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Scott Aaronson's cautious optimism for the MWI
http://www.scottaaronson.com/blog/?p=1103
Eliezer's gung-ho attitude about the realism of the Many Worlds Interpretation always rubbed me the wrong way, especially in the podcast between both him and Scott (around 8:43 in http://bloggingheads.tv/videos/2220). I've seen a similar sentiment expressed before about the MWI sequences. And I say that still believing it to be the most seemingly correct of the available interpretations.
I feel Scott's post does an excellent job grounding it as a possibly correct, and in-principle falsifiable interpretation.
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Comments (70)
As far as I can tell (being a non-physicist), the Transactional Interpretation shares the mathematical simplicity of MWI. And here<PDF> Kastner and Cramer argue that TI can derive the Born probabilities naturally, whereas MWI is said to need a detour through "the application of social philosophy and decision theory to subjectively defined ‘rational’ observers". So maybe TI is simpler.
The "possibilities" they posit seem quite parallel (pardon the pun) to the multiple worlds or bifurcated observers of MWI, so I don't see the philosophical advantage there, that they tout. But integrating the Born probabilities more tightly into the physics is a plus, if true.
With respect to Born probabilities, TI is on the level of MWI, it has no derivation for them. Similarly, its ontology is rhetorical rather than rigorous.
A central issue for any zigzag-in-time or retrocausal theory of QM would be vacuum polarization, which was the stumbling block for the most serious effort, by Feynman and Wheeler. But Feynman-Wheeler theory is also where the path integral was born, so TI advocates could say, we just need to go back and finish it properly.
Stopped reading the linked paper when it made a mistake because of treating "worlds" as literal things being "split off." Gotta use quantum mechanics if you're going to talk about quantum mechanics. Maybe they corrected it later, but I didn't even want to wade through to find out.
Although they do not "split off" in the same envisioned early on by DeWitt, there is definitely some unanswered questions here. Alastair Wilson and Simon Saunders has raised this issue. Are all the worlds in the wavefunction from the beginning of time or do they somehow spring out from one world? This is called overlap vs non-overlap (first discussed by David Lewis).
Since you are the expert, by all means answer this for us.
So, by "world" in this post I'll mean "basis sate for the universe." The basis is arbitrary, so what "world" means will still depend on how I'm choosing what "worlds" are - there's the energy basis, for instance, where nothing ever changes if you look at just one of those "worlds." But you can have animals or computers in your basis states if you want - they aren't energy eigenstates, so they change with time.
Anyhow, currently the universe is spread out over a very wide variety of energy eigenstates, which is a fancy way of saying that lots of stuff changes. If we only allow quantum mechanics (that is, strictly follow MWI), this spread over "energy-worlds" is how the universe has been since the beginning of time. But if we look at the exact same state a different way, you could just call the initial state of the universe a basis state, and then, lo and behold, the universe would have sprung from one world, and the distribution of worlds then changed over time. This way of looking at things is probably pretty useful for cosmology. Or you could use worlds that change over time but don't include the original state of the universe, giving you overlap again. This is what we do unintentionally when we choose worlds that have humans in them, which is also pretty useful :)
For overlap vs. non-overlap to get more complicated than "both are valid pictures," you'd need some model where there weren't any static worlds to talk about - this would be a change to QM though. Also, this does raise the interesting question of how complicated that initial world (if we look at it that way) was. It doesn't have to be too complicated before we see interesting stuff.
Anyhow, it's pretty likely I was too hasty in my mistake-detection. But meh, I rarely regret putting off reading things. And I only occasionally regret putting my foot in my mouth :)
To be perfectly honest, I do not see an answer to my question here.
You do explain some, but it seems that you end up indirectly stating that it is "semantics" whether the worlds overlap or not overlap. From what you say here it all depends on how you look at it, but that there is no "truth" of the matter. But that cannot be, either the worlds are overlapping or they are not. That is just the very fact of objective reality.
So while "both pictures are valid" in terms of math, not both can be the same. Metaphysically they are not the same and they got very different effects on episteomology. Also in terms of for instance quantum suicide. In overlap, it's hard to argue against some sort of Quantum Immortality, whilst in non-overlap death is just as in a classical one world theory.
