3:am magazine (yes, that’s what it’s called) has a very good interview with Craig Callender, philosopher of physics at UC San Diego and a charter member of the small club of people who think professionally about the nature of time. The whole thing is worth reading, so naturally I am going to be completely unfair and nitpick about the one tiny part that mentions my name. The interviewer asks:
But there is nothing in the second law of thermodynamics to explain why the universe starts with low entropy. Now maybe its just a brute fact that there’s nothing to explain. But some physicists believe they need to explain it. So Sean Carroll develops an idea of a multiverse to explain the low entropy. You make this a parade case of the kind of ontological speculation that is too expensive. Having to posit such a huge untestable ontological commitment to explain something like low entropy at the big bang you just don’t think is worth it.
There is an interesting issue here, namely that Craig likes to make the case that the low entropy of the early universe might not need explaining — maybe it’s just a brute fact about the universe we have to learn to accept. I do try to always list this possibility as one that is very much on the table, but as a working scientist I think it’s extremely unlikely, and certainly it would be bad practice to act as if it were true. The low entropy of the early universe might be a clue to really important features of how Nature works, and to simply ignore it as “not requiring explanation” would be a terrible mistake, even if we ultimately decide that that’s the best answer we have.
But what I want to harp on is the idea of “ontological speculation that is just too expensive.” This is not, I think, a matter of taste — it’s just wrong.
Which is not to say it’s not a common viewpoint. When it comes to the cosmological multiverse, and also the many-worlds interpretation of quantum mechanics, many people who are ordinarily quite careful fall into a certain kind of lazy thinking. The hidden idea seems to be (although they probbly wouldn’t put it this way) that we carry around theories of the universe in a wheelbarrow, and that every different object in the theory takes up space in the wheelbarrow and adds to its weight, and when you pile all those universes or branches of the wave function into the wheelbarrow it gets really heavy, and therefore it’s a bad theory.
That’s not actually how it works.
I’m the first to admit that there are all sorts of very good objections to the cosmological multiverse (fewer for the many-worlds interpretation, but there are still some there, too). It’s hard to test, it’s based on very speculative physics, it has a number of internal-consistency issues like the measure problem, and we generally don’t know how it would work. I consider these “work in progress” types of issues, but if you take them more seriously I certainly understand. But “wow, that sure is a lot of universes you’re carrying around” is not one of the good objections.
When we’re adding up our ontological commitments (i.e., the various beliefs about reality we are willing to hypothesize or even accept), the right way to keep track is not to simply add up the number of objects or universes or whatevers. It’s to add up the number of separate ideas, or concepts, or equations. There are an infinite number of integers, and there are only a finite number of integers between zero and a googol; that doesn’t make the former set somehow ontologically heavier. If you want to get fancy, you could try to calculate the Kolmogorov complexity of the description of your theory. A theory that can be summed up in fewer words wins, no matter how many elements are in the mathematical structures that enter the theory. Any model that involves the real numbers — like, every one we take seriously as a theory of physics — has an uncountable number of elements involved, but that doesn’t (and shouldn’t) bother us.
By these standards, the ontological commitments of the multiverse or the many-worlds interpretation are actually quite thin. This is most clear with the many-worlds interpretation of quantum mechanics, which says that the world is described by a state in a Hilbert space evolving according to the Schrodinger equation and that’s it. It’s simpler than versions of QM that add a completely separate evolution law to account for “collapse” of the wave function. That doesn’t mean it’s right or wrong; but it doesn’t lose points because there are a lot of universes. We don’t count universes, we count elements of the theory, and this one has a quantum state and a Hamiltonian. A tiny number! (The most egregious version of this mistake has to belong to Richard Swinburne, an Oxford theologian and leading figure in natural theology, who makes fun of the many-worlds interpretation but is happy to accept a completely separate, unobservable, ill-defined metaphysical category into his ontology.)
The cosmological multiverse, while on much shakier empirical ground than the many-worlds interpretation, follows the same pattern. The multiverse is not a theory, it’s a prediction. You don’t start with the idea “hey, let’s add an infinite number of extra universes!” You start with our ideas of general relativity, and quantum mechanics, and certain plausible field content, and the multiverse comes out, like it or not. You can even get a “landscape of different vacua” out of very little theoretical input; Johnson, Randall and I showed that transitions between states with different numbers of macroscopic spatial dimensions are automatic in a theory with just gravity, vacuum energy, and an electromagnetic field, while Arkani-Hamed et al. showed that the good old real-world four-dimensional Standard Model coupled to gravity supports a landscape of different vacua that depends on the masses of the neutrinos. The point is that these very complicated cosmologies arise from very simple theories, and it’s the theories we should be judging, not their solutions.
The idea of a multiverse is extremely speculative and very far from established — you are welcome to disagree, or even better to ignore it entirely. But please disagree for the right reasons!