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By Root 2067 0

course of developing the general theory of relativity, Einstein became intimately familiar with vast areas of mathematics that most physicists of his day knew little or nothing about. As he groped toward general relativity’s final equations, Einstein displayed a master’s skill in molding these mathematical constructs with the firm hand of physical intuition. A few years later, when he received the good news that observations of the 1919 solar eclipse confirmed general relativity’s prediction that star light should travel along curved trajectories, Einstein confidently noted that had the results been different, “he would have been sorry for the dear Lord, since the theory is correct.” I’m sure that convincing data contravening general relativity would have changed Einstein’s tune, but the remark captures well how a set of mathematical equations, through their sleek internal logic, their intrinsic beauty, and their potential for wide-ranging applicability, can seemingly radiate reality.

Nevertheless, there was a limit to how far Einstein was willing to follow his own mathematics. Einstein did not take the general theory of relativity “seriously enough” to believe its prediction of black holes, or its prediction that the universe was expanding. As we’ve seen, others, including Friedmann, Lemaître, and Schwarzschild, embraced Einstein’s equations more fully than he, and their achievements have set the course of cosmological understanding for nearly a century. By contrast, during the last twenty or so years of his life, Einstein threw himself into mathematical investigations, passionately striving for the prized achievement of a unified theory of physics. In assessing this work based on what we know now, one can’t help but conclude that during those years Einstein was too heavily guided—some might say blinded—by the thicket of equations with which he was constantly surrounded. And so, even Einstein, at various times in his life, made the wrong decision regarding which equations to take seriously and which to not.

The third revolution in modern theoretical physics, quantum mechanics, provides another case study, one of direct relevance to the story I’ve told in this book. Schrödinger wrote down his equation for how quantum waves evolve in 1926. For decades, the equation was viewed as relevant only to the domain of small things: molecules, atoms, and particles. But in 1957, Hugh Everett echoed Einstein’s Maxwellian charge of a half century earlier: take the math seriously. Everett argued that Schrödinger’s equation should apply to everything because all things material, regardless of size, are made from molecules, atoms, and subatomic particles. And as we’ve seen, this led Everett to the Many Worlds approach to quantum mechanics and to the Quantum Multiverse. More than fifty years later, we still don’t know if Everett’s approach is right. But by taking the mathematics underlying quantum theory seriously—fully seriously—he may have discovered one of the most profound revelations of scientific exploration.

The other multiverse proposals similarly rely on a belief that mathematics is tightly stitched into the fabric of reality. The Ultimate Multiverse takes this perspective to its furthermost incarnation; mathematics, according to the Ultimate Multiverse, is reality. But even with their less panoptic view on the connection between mathematics and reality, the other multiverse theories in Table 11.1 owe their genesis to numbers and equations played with by theorists sitting at desks—and scribbling in notebooks, and writing on chalkboards, and programming computers. Whether invoking general relativity, quantum mechanics, string theory, or mathematical insight more broadly, the entries in Table 11.1 arise only because we assume that mathematical theorizing can guide us toward hidden truths. Only time will tell if this assumption takes the underlying mathematical theories too seriously, or perhaps not seriously enough.

If some or all of the mathematics that’s compelled us to think about parallel worlds proves relevant to reality,