# An instrumentalist Everettian

Scott Aaronson posted an interesting piece this week coming out about his favorite interpretation of quantum mechanics. I think the most relevant part is this snippet. (Although the full piece has a lot of nuance well worth reading.)

I don’t mean to say that the interpretations are all interchangeable, or equally good or bad. If you had to, you could call even me a “Many-Worlder,” but only in the following limited sense: that in fifteen years of teaching quantum information, my experience has consistently been that for most students, Everett’s crutch is the best currently on the market. At any rate, it’s the one that’s the most like a straightforward picture of the equations, and the least like a wobbly tower of words that might collapse if you utter the wrong ones.  Unlike Bohr, Everett will never make you feel stupid for asking the questions an inquisitive child would; he’ll simply give you answers that are as clear, logical, and internally consistent as they are metaphysically extravagant. That’s a start.

In truth, this doesn’t seem like much of a revelation. Aaronson’s cautious sympathy with Everett has been evident in his writings and interviews for a long time. Even when he ostensibly was criticizing it, it was done in an obviously sympathetic manner. And his view isn’t unusual among quantum computing theorists. The reason is the dynamics are just easier to think through under an Everettian view. Of course, it is possible to give accounts of quantum computing under other interpretations, and some theorists do, but as Aaronson notes, it’s more work.

But this other snippet, I think, captures the caution in his support.

Do “other” branches of the wavefunction—ones, for example, where my life took a different course—exist in the same sense this one does? If you start with a quantum state for the early universe and then time-evolve it forward, then yes, you’ll get not only “our” branch but also a proliferation of other branches, in the overwhelming majority of which Donald Trump was never president and civilization didn’t grind to a halt because of a bat near Wuhan.  But how could we possibly know whether anything “breathes fire” into the other branches and makes them real, when we have no idea what breathes fire into this branch and makes it real? This is not a dodge—it’s just that a simple “yes” or “no” would fail to do justice to the enormity of such a question, which is above the pay grade of physics as it currently exists.

This is a view I’ve noticed from a lot of Everettians, such as Sidney Coleman or Stephen Hawking. Supporting Everett isn’t necessarily a full throated support for the idea of many-worlds. (This is one reason I’ve started calling it “Everett” instead of using the acronym “MWI”.)

Yes, the many-worlds are an inescapable prediction of Everett. But it’s not a prediction that can currently be tested. The raw quantum formalism has been heavily tested for almost a century now, reportedly more so than any other theory in science, but there’s an enormous amount of “terrain” between the scale of those tests and the broader predictions. All we can currently say is that there’s no evidence for any factors that would frustrate those predictions.

But much of the history of science is discovering previously unforeseen complications. Who knows what might emerge in quantum systems as they scale from the currently tested thousands of elementary particles to something like 1036 particles? Concepts like “cat lives” and “cat dies” are put as variables in Bra-ket notation as though it’s a precise formulation. But we shouldn’t forget the huge assumptions in doing so, that there’s nothing in the cat’s actual wavefunction that might complicate the picture.

On the other hand, Sidney Coleman used to make the point that the world looks exactly as it should if quantum mechanics evolves as the raw formalism dictates. Maybe another way to express this idea is that the straight mathematical models of quantum mechanics successfully predict our observations as if there are macroscopic superpositions, effectively other worlds, even if it should turn out there aren’t.

I sometimes say that weak Copenhagen, the epistemic instrumentalist version, is true. But it’s true in such a cautious logically-positivist manner that another interpretation can also be true. I think something similar can be said for instrumentalist Everett. It’s true, even if another interpretation eventually turns out to be true in some realist sense. And it seems to get there with fewer assumptions and more logical coherence.

Unless of course I’m missing something.

## 43 thoughts on “An instrumentalist Everettian”

1. I don’t know that I’m up for another round of this so soon after the last one, but I will say that I thought the most relevant part was:

I hold that all interpretations of QM are just crutches that are better or worse at helping you along to the Zen realization that QM is what it is and doesn’t need an interpretation.

