Our Mathematical Universe: My Quest for the Ultimate Nature of Reality (2014)
Max Tegmark (1967)
421 pages
Evolution endowed us with intuition only for those everyday aspects of physics that had survival value for our distant ancestors, leading to the prediction that whenever we use technology to glimpse reality beyond the human scale, our evolved intuition should break down. (363)
This observation by physicist and author Max Tegmark comes toward the end of his book Our Mathematical Universe, but it could perhaps have served well as its epigraph, giving readers fair-warning of the strange and profoundly counter-intuitive predictions and hypotheses about our universe that he describes as arising out of the most important and consequential theories in physics from the past century.Given, then, that one must abandon intuition at the door, and despite Tegmark’s best efforts to distill the essence of what, as he himself indicates, at most a handful of modern-day physicists in the world truly grasp, his book is not for the faint of heart. But those who take courage in hand and dive-in will be rewarded with an engaging, if wild, ride through the latest --- yes highly counter-intuitive --- conclusions being explored about the nature of our physical world.
As hinted at in the book’s subtitle, My Quest for the Ultimate Nature of Reality, Tegmark goes beyond reviewing the origins and implications of the theoretical physics he covers, to also describe his role as a physicist in the developments of the past half-century and the conclusions he has drawn from that work about the “nature of reality.” Thus, into his explanations of the science, he works in auto-biographical notes that provide insight into the often incremental nature of scientific development, as well as the complexity of the politics among physicists. Certainly his description of the heated debates and disagreements among proponents of differing understandings of the models physicists have proposed to describe our physical reality, and the seemingly strict demarcation between what is acceptable to discuss or even consider publicly --- and what is not --- put the lie to an idealized view of science as a purely objective discipline driven only by the data.
Tegmark makes clear that the hypothesis that he has developed over the past few decades about the “ultimate nature of reality,” and that he lays out in this book, does not yet enjoy much support among the physics community. He even includes an e-mail from a “senior professor” (243) that implores him to, basically, keep his crazy ideas to himself, and so avoid destroying his own career. But, as evidenced by the irreverent style in which Tegmark has written the book, he is not one to be easily diverted from following where he feels that the mathematics and physics --- and observational data --- lead him.
Before getting to his own hypotheses about the physical world in the third and final part of the book, however, Tegmark sets the stage by reviewing some of the latest understandings and debates of physicists.
The first part of the book, labeled Zooming Out, deals with cosmology --- our understanding of, as the opening chapter is titled, Our Place in Space. Tegmark begins by re-tracing humankind’s gradual discovery of the vastness of space, and Earth’s place in it. Up to his description of the model of the Big Bang the story will be largely familiar to most lay-readers of science, though Tegmark provides fascinating insights, from his vantage point as a physicist doing experimental and analytical work, into especially the recent period of testing of the validity of the Big Bang model.
Then comes time, however, for readers to buckle their seatbelts. After discussing some of the limitations of, and seemingly wildly unlikely coincidences required by the Big Bang model based on the latest data and analysis, Tegmark introduces inflation theory, which was first proposed by physicist Alan Guth. Examining Einstein’s theory of gravity, Guth found that among its implications one can conclude that “once upon a time, there was a tiny uniform blob of a substance whose density was very hard to dilute,” (100) that such a substance can undergo an explosion in which it grows exponentially in size without its density dropping, and that this expansion can continue forever.
Tegmark notes that inflation theory has been found to address many of the issues observed with the Big Bang model. More critically, however, a further consequence of inflationary theory is that it can be understood to imply the existence of multiple, parallel universes, defined cumulatively as a multiverse, a concept that plays a central role in the reminder of the book.
Each of these parallel universes, according to inflation theory, results from the occurrence of a Big Bang in a region of the inflationary space, an event which, in fact, leads to an end to inflation in that particular region. And, as a consequence of the inflation of space going on forever, an infinite number of such parallel universes can exist, each the result of a separate Big Bang, our own universe being one among them. Critically, given different initial conditions for each such Big Bang, history will play out differently in each of these parallel universes: the history in a universe parallel to our own will differ from our own history to the extent that the initial conditions of the Big Bang in that region of space differ from those of our own region’s Big Bang.
One mind-blowing implication of such an infinite number of parallel universes is that somewhere in space, in a universe parallel to ours, history can proceed exactly as in ours except that, say, I stop writing this review after this sentence for whatever reason; and, of course, the same can be said about the next sentence, and so on. Given an infinite number of such parallel universes then, all possible histories can be imagined to be playing out, unaccountably many of them including some version of ourselves.
