Sean Carroll’s February AMA episode is up on his podcast. As usual, there were questions about the Everett many-worlds interpretation of quantum mechanics (which I did a new primer on a few weeks ago). This time, there was a question related to the correlated outcomes in measurements of entangled particles that are separated by vast distances.
From the transcript:
3:27:55.2 SC: Rob Petro says, “You’ve explained on a number of occasions that Everretian Branching happens either instantly or at light speed. Specifically one can choose how to interpret the branching, since presumably they’ll be equivalent… These will be equivalent from the perspective of the observers at the source of the branch. My question relates to how this interpretation interacts with quantum entanglement? If Alice and Bob have entangled particles and travel to a great distance, then Bob observes his particles, how does branching happen? Given that Bob will now know the state of Alice’s particle instantaneously and Alice when she observes will know what Bob had observed.”
So, this is exactly why I prefer to think of it in terms of instantaneous branching all over, even though that is contrary to the spirit of special relativity, even though it’s completely compatible with the letter of the law, as it were, ’cause it’s a completely observable effect… Unobservable effect.
3:28:47.7 SC: If you say that when Bob observes his particle, the branching happens instantly. If you’re many worlds person, then there are now two copies of Alice. There’s an Alice in the spin-up branch and Alice in the spin-down branch, but she doesn’t know as she has no idea that there are now two copies of her, ’cause there are exactly identical copies locally. So, one of them will be on the branch that later when they visit, Bob, will see spin-up, the other will later visit Bob and see spin-down, as everything is perfectly compatible. If you want to believe in the story where the branching sorta spreads out at the speed of light, then you have to have rules when that spreading out branches overlap how they reconcile with each other, right? So, the branch where Alice spin-up, if the spins are initially counter-aligned, it has to have the property that when it joins up with Bob’s branches it joins up with the one where Bob will spin-down, etcetera. So that’s complicated, but you can do it and you can work it out. I just think it’s a little bit of complication we don’t really need.
This was an issue I struggled to understand when learning about the Everett interpretation. Bell’s theorem, along with experimental evidence, seems to demonstrate that local causality can’t be preserved in these correlations. There’s seemingly no room for the values to have been set prior to the measurement. But Everett is usually presented as a locally causal theory. How does it evade Bell? The usual quick answer of Everettians is that Bell assumes only one outcome for a measurement, but since under Everett every outcome is realized, it isn’t an issue. However that still leaves the issue of trying to understand how the correlations across vast distances are maintained.
As Carroll notes, it isn’t much of an issue if we regard the world as instantly splitting, since then each world’s correlations are maintained within that world. It’s harder if we regard the world as gradually splitting since the gradual splits then have to “pair up” with the correlated versions and not the uncorrelated ones. As Carroll mentions, there are ways to understand this, but it’s complicated, and doing it right, per Alyssa Ney, likely requires thinking about the higher dimensional configuration space of the wave function where the correlations are encoded.
Maybe for us lay people, a simpler way is to reconcile the different versions of world splitting. As I’ve noted before, they are really different ways of talking about the same ontology, that of the universal wave function. I tried to explain this a while back. Looking back at it, I’m not satisfied with that effort. Here’s another shot. This time, I’ll focus on what I understand the word “world” to mean in each description.
And of course, this is completely per my own understanding as an interested amateur, a consolidation of what I’ve picked up from many books and some physics papers, so take it with that in mind.
To review, there are at least three ways of looking at how worlds evolve under Everett.
- Gradual split: On a measurement, the world begins splitting from the time and location of the measurement, propagating out into the universe, no faster than the speed of light. In this view, the world split is identical to the divergence in states between the worlds.
- Pre-existing worlds: This is David Deutsch’s view, which I’m gradually starting to see a lot of value in. All the worlds already exist. On measurement, the worlds begin diverging from each other, with the divergence propagating out no faster than light. In this description, there is no world splitting.
- Instant split: On measurement, what we previously regarded as one world, we now regard as two (or more depending on the measurement), with each world diverging from each other at the site of the measurement, no faster than light.
There are different versions of a “world” in each of these descriptions, each one slicing up the configuration space of the universal wave function in a different way.