What I think it needs is an understanding, and we don’t have that yet. I think that, as Gandhi said about religion, all interpretations are ‘a little bit right and a little bit wrong.’

Far better to focus on learning the QM mathematics, since that’s the working part, so to speak.

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1. Don’t worry. I’m not up for another round either. I almost didn’t do this post as a result, but it expresses a concept I just wanted to register, and felt like if I waited I would likely never have gotten around to it.

I agree about the crutch, but I also agree with what he said later, that most of us will never have the time, skill, or inclination to follow the truest path of working with the mathematics for decades.

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1. Which unfortunately puts one in the position of having to pick their “religion” so to speak based on which story they like best. Which is fine and, as you say, inevitable for many, but hopefully one keeps in mind, as with all beliefs, it might not be true. Grain of salt and all that.

I’ve asked Aaronson about some of my larger questions, his first reply seemed contradictory and unsatisfying, so I’ve submitted a second comment trying to make my question more clear. He’s good about replying, so I expect I’ll see an answer soon.

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1. That’s why I focused here on the instrumentalist aspect. The instrumentalist versions of Copenhagen and Everett are both true, in the same sense that the instrumentalist versions of Ptolemy and Copernicus were both true prior to the telescope. Given that, until we have more evidence, the only question is which one is more useful, easier to work and think with, etc.

Glad you’re asking Aaronson questions. It’s a great opportunity. I’ll watch with interest!

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1. I definitely have some instrumentalist sympathies, although the full philosophy goes beyond those. (I think it was one of your posts that made me realize I had an overly simplistic notion of it based on the title.)

Those who do actually work with QM use the math and, regardless of how they interpret that math, effectively are in the “shut up and calculate” zone. At least while they do the calculations. It’s when we sit around the campfire discussing what it all must mean that differences arise. As Aaronson points out, it’s really students (and onlookers) who need the crutches because they don’t have the math. I suspect for many working in the field, the interpretation fades in significance and becomes something like one’s favorite color, song, or movie.

I’m certainly looking forward to his answer to my second question(s). (I added my question about physical coincidence.)

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2. I have to say I’m impressed with Aaronson’s ability to keep up with correspondence on his thread. If I ever got 141 comments in a day, I think I’d crumble and implode. Most people with that kind of volume are far more selective in what they respond to.

Hope he gets around to your Pauli question.

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3. I know what you mean. I’m hard pressed just to read all those comments. (I’m still somewhere around #55 there.) It must be the teacher in him that drives him to respond.

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4. The best I can muster for other people’s threads is to skim them, particularly when they’re long and filled with lengthy dense comments.

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5. Yeah, it depends a lot on both the content of the given post and the general science education level of the participants.

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6. He ignored it. And declined to even post my follow-up comment. His last comment on the thread says he’s going to stop talking about it for a while. I’m very disappointed; I was really hoping for some answers. (If my comment never shows up, I may email him to see if he’ll say why.) This all does not improve my disposition towards MWI.

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7. Sorry Wyrd. One thing to consider. When someone is facing an onslaught of comments, and we want to increase the chance of a response, it pays to be careful how much of a burden we’re putting on them. Asking too many question at once and in too aggressive a manner probably decreases that chance. Just something to think about if you email him.

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8. An email would just ask if my message was stuck in moderation or if I had offended somehow.

I find the progression of events strange. My first comment needed to be moderated. Fair enough; it’s been a while since I posted there, no problem. It was posted and got a reply. My second comment posted immediately, but was ignored. My third comment I’m back to being moderated, and it still hasn’t been posted. Feels like I’ve been ruled persona non-grata.

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9. From the verbiage on the comment form, it sounds like he moderates everyone. You probably just caught him when he happened to be online with the second comment. No idea on the third. It doesn’t sound like he minds being emailed about them. Maybe his spam folder ate it. (That reminds me. I need to check mine since it’s had a higher tendency to eat real comments lately.)