What I am saying is that if one person says "all the worlds have always existed" and another says "the worlds spread out from one world," it's possible that both of them are being consistent, but then they are using two different definitions of "world." I am also saying that there is no basis that is "more real" than the others - only that some are more useful, and it's okay that people use different definitions as long as they're clear about it.
And yes, both pictures can describe the same thing. Have you worked with Bell states at all? Or am I misinterpreting your name and you actually haven't taken a class on quantum mechanics before?
The quantum world is like a diagonal line. One person comes up to it and says "Ah! Here is a diagonal line! It has just as much horizontal as it does vertical, therefore it is a mixture between horizontal and vertical." Another person comes up to it and says "Ah! Here is a diagonal line! It is a perfect rising diagonal, and is not even a little biased towards the falling diagonal." Will these two people argue over whether the line is made of two components or one?
I understand what you are saying, which I think my last post showed quite clearly, but this still does not answer the actual question at hand. What you are saying really amounts to saying that "realism and solipsism are the same", because we cannot really distinguish either through science, all we can do is use logic and metaphysical "reasoning".
Obviously both overlap and non-overlap cannot be true, they are ontologically different, yet you seem to say that "because the equations doesn't decide, reality isn't decided" which is some sort of extreme positivism.
Have you read any of the papers that outline this? Alastair Wilson have written several: http://www.alastairwilson.org/
Maybe you're just used to talking with people who are better at interpreting you, or people who are more similar to you. Clearly understandable to people you talk with every day isn't always clearly understandable to me, as we've seen.
Could you explain this? Is this a metaphor, or are have you interpreted my statements about vectors to actually bear on realism vs. solipsism? Perhaps we have been talking about two different things.
Ah. See, this is the sort of thing I was trying to illustrate with the example of the diagonal line. A line being made of one component is ontologically different from a line being made of two components. Does this matter?
What happens if a one-componenter runs into a two-componenter? Do they argue? Does the first say "because of [insert convincing component-ist argument here], it's ONE component!" Are there valid component-ist arguments? How can the two-componenter respond?
I think it would go more like this: the first one says "hey, if you describe lines in terms of plus and minus diagonals, this one is clearly just a plus diagonal, so why say it has two components?" And the second says "Oh, huh, you're right. But there are lots of horizontal and vertical lines out there, so two-components is more useful." And the first says "yeah, that makes sense, unless you were building a ramp or something." "Well then, cheerio." "Toodles."
The reason this was so anticlimactic is because each participant could frame their ontology in a universal language (vectors!), and the ontologies were lossless transformations of each other - in this case the transformation was as simple as tilting your head. This clarity of the situation leaves no room for appeals to componentism. Arguments are for when both people are uncertain. When people know what's going on, there's simply a difference.
Could you point me to an example? Similar to how we are potentially talking about two different things, Alastair Wilson seemed to be talking about something other than physics in the papers I skimmed. The phrase "the most appropriate metaphysics to underwrite the semantics renders Everettian quantum mechanics a theory of non-overlapping worlds" exemplifies this for me.
Sure I can accept that I might have overestimated how well you should've been able to interpret my post.
Solipsism vs Realism is indeed a metaphor. If you are saying what I think you are saying, then it is quite equivalent.
I do not think that your example of a diagonal line is the same as overlap vs non-overlap at all. In overlap vs non-overlap the ontological differences matter. In a overlapping world, if you are shot, you are guaranteed to survive in another branch, so QI has to be true. In non-overlap, if you get shot, you just die. There is no consciousness that continue on in another branch that it was never connected to...
Also it makes away with the incoherence problem, which is HUGE if you are in the "Born Rule can be derived from decision-theoretic camp".
It is metaphysics, I've already said this in the first post. There is no experiment that can ever distinguish either, just like no experiment can ever tell us if solipsism or realism is true. But obviously (assuming MWI is right) one of them are, only one, not both.
