The nature of splitting worlds in the Everett interpretation

This post is about an aspect of the Everett many-worlds interpretation of quantum mechanics. I’ve given brief primers of the interpretation in earlier posts (see here or here), in case you need one.

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:

  1. 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.
  2. 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.
  3. 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?

83 thoughts on “The nature of splitting worlds in the Everett interpretation

  1. “…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.”

    What about those who’ve given it considerable thought and analysis and still find it absurd?

    Doesn’t the mere fact that proponents can’t even say for sure how the splitting works say something about how absurd the theory is? (Or, for that matter, define how energy can be “thinned”?)

    Liked by 1 person

    1. I wasn’t describing you with that passage Wyrd. You’ve at least read about it and have often been willing to talk about it.

      On your question about the splitting, it seems clear I didn’t get my point across in the post, at least not to you. Oh well, maybe next time. (Doesn’t energy get thinned all the time in physics? What else is an explosion? Or the big bang?)

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      1. While I agree I’m not “most people” the way it’s written verges on the evangelistic ‘if you don’t agree with this, you don’t get it’ mode that I see as making MWI something of a case of groupthink.

        If your point is that it’s dealer’s choice, I got it, and it’s what I’m suggesting makes this not even a theory but a metaphysical belief. Too much is undefined, and there isn’t any math for any of it.

        Energy is never “thinned” out in the sense I think you know I mean (especially in light of any number of previous conversations). In physics, energy is conserved.

        I noticed each of your three options starts with “On a quantum measurement” but what really is a measurement under MWI? Measurements collapse the wave-function, which MWI explicitly denies.

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        1. Wyrd, my friend, based on our other conversations on this, I feel like if I address your points, things are just going to get progressively more heated. I acknowledge you think this theory has zero merit and is utterly misguided. Can we just agree to disagree on this particular topic?

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  2. I must read back into quantum mechanics to be able to comment better on your interesting speculations. What I am wondering is whether it doesn’t all result from the amplitude of the wave function being available to us but the phase always being unavailable and probabilistic. When we make a measurement, the phase of the wave function gets translated into an amplitude accessible to us. A measurement is then just an interaction that is accessible to us.

    Is it then necessary for some ‘wiring up’ behind the scenes to track which particles are entangled (= have correlated phase?), or does that drop out of the universal wave function, evolving according to Schodinger’s equation.

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    1. I have to admit your first paragraph is pushing beyond my understanding. My reading about the phase is that it’s a factor in maintaining coherence, and when it gets disrupted, we lose that coherence, that is, we get decoherence and the disappearance of quantum effects. That might match up with what you’re describing, but I’m not sure.

      It took me a while to appreciate how thoroughly entanglement features in the Everettian view. As I understand it, the wavefunction collapse in Copenhagen and other collapse interpretations ends entanglement. But under Everett, there is no collapse, just the evolution of the wavefunction.
      Decoherence is the quantum system becoming entangled with the environment.

      So with a universal wave function, entanglement is pervasive. When we talk about the entanglement, under Everett, it seems like we’re talking about systems more entangled than the background levels. It’s so pervasive that Carroll, working with others on their on theory of quantum gravity, has proposed that space may be emergent from entanglement.

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          1. You may regret asking…

            Given the canonical “zero” state, |0⟩, defined as:

            \mid\!{0}\rangle=\begin{bmatrix}1\\0\end{bmatrix}

            It’s the case that:

            \begin{bmatrix}1\\0\end{bmatrix}=e^{i\theta}\begin{bmatrix}1\\0\end{bmatrix}=\begin{bmatrix}e^{i\theta}\\0\end{bmatrix}

            The |0⟩ state is indistinguishable for any global phase angle theta. The reason, as PJMartin mentioned, is that the magnitude of that exponential is always 1.0, so the state always looks like the |0⟩ state.

            But given the states |+⟩ and |-⟩, defined as:

            \mid\!{+}\rangle=\begin{bmatrix}\frac{1}{\sqrt{2}}\\\frac{1}{\sqrt{2}}\end{bmatrix},\;\;\mid\!{-}\rangle=\begin{bmatrix}\frac{1}{\sqrt{2}}\\\frac{-1}{\sqrt{2}}\end{bmatrix}

            Which differ by a relative phase, we can apply a rotation operator such that the states become |0⟩ and |1⟩, which we can distinguish.

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          2. Thanks. I think I follow the mathematics, but not sure if I follow the concept. Would it be accurate to say the global phase is the overall background phase of everything in the environment, and the relative phase is the local variance? If so, it makes sense that global phase could never be detected, since anything used to detect it would have the same phase which would just cancel out.

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          3. Both global and relative phase are properties of the quantum system and have nothing to do with the background. A physical intuition might be something like:

            Imagine a rotating ball. The vector pointing along the axis of rotation is, in some sense, rotating, but since its coordinates never change, there’s no way to detect that rotation. For the vectors not aligned with the axis, their coordinates do change under rotation, and we can detect that change.

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  3. The way I read the quote you provided from Carroll is that there is no effective difference, at the level of physics we can do, between universes in which a split happens everywhere at once and words in which it spreads at the speed of light. It makes zero difference to the physics. If you want to imagine the whole universe splits everywhere at once, have a ball. Or if you want to imagine the split having a fixed location in space and spreading at the speed of light, knock yourself out. But… if you start actually doing physics and you want to know which point on a detection screen a photon hit, and you’re ten light-years away, you’ll have to wait ten years to find out. Doesn’t matter if you think you split instantly with the photon, or you split when it arrives. Neither depiction matters because they’re indistinguishable in practice. When the radio signal reaches you with the information, then you’ll know!

    With your Louisiana Purchase example, imagine that what all those different people you described who are rambling around the Territory “know” about the purchase defines their phase correlation. And imagine that the moment of congressional ratification was actually a moment that could have gone either way. That is the quantum system we’re curious about.

    Let’s say the world “splits” everywhere instantly. So then everyone in the Territory is replicated instantly: in one world there is a version of themselves who know the purchase was ratified, and in the other world there is a version who knows the purchase was repudiated. But these two sets of people never interact because they know different things. OR… the replication of all those people doesn’t occur until the news actually reaches them, (traveling at the speed of light), since prior to this news reaching them Louisiana was owned by both the US and France simultaneously (in the quantum sense). But when news reaches them, THEN a version of them takes up residence in both worlds, since the news must be one way or the other. But at the end of the day, it doesn’t matter which version of the splitting worlds story is “right” because there’s no way for anyone in the territory to actually distinguish them…

    There’s also a bunch of people who think it was ratified and bunch of otherwise identical people who think it split. Right?

    Michael

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    1. Hi Michael,
      You parsed it well! I think I agree with everything you wrote here, with a few minor but important quibbles. (Which might come down to just word choices.)