Taken together, Tegmark defines this set of parallel universes, in which the laws of physics are the same across all of them but the history taught in each one is different, as the Level 1 multiverse.
He goes on to define a Level 2 multiverse as the equally infinite number of universes that have the same fundamental laws of physics as ours, but whose effective laws of physics --- the laws as they are experienced --- are different in that key parameters (for example, the number of time dimensions or space dimensions, or the mass of the electron) can take on different values. The result is an infinity of Level 1 multiverses, each with different effective laws of physics, each separated from the others by an eternally expanding space between them, and each, of course, itself containing an infinite number of universes.
Given the weirdness (a word Tegmark himself uses repeatedly) of these ideas, and that they will only get still weirder as one gets deeper into the book, it is perhaps useful at this point to step back and highlight a key point that Tegmark makes: the potential existence of the Level 1 and Level 2 multiverses is not a theory or an unsubstantiated proposal; instead, the possibility of their existence arises as an implication of the mathematics of Einstein’s theory of gravity. And the fact that “Einstein’s theory of general relativity has successfully predicted many things that we can observe … we consider it a successful scientific theory and take seriously also its predictions for things we can’t observe.” (124) As Tegmark goes on to point out: “you have to either accept all [of a theory’s] predictions, or you have to start over from scratch” (125) --- you can’t pick and choose the predictions you like. Of course, as he points out repeatedly, such an understanding has not stopped significant portions of the community of physicists from discounting the idea of the existence of multiverses.
The middle part of the book, entitled Zooming In, turns to the very small, providing a history of the work that led to the development of quantum mechanics, and its still hotly debated meanings and implications. Tegmark summarizes the important conclusion of quantum mechanics as that particles can have “properties both of traditional particles (they’re either here or there) and of waves (they can be in several places at once in a so-called superposition).” (183) This behavior of particles, he recalls, is described by the wavefunction, developed by Erwin Schrödinger.
One implication of the wavefunction is that a particle, or a superposition of many particles such as an object or person, can be in more than one place at one time. But physicists have had to grapple with the fact that a particular particle (or superposition of particles) appears in a particular place when observed --- that is, the wavefunction is said to “collapse” to being a particle located at one particular place. He notes that Niels Bohr and Werner Heisenberg settled on “a remarkably radical remedy that became known as the Copenhagen interpretation, [which said in part that] if something is not being observed, then its wavefunction changes according to the Schrödinger equation, but if it is being observed, then its wavefunction collapses so that you find the object only in one place.” (178)
Tegmark summarizes the concerns some physicists have had with the apparent arbitrariness of the Copenhagen interpretation, then states that “in 1957, Princeton grad student Hugh Everett III had proposed a truly radical answer [to these issues] involving parallel universes” (186). Everett proposed that the wavefunction never collapses, regardless of whether an observation is taking place. The implication of this, according to Everett, was that if the wavefunction shows two possible locations for the particle, then when an observation is made our universe splits, so that in one branch the particle is in one place, while in the other it’s in the other place. As Tegmark describes it: “In other words, parallel-universe splitting is happening constantly, making the number of quantum parallel universes truly dizzying.” (190). This (again infinite) set of parallel universes he defines as the Level 3 multiverse.
Having set the stage by describing modern day cosmology and its implication for the potential existence of Level 1 and Level 2 multiverses, and quantum mechanics and its implication for the potential existence of the Level 3 multiverse, Tegmark gets to the heart of his own thesis in the final part of the book, in which he introduces what he defines as the Level 4 multiverse.
To introduce the conceptual walk he followed to arrive at the idea of this new order of multiverse, Tegmark recalls that scientists have long wondered at the effectiveness of mathematics in describing the physical universe. As an explanation for this he proposes “the hypothesis that there exists an external physical reality completely independent of humans.” (267) As a consequence of accepting this hypothesis, Tegmark argues that “the hypothesis that our external physical reality is a mathematical structure” (267) follows unavoidably. And, as a further consequence, if space (that is, the entire inflationary space in which we live, containing the Level 1, 2 and 3 multiverses) is defined by a mathematical structure --- that is, by the set of fundamental laws of physics that apply in our universe, and by extension in our entire inflationary space --- then it follows that other spaces can exist that have other mathematical structures, with different fundamental laws of physics.
Thus, the Level 4 multiverse contains an infinite number of spaces, each fully described by a different mathematical structure.
