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How Do You Count in A Multiverse? Definitely Not as Easy as 1, 2, 3.. Literally

Cosmologists have been thinking for years that our universe might be just one bubble amid countless bubbles floating in a formless void.

And when they say “countless,” they really mean it. Those universes are damned hard to count. Angels on a pin are nothing to this. There’s no unambiguous way to count items in an infinite set, and that’s no good, because if you can’t count, you can’t calculate probabilities, and if you can’t calculate probabilities, you can’t make empirical predictions, and if you can’t make empirical predictions, you can’t look anyone in the eye at scientist wine-and-cheese parties. In a Sci Am article last year, cosmologist Paul Steinhardt argued that this counting crisis, or “measure problem,” is reason to doubt the theory that predicts bubble universes.

Other cosmologists think they just need to learn how to count better. In April I went to a talk by Leonard Susskind, who has been arguing for a decade that you don’t need to count all the parallel universes, just those that are capable of affecting you. Forget the causally disconnected ones and you might have a shot at recovering your empiricist credentials. “Causal structure is, I think, all important,” Susskind said. He presented a study he did last year with three other Stanford physicists, Daniel Harlow, Steve Shenker, and Douglas Stanford. I didn’t follow everything he said, but I was enamored of a piece of mathematics he invoked, known as p-adic numbers. As I began to root around, I discovered that these numbers have inspired an entire subfield within fundamental physics, involving not just parallel universes but also the arrow of time, dark matter, and the possible atomic nature of space and time.

Lest you think that the whole notion of parallel universes was ill-starred to begin with, cosmologists have good cause to think our universe is just one member of a big dysfunctional family. The universe we see is smooth and uniform on its largest scales, yet it hasn’t been around long enough for any ordinary process to have homogenized it. It must have inherited its smoothness and uniformity from an even larger, older system, a system permeated with dark energy that drives space to expand rapidly and evens it out—the process known as cosmic inflation. Dark energy also destabilizes the system and causes universes to nucleate out like raindrops in a cloud. Voilà, our universe.

Other bubbles are nucleating all the time. Each gains its own endowment of dark energy and can give rise to new bubbles—bubbles within bubbles within bubbles, an endless cosmic effervescence. Even our universe has a dab of dark energy and can birth new bubbles. The space between the baby bubbles expands, keeping them isolated from one another. A bubble has contact only with its parent.

The process produces a family tree of universes. The tree is a fractal: no matter how closely you zoom in, it looks the same. In fact, the tree is a dead ringer for one of the most famous fractals of all, the Cantor set.

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