The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [107]
The ambiguity has a dramatic impact on what we conclude are typical or average properties in a given multiverse. Physicists call this the measure problem, a mathematical term whose meaning is well suggested by its name. We need a means for measuring the sizes of different infinite collections of universes. It is this information that we need in order to make predictions. It is this information that we need in order to work out how likely it is that we reside in one type of universe rather than another. Until we find a fundamental dictum for how we should compare infinite collections of universes, we won’t be able to foretell mathematically what typical multiverse dwellers—us—should see in experiments and observations. Solving the measure problem is imperative.
A Further Contrarian Concern
I’ve called out the measure problem in its own section not only because it is a formidable impediment to prediction, but also because it may entail another, disquieting consequence. In Chapter 3, I explained why the inflationary theory has become the de facto cosmological paradigm. A brief burst of rapid expansion during our universe’s first moments would have allowed today’s distant regions to have communicated early on, which explains the common temperature that measurements have found; rapid expansion also irons out any spatial curvature, rendering the shape of space flat, in line with observations; and finally, such expansion turns quantum jitters into tiny temperature variations across space that are both measurable in the microwave background radiation and essential to galaxy formation. These successes yield a strong case.11 But the eternal version of inflation has the capacity to undermine the conclusion.
Whenever quantum processes are relevant, the best you can do is predict the likelihood of one outcome relative to another. Experimental physicists, taking this to heart, perform experiments over and over again, acquiring reams of data on which statistical analyses can be run. If quantum mechanics predicts that one outcome is ten times as likely as another, then the data should very nearly reflect this ratio. The cosmic microwave background calculations, whose match to observations is the most convincing evidence for the inflationary theory, rely on quantum field jitters, so they are also probabilistic. But, unlike laboratory experiments, they can’t be checked by running the big bang over and over again. So how are they interpreted?
Well, if theoretical considerations conclude, say, that there’s a 99 percent probability that the microwave data should take one form and not another, and if the more probable outcome is what we observers see, the data are taken as strongly supporting the theory. The rationale is that if a collection of universes were all produced by this same underlying physics, the theory predicts that about 99 percent of them should look much like what we observe and about 1 percent to deviate significantly.
Now, if the Inflationary Multiverse had a finite population of universes, we could straightforwardly conclude that the number of oddball universes where quantum processes result in data not matching expectations remains, comparatively speaking, very small. But if, as in the Inflationary Multiverse, the population of universes is not finite, it is far more challenging to interpret the numbers. What’s 99 percent of infinity? Infinity. What’s 1 percent of infinity? Infinity. Which is bigger? The answer requires us to compare two infinite collections. And as we’ve seen, even when it seems plain that one infinite collection is larger than another, the conclusion you reach depends on your method of comparison.
The contrarian concludes that when inflation is eternal, the very predictions that we use to build our confidence in the theory are compromised. Every possible outcome