      The first is I think the word “replicate” gives the wrong impression. It implies a copy is being made. But that’s wrong. “Split” really is the right word for what’s happening, if we want to think about one world becoming two. Think of it that every world has a certain “thickness”, a certain energy. When a split happens, the resulting worlds are thinner. (Which raises the question of how thin things can get. Carroll says it may be infinite, but if not, based on a maximum entropy calculation, he estimates it should allow at least e^10^122 slices of the observable universe.)

      Or we can think about it as two worlds that were always there with the thinner thickness. They were identical, running side by side, until the ratification vote, then they started having differences after the vote went different ways in each one.

      Where we draw the boundaries and when we change them is really up to us, because the boundaries are just accounting, something to make it easier for us to think about it. No matter which way we do it, the actual dynamics only propagate under the speed of light (or the speed of early 1800s mail in the analogy).

      So, on the second quibble, it’s important to understand that it’s not a matter of not knowing which of different ontologies is “right” but all of them being compatible with the mathematics. It’s that both versions are the same. The underlying ontology (if Everett is correct) is identical. The variance is just in how we choose to slice up the universal wave function in our accounting.

      Hope that makes sense (and I got it all right on my end).

      Liked by 1 person

      1. I have no quibbles with your quibbles, Mike. Replication was meant to suggest that when a split occurs there’s potentially two of me now–one where the purchase was ratified and one where it wasn’t. But I realized after I hit ‘Send’ that this was based only one of the three scenarios you had described. Both could have been there all along in some of the others. So no issue.

        On the issue of an ontology being “right” or not, this gets interesting to me in the following sense: I think what you’re saying is that both scenarios are fictional representations of processes that don’t exist quite as imagined to begin with, and because both are compatible with the observable processes that do exist, they are the “same.” But to one disinterested in physics, they seem like they could be different. To the non-technical part of me, for instance, it sure seems like a split that happens everywhere at once is not the same as one that propagates in time. I understand it is a difference without distinction, but maybe the pause that arises when we consider this is worth attending to…

        If the mathematics equates two scenarios which common sense tells us are not in all ways equal, then what is happening? This was prompted by thinking further about this equality of conditions that don’t seem equal–but ultimately are in terms of how they cash out. It’s not an objection… more of a curiosity.

        Michael

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        1. I understand the difficulty Michael. Remember, I did a whole post questioning Deutsche’s view and had a hard time for months thinking of it as the same theory as Everett’s. The idea that they’re discussing the same reality isn’t obvious.

          What is a fiction is the idea that worlds are definite things in Everettian theory. It’s more of a continuum in which we can interact with a narrow slice. I think about a post Chad Orzel did on the Everett interpretation, which I linked to in my post about Carroll’s book.
          https://www.forbes.com/sites/chadorzel/2019/09/17/many-worlds-but-too-much-metaphor/?sh=2adbe921625d
          At the time, I misinterpreted his post as taking an anti-real stance toward the worlds because he used the word “metaphor”. But when I recently went back to it, I realized that I (and many other people) had missed his meaning. He meant the same thing that Carroll meant. The main reality is the evolution of the wave function. What we call “worlds” or “universes” are just a convenient way for us to think about that reality, to relate it to our experiences.

          Lev Vaidman, in the SEP article on the many-worlds interpretation, describes the theory as having two components:

          The MWI consists of two parts:

          i. A mathematical theory which yields the time evolution of the quantum state of the (single) Universe.

          ii. A prescription which sets up a correspondence between the quantum state of the Universe and our experiences.

          Part (i) is essentially summarized by the Schrödinger equation or its relativistic generalization. It is a rigorous mathematical theory and is not problematic philosophically. Part (ii) involves “our experiences” which do not have a rigorous definition.

          https://plato.stanford.edu/entries/qm-manyworlds/

          It’s funny that we use the word “interpretation” to refer to theories like Copenhagen, deBroglie-Bohm, and Everett, when they have different postulates and make different predictions. They really are different theories. (I think the word “interpretation” in this case arose for historical reasons, an attempt to get these alternate theories past the old guard.) But what Vaidman calls Part(ii) is actually an interpretation of Everettian physics, and there are multiple. But unlike what we normally call “interpretations”, these really are interpretations, all with exactly the same cash out predictions.

          I should also note that there are plenty of Everettians who do take either an anti-real stance toward the worlds, or an agnostic one. Stephen Hawking was one. He was an Everettian, but also an instrumentalist. His attitude was that Part(i) was the important part and that it was predictive of our observations. He stopped there. As someone with instrumentalist sympathies, it’s a view I can understand.

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          1. Hi Mike,

            Thanks for the link; I enjoyed Chad Orzel’s article. What it reinforced for me personally is that MWI suffers from the same problem every other form of QM suffers: there is no explicit connection between the mathematical theory and our experience of the world, which is to say, something in addition to the core mathematical theory is required to derive the world we experience. And that something in addition is always a little wonky compared to the underlying mathematical structure. This is Vaidman’s point I think.

            If you posit the wave equation is describing what is real, then our collective, objective perception of a classical world is a shared hallucinatory negation of everything else, and some physical vehicles or mechanisms are required to explain how this “filtering” occurs. And it isn’t just a filtering of conscious perceptions, but something more extensive. We know this because the “me” on one branch doesn’t bump into the “me” on another branch in the hallway. So if all branches are equally real, a mechanism for physical differentiation or divisibility is required. I’m not aware of any hypothetical means by which this shared hallucinatory negation or physical divisibility of elements of reality occurs. And I’m probably missing something because physicists don’t seem to bothered by this. In this notion, the “we” that we think we are, are ghosts. We pass through everything else.

            It seems more likely to me, as an explanatory position, that the wave equation is describing a universe of possibilities that are all quite real to one another at the level they exist, and that they can interact on this level, but that only a subset of particular conditions or branches are then physically instantiated somehow through a process we have yet to even imagine. And that produces the collective, objective reality. In this notion what is “real” is only what is instantiated, and the wave equation is actually describing a realm of ghosts. The “we” that we think we are is what is “real” and everything else is a ghost.

            Not sure it matters which is correct, but how do you reconcile the basic claim of MWI and the human experience without needing to define different notions of what is “real?”

            Michael

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          2. “So if all branches are equally real, a mechanism for physical differentiation or divisibility is required. I’m not aware of any hypothetical means by which this shared hallucinatory negation or physical divisibility of elements of reality occurs.”

            Nor am I. (Normally Fermi exclusion principle prohibits matter from coinciding.) The claim is that some magical form of decoherence is responsible, but decoherence as we know it does the opposite. You don’t sink through the chair you’re sitting in because you and the chair are both decohered.

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          3. Hi Michael,
            I’m not wild about the word “hallucinatory”, but I think from your full description you don’t mean something that should be perceptible by the nervous system. It happens at a much lower level.

            I wouldn’t say that physicists aren’t bothered by the concept you’re describing. In fact, the first physicist to be bothered by it was Albert Einstein, since the basic mechanism which would allow this to work is entanglement. The physicists have just been wrestling with it for a lot longer than we have. It’s old hat to them. It’s entanglement that allows for multiple particles to be in a combined superposition. The Everett interpretation is that entanglement doesn’t end on measurement, but propagates into the environment (decoherence results from the system becoming entangled with the environment).