I think 5 of those papers are directly about non-overlap vs overlap, and I can't remember which makes the point best right now, so read any of them you'd like. Or you can read Simon Saunders paper which was in a chapter of the Many Worlds? 2010 book here: http://users.ox.ac.uk/~lina0174/chance.pdf
Ah, I see. "Metaphysics."
By which you mean "taking human morality and decision-making, which evolved in a classical world, and figuring out what decisions you should make in a quantum universe."
Would you agree that overlap vs. non-overlap cannot be answered without looking inside humans, and in fact has little to do with the universe apart from a few postulates of quantum mechanics? For some reason I thought we were talking about the universe.
Anyhow, I think Shane Legg had a nice paper on porting utility functions, though of course humans are inconsistent and you immediately run into problems of how to idealize them. The basic idea being that you split up changes into "new things to care about" and "new ways to express old things." Quantum suicide is probably the easiest thing to deal with via this method.
He says that the math is simpler under MWI.
Can someone explain why that's true (or false)?
In non-relativistic MWI, the evolution of the quantum state is fully described by the Schrodinger equation. In most other interpretations, you need the Schrodinger equation plus some extra element. In Bohmian mechanics the extra element is the guidance equation, in GRW the extra element is a stochastic Gaussian "hit".
In Copenhagen, the extra element is ostensibly the discontinuous wavefunction collapse process upon measurement, but to describe this as complicating the math (rather than the conceptual structure of the theory) is a bit misleading. Whether you're working with Copenhagen or with MWI, you're going to end up using pretty much the same math for making predictions. Although, technically MWI only relies on the Schrodinger equation, if you want to make useful predictions about your branch of the wave function, you're going to have to treat the wave function as if it has collapsed (from a mathematical point of view). So the math isn't simpler than Copenhagen in any practical sense, but it is true that from a purely theoretical point of view, MWI posits a simpler mathematical structure than Copenhagen.
In other words, MWI says: apply Copenhagen for anything useful.
MWI says that you apply no more than one collapse in every experiment, and you know why it is a collapse from your point of view. Copenhagen requires you to decide without guidance whether to apply collapse inside the experiment.
Yeah, just like statistical mechanics requires us to model systems as having infinite size in order to perform many useful calculations (e.g. phase transitions, understood as singularities in thermodynamic potentials, can only take place in infinite particle systems). It doesn't follow that we should actually believe that these systems have infinite size.
Also, the claim is not that MWI is mathematically identical to Copenhagen, just that it works out that way in most practical cases. The Copenhagen interpretation is sufficiently ill-defined that it's unclear what its mathematical structure actually is. But as Aaronson points out in the post, there are predictions that distinguish between MWI and Copenhagen.
I don't believe that he said anything of the sort. At about 50min Scott talks about quantum speedup as utilizing the computational power of many worlds, provided they exist, not as any kind of experimental distinction (indeed, quantum computing is interpretation-agnostic).
I was talking about the blog post, not the bloggingheads video. He doesn't outright declare that the two interpretations are distinguishable, but that position is strongly suggested by both his discussion of betting on the extension of linearity to macroscopic scales and his subsequent discussion of the Wigner's friend experiment.
Hmm, if anything, the most interesting near-future experiment he mentioned is the one by Dirk Bouwmeester's group. No one has the foggiest idea about how to construct the Wigner’s friend experiment, not even in principle, given that it is no different from the original (though non-lethal) Schrodinger cat experiment, where Wigner’s friend is the cat and Wigner is the observer.
Surely there's a difference between thinking that experiments that can distinguish MWI and Copenhagen are infeasible for various technological reasons, and thinking that MWI and Copenhagen are empirically indistinguishable. I usually interpret empirical indistinguishability as "no conceivable distinguishing experiment" rather than "no feasible distinguishing experiment".
There are certain observables for which MWI and Copenhagen predict different expectation values, provided decoherence is contained. The problem is, we do not currently have much of an idea of how we could go about making the relevant measurements, mainly because we do not know how to keep systems as large as Wigner (or Schrodinger's cat) informationally isolated for a sufficiently long period of time.
