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To Carlo and Lee For entrusting me with your stories
Preface ix List of Abbreviations xvii About the Author xix
Prologue: An Irresistible Longing to Understand the Secrets of Nature 1
part i: foundations
1. The Laws of Physics are the Same for Everyone 11
2. There’s No Such Thing as the Force of Gravity 27
3. Why Nobody Understands Quantum Mechanics 45
4. Mass Ain’t What it Used To Be 65
5. How to Fudge the Equations of the Universe 83
part ii: f ormulation
6. To Get There I Wouldn’t Start from Here 107
7. A Gift from the Devil’s Grandmother 123
8. Our Second or Third Guess Solved the Equations Exactly 141
9. I Used Every Available Key Ring in Verona 159
10. Is There Really No Time Like the Present? 183
11. Gravitons, Holographic Physics, and Why Things Fall Down
12. Fermions, Emergent Particles, and the Nature of Stuff
13. Relational Quantum Mechanics and Why ‘Here’ Might Actually be ‘Over There’ 243
14. Not with a Bang: The ‘Big Bounce’, Superinflation, and Spinfoam Cosmology 263
15. Black Hole Entropy, the Information Paradox, and Planck Stars 285
16. Close to the Edge: The Reality of Time and the Principles of the Open Future
Like Being Roped Together on a
PREFACE
Let’s get one thing straight.
This is a book about loop quantum gravity, one of several contemporary approaches to the development of a quantum theory of gravity, perched right on the very edge of our current understanding of space, time, and the physical universe. One hopes that science at the frontiers will always make for entertaining reading but, make no mistake, like all such theories, as of today there is not one single piece of observational or experimental evidence to support it. 1
You might then wonder why I think you ought to be interested in this.
Here’s why. There’s little doubting that in these first few decades of the twenty-first century we face some tremendous economic, political, and environmental challenges, some much more stubborn and intractable than others. But when it comes to our ability to comprehend the nature of space and time, to understand the very fabric of physical reality, the quantum theory of gravity is simply the greatest scientific problem of our age.2 It addresses the ultimate ‘big question’ of existence. Resolving this problem demands a real depth of scientific expertise; it demands unique moments of insight and inspiration; and it demands intellectual creativity likely to be unsurpassed in the entire history of physics.
The reason is simple. Today we are blessed with two extraordinarily successful theories. The first is Albert Einstein’s general theory of relativity, which describes the large-scale behaviour of matter in a curved spacetime. It tells us how gravity works: matter tells spacetime how to curve, and curved spacetime tells matter how to move. This theory is the basis for the so-called standard
model of Big Bang cosmology. We use it to describe the evolution of our universe from almost the very ‘beginning’, which on current evidence happened about 13.8 billion years ago. The discovery of gravitational waves at the LIGO observatory in the USA (and now Virgo, in Italy) is only the most recent of this theory’s many triumphs.
The second is quantum mechanics. This theory describes the properties and behaviour of matter and radiation at its smallest scales; at the level of molecules, atoms, sub-atomic, and subnuclear particles. In the guise of quantum field theory it is the basis for the so-called standard model of particle physics, which builds up all the visible constituents of the universe (including stars, planets, and us) out of collections of quarks, electrons, and forcecarrying particles such as photons. It tells us how the other three forces of nature work: electromagnetism, the strong force, and the weak interaction. The discovery of the Higgs boson at CERN in Geneva is only the most recent of this theory’s many triumphs.
But, while they are both highly successful, grand intellectual achievements, these two standard models are also riddled with holes. There’s an awful lot they can’t explain, and they leave a lot of important questions unanswered. If anything, their successes have only served to make the universe appear more elusive and mysterious, if not downright bizarre. The more we have learned, the less we seem to understand.
The two theories are also fundamentally incompatible. In the classical mechanics of Isaac Newton, objects exist and things happen within a ‘container’ of absolute space and time which somehow sits in the background. If we could take everything out of Newton’s universe we must suppose that the empty container would remain. General relativity gets rid of this container. In Einstein’s universe space and time become relative, not absolute, and the theory is said to be ‘background independent’. Spacetime
is dynamic; it emerges as a result of physical interactions involving matter and energy.
Quantum mechanics, though exasperatingly bizarre yet unfailingly accurate in its predictions, is formulated in a different way. Interactions involving the elementary particles of matter and radiation are assumed to take place in precisely the kind of absolute spacetime container that general relativity eliminates. Quantum mechanics is background-dependent.