            Consider quantum computers. A 50 qubit circuit can be in up to 2^50 concurrent states (over a quadrillion) simultaneously. When changes ripple through the circuits, how do the qubit states in each version of the circuit “know” which version they’re in? Because they’re still in a coherent state, there is detectable (and usable) interference between the versions, but each version is still distinct. Under collapse interpretations, when the circuit is measured, it collapses to one classical state. Under Everett, the entanglement instead spreads into the environment. The success of quantum computing is actually one of the things that led me to take another look at this stuff a few years ago.

            On only a subset of the branches being real, well, that’s the rub. Collapse interpretations say only one is real, but no one can identify a mechanism to identify why any particular one should be more real than any other, except to just say it’s random. But there’s nothing in the raw quantum formalism, the part of QM that has been validated through almost a century of experiments, to indicate any outcome should be any more real than the others. Doesn’t mean some experiment might not find one tomorrow, and so falsify Everett, but that’s where we are.

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          4. “It’s entanglement that allows for multiple particles to be in a combined superposition.”

            Except that entangled particles are distinct particles with their own energy/mass, and are subject to the Fermi exclusion principle. They cannot physically coincide, which, I believe, is what Michael is getting at.

            In a Stern-Gerlach experiment, for instance, under MWI there are suddenly two silver atoms where there was only one entering the apparatus. If the claim is there were two silver atoms all along, then how did they coincide? If the branch split one atom into two atoms, how does that happen? Either way you seem to need new physics.

            re QC: In all the reading I’ve done, most texts don’t mention MWI in the context of QC. I finally did find a reference to it. Deutsch believes the power of QC comes from the myriad branches, which really raised my eyebrows.

            For one, how do other branches return the result of their computations? MWI suggests branches cannot affect each other. For another, QC is fully explained in its own mathematics. Deutsch seems to treat QC like binary computing, but it’s not, it’s a form of analog computing, hence its ability to have those myriad superposed states.

            It’s like saying we need multiple worlds to explain the different timbres of diverse musical instruments playing the same note. The notes sound different because they are different superpositions of harmonics. The notes, and QC, are analog and fully capable of having myriad wave forms combined.

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          5. Do you mean the Pauli exclusion principle? As I understand it, that states that no two fermions can be in the same quantum state at the same time. Since the various states of a particle in superposition are, by definition, different states, I don’t think there’s an issue here. I’ve said it before, but when we think we’ve found a cheap way to dismiss Everett, we’re almost certainly missing basic stuff.

            On QC, most books on it don’t go into quantum interpretations because they’re controversial and it’s not needed to explain the techniques. But many of the theoreticians, like Deutsch or John Preskill, thought through it within the Everettian paradigm. That, in and of itself, doesn’t make that the only paradigm it can work in, just the one it does most straightforwardly. In any case, I can’t imagine anything Deutsch might say about the Everett interpretation that you wouldn’t have a strong reaction against. 🙂

            I’ll repeat what I said above, over a quadrillion concurrent states, each one able to do its own calculations. At 300 qubits, there will be more states than there are particles in the observable universe. When we get into the thousands and higher, the alternative explanations to quantum states are going to get increasingly strained.

            As to how the branches return their results, remember that Deutsch is looking at this from Option 2 in the post. The main thing is these branches aren’t yet decohered from each other. They still have coherent interference. Under option 2, that interference is between worlds / universes. I think you know the interference is utilized and manipulated to promote the correct answer so that it has a high probability of being in the measured version.

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          6. Oops, yes, Pauli, not Fermi. I jumped from fermion to Fermi there!

            This is why I mentioned silver atoms (which are made of fermions). In particular, the electrons already occupy all available quantum states, except for the lone valence electron in the 5s shell. It’s that electron that allows a silver atom to have an over all spin. The other 46 electrons pair off in spin-up+spin-down pairs.

            And those 46 electrons are fully described within the silver atom, there are no extra quantum states they can have to differentiate from supposedly superposed “identical” electrons.

            Think of it this way: When Sean Carroll gives a lecture about MWI and uses his beam-splitter and then jumps one way or the other depending on the result, the implication is he, the podium, the stage, the audience, and the auditorium, all branch into closely identical versions that physically coincide.

            What magical quantum state allows all those fermions to do that in violation of Pauli?

            The usual explanation is “decoherence” but that’s magical, too, at least in terms of how we currently understand decoherence.

            “On QC, most books on it don’t go into quantum interpretations because they’re controversial and it’s not needed to explain the techniques.”

            Or the outcomes. Exactly. It’s not the controversy. It’s that there’s no need for it.

            “I’ll repeat what I said above, over a quadrillion concurrent states, each one able to do its own calculations.”

            It’s just one calculation — one set of operations performed on the qubits.

            The thing about interference, which yes, is where the QC power comes from, is that, as in the two-slit experiment, which we previously agreed didn’t seem to invoke MWI except in where the particle actually gets measured (as in a beam-splitter experiment), interference is a single-world phenomenon that, while we don’t fully understand it, doesn’t seem to require, or even suggest, multiple worlds.

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          7. Mike,

            Wyrd seems to understand pretty well the question I was trying to ask. I wasn’t sure from your answer you fully understood what I was driving at, or if you did, your own reading may have given you a perspective on this I don’t grasp, which results in our talking past one another just a bit.

            Imagine I am in a room observing a double-slit experiment. And there are various possibilities for the outcome I might observe. If I understand MWI, they all occur. And in popular writing about this, it seems to imply there is a “me” who sees one outcome, as well as a “me” in another branch that sees another. Let’s say I’m sitting behind a desk where a computer is telling me what the detector in “my” branch of the wave function registered. Presumably, in another branch, a completely independent instantiation of “me”, seated at the same desk (albeit an independent instantiation of the desk), registers a different result for where the photon landed. Now, the entanglement that allows the double slit experiment to create the interference pattern presumably is a physical process occurring within this room. So there are all these instantiations of me seated at this desk, by they do not “bump” into one another or know of one another or interact in any way. So it’s a lot like the Exclusion Principle problem, only we’re talking about entire portfolios of nearly identical physical systems that would seem to exist in the same physical space but don’t interact.

            When I asked if this issue concerned physicists, I wasn’t speaking about entanglement itself, which I know Einstein objected to–I’m wondering what it is I’m missing about all these nearly identical physical systems along separate branches that would intuitively be in the same room. If they are all in parallel “worlds” then where are those worlds? This seems like a straightforward question to ask if the premises are right: the key premise being that in branches with different outcomes than the one I know about, there is a version of “me” there also who witnesses the other outcomes. Where do these versions of “me” reside that all witness different outcomes of the same physical experiment, but never physically interact?

            Because it seems an obvious question, and because many people smarter than me don’t seem worried about it, I am wondering if I’m misunderstanding something essential about the MWI to begin with.

