13 July 2021

Musing on infinity

I remember as a quite young kid, maybe 12, thinking along the lines of "if the universe is really infinite, then that means there are an infinite number of me out there, doing exactly the same thing I'm doing, on a world exactly like Earth, and on an infinite number of them I'm thinking this right now, but just as many I'm not, and things turn out different." To me, even then, the logic of this was inescapable. In infinity everything that's possible actually happens. I remember trying to justify this thinking to a couple of friends, but they didn't see it.

Later I came to (mis)understand from reading about the Big Bang that the universe likely was not infinite, just very large, so this kind of thinking, with all the weirdness it entails, probably meant nothing, and that's been my tacit or explicit working worldview thereafter until some really novel ideas emerged in recent years. All of this was before Alan Guth proposed inflation, and others following on him realized that inflation actually can result in a universe composed of infinite space, and infinite mass and energy, referred to as "Eternal Inflation."

Now I read in Max Tegmark's remarkable book, "Our Mathematical Universe," that the best match to observation is this "Eternal Inflation," and that, indeed, in all likelihood, the universe causally connected to the so-called Big Bang (in other words excluding the higher levels of Multiverse, but including all the stars and galaxies even beyond the horizon where we can ever see (the so-called "observable universe" horizon), probably IS infinite, after all, and, well, my musings from more than 50 years ago were spot on. A fairly lengthy quote from the aforementioned book (paraphrased a bit because he uses the phraseology "Level I Parallel Universe" to refer to regions of the Big Bang Universe where detailed patterns are repeated by pure chance, inevitable in the case of infinity; I prefer to call them "regions" of our universe):

"…the quantum induced differences between [different regions of the universe] get amplified over time into very different histories. Students [in different regions] would learn the same thing in physics class but different things in history class.

"But would those students exist in the first place? It seems extremely unlikely that your life turned out exactly as it did, since it required so many things to happen: Earth had to form, life had to evolve, the dinosaurs had to go extinct, your parents had to meet, you had to get the idea to read this book, etc. But the probability of all these outcomes happening clearly isn't zero, since it in fact happened right here in [our part of the] Universe. And if you roll the dice enough times, even the most unlikely things are guaranteed to happen. With infinitely many … parallel (regions of the universe] created by inflation, quantum fluctuations effectively rolled the dice infinitely many times, guaranteeing with 100% certainty your life would occur in one of them. Indeed, in infinitely many of them, since even a tiny fraction of an infinite number is still an infinite number.

"And an infinite space doesn't ONLY contain exact copies of you. It contains many more people who are almost like you, yet slightly different. So if you were to go out and meet the closest person out there in space who looked like your spitting image, this person would probably speak an alien language you couldn't understand and would have experienced a life quite different from yours. But of all your infinitely many look-alikes out there on other planets there are also [an infinite number] who speak English, live on a planet identical to Earth, and have experienced a life completely indistinguishable from yours in all ways. This person subjectively feels exactly like [how] you feel. Yet there may be some very minor difference in how the particles move in your alter ego's brain that's too subtle to make a perceptible difference for now, but which in a few seconds will make your alter ego put this book aside while you read on, causing your two lives to start diverging."