An Objection To Many Worlds

From anthropics

Before I begin this article, let me say: I am not an expert on the many worlds interpretation of quantum physics. You shouldn’t really trust what I have to say on this subject. The extent of my expertise is having gotten an A in high school physics and read some Eliezer Yudkowsky articles about many worlds. I could tell you almost nothing about the physics behind many worlds. Fortunately, my argument doesn’t hinge on highly precise facts about physics.

The basic idea of many worlds is that each time a quantum mechanical event happens, the universe splits so that there’s a world where it turns out each of the ways it could have. So, for instance, if a particle can either go left or right, the world splits and there’s one world where it goes left and another where it goes right. This may sound ridiculous and gerrymandered, but it allegedly falls straightforwardly out of existing physical equations rather than requiring an epicycle.

How much splitting happens? A lot! Likely an infinite amount of splitting happens per second. If the amount is finite, it’s likely on the order of 2^10^18 new universes per person per second, and obviously much more caused by all the rest of the universe.

To introduce my objection, let me give an analogy. Let’s imagine that the human population is increasing massively. The first generation has just 100 people. The next has 100^100 people. The one after that has 100^100^100 people. And so on. Given the massive expansion in the number of people, you should expect—with near certainty—to be born right before the end of the world. Given the massive growth in numbers of people, nearly everyone who ever lived will be born at that time. So given that you exist, you should think probably you would be born at that time.

This is analogous to how if you know that almost no one lives in Antarctica, you should think probably you don’t live in Antarctica. If you woke up in Antarctica, unsure of how you got there, this would be a bit of evidence that a larger percentage of people are in Antarctica than you thought. If you woke up in Asia, and were considering between the theories that Asia has the most people and that Antarctica does, your evidence would favor the theory that Asia does.

The core idea is that if almost everyone has some property X then you should expect to have property X.

But now let’s apply that to many worlds. On many worlds, the number of worlds is constantly increasing at extreme rates. Nearly everyone who has ever lived will live right before the end of civilization. Conditional on many worlds, therefore, it’s overwhelmingly likely that you currently live at the end of the world.

Counterpoint: you don’t. So because many worlds gives you reason to expect that you would live at the end of the world, this is strong evidence against many worlds. Just like in the earlier case, if you find that you’re not at the end of the world, you get extremely strong evidence that the theory is false.

Now, you might object that there could be multiple ends of the world. To simplify, let’s say that there is one world A. A branches into B and C. Then C ends but B branches into D and E. There might be no single end of the world but just ends of individual branches. This is correct, but you should expect to be at the end of whichever branch is yours. That’s where most people are. At the very least, you should expect to find yourself quite late in the universe, which we do not.

In fact, because in the distant future there are likely to be many more Boltzmann brains, by this logic, you should suspect that you’re a Boltzmann brain on many worlds. A Boltzmann brain is a brain that randomly fizzes into existence in the recesses of outer space, rather than evolving on a planet. It forms randomly as a result of chemicals coming together. During heat death, after the last black hole has burned out, Boltzmann brains will still be able to form but there won’t be any complex structures. Thus, it seems like if many worlds is true, you should suspect you’re almost definitely a Boltzmann brain. Almost everyone who lives will do so after heat death.

Another reply: on many worlds, it looks like the number of worlds will be infinite in any case. At every time, there will be infinite people of the same cardinality. A cardinality, for those who don’t know, is a measure of the number of elements of a set. Two sets have the same cardinality if you can pair their members one to one: a set of two apples and two bananas have the same cardinality because you can pair their members one to one. Infinities are usually measured by cardinality; the number of natural numbers (…-2, -1, 0, 1, 2, 3, 4) has the same cardinality as the number of prime numbers as you can pair them off one to one.

Thus, a defender of many worlds could reply that at every single time, the cardinality of worlds will be the same—aleph null perhaps. Thus, it’s not really increasing and you shouldn’t expect to find yourself in a later world.

This has several problems. The first one is that it’s probably the wrong analysis of infinity. Imagine there are aleph null people. They each have ten kids. You’re created but don’t know if you’re part of the first generation or a later generation. It seems obvious that you should think at 10:1 odds that you’re in the later generation. Even if the cardinalities don’t change, you should probably still think that you’re in the later generation. If you deny that, then you should think that in the actual world, so long as it’s infinite, you’re no likelier to be born after the first generation of humans than to be the first generation of humans.

Similarly, with many worlds, if aleph null universes repeatedly split, you should expect to be in one of the later universes, rather than one of the originals.

The second big problem is that if this is right then credences turn out undefined. If there are aleph null people with each of several properties, generally your credence in having any of the properties will be undefined. If this is right, then before learning your birth rank, you should have undefined credence in each of the times you could be born at. But then, because later periods have mostly Boltzmann brains, you’ll have undefined credence in your being a Boltzmann brain.

This objection strikes me as pretty strong. But I could easily be missing stuff. As I’ve said before, I don’t really get the physics of many worlds. So proponents of many worlds tell me: why am I wrong?