Key to acknowledging the essential nature of the mathematical structure of our space, according to Tegmark, is to not allow what he refers to as the “baggage of language” to interfere with our understanding; we must recognize that the names we give things are only for our own convenience, and don’t imply or represent any inherent property of those things. Thus, a “ball” or a “star” are convenient names we use to describe objects that are actually groupings of particles fundamentally described by the mathematical relationships between the particles. More broadly, the entirety of reality, Tegmark argues, can be fully describe by a set of mathematical relationships, independent of the descriptions any particular observer may give them, and in fact independent of the existence of any observer.
He points out that some, perhaps many, of the mathematical structures in the Level 4 multiverse may not be capable of leading to life, in any sense that we can imagine it. And as other mathematical structures may lead to vastly different fundamental physical laws, it can also be that the multiverses that have been proposed to exist in our space (our mathematical structure) may not exist in these other mathematical structures, though at the same time other kinds of multiverses that we can’t imagine may be present.
Over several chapters, Tegmark goes on to examine the mathematical structure of our particular universe, to the extent it is currently understood, and more generally the implications of his hypothesis for the existence a multiverse of different mathematical structures. He discusses how his hypothesis can address some of the currently unresolved mysteries of our universe, including the implications for the concepts of time, randomness, and complexity, and why the fundamental laws of physics in our universe seem to be tuned just right to support life. He also addresses how his hypothesis could be tested and verified.
The book concludes with a chapter whose title, Life, Our Universe and Everything, recalls the title of the first book in Douglas Adams’ series, The Hitchhiker’s Guide to the Galaxy: Life, the Universe and Everything. (“Our” universe for Tegmark, of course, instead of Adams’ “the” universe, because the very subject of Tegmark’s book is that we live in one universe among infinitely many.) In this final chapter, Tegmark examines the potential ways in which our universe could one day end, based on current understandings. He then focuses more directly on the future of life, and in particular what could destroy life as we know it --- from near-term threats such as a global pandemic, nuclear war or climate change, to more distant threats such as the death throes of our sun or the eventual collision of our Milky Way with the Andromeda galaxy. He concludes with a plea that we recognize what he feels may be the nearly unique gift of consciousness that humankind enjoys on “Spaceship Earth” (398), and the importance of dealing with the near-term problems that place the existence of our life as a species at risk.
The link to Douglas Adams reflects the style and approach Tegmark uses throughout the book. He includes a variety of references to popular culture, from the The Hitchhiker’s Guide to the Galaxy to Star Trek and others. He also tells stories of his own experiences studying and working in the field of physics, to highlight the challenges of doing work in this highly competitive field, including the difficulties and risks of bucking the status quo. Though he occasionally goes into some details of the mathematics and physics, he generally relegates the most technical aspects to the footnotes, and so keeps the main text at a more descriptive level, using prose and helpful diagrams to make his points.
At times this almost folksy nature of his writing can seem to overly simplify the explanation, failing to highlight the importance of particular points. More than once I encountered a statement along the lines of ‘as we saw in the previous chapter…’ and when I referred back, it was a single line buried in a paragraph, one that hadn’t seemed particularly consequential on the first pass, and so the implications of which I had missed.
This is a minor quibble, however. In Our Mathematical Universe, Tegmark has provided an entertaining, engaging and profoundly fascinating exploration of the cutting edge of physics and its implications for our understanding of reality. In a tradition that goes back to the earliest human urge to understand and explain our physical world, we continue to learn that that which we can see occupies an ever smaller and less central part of our latest understanding of the whole of what is.
Other reviews / information:
In a coincidence that seems to highlight a focus of many physicists
working today, the title of Tegmark’s opening chapter --- which serves
as a kind of preface for the rest of the book --- has strong parallels
to the title of a book published by physicist Carlo Rovelli in the same
year. (Rovelli’s book, originally in Italian, didn’t appear in English
until several years later.) Tegmark’s first chapter is titled, What is Reality, and opens with the section heading Not What It Seems, while Rovelli’s book is titled Reality is Not What it Seems;
both physicists make clear reference to the breakdown in our intuition
as we attempt to grasp the complexity of our physical world. (My review
of Rovelli’s book is linked to at left.) Sam Harris, as part of his podcast Waking Up, has had several fascinating discussions with Tegmark, on topics ranging from the multiverse, to the future of artificial intelligence. Links are provided below.
The Multiverse & You (& You & You & You…)
The Future of Intelligence
What Is and What Matters
with Max Tegmark and Rebecca Goldstein
Have you read this book, others by this author, or even similar ones by other authors? I’d enjoy hearing your thoughts.
Other of my book reviews: FICTION Bookshelf and NON-FICTION Bookshelf
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