And there you have it. We have a classical (non-quantum) theory of spacetime which is background-independent. And we have a quantum theory of matter and radiation which is background-dependent. Our two most successful theories of physics are built on incompatible interpretations of space and time. They are woven on different kinds of fabric, one co-generated by the physics and the other pre-supposed and absolute.
We have two incompatible descriptions but, as far as we know (and certainly as far as we can prove), we’ve only ever had one universe. This is a problem because we also know that in the first few moments following its birth in the Big Bang, the universe would have existed at the quantum scale, at the mercy of a quantum mechanics. Now, the fact that we can’t explain the origin and earliest moments of the universe might not trouble you overmuch, but the track-record of physics in the past hundred years or so has encouraged us to have greater expectations. What we need is a quantum theory of gravity.
So, do I have your attention yet?
The Chinese philosopher Laozi once said that a journey of a thousand miles begins with a single step. The first thing we can do is recognize that the only way to bring together quantum mechanics and general relativity is to find a new fabric, a new way of conceiving of space and time, one that is compatible with physics on any scale. preface . xi
Charged with a newfound sense of purpose, we must now choose which road to take. Do we start with the pre-supposed, absolute spacetime fabric of quantum mechanics? Or do we start with the co-generated fabric of general relativity?
In the past forty years or so, judgments concerning the ease of passage along these two roads have split the theoretical physics community along essentially tribal lines. This split is very visible in a recent attempt to map the relationships between all the different ways of developing a quantum theory of gravity, which identified two distinct ‘fundamental’ branches: string theory and loop quantum gravity.3 This divide isn’t simply the result of differences of opinion between general relativists and particle theorists, as theorists on either side frequently borrow ideas and techniques from both general relativity and quantum field theory.
It is, however, true to say that the theoretical physics community is dominated by particle theorists, and particle theorists tend to favour the string theory approach. In the past twenty years or so, their highly successful PR has spilled into the popular science literature, with the result that few readers are even aware that there’s more than one game in town, or more than one road that can be taken. For example, in one recent popular book about gravity, loop quantum gravity is mentioned only in passing, relegated to a footnote.4 There are all sorts of reasons for this, and I will discuss some of these in what follows.
This book is about the road less travelled. It starts from general relativity, borrows ideas from quantum chromodynamics, and involves finding a way to turn the result into a quantum field theory of gravity. At the destination we find a fabric in which space is not continuous, but quantized. It comes in ‘lumps’ just like matter and radiation. The fabric is a system of interlinking ‘loops’ of gravitational force which form a ‘spin network’. There are fundamental limits on the geometries of these loops, which xii . preface
preface . xiii
define quanta of the area and volume of space in terms of something called the Planck length, which is about 1.6 × 10−35 metres, or about a hundredth of a billionth of a billionth of the diameter of a proton.
Different spin networks—different ways of interlinking the loops—define different quantum states of the geometry of space. The evolution of spin networks (the changing connections between one geometry and the next) then gives rise to a spinfoam. Adding spinfoams in something called a superposition describes an emergent spacetime, a fabric co-generated by the quantum physics.
This is loop quantum gravity, or LQG for short. It is now thirty years old and currently occupies the attentions of about thirty research groups around the world. The road from relativity has been difficult, with many highs and lows. There remain many challenges yet to be overcome, not least that of finding a way to torture the theory into providing one or more definitive empirical tests. But as Carlo Rovelli, one of the principal architects of LQG, explained a little while ago, ‘the situation in quantum gravity is in my opinion . . . far better than twenty-five years ago, and, one day out of two, I am optimistic.’5
Readers of popular science may have heard about LQG from Lee Smolin, another of its principal architects, whose Three Roads to Quantum Gravity was published in 2000. Smolin briefly touched on LQG again in The Trouble with Physics, published ten years ago, and most recently in Time Reborn. Rovelli mentions LQG in his best-selling Seven Brief Lessons on Physics, and in his most recent book Reality is Not What It Seems.
My mission in Quantum Space is to correct an imbalance in public perception. I want to persuade you that LQG is not only a good game, it offers a genuine, credible alternative to the string theory approach. To do this I will share with you a little more
xiv . preface
detail about the theory than Smolin and Rovelli have so far shared in their own popular books. I not only want to give you some sense for what LQG tells us about space, time, and the universe, but also how and why it tells us these things.