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10. I don’t believe that’s the case. I just tried another comment to another poster (#201), and, as with my first and third comments, it says the comment is in moderation. My second comment posted immediately without that notation. If #3 got stuck, I figure #4 should get posted. If not, well, I guess I’m not welcome at the table. 😦

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11. I did email Scott Aaronson and he replied (very quickly). My comment simply got missed, and he approved it (even changed the timestamp so it shows up at the end of the thread), so we’re cool. I’m relieved!

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2. As I understand, the underlying equations of all QM interpretations are the same. What I would like to understand better is what the differences are (if any) in the predictions of each of the QM interpretations. I once read that there are two criteria for deciding whether one theory is better than another: (1) does it explain more or better than any other theory, or (2) does it make better or more accurate predictions than any other theory. Of course, no theory can ever claim to be the “last” theory; only the “latest” theory. Interesting post, Mike, as always!

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1. Thanks Mike!

On the equations, it depends. The underlying equations are the same for Copenhagen and Everett. Copenhagen adds a non-mathematical collapse postulate that Everett eschews. That postulate’s presence or absence does result in different predictions, but not currently testable ones. Everett would be falsified if an actual collapse were ever discovered, and Copenhagen seems on less firm ground as progressively larger objects are able to be held in quantum superposition.

But there are interpretations where the math is amended or altered. These are often called hidden variable theories. de Broglie / Bohm pilot wave has Bohmiam mechanics which includes both a particle and wave co-existing. And there are various objective collapse theories that add the collapse in a mathematical fashion. But all make the same testable predictions as Copenhagen and Everett, albeit with more assumptions, some of which are significant.

How to evaluate a theory is a controversial subject. My take is that we should look at what assumptions a theory asks us to make, that is, what concessions do we have to make to get it off the ground, the theory’s logical coherence, and its testable predictions. I think other predictions that can’t be tested, and which don’t conflict with other reliable theories, should be ignored, at least for scientifically assessing the theory. Of course, that doesn’t happen. People often have strong opinions about the untestable predictions.

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1. I don’t think Bohm, or some other theories, should be regarded as an “interpretation” in the narrowest sense. My first introduction to these issues was an article by David Albert in Scientific American titled “Bohm’s Alternative to Quantum Mechanics”. Not that “interpretation” needs to be read in its narrowest sense all the time – but it’s good to be aware of the fact that some theories diverge in yet-untested areas.

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1. I think the only reason we call these things “interpretations” is historical. Heisenberg referred to the “Copenhagen interpretation” in the 1950s. (He had previously called it the Copenhagen “spirit”.) Wheeler used the tact when trying to sell Bohr on Everett’s theory that it was merely a clarification, a re-interpretation of Bohr’s own theory. (Bohr didn’t buy it of course.) But ever since then, we’ve had interpretations.

But as far as I can see, most of these are different theories, with different assumptions and predictions, albeit currently untestable ones. In my view, different interpretations would be like the different ways of looking at world splitting I discussed in the post a couple of weeks ago. They all cash out the same, even in principle, so different ways of talking about the same reality. But that doesn’t seem true for many quantum interpretations overall, unless we restrict ourselves to currently testable predictions.

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3. I like the point Aaronson makes about “reality” and basketball games. I think he and I might like it for different reasons though – I have very liberal views about what’s real, so I think there’s a right answer to “are basketball games real or merely conventional?” Namely, yes both.

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1. You know my criteria. Is it causal? A basketball game certainly seems to be. Although the nature of its realness is another matter.

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1. And there is a difference between “the game of basketball” and any given actual game of basketball.

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4. I enjoyed Aronson’s attempt to make sense of what Integrated Information Theory implies in 2014 where he reduced it back to some sort of bipartite expander graph. But ultimately his answer was simply a mathematical statement rather than anything tangible. It took a philosopher (Eric Schwitzgebel) to do better, or to show that IIT implies that the whole of the United States would thus have its own subjective experience. Furthermore this seems to apply to many other popular consciousness theories. (Friends of IIT were so concerned about this that they made an amendment that they thought would fix things, not realizing that the professor would be able to ridicule their new version no less.)