Let’s call the pre-existing world concept a “base-world”. In my mind, base-worlds could be thought of as worlds distinct from each other down to, perhaps, the Planck scale (or smaller if Planck lengths eventually turn out to not be fundamental). Base-worlds never split on measurement, they only diverge from each other.
(A natural question here is, how many base-worlds are there? The theory is silent on that. Deutsch just says it’s infinite and moves on. It seems like it would depend on whether there is some base unit of reality. Carroll occasionally mentions something like 210122 as a lower estimate.)
Now, let’s take a set of base-worlds that are macroscopically identical with each other, and let’s give that type of set a name: a “macro-world”. The base-worlds in this set vary microscopically from each other, but those variances average and cancel out over macroscopic scales. Macro-worlds are macroscopically distinct from each other across all of space, and are composed of a vast multitude of base-worlds.
Let’s say someone in this set of base-worlds measures the spin of a particle. In one portion of the constituent base-worlds, the result is spin-up, in the other portion, spin-down. Each portion of the set of base worlds therefore begin to diverge from the other.
But what of our macro-world? Remember, the definition here of a macro-world is a set of base-worlds that are macroscopically identical. The measurement has changed that set. It now makes sense to say that the set has instantly split into two separate sets, two macro-worlds. But also remember, there has been no splitting of the base-worlds themselves, just in the macro-world set that they belong to.
The macro-world is the one used in scenario 3, the instant split.
Now, let’s consider a set of base-worlds which, in an isolated quantum particle, are locally similar enough that they participate in the interference effects of that particle. That is, the wave function of the isolated particle spans the base-worlds of this set. In Deutsch’s description, each base-world has its own version of the particle, all of which are close and similar enough to coherently interfere with each other.
Let’s give this new type of set a name: an “interfere-world”. An interfere-world will span the base-worlds of one or more macro-worlds. In reality, it will probably span a vast multitude of macro-worlds, which of course are an even vaster multitude of base-worlds. But the spatial scope of an interfere-world is less than that of the others. Which interfere-world you’re in any instant in time depends on your location.
For example, if someone has just done a spin measurement close to you with a 50% chance of each outcome, such that the causal effects of that measurement have reached you, then your interfere-world will have half the base-worlds of someone further away who the effects haven’t reached yet. (Assuming of course that the effects of some other measurement event, natural or engineered, don’t reach them first.) In other words, each measurement splits an interfere-world, and that split propagates with, actually is equivalent to, the divergence.
The interfere-world is the one used in scenario 1, the gradual split.
So, to review.
- Base-worlds are microscopically distinct from each other. Base-worlds never split, only diverge from each other no faster than light.
- A macro-world is a set of base-worlds that are macroscopically identical. Macro-worlds are macroscopically distinct from each other. A macro-world, on measurement, splits instantly, but this split is a definitional one, not a physical one. The physics in in the divergence.
- An interfere-world is a set of base-worlds that are locally similar enough to contribute to the interference effects of an isolated quantum system. An interfere-world, on measurement, splits with the causal effects of the measurement, the wave of entanglement, through the universe, no faster than light. Which interfere-world you’re in in any instant depends on your location.
- Scenario 1, gradual split, uses interfere-worlds.
- Scenario 2, pre-existing worlds, uses base-worlds.
- Scenario 3, instant split, uses macro-worlds.
Here is my feeble and oversimplified attempt to show these relations visually. I hope it helps. The vertical are the configuration space dimensions that separate worlds, and the horizontal is the spatial extent of those worlds.
So what does all this tell us? As noted before, these descriptions are not alternate ontologies. They just discuss the same ontology, that of the universal wave function, by slicing it up in different ways. When considering the different descriptions, you really can choose whichever works best for you depending on your goals. You’re not giving up the benefits of the others when you choose one.
If your goal is to understand Everett’s take on Schrödinger’s cat or Wigner’s friend type scenarios, then I think the interfere-world works better. If you want to understand how probabilities might make sense in Everett, then the base-world seems better since we can coherently talk about the probability of an outcome in any one base-world. And the base-world version feels far less existentially disturbing, since in it, we are who we are and never split.
And to Carroll’s point and that of this post, if you want to understand Bell correlations, then either the macro-world or base-world seem easier to do that with.
Unless of course I’m missing something?