In researching and writing this book I’ve been very fortunate to receive considerable encouragement, support, and insight from both Smolin and Rovelli. This book is their story, but we also need to get a couple of other things straight. LQG is the result of a collaboration involving many theorists over many years of effort. I’ve tried as far as possible to acknowledge as much of this effort as is feasible in a popular presentation, and can only offer my sincere apologies in advance to any member of the community reading this who feels that their efforts are under-represented or, even worse, overlooked. By the same token, as this book focuses principally on the efforts of two prominent contributors, it is not intended to provide a comprehensive summary of everything that’s been done in the name of LQG.6
The book is structured in three parts. Part I sets the scene. It tells us about the things that Smolin and Rovelli learned about relativity, quantum mechanics, and Big Bang cosmology as young students and then as mature theorists. Readers already familiar with this background can safely skip it (but I hope they won’t). Part II tells the story of the birth and evolution of LQG, starting with efforts to bring relativity and quantum mechanics together in the late 1950s, through Abhay Ashtekar’s discovery of the ‘new variables’ that would make this possible, to the collaboration among Ashtekar, Smolin, and Rovelli (and many others) which yielded quanta of area and volume and the spinfoam formalism towards the turn of the previous century. Part III brings us reasonably up to date. It summarizes efforts to perform calculations of familiar physical quantities using LQG and the implications of the theory for quantum cosmology and the physics of black
preface . xv
holes. On this part of the journey we will also explore the interpretation of quantum mechanics and the reality (or otherwise) of time.
I want to be straight with you about one final thing. Like the string or M-theory framework, LQG is still a work in progress. It is not finished and we don’t yet have all the answers. Smolin and Rovelli are, of course, enthusiasts, and although I’ve tried to take a balanced view, a lot of their enthusiasm is inevitably reflected in my choice of words. But it is important not to get too carried away. Many other theorists who have been involved in various stages of the journey have since lost faith, the optimism of the late 1990s giving way to more sober (and sombre) assessments. Some have chosen to leave the field entirely and work on different problems. I hope that readers will at least get some sense of the scale of the challenge—chasing a theory of quantum gravity is most definitely not for the faint of heart. The book closes with a three-way exchange among Smolin, Rovelli, and myself which looks back at recent history, and forward to the future.
There’s a lot at stake. The great revolutions in science that have shaped the way we seek to comprehend reality have profoundly changed the way we think about space, time, and the universe. Could another revolution be close at hand?
This book would not have been possible had Lee and Carlo not entrusted me with their stories. It’s therefore a real pleasure to acknowledge their commitment to this project, reading over my shoulder as I worked on the manuscript, nudging me in the right direction and putting me right when I got it wrong. Having said that, it’s important for you to know that the views expressed in this book are entirely my own, and whilst Lee and Carlo agree with much of what I’ve written, you shouldn’t assume they agree with everything.
xvi . preface
In addition to thanking Lee and Carlo, I also need to acknowledge the efforts of many other busy scientists who gave up their valuable time to read through my draft manuscript, correct many of my misinterpretations and mistakes, and add insights of their own. These include Abhay Ashtekar at Pennsylvania State University, John Baez at the University of California, Riverside, Martin Bojowald at Pennsylvania State University, Alejandro Corichi at the National Autonomous University of Mexico, George Ellis at the University of Cape Town, Ted Jacobson at the University of Maryland, Kirill Krasnov at the University of Nottingham, Jorge Pullin at Louisiana State University, and Peter Woit at Columbia University.
Now, LQG is a theory that is far from complete. This means that even those who have been involved most closely in its development don’t all agree on the answers to the theory’s many open questions. In order to produce a hopefully coherent, readable narrative about a subject in which virtually everything can be challenged, I’ve had to be somewhat selective in what to present. I’m pretty sure I haven’t got this right all the time, and it goes without saying that I’m happy to take the credit for all those errors that remain.
I must also once more acknowledge my debts to Latha Menon, my editor at Oxford University Press, and to Jenny Nugee, who have again worked industriously behind the scenes to produce the book you now hold in your hands. Without their efforts, the book would certainly have been poorer.
Shall we begin?
