Max Tegmark on being seduce by infinity.

 I was seduced by infinity at an early age. Cantor's diagonality proof that some infinities are bigger than others mesmerized me, and his infinite hierarchy of infinities blew my mind. The assumption that something truly infinite exists in nature underlies every physics course I've ever taught at MIT, and indeed all of modern physics. But it's an untested assumption, which begs the question: is it actually true? 

There are in fact two separate assumptions: "infinitely big" and "infinitely small". By infinitely big, I mean the idea that space can have infinite volume, that time can continue forever, and that there can be infinitely many physical objects. By infinitely small, I mean the continuum: the idea that even a liter of space contains an infinite number of points, that space can be stretched out indefinitely without anything bad happening, and that there are quantities in nature that can vary continuously. The two are closely related because inflation, the most popular explanation of our Big Bang, can create an infinite volume by stretching continuous space indefinitely.

The theory of inflation has been spectacularly successful, and is a leading contender for a Nobel Prize. It explained how a subatomic speck of matter transformed into a massive Big Bang, creating a huge, flat and uniform universe with tiny density fluctuations that eventually grew into today's galaxies and cosmic large scale structure, all in beautiful agreement with precision measurements from experiments such as the Planck satellite. But by generically predicting that space isn't just big, but truly infinite, inflation has also brought about the so-called measure problem, which I view as the greatest crisis facing modern physics. Physics is all about predicting the future from the past, but inflation seems to sabotage this: when we try to predict the probability that something particular will happen, inflation always gives the same useless answer: infinity divided by infinity. The problem is that whatever experiment you make, inflation predicts that there will be infinitely many copies of you far away in our infinite space, obtaining each physically possible outcome, and despite years of tooth-grinding in the cosmology community, no consensus has emerged on how to extract sensible answers from these infinities. So strictly speaking, we physicists are no longer able to predict anything at all!