            Michael

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          8. Michael: You’re right on point with the coincidence issue.

            I think the understanding required is this: MWI places the Schrödinger equation as central to its ontology, and proponents have faith the coincidence issue, the energy issue, the probability issue, the preferred basis issue, and the Hilbert space ontology issue, all have reasonable explanations we’ll someday understand based on the central notion that the Schrödinger equation explains everything.

            Those on the Copenhagen side of things have faith that wave-function “collapse” has a reasonable explanation we’ll someday understand based on, or extending, QM principles. (As I tried to illustrate with the spin experiments, even MWI experiences sudden changes to the wave-function in experiments, so it actually does include a form of “collapse” — that wave-function vector suddenly jumps to a known eigenstate.)

            The irony to me is that MWI is often claimed as the more parsimonious view based on the simplicity of the premise. I think the consequences of a premise need to be considered as well, and as total views there is far more physics unexplained under MWI and it is therefore the less parsimonious view overall.

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          9. Michael and Wyrd,
            On the exclusion principle, I don’t have a researched answer. However, I’ll note again that the Everett interpretation is not going to be dismissed on the cheap. If it was incompatible with something as fundamental as the Pauli Exclusion Principle, Hugh Everett wouldn’t have gotten it past John Wheeler, or his thesis committee, or the peer review for publication, not to mention all the people who’ve attacked the theory over the decades. So my answer here might not be right, but if it isn’t, it just means we’re overlooking something a first year physics graduate student probably knows.

            I think the answer is that the exclusion principle is based on interactions, on bosons being exchanged by fermions. However, in a group of entangled particles, such as all the elementary particles in an atom or molecule in superposition, those types of interactions can only happen between versions of the particles in the same element of the composite superposition. In other words, an electron in one version of an atom in superposition isn’t going to exchange photons with the same electron in another version of that atom. Remember that the photons are part of the entanglement too, so there will be versions for each element of the overall entangled superposition. (I wish I knew less awkward language to express this.)

            I’ll admit I’m not sure how interference factors into this, except to say it’s only a factor until decoherence. Wyrd laid the entire explanation on decoherence, but I’m not sure that’s true. I think there is already a separation before then. It’s just that interference is gone (or well, no longer significant) after decoherence.

            Anyway, that’s my amateur (possibly very wrong) shot at the answer. It’s the way I’ve assumed it worked for a while. I might do some digging around to find out how the exclusion principle and superpositions relate to each other. I think it’s where the answer lies.

            Liked by 1 person

          10. Mike,

            It is precisely because I agree MWI won’t be dismissed on the cheap that I’m wondering what I’m missing.

            I think the focus/discussion above on the Pauli Exclusion Principle has perhaps led you away from the bigger picture, even simpler question I was asking. I think to your point, it’s easy enough to deal with the Exclusion Principle. Might we note for instance that the Pauli Exclusion Principle holds in any given branch or world, and that when we deal with entanglement all the “versions” of an electron, say, in MWI, have something unique about them (a different spin or position or momentum), which is why they’re in another branch to begin with.

            I’m less concerned about such a specific and technical nuance of the theory, and more curious about where the physicists think all the various branches of the wave function reside such that they are all equally “real” but utterly hidden from one another on the large.

            Michael

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          11. Michael,
            I think the principle remains the same on broader considerations. Our ability to detect something depends on interactions. For example, we only see something by having photons from it strike our retina. When we touch something, it’s electromagnetic interactions that stop our hand from going through it, etc. This is one of the reasons dark matter is supposed to be so hard to detect, because it only seems to interact gravitationally. We could think of the other “worlds” as dark matter without the gravitational interactions. (Although each world obviously interacts with itself.)

            We can only interact with the slice of the wave function we’re on, essentially with the stuff in the same element of the superposition of the entangled environment we’re a part of. The other worlds are all right here, but we can’t interact with them, and they can’t interact with us. (At least aside from interference that is so fragmentary and canceled out that detecting it would require knowledge of all the relevant microstates.)

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          12. “The other worlds are all right here, but we can’t interact with them, and they can’t interact with us.”

            Nothing in physics explains how that can be true of normal matter. It’s an unfounded assertion.

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          13. I think that shoe is actually on the other foot. It’s my logic you have consistently denied in all these conversations. MWI doesn’t really have logic so much as assertions based on the notion that the Schrödinger equation must be the whole and entire truth.

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          14. I’m recalling now we had this discussion once before, Mike. I understand the notion that dark matter doesn’t interact with us except gravitationally so it’s in essence right here all the time though we never sense it. But I think what you’re suggesting here is that not only is red different from blue in the branch of reality in which we’re having this conversation, but that in 10^(10^120 something) co-located branches of reality, there is a red that is different from every other red in some way that doesn’t reduce it’s redness. I can imagine ways of describing this, but I think it requires additional properties of matter, and a HUGE range of them. I guess the question is: are these properties part of the wave equation? I think this is part of the extra stuff that is needed to relate the theory to our experiments. All the versions of QM have a problem with that specific issue I think.

            When you say we only interact with the stuff in the same element of the superposition of the entangled environment we’re a part of, I don’t really know how to parse that. I think of the double slit experiment again, and understand at some conceptual level that the entanglement between possible outcomes of the experiment is replaced by new entangled relationships that spread through the environment. But where this gets confusing is that if I’m listening to channel 96.5 on the FM band, everything on this station must be somehow related in a way that everything else is not. When we do a double slit experiment, the entanglement passes from all possible electron states to a specific electron and the detector, and then it bangs around the detector as a whole as atoms interact or what have you. Point being: the baton of entanglement is passed through specific interactions is it not? Two particles collide and now we don’t know which one has more of the energy. Entanglement doesn’t just get broadcast to every atom in our light cone once the electron hits the detector right?

            So if I’m correct that entanglement disperses through chains of interaction, then at some level it seems like we’re saying every element of matter/energy touched by this chain has to obtain or activate some underlying property that unifies them on the one hand, and differentiates them from all the other chains going on out there, right? I just don’t see how such a world practically works, or even is contained in the wave equation if there are no variable properties that are shared to unify all the matter and energy contained in a particular branch.

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          15. Michael,
            From what I’ve read, entanglement is a complex topic. It can exist on various properties (like spin) while not on others. And there can be different degrees of it. One of the sources that helped me think about it was this post.
            https://www.askamathematician.com/2018/10/q-what-is-the-monogamy-of-entanglement/
            But at a fundamental level, I generally take entanglement to be correlation, which makes sense when you think about how correlations form and that they can exist to greater or lesser degrees.

            Of course, under collapse interpretations, it must be something stronger than that. And even under Everett, it feels like that isn’t sufficient. This feels particularly true when we’re talking about a quantum circuit in a superposition of quadrillions of composite states, much less of a whole environment that, under Everett, is also in a superposition of some unfathomable number of composite states. The feeling that there must be something else, some hidden variables to keep everything straight, is very strong. But there’s a good chance our intuitions here are simply not reliable.

