Many-worlds and Bell’s theorem

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.

  1. 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.
  2. 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.
  3. 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.

Everett world concept relations

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?

11 thoughts on “Many-worlds and Bell’s theorem

  1. I don’t understand why we need to complicate what is not. Rene Descartes wrote ‘I think, therefore I am’. The conscious form breaks everything here including experiments upon observation. And other objects do the same when observed or when a human acts and thereafter. The wave of the particle later-on is up to the nature or God or luck which ever way you care to lean. It seems that consciousness is a massive influence on our understanding and also how a particle acts. Copenhagen has always made more sense to me.

    Liked by 3 people

    1. Until one of the interpretations manages to rack up evidence uniquely in its favor, no one can authoritatively say what is or is not. The idea that consciousness causes the collapse goes back to musings by John von Neumann in 1932, and later writings by Eugene Wigner. There were a substantial portion of physicists who agreed. That started to decline in the 70s and 80s with the development of decoherence theory. Today, it’s far more popular outside of physics than in it.

      But for me, consciousness causing the collapse is difficult to reconcile with the engineering involved in quantum computing. Maintaining quantum effects in these systems requires extraordinary isolation from the environment. If the only thing engineers had to do to maintain those effects was keep any conscious entity from observing them, their job would be a lot easier. But those effects are routinely lost without any conscious interaction.

      Of course, someone could argue that the QC issues are only about decoherence, that the collapse itself doesn’t happen until conscious observation. But then, that is observationally indistinguishable from there being no collapse. If we have a choice between assuming a collapse, or not assuming one, then is it really simpler to assume one?

      Liked by 1 person

  2. So Mike, I always just assumed that in MWI, the split doesn’t happen with “measurement” as you wrote in scenarios 1 and 3, but rather whenever the wave function develops new possible branches. For the Bell Test, as soon as down conversion (or whatever is used to create a correlated pair of photons) occurs, then in my mind the split happens then, because every “possibility” that results from that moment comes into being. It makes very little sense to me to imagine the splitting or branching only occurs much later when this thing called “measurement” happens. Because I thought a big attraction for MWI was to avoid these measurement issues altogether? Everything is real simultaneously so no special power is assigned to this measurement event…

    In this that I’ve described the Bell Test is local in every branch, because the results are, in essence, entirely described by the correlations that exist in the various branches from the instant down conversion occurs. Unless I’m mistaken you’re describing something very different and I guess I don’t understand why the worlds don’t split when the math splits…? Because it’s based on the wave equation being “reality” no?

    Liked by 2 people

    1. Hi Michael,
      I think that’s another valid way to look at it. But it seems like you’ve defined a new type of world, somewhere between the base-world and macro-world concepts. For now, let’s call it a prep-world, since it splits based on the preparation of those pairs. So a prep-world is the set of base-worlds that are identical at the resolution of the prepared state, but are distinguished from each other by the different versions of that state.

      The thing to keep in mind though, is that at the point of that preparation, while the particles remain in their unmeasured states, all the new prep-worlds remain macroscopically identical. If the particles are never measured (either in a lab or naturally) then those worlds will never diverge from each other macroscopically (at least not due to this prepared system). So they remain one macro-world. A prep-world could be viewed as a potential macro-world, but only if its effects are able to propagate.

      A note on measurement. When I use that word, I’m lumping it in with decoherence, the amplification of the causal effects of the measured particle into the environment. Without that amplification, any divergence only exists only at the micro-level and gets averaged out. To have a split at the macro-world level, we need a measurement / decoherence event.

      Something to note on the math. It can describe things at various levels. Describing a photon seems pretty primal, but it can also describe the state of a composite system, like an atom, molecule, table, etc. If we ever discover that photons have constituents, then the variables could model those constituents. So, if we regard the world as split based on mathematical variables, the resolution of that split will depend on what level that variable is modeling. Which means, for your final question, under realism, the wave equation, in and of itself, isn’t reality, it describes reality (at some chosen level).

      Hopefully the idea is coming across here that a “split” isn’t an ontological thing, but a descriptive one, a strategy for us to think about the underlying reality (if there actually is a universal wave function).

      Liked by 2 people

      1. Thanks, Mike. The easy part is I understand the equating of decoherence and environmental interactions of some sort and the notion of “measurement,” so follow what you’re saying there.

        But I do get lost in the various sets of worlds you have described. What’s new to me in your description is that I had always thought, as I wrote earlier, that since all the possible outcomes of a quantum event are equally realized in MWI, any branching occurs then. Having the branching delay until some other point in time seems weird to me, but I guess the delay can only be one in which “nothing is happening” in the sense that the system in question hasn’t interacted with the environment. The cost of this “delayed branching” (in quotes to convey merely that this is expression is my own, likely due to my ignorance on the topic) is the loss of locality as you noted. Because in a Bell Test, if the photons are conveyed in opposite directions for a good ways, and THEN measured, and if branching hasn’t already occurred, then it’s back to non-locality in every world branch as near as I can tell? While if the branching occurred in the moment when a superposition comes into being, then in any given world everything is local because no matter how far apart the photons are conveyed… they are what they are.

