The problem with hierarchical multiverses

Lee Smolin

In an earlier post in this blog I mentioned a list of theories about multiverses, independent and often mutually contradictory, prepared by George Ellis, the cosmologist. These multiverses can be divided into two large groups:

• Non-hierarchical multiverses: such as the chaotic inflationary multiverse, where each universe is supposed to be a bubble that has stopped its inflationary growth, amid a permanent and total inflationary environment.
• Hierarchical multiverses: like Smolin's (which Ellis does not mention) and the multiverse of universe simulations (in other words: that we live in a simulation). In this post I speak exclusively about this type of multiverses, which share a property that, in my opinion, makes them implausible, if not impossible.

Smolin’s selective multiverse, where every black hole in a universe becomes the Big Bang of a new universe, is selective because the number of universes capable of producing black holes in that multiverse would be much greater than that of universes incapable of it, since these wouldn’t leave any offspring. In Smolin’s opinion, this would solve the fine tuning problem, since universes similar to ours would also be more apt for life to appear.

Smolin’s multiverse gives rise to a hierarchical structure (the genealogic tree) where each level is clearly less powerful than the previous level. Indeed, by applying the Einstein cosmological equation to the standard cosmological model, our universe is computed a mass of the order of 10⁵² kg. Each of our descendant universes would have a much lower mass. The largest, those black holes that appear to be in the center of the biggest galaxies, have a mass several million times larger than the sun (about 10³⁶ kg), which means a loss of 16 orders of magnitude by descending one level in the hierarchy. It also means that the universe from which ours came would have a mass much higher than ours (above about 10⁶⁸ kg). Sooner or later, when descending through the hierarchy, a level would be reached where the universes would no longer be able to generate new universes similar to ours, because they would not have enough mass to give rise to black holes, and so the hierarchy would come to an end.

ΛCDM cosmic model simulation
Michael L. Umbricht - Wikimedia

Something similar would happen with the multiverse of universe simulations on computers. As I indicated in the previous post, and one of my readers pointed out in a comment, it has been shown that each simulated universe must be less complex (or less powerful, to use another word) than the universe that simulated it. Therefore, the hierarchy made up by simulated universes also decreases in complexity, like that of Smolin in mass. Consequently, sooner or later a level would be reached at which the simulation of universes like ours is no longer possible, where intelligent life may appear. And there the hierarchy would come to an end.

The fact that these multiverses give rise to the appearance of a hierarchical structure has two consequences:

• The number of universes in each hierarchical level grows very rapidly with the degree of descent of the hierarchy: Thus, for instance, in our universe there are many supermassive black holes, so the next level, if still viable, would contain many more universes than our level. And if we live in a simulation, the number of universes simulated by each higher level universe would be much greater than the universes in that higher level. This law would apply at all levels.
• As a result of the above, the number of universes would be maximum at the last level of the hierarchy. This has a remarkable consequence: according to the law of probabilities, if we are in a hierarchical multiverse, we must be precisely in a universe of the last level, since they would be much more abundant than the others.

If Smolin’s multiverse were correct, our universe must be one of the last that would allow the apparition of life. And if we live in a simulation, we are forbidden the simulation of universes where intelligent life can arise, for we won’t be able to simulate universes sufficiently complex. In other words: if we really live in a simulation, we’ll never be able to simulate anything really interesting. This is not an immediate proof that we don’t live in a simulation, but it does offer a possible way to prove that this theory is false: if we ever manage to simulate intelligent life, we’d automatically prove that we don’t live in a simulation.

The same post in Spanish
Thematic thread on Multiverse and Fine Tuning: Preceding Next

Manuel Alfonseca