            My understanding is that entanglement, under normal conditions, is constantly being “broadcast”. Remember that this is often described as information about the quantum system leaking into the environment. But what we’re really saying is that the system in question is having causal effects on the environment, while the environment is also having causal effects on it. A lot of the effort involved in keeping quantum circuits coherent involves inhibiting those causal interactions with the environment as much as possible until the desired result is ready. When it is ready, it is then allowed to causally cascade into the environment (i.e. be measured).

            What this means is that, under Everett, there’s a background level of entanglement, which we don’t notice because it’s everywhere. When we discuss whether or not particles are entangled, we’re really discussing whether they’re more entangled then that background level. All of this makes sense when you remember that we’re talking about a universal wavefunction.

            But as I mentioned somewhere else on this thread, entanglement is so pervasive that there are physicists now thinking that space could be emergent from it. Conversely, in the context of multiple worlds, it might be that entanglement’s broad ranging correlations are depending on space itself branching. That’s something we haven’t discussed here. Everett requires gravity to eventually be brought into the quantum fold. Which might help with keeping all those reds from each other. Although when we remember that red only comes about through interactions, I’m not sure it’s strictly necessary.

            This reply feels somewhat rambling. Hopefully somewhere in it your concerns were addressed.

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          16. Thanks for additional info. This is a very interesting topic…

            Focusing on your paragraph that begins, “What this means is that, under Everett, there’s a background level of entanglement…,” there are definitely questions that arise. I’ve read a few books on entanglement–Amir Aczel’s and Louisa Gilder’s–but it’s been a while. I don’t recall either of them spending much of any time on widespread universal entanglement networks, as they were focused moreso on the “more entangled” situations of experiments. In the experiments and in quantum computing, the entanglement is very fragile and has to be kept isolated, but I think what you’re saying is that in the most general case, entanglement is a pervasive condition of things. I want to say something like, “I can see that…,” but the truth is I’m pretty fuzzy on what that really means. Doesn’t mean I’m opposed to it. It’s just that the properties of such a reality would have to be explained a bit to me I think so I could understand it better.

            What I understand entanglement to mean is this: two or more particles are said to be entangled when a) they are in a superposition and haven’t interacted with the environment or otherwise been “measured” and b) when conservation of spin or momentum or something requires that their states, whenever they are actually determined, are mathematically related such that if I know the state of one I also know the state of the other. Perhaps as I ramble here in return, an important element of what you’re describing is noting that in an Everettian universe, the wave function never collapses, so the entanglement never really dissolves. Particles are never released from their obligations to one another, although they can trade those obligations with one another. Say particle A and B are entangled. Particle B could have a drink with Particle C, and they could agree to share somehow in the fulfillment of the obligation Particle B originally had with Particle A. This could go on and on and on. It’s kind of like those financial securities that got us in so much trouble in 2008. Pretty soon everyone has an obligation to everyone else and no one knows who owes who.

            But, it seems to me that all these trading of mutual obligations are actually moments when the wave function branches–since it doesn’t collapse, it must branch–and the question in my mind remains: how does one speak meaningfully about the “classical” world we experience in this case?

            So what keeps coming up for me, Mike, is this. There’s an intriguing “truth” I’ve encountered in a number of contexts: everything and nothing are indistinguishable. There is nothing interesting about either one. They are the alpha and the omega. Things only get interesting when one thing happens and other things do not, so I cannot help but think this notion of an ever-evolving wave function in which everything happens is only one part of what’s really happening, and that there are very likely selection processes at work. It’s just a suspicion.

            Otherwise, this notion of extended entanglement networks, which is a lot like an economy as Orzel noted, doesn’t quite explain how you could have trillions of such economies that are mutually exclusive. But it makes for interesting thought experiments and I’m inclined to run a few before saying anything more. Haha.

            Michael

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          17. Thanks Michael. I hadn’t heard of those books. Interesting. I picked up a couple myself late last year, but was disappointed in them. They were fairly shallow pop-science books, and only lightly touched on Everett.

            One source that gave me a little insight about the relationship between entanglement and Everett was briefly discussed by Matt O’Dowd in this video. (Hopefully I got the timestamp right. He takes the option 1 approach from the post.)

            Sean Carroll occasionally veers into this on his podcast, particularly on the solo eps, although most of it is him interviewing others about their ideas.

            Thinking through scenarios is the way to approach this. Every time I think I’ve found a fatal flaw, it turns out to have a solution. As long as the raw quantum formalism continues to be validated in experiments, it’s hard to dismiss. Of course, that could change at any time with new evidence.

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          18. I skipped ahead to the eight minute mark that Wyrd pointed out. It was interesting and it was consistent with what I’ve heard on this topic before I think. Statements like this, at the 10:20 mark, are the ones I think require additional assumptions on top of the wave equation, “The evolution of the wave function is deterministic. That means all future branching of the wave function of your present, by which I mean the entanglement network that you currently belong to, is pre-defined. What isn’t defined is your own experience of that future branching. You will be the thread of conscious experience that travels one of those branches. You’ll also travel the others, but each version of you will only feel like you travel one of them. (emphasis added)” This gets quickly into the relationship of the wave function to conscious experience that I said earlier is tricky.

            More scenarios to ponder… 🙂

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          19. FWIW, the first paragraph of the “Meaning of entanglement” section of the Wiki article for quantum entanglement does a fair job of describing it:

            An entangled system is defined to be one whose quantum state cannot be factored as a product of states of its local constituents; that is to say, they are not individual particles but are an inseparable whole. In entanglement, one constituent cannot be fully described without considering the other(s). The state of a composite system is always expressible as a sum, or superposition, of products of states of local constituents; it is entangled if this sum cannot be written as a single product term.

            (In general, Wiki is a pretty good resource for QM. It’s one of the first places I check when I have a question about some aspect of it.)

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          20. As I said, this isn’t a researched answer. It’s possible bosons aren’t involved, but the relation with superposition still applies.

            Or not. I think whatever it is, it’s standard physics that we’re simply missing.

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          21. Okay, good, I would have been surprised. I’m pretty sure Fermi-Dirac statistics (which may be why I confused the names) are due entirely to fermions having 1/2 integer spin. It’s a fundamental part of how such particles behave, and it comes from their mathematics.

            The thing about all these interpretations of QM is that there’s a metaphysics aspect to them, and metaphysical positions are easy to believe in a hard to refute. Ask why billions believe in some form of God. The only available tool is logic, and its value depends on people accepting the premises involved.

            I have long suspected the commitment to MWI comes, in part, from seeing its viability on the quantum scale and, from the premise “everything is quantum,” assuming it scales up to the classical world. As such, I’ve also long suspected the key to refuting MWI lies in figuring out the Heisenberg cut.

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          22. It seems like fermions have to interact with each other in some manner, otherwise how does one “know” where to avoid?

            If a Heisenberg cut were ever found, it would falsify Everett. As would evidence for an objective collapse. I also understand Everett needs gravity to be quantized.