        The issue of macroscopic identity and differentiation is one I don’t follow yet and maybe need to think about. I don’t understand how it “matters” to MWI whether a state is distinguishable macroscopically or not, as that kind of depends on the eye of the beholder doesn’t it? Or at least on the context of a particular interaction. Some events will be much more significant to macroscopic states than others, and I don’t know the mathematics, but I don’t think the significance enters into it much? This seems like an extra layer of interpretation layered onto MWI in order to relate it to human experience. I only say that because I saw various possible outcomes of a quantum event as all equally relevant, meaning they all come to fruition somewhere.

        On base worlds never splitting I guess I don’t follow that either. Is the idea that more base worlds come into being, but never actually split? Or is this to do with Deutsch’s view, where all base worlds possible—an infinite array—already exist and MWI is simply the various ways they interact? If that’s the case, then I could understand how base worlds never split, just interact and diverge.

        Liked by 2 people

        1. I was worried that those three world types might get confusing. It’s why I had the review step, and pulled back from abbreviating them. Sounds like it was still a fail. Sorry Michael.

          The word “branching” is, unfortunately, a bit vague, and used by different people in different ways. But you’re right that any post-decoherence branch is a continuation of the elements of the superposition that existed prior to decoherence. So you could say the branches began as soon as the differentiation in states emerged, although the word “branch” is often held for use after decoherence. Decoherence is just the process of the measured entity becoming entangled with its environment, that is, its causal effects (all branches of them) propagating into that environment. But with or without measurement, the initial entanglement of the photons never disappears. It remains encoded in their wave function and is why the correlations persist across large distances. Nothing in the post should be seen as negating that. So if that’s how you understand local causality being maintained, it’s still good.

          What the different world types do provide, however, is an easy way to think about the encoding of the entanglement. Let’s just focus on base-worlds, which you’re right is Deutsch’s idea of a world. In this view, they all already exist, never split, and, for our purposes here, their number is static (albeit infinite or sublimely large). In terms of branches, you could view it as all the branches that will ever exist, already exist. They’re just not distinct yet.

          The combined wave function of our entangled particles spans many base-worlds, including any that are similar enough for interference to happen between them. Each base-world has its own version of each particle and their correlation. The interference between the particles in the various worlds creates the overall wave effect. So each correlation is easy to understand because they each exist in their own separate base-world. There is no world splitting here, just the different worlds diverging, evolving to be different from each other. Although the number of base-worlds should be thought of as profoundly high so there are always plenty left identical enough for additional quantum interference effects.

          Does that help in seeing how it’s compatible with the understanding you described?

          The only reason to bring in the other types is to reconcile with the other ways people talk about worlds in Everett, but it’s not necessary. They’re just different ways of talking about groupings of base-worlds.

          Liked by 2 people

          1. Mike, this explanation was helpful and I was able to follow your description of the worlds better. Thank you! The key realization was the base worlds go with Deutsch’s ideas, and then the rest fell into place much better.

            Liked by 1 person

          2. Thanks Michael. I actually started off calling them “Deutsch-worlds”, but some writers assert that version didn’t start with him, so it felt better to just go generic. I also considered “Planck-worlds”, but didn’t want to make an assertion about the Planck scale, and “micro-worlds”, but at one point I was planning to abbreviate them and that would have collapsed to “m-worlds” for both the micro and macro version.

            Effective naming is hard. 🤔

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        2. “While if the branching occurred in the moment when a superposition comes into being,”

          But which superposition? How would it know at that point which axis (or axes, if different) Alex and Blair use?

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  3. The violation of Bell’s inequality does not necessarily imply non-locality. It implies that QM is either non-local OR without hidden variables. Meaning it can be non-local but still with hidden variables (e.g. DeBroglie Bohm theory, MWI or supereterminism) or it can be also a local theory, but then it must be without hidden variables (e.g., Gherardi-Rimini theories) or both non-local AND without hidden variables (orthodox theory and, IMHO, the most plausible option).

    Liked by 2 people

    1. Thanks for commenting!

      My understanding is that Bell implies (a) non-local causality and inseparability, (b) local causality with inseparability with many-worlds, or (c) local causality and separability with superdeterministic loopholes.

      It does seem like deBroglie-Bohm falls into (a). Superdeterminism, as I’ve seen it pitched, usually promises full locality with hidden variable, albeit at the expense of assuming the whole universe works to enforce improbable correlations.

      I’m curious where you see the local variables in many-worlds. It’s generally seen as just following the mathematical formalism.

      I’ve usually regarded GRM as non-local and so in (a), although Alyssa Ney in her book argued that due to its spontaneous and uncaused nature of its collapses, it could be seen as causally local. (Still trying to wrap my brain around that one.)

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