Jim Baggott July 2018
LIST OF ABBREVIATIONS
ADM Arnowitt, Deser, Misner
ATLAS A Toroidal LHC Apparatus (detector)
CDM cold dark matter
CERN Conseil Européen pour la Recherche Nucléaire
CMS Compact Muon Solenoid (detector)
COBE Cosmic Background Explorer
CODATA International Council for Science Committee on Data for Science and Technology
GeV giga electron volt
GUT grand unified theory
Λ-CDM lambda-cold dark matter
LHC large hadron collider
LQC loop quantum cosmology
LQG loop quantum gravity
MeV mega electron volt
MSSM minimum supersymmetric standard model
NSF National Science Foundation
QCD quantum chromodynamics
QED quantum electrodynamics
SLAC Stanford Linear Accelerator Center
SUSY supersymmetry
TeV tera electron volt
WMAP Wilkinson Microwave Anisotropy Probe
ABOUT THE AUTHOR
Jim Baggott is an award-winning science writer. A former academic scientist, he now works as an independent business consultant but maintains a broad interest in science, philosophy, and history and continues to write on these subjects in his spare time. His previous books have been widely acclaimed and include the following:
Mass: The Quest to Understand Matter from Greek Atoms to Quantum Fields, Oxford University Press, 2017
Origins: The Scientific Story of Creation, Oxford University Press, 2015
Farewell to Reality: How Fairy-tale Physics Betrays the Search for Scientific Truth, Constable, London, 2013
Higgs: The Invention and Discovery of the ‘God Particle’ , Oxford University Press, 2012
The Quantum Story: A History in 40 Moments, Oxford University Press, 2011, re-issued 2015
Atomic: The First War of Physics and the Secret History of the Atom Bomb 1939–49, Icon Books, London, 2009, re-issued 2015 (shortlisted for the Duke of Westminster Medal for Military Literature, 2010)
A Beginner’s Guide to Reality, Penguin, London, 2005
Beyond Measure: Modern Physics, Philosophy and the Meaning of Quantum Theory, Oxford University Press, 2004
Perfect Symmetry: The Accidental Discovery of Buckminsterfullerene, Oxford University Press, 1994
The Meaning of Quantum Theory: A Guide for Students of Chemistry and Physics, Oxford University Press, 1992
PROLOGUE
An Irresistible Longing to Understand the Secrets of Nature
It’s probably not unreasonable to say that theoretical physics attracts particular kinds of people to work on it. This is a discipline that demands an agile, creative mind and a certain facility with abstruse concepts and dense, complex mathematics, so a degree of selfselection can be expected. A general lack of desire for material wealth is also useful. But if we’re dealing with a physics perched right on the edge of our understanding of the nature of reality and physical existence, then we must admit that there’s a further characteristically human trait that can often be helpful.
Theoretical physics loves a rebel.
Put it this way. You don’t get the opportunity to transform our understanding of the very fabric of space and time; you don’t get to turn the world upsidedown and subvert our cosy notions of the larger universe if you’re inclined to worry about what other people will think.
Many rebels come to theoretical physics seeking a refuge, a safe haven from the perceived injustices and unpredictability of human affairs and the social disappointments of youth. They come seeking a place where their instincts are more likely to be
appreciated as, unlike many other walks of life, rebellion in science is not only encouraged, it is necessary.
At Walnut Hills High School in Cincinnati, Ohio, the sixteenyearold Lee Smolin was principally interested in revolutionary politics, rock stardom, mathematics, architecture, and his girlfriend, not necessarily in this order or with this priority. His teachers had advised him that he wasn’t smart enough to take the advanced track in mathematics and, to prove them wrong, in a singular act of rebellion he completed the three year advanced course in just a year. Not everyone’s idea of radicalism in action, perhaps, and not as subversive as rock music or publishing an underground newspaper, but Smolin discovered that ‘it was almost as much fun’.1
His interest in architecture was kindled when, in the eleventh grade, he invited the eccentric architect and system theorist Richard Buckminster Fuller to speak at the school. A fascination with Fuller’s geodesic domes led him to a branch of mathematics called tensor calculus. Books on tensor calculus led him to Einstein’s theories of relativity, and to Einstein himself.
Smolin’s world crumbled at the beginning of his senior year. His rock band had split, his girlfriend had left him, and his political revolution had failed to come to pass. He had flunked chemistry, and a perceived lack of aptitude meant that he had been refused admission to the physics class. He decided to drop out of high school altogether.
It was therefore in the public library that he would find the book that would change his life. It was called Albert Einstein: Philosopher-Scientist, edited by Northwestern University philosopher Paul Arthur Schilpp, and first published in 1949. The book opens with a chapter of ‘Autobiographical Notes’, written by the 67yearold Einstein as ‘something like my own obituary’.2 His words spoke directly to the disillusioned Smolin.