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          23. Ha, yeah, we all need gravity to be quantized!

            To answer your question (as best I can), the mathematics of 1/2 integer spin only allow for a fixed set of quantum states. Recall that particles act like waves, and it’s in the interaction of those matter waves that the particles “know” what they can, or cannot, do. The matter waves for fermions act differently than the matter waves for bosons. (In fact, because of the dynamics of the wave behavior, bosons like to clump together. I think that pop sci series you’ve mentioned got into that in one of the essays.)

            Tunneling, for instance, is because when a particle is near a barrier its wave-function extends beyond the barrier and, because the wave-function determines the probability of finding the particle in a given position, there is therefore some probability the particle is on the other side of the barrier. With particles, the wave description always obtains until the particle is somehow observed.

            (FWIW, my abiding belief is that the Heisenberg cut will be figured out. We’re currently vexed because it all takes place down on the Planck level which we can’t see.)

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          24. Thus sayeth Schrödinger: “He who hath an ear let him hear. My equation was from the beginning, it is the premise upon which all understanding of the natural world rests. The great Schrödinger speaks; my equation is a probabilities mathematical synthesis, an Immortal Law derived from a quantum wave that has never been demonstrated to exist. He who hath an ear, let him hear…”

            As mother calls; “Children, it’s time to quit playing in the sandbox of discourse; it’s nappy time…”

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          25. This snippet from last week’s Ars Technica article on quantum physics is worth noting:

            Quantum mechanics is not only written in math, but there are three completely different versions of the math in widespread use: the Schrödinger wave approach, the Dirac formulation, and Feynman’s path integrals. The Schrödinger approach emphasizes the waviness of particles and uses differential equations. The Dirac formulation focuses on quantum mechanics’ sensitivity to measurement order and uses the language of linear algebra.

            Feynman’s path integrals also have a wavy point of view and can be seen as an extension of the Huygens–Fresnel principle of wave propagation. This leads to some truly terrifying path integrals, covering all possible paths and possibilities. Feynman diagrams are a shorthand for keeping track of the approximations you need to make to actually solve things. While the mental models behind the three mathematical traditions are quite distinct, they always give the same answers.

            So why are there three equivalent versions of quantum mechanics? Depending on the problem you are worrying about, it turns out that it can be easier to get the answer using one of the three approaches. And physicists are all about using the path of least resistance.

            https://arstechnica.com/science/2021/02/a-curious-observers-guide-to-quantum-mechanics-pt-6-two-quantum-spooks/

            So it’s not really about the Schrodinger equation in and of itself, but about what it models. But yes, the Everett view is that we live in a quantum universe. If right, it’s far from the first time science would be shifting our view of reality out from under our feet.

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  4. Hmm. I think that what Sean Carroll is hinting at when he playfully says, “So the nice answer is, it’s up to you,” is that the universe isn’t really splitting in the way MWI is popularly presented. If I understand the first thing about MWI, it’s that the “world” doesn’t “split” when a “quantum measurement” occurs, but is constantly accessing multiple states.

    To put it in mathematical terms, there is no measurement in the Schrodinger equation. It simply describes a time-dependent system whose solution is a superposition of eigenstates.

    And your assertion that “And each split effectively divides up the energy of the world among the new worlds, which many find difficult to accept,” is something we’ve discussed before and I thought you’d moved on from that misconception. The energy is not divided up between worlds. There aren’t different universes.

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    1. The main thing to understand about the Everett interpretation is that the core theory is simply the evolution of the universal wave function, the raw quantum formalism applied to the whole universe, a deterministic theory with local dynamics. Everything else is us interpreting the interpretation. So yes, Carroll is making clear that that’s the core theory, the main reality.

      I don’t think it’s accurate to say there’s no measurement in Everett, it just doesn’t have the ontological role it does in Copenhagen. Any magnification of an individual quantum outcome to macroscopic scale is a measurement like event. So when a cosmic ray knocks an atom loose in DNA resulting in a mutation, that is a measurement type event, even though there’s no conscious observer.

      When I talk about splits and dividing up the energy, that is about the interpretation of the interpretation. You can interpret it in different ways. Whether there are different universes, or portions of the same universe which don’t have access to each other, is just semantics. It’s like when other galaxies were discovered in the 1920s, they were often referred to as “island universes”, before the term “universe” got reserved for all of space.

      So if it makes you feel better to think of it all as one universe, that’s fine. It was the approach that Everett himself seemed to prefer. I use the term “world”, in the sense that there are many classical worlds in the universe. Others prefer to go with explicit multiverse language. Or you can think of it as the one universe in a superposition of many and an ever growing number of quantum states. It’s all compatible ways of thinking about the core theory.

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      1. The problem is that measurement necessarily alters — “collapses” — the wave-function, so figuring out what “measurement” actually means under MWI is one of the many undefined things about it.

        Which is why I pointed to your three options that all start with: “On a quantum measurement…”

        Under MWI, what does it mean to “measure” something?

        If Alex does a spin experiment and branches into Alex-Up and Alex-Down, both versions have a different wave-function than prior to the experiment.

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        1. There is a phenomenological collapse. That’s true in every interpretation. But if you want to say there’s an ontological collapse, then that’s not accepting the most fundamental thing about Everett, and I wouldn’t expect the theory to make much sense from there.

          From what I’ve read, the best way to think of a measurement under Everett is the magnifying of the effects of a quantum event. As I mentioned to Steve, there are natural measurement events.

          Certainly the wavefunction evolves and changes, and measurement has effects (such as decoherence). In the Alex scenario, each branch of Alex is dealing with a different element of the superposition of the spin of the particle in question.

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          1. “In the Alex scenario, each branch of Alex is dealing with a different element of the superposition of the spin of the particle in question.”

            The problem is that the experiment “picks out” a specific part of that superposition, the up and down on the selected axis, and now they each have a wave-function in a suddenly altered state. They can demonstrate this by repeating the same measurement and with 100% probability getting the same result they got the first time.

            Their respective shares of the wave-function have superpositions of possible measurements on other axes. If they first measured Z-axis, both would expect “random” results on the X-axis, because the Z-axis measurement eliminates any knowledge of the state of the X-axis. Doing such a test would cause further branching, whereas repeating the Z-axis test would not.

            Say they measure the Z-axis, branch into Alex-Z.up and Alex-Z.down, and both now measure the X-axis. Now there is: Alex-… Z.up-X.up, Z.up-X.down, Z.down-X.up, and Z.down-X.down. For each of the four branches, Alex now has knowledge of X-axis spin and has eliminated knowledge of the Z-axis spin.

            Considering just one Alex, say the one who got Z.up-X.up, what do you think they would get if they measured the Z-axis again?

            Note that these experiments are set up so only the final result is actually measured. The various branches of Alex only ever see the final result (e.g. Z.up-X.down-Z.up), although they know the path the particle took through the system and, hence, the outcome of each step along the way. (Note also that the tests I’m describing are physically possible and have been done and verified.)

