Our Mathematical Universe: My Quest for the Ultimate Nature of Reality
“. . . a fun and interesting introduction to cosmology and multiverse theory.”
[Disclaimer: Both the author and the reviewer are employed by MIT but neither knows the other nor do they work together.]
Our Mathematical Universe is an eminently readable introduction to cosmology for the non-scientist—a less textbook-like version of The Life and Death of Stars by Kenneth R. Lang, previously reviewed on this website.
In Our Mathematical Universe Professor Tegmark addresses such aspects of cosmology as how to calculate the distance to stars, stars’ chemical composition, the behavior of gas clouds that lead to star and galaxy formation, Einstein’s theories and the nature of the Universe. What makes this book different and controversial is his consideration of the theory of multiple universes, also called the Multiple Universe Hypothesis (MUH) or the Multiverse.
The preface outlines the book’s organization, which is in three sections: mainstream physics, controversial physics, and more controversial physics. Each section is divided into chapters, with the first four chapters the introduction to cosmology. Beginning with chapter five the science gets more hardcore though chapters end with a summary of key points called, “The Bottom Line.”
The first chapter begins with questions the professor is most often asked on cosmology. For example, “How could space not be infinite?” and “If our universe is expanding then what is it expanding into?” He answers these questions simply and clearly using diagrams, charts, photos and illustrations to support his explanation.
Along the way he provides interesting tidbits on cosmology’s historical notables and points out his own efforts in cosmology research. He describes his excitement on seeing the very first three-dimensional galaxy map of the cosmic background radiation, pointing out that we have entered the era of “precision cosmology,” the ability to measure cosmic quantities to percent level precision.
Professor Tegmark compares his job as cosmologist to that of a detective, telling the story of how the ancient Greeks (who also acted as detectives) were able to estimate the size of and distance to the Sun, which if not perfect measurements were at least good enough for the tools of the time. He describes more modern and more accurate measurements; pointing out the central doctrine of physics—that the laws of nature hold true everywhere—that Newton’s laws on Earth could be extrapolated and applied successfully to more distant objects in outer space. A key process of scientific progress is in acquiring data from experiments to improve models used to make predictions that lead to new experiments that lead to new data for models in a neverending cycle.
The controversial aspects of Our Mathematical Universe begins in its second section with consideration of one of cosmology’s mysteries: that our universe appears to be tuned for life, yet as far as we can tell we’re on the only planet where life exists. The background to this mystery includes the theory of the origin of the universe, the Big Bang theory, which depends on the theory of “inflation,” a speeded up period of time where the Universe expanded rapidly. Inflation explains the universe’s homogeneity across great distances but was necessarily limited in time; only when inflation ends can galaxies form. And though halted in our portion of the universe, inflation is continuing in other parts, driven by dark energy.
The idea of the multiverse comes from solutions to models used to estimate the universe going backward in time (and space) from the inflationary period to the Big Bang. These models show that the phase of space can change when there’s a tremendous amount of energy in a very small space. They also show the Big Bang allows for more than one solution going forward.
Each has implications for cosmological theory. The first is that “phase change” provides control knobs for the laws of physics, implying that the fundamental laws of physics can vary from place to place. The second is that having a model with more than one solution leads to the possibility of multiple universes having different laws of physics—not just a few parallel universes but a near infinite number of parallel universes.
Our very existence suggests but does not prove the existence of a multiverse, but does provide a solution to the improbability of the fine-tuning of the universe. Cosmologists call the near perfect tuning of the laws of physics that allow life to exist “the anthropic principle of the universe.”
Many cosmologists don’t like the anthropic principle as it suggests the universe was created by accident or by God (hence the book’s title: Our Accidental Universe). The multiverse makes the anthropic principle more attractive as it does not require an accident or intervening God. The reasoning goes like this: Because we exist and because our existence is unlikely, the possibility that there are a near-infinite number of universes with a near infinite variety of physical laws leads to the greater chance of our universe to exist with the laws of physics being tuned just right for life.
Of the near infinite number of universes in the multiverse, some may be at different levels with respect to the laws of physics, and Professor Tegmark provides a chart showing the number of dimensions versus the kind of universes that would result, if any.
The first level universes would have the same laws of physics that exist in ours, though most of these would not have life or galaxies or stars or planets. The second level would have different laws of physics and would forever be unobservable. As to what those laws would be, we can only guess. From informal polls conducted by the author over a period of time, increasing numbers of cosmologists are beginning to accept the possibility of a first level multiverse.
Professor Tegmark poses rhetorical questions and suggests possible answers about the first level multiverse, such as: Where would it exist? Here, but because of inflation very far away, or here, but in a different “quantum wave function”?
He considers the possibility that the first level multiverse may not even be at anything that corresponds to a location, and he reminds the reader more than once that the multiverse is not a theory but a prediction of certain theories—though the possibility of parallel universes appears unavoidable it doesn’t have to be correct. He adds, “If I’m wrong and the MUH is false, then physics will eventually hit an insurmountable roadblock beyond which no further progress is possible.”
What can we predict from having a multiverse theory? Professor Tegmark believes that a near infinite number of first level multiverses permit everything that could happen within the laws of physics to happen a near infinite number of times, though he recognizes that this too may strain credulity. Having a multiverse theory also leads to negative predictions, such as removing the hope of ever knowing what everything ultimately is made of, or of ever understanding why the constants of nature are what they are, which increasingly appear to be random.
The fine-tuning that allows alternative universes does so by changing the fundamental constants of the elementary particles, and in chapter eight, professor Tegmark turns from the cosmos to quantum theory. As in earlier sections, he begins reasonably, pointing out that particle physics are no more than a rearranging of energy, momentum, charge and other conserved characteristics that can’t be create or destroyed, only converted in new ways. And again he makes quantum mechanics personal, going back to his graduate education, reminiscing about eccentric classmates and teachers.
Then seemingly out of nowhere, Professor Tegmark expresses his belief that randomness is an illusion—something our mind feels when it is cloned into a diverging parallel universe, and proposes a thought experiment based on Schrodinger’s cat to prove this. To explore Tegmark’s theory one replaces the cat with a human who must risk certain death. As to why the subject has to be human and why risk certain death are not well explained—though the implication is that surviving isn’t luck so much as dying in all possible universes but one.
The author jumps from that to the possibility that we living in a simulation, a possibility he disagrees with—but again provides little explanation. This chapter leaves the reader to wonder just what’s going on in the author’s mind and leaves the impression of non-sequiturs standing in for well-reasoned thought.
In chapters nine and ten Professor Tegmark provides his thoughts on the meaning of reality. Though he accepts the existence of reality, he refers to it as an unproven hypothesis. His tendency toward solipsistic thought then extends to claiming reality is a mathematical structure, not represents a mathematical structure. By the end of chapter ten, though the reader may disagree with the author, there should be good understanding of where he is coming from. As Tegmark says of others, “Sometimes scientists get attached to an idea with almost religious fervor, so that no facts can dissuade them.” Clearly the professor is unwilling to apply that possibility to himself.
After chapter ten, the concluding chapters of Our Mathematical Universe become less compelling, though some of the material does stand out, for example when the author refers to human subjectivity as “baggage,” and when using chess for an example of “baggage” says the game is no more than the solution to a mathematical equation. Despite all that came before leading up to this, this reviewer was, for no better word, gobsmacked.
Max Tegmark in Our Mathematical Universe is informative, chatty, and engaging. Though the author exhibits humor and high self-regard, there are instances where the difference between the two remains unclear. Our Mathematical Universe is (at least in the first two sections) a fun and interesting introduction to cosmology and multiverse theory.