Sean Carroll, as he does periodically, did an AMA on his podcast. He got a number of questions on the Everett interpretation, one of which in particular I want to look at, because it’s about an issue that bugged me for a long time. From the transcript:
0:26:50.1 SC: David H says, “When the universe splits a la Everett, is the split instantaneous across the whole pre-existing universe, or does it propagate at the speed of light?”
So the nice answer is, it’s up to you. And this goes exactly back to what we were talking about, about Laplace’s demon earlier. The branching of the wave function of the universe into separate worlds is not part of the fundamental theory. The fundamental theory is, there’s a wave function and it evolves according to the Schrödinger equation. That’s the entire theory. The splitting into worlds is something that we human beings do for our convenience. So, the right way to ask this question is, is it more convenient to imagine the world splitting all at once across all of space, or propagating at the speed of light?
0:27:31.0 SC: And for that, it’s completely dependent on what your purpose is, right? I actually tend to think of it as simpler just to imagine the universe splitting all at once, pre-existing, simultaneously across the whole pre-existing universe. That bothers some people, because they say, “Well, that’s not compatible with special relativity, which says that signals can’t travel faster than the speed of light.” But there’s no signal traveling faster than the speed of light; it’s just our description is traveling faster than the speed of light, and that’s perfectly okay.
While this answer makes sense to me now, I don’t think it would have when I was struggling with it. This post is my attempt to explore the answer in such a way that someone who doesn’t yet get it, might.
Let’s start with an analogy, the Louisiana purchase. In 1803 France sold a large chunk of territory in North America to the United States. Consider this question. When did the territory become part of the US? From a legal perspective, that would have been when the US Senate ratified the purchase agreement with France, which happened on October 20, 1803. On that ratification, all of the territory became part of the US, and all of the inhabitants became US residents.
Of course, news of the purchase took time to spread. There was a ceremony in New Orleans on December 20, 1803. But the news took longer to reach many residents. In particular, no one had really bothered to consult or inform most of the Native Americans living in the territory. So while the legal transfer happened instantly, the social results took time, years in fact, to be felt throughout the territory.
Which way is the right way to look at when the Louisiana territory became part of the US? The legal transfer date? The boots on the ground occupation? Or the overall assimilation into US culture? There isn’t really a fact of the matter here. Borders and nationality are human conventions. The land is the land. Nature doesn’t care. So we can validly talk about it in different ways.
That’s what Carroll is trying to get at when he talks about the raw theory, the universal wave function, versus our ways of talking about worlds or universes splitting. Similar to the transfer of the Louisiana territory, there are multiple ways of looking at and talking about the same reality. Here are three:
- On a quantum measurement, the world begins splitting at the time and location of the measurement. The split propagates out at the speed of quantum interactions. The propagation can happen no faster than the speed of light.
- On a quantum measurement, previously existing worlds, which had until then been identical, begin to diverge from each other at the time and location of the measurement. The divergence propagates out at the speed of quantum interactions, no faster than light.
- On a quantum measurement, what we considered one world, we now instantly consider split into multiple whole worlds, which had until then been identical. They begin to diverge from each other at the time and location of the measurement, propagating out via quantum interactions no faster than light.
The thing to remember here is that a “world” or “universe” in Everett is a slice of the universal wavefunction. But our divvying up of the wavefunction is a human convention. In nature it’s just a continuum. So we can talk about the slice we’re on “splitting” into two or more slices, or nearby slices “diverging” from each other, or even decide that what we once divvyed up as one slice we’re considering multiple slices. It’s all different ways of talking about the same reality.
Option 1 has historically made the most sense to me. It was how I needed to think of the Everett interpretation to consider it a viable possibility. It also makes more sense when considering something like an isolated quantum system, such as a quantum computer, which has qubit circuits in combined superposition. Under 1, these could be seen as world splits that are contained for a time, until the measurement magnifies the quantum state differences into the universe.
But 1, which is us constantly being split into multiple people, is an existentially disconcerting way to think about this. It also makes the probability of observed measurement outcomes awkward to talk about since all possible outcomes happen. And each split effectively divides up the energy of the world among the new worlds, which many find difficult to accept.
Option 2 is David Deutsch’s preferred way of looking at it. In this view, we are who we are, and there are other people in parallel worlds identical to us but diverging away anytime a quantum event is magnified, so we can see ourselves as having a classical timeline. Isolated quantum superpositions are basically the conditions necessary to detect the interference between worlds. Talking about probabilities is much easier since we’re now talking about the probabilities of outcomes in this world. And the energy of this world is what it is. It’s also easier to understand why Bell’s theorem isn’t an issue for Everett within this view, because within any one world, the correlations can exist from the beginning. The drawback of this option is it requires more explanation.
Option 3 is Carroll’s preference, and this is the way Everett is usually presented in quick summaries, although without the explanation of why it doesn’t violate relativity. It also seems to inherit the existential angst and other issues from 1. I’m not sure why Carroll prefers it. It might be because the existential issues can also be seen as exciting. And the hybrid model can be seen as preserving that while also making clear why Bell isn’t an issue. But it seems to have the highest explanatory burden.
Of course, all of this is about a theory that already requires a lot of explanation, one most people won’t wait on before summarily dismissing the whole thing as absurd and outrageous. So maybe worrying about additional explanatory burden isn’t productive.
Which option works for you? Or is the least problematic? Is there another way of looking at it?