Here Aronson seems to have fallen short again. Mentioning that “Everett will never make you feel stupid for asking the questions an inquisitive child would”? Maybe he didn’t realize that when you inform an inquisitive child that bazillions of full universes emerge (or whatever) each moment from ours, that they tend not to ignore the substance of your amazing claim. So if these countless universes that theoretically emerge from ours each moment are essentially like ours except they took different superposition paths, doesn’t this mean that bazillions of universes would emerge from each of them each moment as well given their own non realized super positions? If so then wouldn’t this mean we’re discussing the existence of infinite regress beyond the mere construct of language? Wouldn’t this be even more funky than the QM funkiness that we were trying to dismiss by means of an unfalsifiable proposal?

Instead of a story like this I don’t see what would be wrong with plainly stating that we don’t understand what’s happening in QM, though either it’s deterministic in a causal capacity, or it’s supernatural. Wouldn’t that be a reasonable crutch too, and one that we could tell children without them asking us questions which illustrate fantastic rationalizations?

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1. Eric,
It doesn’t seem like you’re engaging with what Aaronson or I actually wrote here. It doesn’t leave much for me to respond to.

On your final point, you’ve said yourself many times that it’s not whether an idea is true or false, but how useful it is. That’s what these posts were actually about.

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1. I thought I was engaging with the point that children wouldn’t ask us difficult questions given this scenario Mike. From there I noted that it quickly leads to worldly infinite regress, or something that I consider a causal impossibility. If you inform me however that you and Aaronson (and Carrol and so on) have merely been speaking of a potentially useful QM teaching tool, then I drop my objection. Teach on! I have no problem with a hypothetical “Think of it like this…” crutch, that is if openly pedagogical. In that case I suspect Wyrd would cease his opposition as well.

You’re right that I do not demand explanations to be “true”, but rather “useful”. Keep in mind however that I consider no answer useful which depends upon supernatural dynamics. We know “Force equals accelerated mass” to not be true, though is causal and remains quite effective in general. Conversely “Because God did it” could conceivably be true, though conflicts with my own brand of metaphysic and so I don’t consider this to be a useful explanation for anything (even if/when it’s true). To me theorizing the existence of full otherwise separate universes to account for our measurements (unless purely pedagogical), seems more like “Because of God” than “F = MA”. The former should inherently conflict with better natural theories, while the latter clearly has not.

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1. Aaronson’s remark about the child asking questions was in reference to the reply many advocates of other interpretations have to certain questions, often saying, “It’s meaningless to ask that question,” or something along those lines. For example, strong Copenhagenists will often say it’s meaningless to ask about the state of the particle prior to measurement, as though the act of measurement brings it into existence somehow. Or RQM advocates will say it’s meaningless to talk about the state of the particle between interactions.

His point is that the Everett interpretation doesn’t do that. It just relentlessly follows the quantum formalism. You may not like the resulting answers, but it doesn’t tell you to just shut up.

As to the other worlds, Carroll is an all-in many-worlder. (Although he stays open to the possibility that it could be falsified at some point.) I can’t say for sure with Aaronson, but if I understand his remarks, he’s far more cautious. Myself, I’m agnostic on the other worlds. They’re predicted by the heavily tested formalism, and there’s nothing currently known to prevent them from existing, but we also don’t have a way to test that existence. That might change someday.

As I’ve pointed out many times, the other worlds are not an assumption made to solve the measurement problem. They’re a prediction, a consequence of just letting the quantum formalism play out.

As a result, I find confident rejection of the other worlds unjustified, and the vehemence and overall emotion associated with it striking.

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1. Okay Mike, I’ve asked Scott if he supports Everett merely as a pedagogical tool, or “all in” like Sean Carroll. https://www.scottaaronson.com/blog/?p=5359#comment-1882021

I do see however that he’s just mentioned that he won’t be commenting for this one further. At the end there he also mentioned that he doesn’t object to being referred to as either “essentially Everettian”, or “non-Everetttian”, which suggests that he doesn’t back this more than pedagogically.

