatible with solutions like ‘unbreaking’ waves, provided that sufficiently many objects are involved. There is no absolutely irreconcilable conflict with the laws of nature even if one has to invoke something close to divine intervention. De facto, this is what physicists are forced to do. They have to assume that at some time in the distant past, most probably at the big bang, the universe was in a special state of extraordinarily high order, the ultimate origin of all time’s arrows.

The philosopher of science David Albert has dubbed this assumption the ‘past hypothesis’. It was first proposed by the great Austrian physicist Ludwig Boltzmann in the 1890s as one possible way to explain what is now called the arrow of time. But it’s a stopgap he did not favour because it does not respect temporal symmetry. Science aims to explain phenomena by laws, not by inexplicable initial conditions arbitrarily imposed. By that criterion, the hypothesis fails, as I think Albert himself would not deny. But this leaves us in a very uncomfortable place: the most profound aspects of existence are attributed not to law but to a special condition ‘put in by hand’. It’s not a resolution; it’s an admission of defeat. However, I would not be writing this book if that were all I had to say. Plenty of other writers have already done a good job of describing the problem; their books are included in the bibliography and there are brief comments about them in the notes to this chapter.

INSTEAD, I’M GOING to suggest that the problem could have a genuine—and surprisingly simple—resolution. My collaborators and I stumbled on it a few years ago while working on a different problem. In this chapter I will give you an outline of our proposal and then fill out the necessary details in the chapters that follow. If the proposals that I present are on the right lines, I think that, taken together, they do amount to a new theory of time itself and not just its arrows. While the arrows by themselves represent a major aspect of time and a huge part of our deepest and most intimate experience, a proper understanding of their nature is impossible without a radical transformation of our notion of time. Accordingly, this book has two parts. The first sets the scene with a brief history of thermodynamics, formulates its principles, and explains why they fail to solve the problem of time’s arrows. The second presents the proposed solution; it takes up the bulk of the book.

We need the history because thermodynamics grew out of a specific problem which arose at a particular point in time: the industrial revolution and Sadi Carnot’s search for the most efficient way to operate steam engines. In that slim booklet published in 1824 he laid down principles of remarkable robustness—they have stood now for almost two hundred years—but they all apply in a ‘box scenario’, that is, to steam, gas, or any fluid in an impermeable and insulating container. Despite this critical condition, it is widely assumed that the laws of thermodynamics and the notion of entropy can be carried over more or less unchanged to cosmology. But the universe is not in a box; it is expanding, seemingly without impediment.


  • "It's worth the effort."—Andrew Crumey, The Wall Street Journal
  • "In The Janus Point, physicist Barbour argues with poetic erudition for a solution to the vexing problem of time's apparent one-way flow: a mirrorlike temporal duality in which the big bang is not an explosive cosmic beginning but rather 'a special point on the time line of the universe.'"—Lee Billings, Scientific American
  • “[Barbour]’s provocative theory offers an optimistic view of our cosmic destiny….An engaging and inspiring read.”—Matthew Johnson, Science magazine
  • "In his radical new book, Julian Barbour argues that...time flows in not one, but two ways.... Such an argument might seem overly technical, but it's explained simply and accessibly for all to understand."—BBC Science Focus
  • "The origin of the arrow of time is arguably the most important conceptual problem in cosmology, and the prospect that it can be solved in a universe where time flows 'backward' in the far past is as exciting as it is provocative. In this engaging book, Julian Barbour conveys this excitement admirably, complete with just a bit more detail than professional physicists usually share with the public."
    Sean Carroll, author of From Eternity to Here
  • "With a rare humanity and a perspective based on a lifetime of study of the history and philosophy of cosmology, Julian Barbour writes a book that is both a work of literature and a masterpiece of scientific thought."—Lee Smolin, author of The Trouble with Physics
  • "Julian Barbour's infectious enthusiasm for the big ideas in physics is addictive. He has a complete mastery of the history of ideas yet a remarkable lightness and clarity in explaining what are profound concepts. The Janus Point is controversial and gripping, an extraordinary introduction to his view of the universe."—Pedro G. Ferreira, author of The Perfect Theory
  • "By abandoning the prejudice that particles (atoms, stars...) are confined in a box, Julian Barbour has discovered an unexpected and remarkably simple feature of Newtonian dynamics. It is the basis of his seductive and eloquently presented explanation of the history of the universe, even time itself. Is his cosmology correct? 'Time' will tell."—Michael Victor Berry, MelvilleWills Professor of Physics (Emeritus), Bristol University
  • "Julian Barbour has no peer when it comes to explaining scientific ideas in a way that is accessible without being simplistic.... This is a fitting sequel to his earlier work and helps to pull together several big ideas that some of us have been watching with fascination for decades."—Neal Stephenson, author of Snow Crash
  • "Julian Barbour is a profound and original thinker, with the boldness to tackle some of nature's deepest problems. He is also a fine writer, and this renders his book -- despite its conceptual depth -- accessible to anyone who has pondered the mysteries of space and time. It's a distillation of the author's prolonged investigations, and the insights that he offers deserve wide readership."—Martin Rees, author of On the Future
  • "For me the main point of the book was to show history-in-the-making.... The book has given me a lot to ponder. As Gauss said of Riemann's habilitation lecture, ‘it exceeded my expectations.'"—Bill Unruh, professor of physics, University of British Columbia
  • "In this delightful, provocative book, Julian Barbour shares his learned insights and passion about deep questions of time, change, and the origin of the universe with all its creative variety. A cosmic physics adventure, enlivened with history and poetry."—Theodore A. Jacobson, professor of physics, University ofMaryland

On Sale
Dec 1, 2020
Page Count
400 pages
Basic Books

Julian Barbour

About the Author

Julian Barbour is the author of the highly regarded The Discovery of Dynamics and the bestseller The End of Time. He received his PhD in physics from the University of Cologne in 1968. He is a past visiting professor of physics at the University of Oxford and lives on the edge of the scenic Cotswolds, UK.

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