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          2. One of the physicists I read, possibly the Ask a Physicist guy, said that a definite spin result on a particular axis just is a superposition of the other perpendicular axes. (I know it’s more complicated for the diagonal ones.) So I think the sequence would happen as you describe. Every time the superposition gets measured there is branching.

            Note that we could actually think of it as every time the same axis gets remeasured with no other axes measured in between, there’s also branching, but the branches are all the same, so it’s not usually thought of as branching.

            On running the experiment so the results aren’t measured until the end, are you saying they could know the intermediate spin results? I think I’d want more details on how that works. Speculating a bit (and possibly getting it very wrong), I suppose you could keep all the particles involved (electrons, photons, etc) isolated so that the changes to spin happen. But all the particles that interact would end up entangled with each other, and when information from the system did finally spread into the environment, it would all become entangled with the environment, with every element in the composite superposition of the entangled particles having its own branch.

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          3. Yes, we treat a Z-axis measurement as an equal superposition of up-down on other orthogonal axes because knowledge of spin on orthogonal axes is mutually exclusive (very similar to position and momentum being mutually exclusive).

            “On running the experiment so the results aren’t measured until the end, are you saying they could know the intermediate spin results? I think I’d want more details on how that works.”

            Spin of particles can be measured by a Stern-Gerlach experiment. Essentially a magnetic field cases a deflection of the particle such that there is one path into the “spin box” and two paths out, one representing spin-up and one representing spin-down.

            Under MWI we’d say that the particle interacting with the magnetic field causes a superposition (branch) and the particle follows both exit paths. When the particle hits a detection screen, it’s “measured” and we only see it in one place. (Not unlike a beam-splitter experiment.) Detection, of course, prevents further tests of the particle’s spin because it’s been splatted against the screen.

            But we can direct the output paths into a second stage pair of “spin boxes”. For instance, we could measure the Z-axis in both stages. If we do, we find the spin-up path from the first stage results in 100% spin-up particles and the spin-down path results in 100% spin-down.

            Or we can measure a different axis the second time. If we measure the X-axis, we see a 50/50 split from both second stages. In the first case, Z-Z, we see a [50%, 0; 0, 50%] distribution. [Z-up+Z-up, Z-up+Z-dn; Z-dn+Z-up, Z-dn+Z-dn] In the second, Z-X, the distribution we see is [25%, 25%; 25%, 25%]

            The final result tells us what path the particle had to take, so we know what its spin was at different stages of the experiment. Note that, until the detection screen at the end, the particle does not interact with other particles, only the magnetic field of the S-G device.

            So let me ask my question about the results of a Z-X-Z experiment again. The particle distribution after two stages is, as mentioned, [25%, 25%; 25%, 25%]. After the third stage, a second Z-axis test, there would be eight outcomes (branches). My question is: What is the final distribution?

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          4. BTW, with regard to a known eigenstate such as Z-up being a superposition, note that such a superposition is different if the known eigenstate is Z-down.

            For Z-up:

            \frac{1}{\sqrt{2}}(\mid\!{0}\rangle+\!\mid\!{1}\rangle)

            But for Z-down it’s:

            \frac{1}{\sqrt{2}}(\mid\!{0}\rangle-\!\mid\!{1}\rangle)

            Note the plus-minus difference between them. Both superpositions give a 50/50 probability for X-axis measurements. The difference means there are certain unitary operations that can change the state, and further such operations can return it to the original state. (Measuring the spin state would not be such an operation.)

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          5. I should maybe emphasize that, after measurement, the definite eigenstate itself is considered to be just |0⟩ for spin up and |1⟩ for spin-down.

            The superposition applies to the possibility of a measurement on some other axis. There are, in fact, infinite superpositions of measurements on other possible axes. In general:

            \alpha\mid\!{0}\rangle+\beta\mid\!{1}\rangle

            Where α and β are normalized coefficients that depend on the angle of the axis, and there is an implicit such superposition for every possible angle.

            The superpositions I showed you above involve an orthogonal axis where both coefficients are 1/sqrt(2). (Remember that we square the coefficient to get the probability of seeing that result, and that the sum of the squared coefficients must be 1.0.)

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          6. On the experiment, thanks. I had forgotten about that setup in the MIT lecture.

            On your question, not sure what you’re looking for. I agree there would be eight outcomes and so eight branches.

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          7. That there are eight outcomes is a given. My question involves the distribution of outcomes. In the two-stage versions, in the Z-Z version, the distribution is [50%, 0%; 0%; 50%]. In the Z-X version, it’s [25%, 25%; 25%, 25%].

            I’m asking about the three-stage version comprised of Z-X-Z. [?, ?; ?, ?;; ?, ?; ?, ?]

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          8. Nope, exactly right.

            The point is that, after the first Z measurement the particle is in a known state, either |0⟩ or |1⟩, but in a superposition of measurements on other axes. In particular, the orthogonal X-axis is a 50/50 superposition so the second test on the X-axis has a “random” (uncorrelated) result.

            That second test gives us a definite state for the X-axis, often thought of as |+⟩ and |-⟩ in contrast to the Z-axis. This again puts the particle’s wave-function into a superposition of states for other axes, and again the orthogonal Z-axis is uncorrelated so there is again a 50/50 chance of measuring |0⟩ or |1⟩.

            For a single particle going through the apparatus, its wave-function changes as a result of each test. Importantly, the first state, either |0⟩ or |1⟩, is erased during the second test, which is why the third test has 50/50 odds.

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    2. I like this 4th option, “there aren’t different universes.” But to me it’s just one option; each option is useful for understanding certain aspects and each poses a danger of misleading when taken overly literally. This 4th option is good for correcting some of those dangers of the other three.

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  5. And when the final curtain falls, materialists sit around scratching their asses wondering why idealists think that materialism is such a screwed up metaphysical position!!??!!☹️ Party on Sean Carrol…..

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      1. Same difference right Mike? MWI is materialism’s archetype of idealism’s M@L.

        Sean Carrol professes to be physicist; one would think that Sean would use his high profile celebrity status as an academic in the profession of adult day care for more productive means other than promoting himself so he can write and market more ridiculous books.

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          1. M@L is Mind at Large; an imbecile god who has Dissociative Identity Disorder (DID) and splits off into multiple personalities…. Sound familiar? M@L, MWI……. pick your ridiculous construct, only you can choose.

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          2. Sounds like Kastrup’s theory. We’re all one big mind with multiple personalities. Kastrup is pretty vehement in his opposition to the Everett interpretation. I can understand why, since it undercuts the quantum physics justifications for his philosophy.

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  6. Is this a case of perspective? Outside looking in vs being inside, living it?
    And then the thought (and it’s only a thought) of instantinaity? Some human transaction or statement that theoretically impacts the subject instantly. “I’m king of the world!” would travel at the speed of thought, instantly. And it’s due to perspective how such a declaration is evaluated.
    It all sounds like fun mind-games to me. (Until you unscroll the deed to The People’s land and tell them to leave, ‘cuz you now own it.)