Einstein wrote of the ‘nothingness of the hopes and strivings which chases most men restlessly through life’. As a young man he had himself ‘soon discovered the cruelty of that chase, which in those years was much more carefully covered up by hypocrisy and glittering words than is the case today’. Rejecting any solace that might be found in organized religion, Einstein had instead found comfort in physics:3
Out yonder there was this huge world, which exists independently of us human beings and which stands before us like a great, eternal riddle, at least partially accessible to our inspection and thinking. The contemplation of this world beckoned like a liberation, and I soon noticed that many a man whom I had learned to esteem and admire had found inner freedom and security in devoted occupation with it.
Smolin decided to become a theoretical physicist later that evening. Like Einstein, he was ‘motivated by an irresistible longing to understand the secrets of nature’.4 ‘[I]t occurred to me then and there that if I could do nothing else with my life, perhaps I could do that.’5
It was not an entirely auspicious decision. He had already been accepted to study architecture at Hampshire College, a radical liberal arts college in Amherst, Massachusetts, and he now scrambled to switch subjects. But he was not totally unprepared. His mother, a Professor of English at the University of Cincinnati, helped enroll him on a graduate course on general relativity, taught at the university by Paul Esposito. This was his first physics course.
He also spent the hot summer months between school and college in Los Angeles working as a sheet metal apprentice at Van Nuys Heating and Air Conditioning, reading about basic physics, relativity, and quantum mechanics in his spare time.
Carlo Rovelli’s journey to theoretical physics took place on a different continent, in a different language, and differs in its details. Yet it shares some remarkable similarities.
He, too, had come to have little faith in a world organized by adults in ways that seemed far from just and right. As he grew up in Verona, in northern Italy not far from Venice, he railed against the creeping nostalgia for fascism that had leached into all parts of provincial society. He clashed frequently with his teachers and rebelled against the authority of the classical lyceum, his upper secondary school, teaching basic subjects in preparation for university. He also needed to escape from his own family. A mother’s love for her only child is comforting, but it can also be stifling.6 Rovelli needed to breathe.
He read voraciously on politics, sociology, and science, and devoured novels and poetry. At the age of twenty he set off on a nomadic quest around the world in search of truth. On his travels he acquired a strong sense of liberty; he learned how to take his life in his own hands and follow his dreams. But by putting some distance between himself and the place that represented everything he had come to resent, he began to see things a little differently. There was still plenty to be angry about, but he began to realize that there were also rich possibilities for learning back in Italy. And he was also missing his Italian girlfriend.
On his return he enrolled to study for a degree in physics at the University of Bologna, the world’s oldest, founded in 1088. This was more accident than design. At school he had demonstrated some capability in physics and mathematics but his first love was philosophy. He had chosen not to enroll for a philosophy degree because he simply didn’t trust established educational institutions to treat philosophical problems with the importance and seriousness the young idealist demanded.
Bologna is a city famed for its art, culture, and historic architecture—notably its red tiled roofscape, reflecting the colour of its communist politics. It suited him well. During his time as a student he made common cause with a likeminded community, one which embraced a posthippy counterculture. The group experimented with mind altering drugs, and different ways of living, and loving, as they tended their goat, Lucrezia. They dreamt of a peaceful, cultural revolution that would make the world a better place.
Despite the distractions of communestyle living, Rovelli had no problem maintaining his focus on physics. He would become so absorbed in study that he would remain blissfully unaware of everything else going on around him. One day, a builder arrived to demolish an interior wall in the dilapidated house in which they were living. This took several hours of noisy effort. Rovelli was working in the room, sitting just a few metres from the wall in question. When asked if the builder had disturbed him, he looked up from his books and asked: ‘What builder?’7
In February 1976 he joined the group that established Radio Alice, a free radio station which provided: an ‘open microphone for everybody, where experiences and dreams were exchanged’.8 Topics included labour protests and political analysis, poetry, yoga, cooking, declarations of love, and music by Beethoven and Jefferson Airplane.
This was one of the defining periods of Rovelli’s life, but as the dream faded he learned that ‘one does not change the world so easily’.
Confused and greatly disillusioned, Rovelli now had to come to terms with the challenge of deciding what to do with the rest of his life. The timing was perhaps fortuitous. He had chosen to learn physics because he had to study something (other than philosophy), and he preferred to postpone the call to obligatory