I see what you mean about many worlds being able to answer certain questions that other interpretations don’t. I’ve presented an observation however which seems to render this interpretation supernatural, or at least if taken literally rather than as a mere education tool.

I get your point that the many worlds are just a prediction or consequence of this interpretation, but in science that’s how things work in general. We figure out all sorts of implication of a given proposal and try to assess them as best we can to help provide support or the converse. I’m pointing out that one of the implications of positing “many worlds” as an explanation for QM observations, is that reality would then function supernaturally given an apparent material infinite regression.

I do not absolutely reject this proposal, but merely classify it as something which seems to have supernatural implications. I don’t consider myself particularly emotional here, though I can see how a person who backs it could get emotional if they were unable to effectively deny my observations. And yes I have had some hesitance discussing this with you just in case you decide that I’m being disrespectful. It’s the same with my thumb pain thought experiment. I don’t want to push too hard, but realize that you’re a naturalist first, and even though you don’t quite grasp the supernatural implications of non mechanistic qualia.

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2. Eric,
My advise, if you want to have productive conversations, is to table the word “supernatural”, unless someone is explicitly talking about supernatural concepts. Used for discussions about scientific or philosophical concepts, it’s polemical and seems more aimed at agitation than conversation.

If I understand your criticism above, it’s centered on the infinite regress thing. Is the concern that the world is being split into an infinite number? If so, that’s a common concern. But to use the Ask a Physicist’s response: the math works.
Carroll admits that there might be some finite number of combined quantum states the observable universe could be in, but using a maximum entropy calculation, he thinks it would be at least e^10^122. He notes that could cause issues before the final heat death of the universe, but we’re talking about periods where, due to dark energy, matter interactions would have become rare.

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3. Mike,
It seems to me that whenever someone invokes dynamics which occur that seem to have no worldly causal reason for their existence, that something supernatural will be proposed. Theoretically there will be existence without cause, or what may also be referred to as “magic”. I think we need to be on guard for magical proposals wherever science remains “soft”, since they’re essentially a way to cheat. The topic of consciousness seems rife with this. At least David Chalmers is reasonably honest about his supernaturalist tendencies. Many distinguished people not only fool others with their proposals, but themselves. It seems to me that the reason that people who propose magical answers tend to hate thought experiments, is because they provide a vehicle from which to potentially expose magical ideas. Surely you agree that magic should be exposed as such if/when it exists?

If it helps however I suppose that I could diplomatically refer to theorized “supernatural dynamics” as “non causal dynamics”. I guess this would be the same thing, though without the rhetorical bite. I can’t promise anything at the moment, though I will keep your concern in mind.

It’s not exactly that I worry about the MWI saying that our world gets “split” (and in e^10^22 ways or more). Regardless of how many ways you divide something it should still add up to just one of them. My concern is instead that MWI seems to say that our world gets multiplied. Furthermore if these other worlds function the same as ours then they would need to be multiplied as well, creating infinite regress. That’s a hell of a lot of theorized new stuff to account for our inability to grasp what’s going on in this world! If the theory is instead that our world gets “split” however then I could see how there wouldn’t inherently need to be any new mass/energy. Is that your perception of this theory? Super positions not realized here don’t actually exist in other full universes, though we momentarily imagine they do in some kind of accounting split of ours?

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4. Eric,
Your call on “supernatural”. I could use it when discussing your views, but I think it would just tend to end discussion. I’d rather point out the gaps and assumptions and give you a chance to speak to them.

Everett doesn’t involve multiplication of matter or energy. There’s no creation ex-nihilo, although that’s a common misconception. It’s the branches of the wavefunction, and the existing energy within them, evolving away from each other. In terms of talking about worlds, as I noted in the post a couple weeks ago, we can talk about the existing world splitting into new ones, or pre-existing multiple worlds diverging from each other. Or we can talk about aspects of the one universe becoming inaccessible. All of those are different ways of talking about the same ontology. But talking about new worlds created out of nothing isn’t compatible with the theory.

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5. @Mike: “we can talk about the existing world splitting into new ones, […] But talking about new worlds created out of nothing isn’t compatible with the theory.”

