The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [183]
The Simulated and Ultimate Multiverses are horses of a different color; they don’t emerge from particular physical theories. Yet, they too have the potential to shift the nature of our questions. In these multiverses, the mathematical laws governing the individual universes vary. Thus, much as with varying initial conditions and constants of nature, varying laws suggest that it’s as misguided to ask for an explanation of the particular laws in operation here. Different universes have different laws; we experience the ones we do because these are among the laws compatible with our existence.
Collectively, we see that the multiverse proposals summarized in Table 11.1 render prosaic three primary aspects of the standard scientific framework that in a single-universe setting are deeply mysterious. In various multiverses, the initial conditions, the constants of nature, and even the mathematical laws are no longer in need of explanation.
Should We Believe Mathematics?
Nobel laureate Steven Weinberg once wrote, “Our mistake is not that we take our theories too seriously, but that we do not take them seriously enough. It is always hard to realize that these numbers and equations we play with at our desks have something to do with the real world.”1 Weinberg was referring to the pioneering results of Ralph Alpher, Robert Herman, and George Gamow on the cosmic microwave background radiation, which I described in Chapter 3. Although the predicted radiation is a direct consequence of general relativity combined with basic cosmological physics, it rose to prominence only after being discovered theoretically twice, a dozen years apart, and then being observed through a benevolent act of serendipity.
To be sure, Weinberg’s remark has to be applied with care. Although his desk has played host to an inordinate amount of mathematics that has proved relevant to the real world, far from every equation with which we theorists tinker rises to that level. In the absence of compelling experimental or observational results, deciding which mathematics should be taken seriously is as much art as it is science.
Indeed, this issue is central to all we’ve discussed in this book; it has also informed the book’s title. The breadth of multiverse proposals in Table 11.1 might suggest a panorama of hidden realities. But I’ve titled this book in the singular to reflect the unique and uniquely powerful theme that underlies them all: the capacity of mathematics to reveal secreted truths about the workings of the world. Centuries of discovery have made this abundantly evident; monumental upheavals in physics have emerged time and again from vigorously following mathematics’ lead. Einstein’s own complex dance with mathematics provides a revealing case study.
In the late 1800s when James Clerk Maxwell realized that light was an electromagnetic wave, his equations showed that light’s speed should be about 300,000 kilometers per second—close to the value experimenters had measured. A nagging loose end was that his equations left unanswered the question: 300,000 kilometers per second relative to what? Scientists pursued the makeshift resolution that an invisible substance permeating space, the “aether,” provided the unseen standard of rest. But in the early twentieth century, Einstein argued that scientists needed to take Maxwell’s equations more seriously. If Maxwell’s equations didn’t refer to a standard of rest, then there was no need for a standard of rest; light’s speed, Einstein forcefully declared, is 300,000 kilometers per second relative to anything. Although the details are of historical interest, I’m describing this episode for the larger point: everyone had access to Maxwell’s mathematics, but it took the genius of Einstein to embrace the mathematics fully. And with that move, Einstein broke through to the special theory of relativity, overturning centuries of thought regarding space, time, matter, and energy.
During the next decade, in the