What’s In a Number: Unravelling a Multiversal Paradox
Still, let’s say the number of universes is infinite. In that case, the reader’s argument goes like so:
A. The number of universes is infinite.
B. A universe exists in which the number of universes is not infinite.
C. This might be it.
Stated this starkly, the flaw in the argument becomes pretty clear. B contradicts A. “The number of universes is infinite” and “the number of universes is not infinite” can’t both be true. The contradiction, however, is obscured by the inclusion of “A universe exists in which.” The implication is that there’s something special about universes, something that, for instance, doorknobs don’t have. “Since there is an infinite number of doorknobs, there must be one for which there isn’t an infinite number of doorknobs” wouldn’t make anyone’s head asplode, except perhaps in bewilderment.
So what’s so special about universes that the existence of an infinite number of them would, for physics-savvy readers, somehow seem to suggest the necessary existence of one that allows the impossible?
I suspect the answer is quantum probability. According to quantum theory, everything is a matter of probability; therefore anything is possible. Anything. The probability that a butterfly will give birth to a dragon or that I will one day fall into the Thames is vanishingly small-but, technically, it’s not zero. Same with the emergence of a universe, or a cornucopia of universes, from nothing. The laws of physics allow it.
And that’s the implicit, but missing, “something special” in premise B: the laws of physics. As in “A universe exists in which the laws of physics require the number of universes to not be infinite.” What prompted the New Scientist reader, and what posed a threat to Sally’s noggin, was an unthinking assumption: that “the laws of physics” — in particular quantum theory — are part of the argument.
It’s a tempting assumption. According to current cosmological thinking, if an infinite ensemble of (or 10500, anyway) universes exists, then presumably each could come equipped with its own laws of physics. So couldn’t our universe be the one in which the laws of physics require that other universes don’t exist?
Yes — but only if our laws of physics have something to do with the other universes. We all, however, went our separate ways 13.7 billion years ago. Our laws of physics affect what happens within our universe, but there’s no reason to think they would influence the multiverse at large. Doorknobs, after all, don’t dictate the laws of physics.
I recommend reading the full article to puzzle this out.