The thing that always gets me here is what is the difference between an existing world splitting into two and creating a new world? There was one cat; then there are two cats. (As someone pointed out on Aaronson’s blog post, there are really many, many cats, since the particle could decay at any point during the test period, and cats dead for 1, 30, or 59, minutes are different cats.)

One is forced to the ontology that such worlds always existed but only branch due to quantum events. It’s the only way I can see to balance the energy question. And, indeed, the notion of a universal wave-function does suggest just that.

I’ve come to think one problem with discussing the MWI is that people focus on specific (small) scenarios, but a wave-function always describes the evolution of the entire system, however large that system may be.

@Eric: It isn’t just that the term “supernatural” is provoking, it’s that for most it carries the connotations of ghosts and witches and H.P. Lovecraft. To many it then labels you as a nutcase. FWIW, I use the term “non-physical” to say the same thing.

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6. “One is forced to the ontology that such worlds always existed but only branch due to quantum events.”

That’s a valid way to look at the universal wavefunction. It actually is David Deutsch’s preferred view.

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7. I’ve come to believe it’s the only way to view it. I’m sure you remember that Everett’s paper is titled “The Theory of the Universal Wave Function”. The Schrödinger equation has a single state vector that encodes the entire system described at any one time. (You likely also recall that, given that state vector at any given time, it can be evolved forward or backward to any other time.)

As I understand it, it is not the case that the SE describing a composite system can be broken down into “sub” expressions that encode parts of that system. One wave vector, with an unimaginable number of Hilbert space dimensions, encodes the whole ball o’ wax.

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8. I do remember that title. It took me a long time to understand it.

Not sure if I understand your final paragraph. It seems like a typical wavefunction does have components. And every wavefunction anyone actually works with would be a small subset of the overall universal wavefunction. Or am I missing the point?

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9. My understanding on this is a big hazy, because at this point in my learning curve texts mostly deal with single particle systems, often in only one physical dimension. That MIT course, for instance, spends the entire semester on 1D single particle systems.

But I’ve heard what I said there asserted a number of times. Roughly speaking, the putative wave-function of my hand is not, in any way, a subset of the putative wave-function of my body. However, a wave-function describing my body doing two different things, those two things would each be components of the total.

So for some wave-function:

$|\Psi\rangle=c_1|\phi_1\rangle+c_2|\phi_2\rangle+c_3|\phi_3\rangle+\ldots$

Each contributing wave-function, Φ, with complex coefficient, c, is some possible state of the entire system, Ψ, not a wave-function of a sub-system of Ψ, if that makes any sense.

It’s similar, perhaps, to how the texture of a given musical note, which differs depending on whether produced by a saxophone, guitar, or piano, is a linear sum of contributing sine wave harmonics. Each contributing sine wave is a complete “system” — a complete sound on its own — not a moment of this sound followed by a moment of that sound followed by some other sound.

That make any sense?

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10. I meant “bit hazy” but “big hazy” isn’t that far off. 🙂

Put in MWI terms, each component Φ would be a complete world in the universal wave-function Ψ.

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11. Thanks. I think I get it.

And in retrospect, I should have remembered the whole entanglement issue. The universal wave function would have widescale entanglement. If we have a wavefunction of two entangled particles, the wavefunction of either particle isn’t strictly a subset of the wavefunction of the entangled particles. We can model one of those particles with a wavefunction, but it would be missing information, and it would be accurate as far as that one particle, but we can’t just add the wavefunctions of the two particles together and get the entangled version. It’s those nonlocal relations again.

All of which means that any wavefunction we might work with, strictly speaking, isn’t a subset of the universal wavefunction.

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12. Yes, exactly so. However, to jump into the weeds, entanglement is a separate topic. None of what I wrote above implies, let alone requires, entanglement. A wave-function describing a multi-particle system contains terms for each particle’s position and the energy potential affecting that particle, and the wave vector encodes all that, but the particles are not entangled.