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    1. It definitely is a case of perspective. You also just reminded me about this from one of Terry Pratchett’s stories:

      The only thing known to go faster than ordinary light is monarchy, according to the philosopher Ly Tin Wheedle. He reasoned like this: you can’t have more than one king, and tradition demands that there is no gap between kings, so when a king dies the succession must therefore pass to the heir instantaneously. Presumably, he said, there must be some elementary particles — kingons, or possibly queons — that do this job, but of course succession sometimes fails if, in mid-flight, they strike an anti-particle, or republicon. His ambitious plans to use his discovery to send messages, involving the careful torturing of a small king in order to modulate the signal, were never fully expanded because, at that point, the bar closed.

      https://www.goodreads.com/quotes/66881-the-only-thing-known-to-go-faster-than-ordinary-light

      Liked by 2 people

          1. Now that you mention it, I do believe I’ve used it fairly recently. It’s one of the many, many bits I love about Pratchett — his twisted use of physics of which he seems to have a very good grasp.

            Liked by 1 person

  7. FWIW: I was looking for a good explanation of global versus relative phase, and I found the following, which nails it. It’s inescapably mathematical, but you said you were doing okay with the math.

    We can define a two-state quantum system like this:

    \mid\!\Psi\rangle={r_1}e^{i\theta_1}\!\mid\!{0}\rangle+{r_2}e^{i\theta_2}\!\mid\!{1}\rangle

    Where r_i are normalized real-valued constants and θ_i is the phase.

    Then we can have:

    \mid\!\Psi\rangle=e^{i\theta_1}({r_1}\!\mid\!{0}\rangle+{r_2}e^{i(\theta_2-\theta_1)}\!\mid\!{1}\rangle)

    Doing the math:

    \mid\!\Psi\rangle=e^{i\theta_1}\begin{bmatrix}{r_1}\\{0}\end{bmatrix}+\begin{bmatrix}{0}\\{r_2}e^{i(\theta_2-\theta_1)}\end{bmatrix}

    And then:

    \mid\!\Psi\rangle=e^{i\theta_1}\begin{bmatrix}{r_1}\\{r_2}e^{i(\theta_2-\theta_1)}\end{bmatrix}

    As I showed you before, that leading term (the global phase) isn’t something we can detect, but the relative phase, θ_2-θ_1, is significant and accounts for interference.

    Mathematically it doesn’t get more clear than that. Intuitionally is another matter… 🙂

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  8. Much of the distinction seems irrelevant. Anything changing in our galaxy, for example, is irrelevant to things happening in other galaxies. So, whether the result of the change spreads instantaneously or at the speed of light matters little. The amount of change or repercussion of a change fades with an inverse square law, no? So, this “transmission” of the world split is a local affair.

    Basically what would happen if the effect of a split here on Earth weren’t noticed in a galaxy 100,000 light years away for 100,000 years? I argue, nada.

    Liked by 1 person

    1. It’s definitely true that under all the options, the dynamics are always local. An analogy might be if we decided to change the name of the Andromeda Galaxy to Ralph’s Galaxy. In our mind, the change would be instantaneous. But if we sent a signal to that galaxy telling any inhabitants what we’d decided, it wouldn’t have any causal effects for at least 2.5 million years.

      So the various options could be seen as how we decide to account for the name change. Whatever we decide, it’s irrelevant to the physics.

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  9. I don’t know why I’ve never thought about this, but I just realized there’s a conundrum in MWI regarding “particles” — observing a particle requires collapsing the aspect of the wave-function that describes the position of the “particle.”

    In the two-slit experiment, for instance, the (unobserved) particle in flight is described by its momentum (its energy) which means its position is unknown. Until it hits something, and then its position is known. Even if we assume branching, each branch sees a “particle.”

    But that “collapses” the wave-function, so how can there ever be point-like interactions (“particles”) unless MWI does have wave-function collapse? Even positing a universal wave-function comprised only of interactions still seems to require abrupt changes to the state vector.

    Liked by 1 person

    1. So tell me if this is crazy or not, but is this another way of expressing what I see as a fundamental question of QM in all its forms, and that is: how does the wave equation–which regardless of interpretation clearly has some part of the picture pretty well-nailed–relate to the reality we experience? And none of the QM theories can explain this without some assumptions that are in addition to the fundamental mathematical theory, unless I’m mistaken.

      Thinking about Newton’s equations of motion is (perhaps?) helpful as a view of a theory where this is not an issue. When we define “x” as the distance of a flying cannonball from the cannon, there are really no additional steps required to relate the math to the world we experience. If we use the equations to show that the cannonball is “x” = 73.5 meters from the cannon when “t” (time) = 0.9 seconds of flight, we know exactly what that means. There really aren’t additional assumptions required, just our definition of “x.”

      In QM, we have the wave equation, but it doesn’t describe a single outcome like Newton’s equations of motion do. So the rub in all QM interpretations is that we only see one thing, and the math predicts many things, no? And I think your point is related: we don’t see waves, whenever we measure something what we see are discrete quanta, or particles. So there are a number of ways it seems challenging to relate the fundamental mathematics to what is actually observed.

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      1. You’re not crazy. QM is the only branch of science I know that requires interpretation, even though it has very precise and extremely well-tested mathematics. I suspect that speaks to our ignorance of it. Its complete lack of compatibility with GR is another indicator we’re missing a big part of the picture.

        Comparisons with Newton’s F=ma are quite apt, and, as you say, seem complete at the classical level. And, also as you say, classical calculations predict single future results — the cannonball will strike here with this much force.

        The wave equation says, well, if you decide to look for a free particle here, there’s this probability of seeing it there, but that much probability of seeing it there, if you look there. And because the wave equation implicitly includes all possible locations (in the universe) there is some (vanishingly small) probability of finding it a zillion miles away.

        Liked by 1 person

      2. I think it’s worse than that. We see interference effects, or what we infer to be interference effects, and from that infer waves. But we also never see a particle. Ever. We infer their existence as well though instruments we hope work according to our theories. Neils Bohr made the point that the quantum realm is inaccessible. Our data comes from the macroscopic effects of our interactions with it.

        But really, this just calls attention to something that always exists, because our senses work by inferring things in the world as well. We just feel like it’s more concrete at the classical level. There may be fewer levels of inference at classical scales, but all observation is inescapably theory laden.

        Liked by 1 person

        1. “But we also never see a particle.”

          They’re too small to be seen by any instrument, but devices such as cathode ray tubes give us the same inference about, at least, point-like interactions, that interference gives us about waves.

          Einstein’s Nobel was another strong inference about the existence of particle-like behavior.

          Liked by 1 person

          1. Schrodinger was inspired by de Broglie’s discovery. He intended his equation to model how the waves worked. But from what I’ve read, he couldn’t complete it until spin was discovered. (The Copenhagen camp played down the physicality of the waves. Schrodinger never agreed with that move. Obviously the Everettians agreed with him.)

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