A simple treatment of entanglement involves what’s called a Bell state, usually represented as:

$\frac{1}{\sqrt{2}}|00\rangle+\frac{1}{\sqrt{2}}|11\rangle$

Which is a superposition of the two possible measurements, |00⟩ and |11⟩. These states cannot be reduced to wave-functions that describe the individual particles — the wave-function necessarily describes both.

The state |00⟩, for instance, is a tensor product of |0⟩ and |0⟩:

$\begin{bmatrix}{1}\\{0}\end{bmatrix}\otimes\begin{bmatrix}{1}\\{0}\end{bmatrix}=\begin{bmatrix}{1_1*1_2}\\{1_1*0_2}\\{0_1*1_2}\\{0_1*0_2}\end{bmatrix}=\begin{bmatrix}{1}\\{0}\\{0}\\{0}\end{bmatrix}$

And for the |11⟩ state:

$\begin{bmatrix}{0}\\{1}\end{bmatrix}\otimes\begin{bmatrix}{0}\\{1}\end{bmatrix}=\begin{bmatrix}{0_1*0_2}\\{0_1*1_2}\\{1_1*0_2}\\{1_1*1_2}\end{bmatrix}=\begin{bmatrix}{0}\\{0}\\{0}\\{1}\end{bmatrix}$

$\begin{bmatrix}{1}\\{0}\\{0}\\{0}\end{bmatrix}+\begin{bmatrix}{0}\\{0}\\{0}\\{1}\end{bmatrix}=\begin{bmatrix}{1}\\{0}\\{0}\\{1}\end{bmatrix}$

And applying the coefficients:

$\frac{1}{\sqrt{2}}\begin{bmatrix}{1}\\{0}\\{0}\\{1}\end{bmatrix}=\begin{bmatrix}{\frac{1}{\sqrt{2}}}\\{0}\\{0}\\{\frac{1}{\sqrt{2}}}\end{bmatrix}$

Which cannot be decomposed into separate wave-functions.

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13. Drat! No matter how many times one proof reads…

The |11⟩ state should be:

$\begin{bmatrix}{0}\\{1}\end{bmatrix}\otimes\begin{bmatrix}{0}\\{1}\end{bmatrix}=\begin{bmatrix}{0_1*0_2}\\{0_1*1_2}\\{1_1*0_2}\\{1_1*1_2}\end{bmatrix}=\begin{bmatrix}{0}\\{0}\\{0}\\{1}\end{bmatrix}$

Which probably makes a lot more sense.

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14. Alright guys, I guess I could mostly stop using terms like “supernatural” and “magic” to refer to various theories that I consider to rely upon non-causal dynamics. I certainly don’t mean to imply that anyone’s casting spells! Terms like “non-physical” and “non-causal” may not be sufficient replacements however, since most probably wouldn’t grasp the significance. Even in science it seems common for people to think of the world as something more than just “physical”. I’ll probably go with terms like “non-natural”, “non-worldly”, and even “spooky” from time to time.

I presume that all events are perfectly caused to happen exactly as they do happen (even regarding QM), and don’t mind thinking of anything else to thus be magical. But if such terms are loaded then I’ll try to do without. Regardless wherever there are problems in science, such as for QM and the mind, should be fertile grounds for non-natural explanations to take hold. I believe that we’ll need various accepted principles of philosophy to help scientists make better progress in these regards.

Mike if you ever suspect that I support a spooky idea, please do state your concerns explicitly as such. I’d like to know, and even if valid, and even if I’ve become highly invested in this idea. Note that I get explicit with you regarding your strong support for medium-less qualia, which I consider outside the causal domain. On some level I suspect that’s where this is coming from, but either way.

On the Everett interpretation, I’ll let this go on the hope that the “many worlds” title is somewhat of an exaggeration. If it merely implies that there is one world which functions as if there were many given the apparent duality of mass/energy, then that’s fine. My beef is with taking something we don’t understand and then “explaining it” by holding a theoretical extra universe responsible that’s otherwise beyond us. What couldn’t we explain with such a scenario? Why are my keys gone! Maybe they were eaten by another universe? 😀

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