Yes, indeed. And it seems like there is a way to potentially falsify MWI, after all (see below). There is no way of falsifying the orthodox approach ("shut up and calculate, unless you can say something instrumentally useful") as yet, because it does not treat collapse as "objective", only as a calculational prescription (this is the part EY completely refuses to acknowledge, and instead goes on constructing and demolishing some objective collapse model). To falsify the orthodox approach one has to show that the Born rule is violated macroscopically, e.g. that you can see something other than a single eigenstate after a measurement, or that the measured probability of it is not the square amplitude.
Now, back to the experimental testing. If I understand it correctly, the quantum cantilever experiment of Bouwmeester, once performed, is likely to show one of two things:
Such a macroscopic object can be put into a superposition of two different spatial states, thus violating the decoherence limit proposed by Penrose. This will falsify his specific model of gravity-induced single world, and would thus be a reason to update toward MWI, though there is still no contradiction with the orthodox (unitary evolution+Born rule) prescription, unless the cantilever remains in the superposition of states after the measurement (not a chance in hell).
The cantilever remains in a single state, despite the predictions of gravity-less QM. This is by far a more interesting outcome, as it would for the first time show the macroscopic limits of the quantum world. This would score a point for gravity-influenced decoherence and single world, and would be a significant blow to MWI.
There is always a chance that the experiment will show something else entirely, which would be even more exciting.
That doesn't sound right. Famously, matrix mechanics is "equivalent to the Schrödinger wave formulation", and matrix mechanics doesn't have multiple interpretations.
I view this whole subject as a colossal waste of time.
As you say, matrix mechanics (or the Heisenberg formulation) is equivalent to the Schrodinger formulation, so it has exactly the same range of interpretations as the Schrodinger formulation.
If you want a concrete example of an experiment that would distinguish between MWI and Copenhagen, here it is:
Prepare an electron so that its z-spin state is the superposition |up> + |down> (I'm dropping the coefficients for ease of typing). Have a research assistant enter an appropriately isolated chamber with the electron and measure its z spin. If Copenhagen is correct, this will lead to the collapse of the superposition, and the electron's state will now be either |up> or |down>. If MWI is correct, the electron's state will become entangled with your research assistant's state, and the entire contents of the chamber will now be in one big superposition from your perspective.
Now have your research assistant record the state she measures by preparing another electron in that quantum state. So if she measures |up> she prepares the other electron in the state |up>. Again, if Copenhagen is correct, this new electron's state is either |up> or |down>, whereas if MWI is correct, its state is in an entangled superposition with the original electron and the research assistant. Call this entangled state predicted by MWI psi.
Now you (from outside the chamber) directly measure the difference between the x-spin (not the z-spin) of electron 2 (the one prepared by your assistant) and the x-spin of electron 1. I can't tell you off the top of my head how to operationalize this measurement, but the fact remains that it is a bona fide observable. If you do the math, it turns out that the entangled state psi is an eigenstate of this observable, with eigenvalue zero. So if MWI is right, whenever I make this measurement I should get the result zero. On the other hand, neither of the states predicted by Copenhagen are eigenstates of this observable, so if Copenhagen is right, if I keep repeating the experiment I will get a distribution of different results.
tl;dr: Basically, all I've done here is take advantage of the fact that there are observables that can distinguish between mixtures and superpositions by detecting interference effects.
Of course, in order for this experiment to be feasible, you need to make sure that the system consisting of the two electrons and the assistant doesn't decohere until you make your measurement. With current technology, we're not even close to making this happen, but that is a problem with the feasibility of the experiment, not its bare possibility.
MWI says: apply Born's rule to get anything useful.
If that's what you call Copenhagen, then sure they're the same thing - but then why was Everett so scandalous and ridiculed? Something had to be different.
No idea, I don't find MWI ridiculous, just not instrumentally useful, given that you still have to combine unitary evolution with the Born rule to get anything done. This is a philosophical difference with EY, who believes that territory is in the territory, not in the map.
... territory is in the territory.
Umm. That sounds... non-controversial. Did I read that wrong somehow?
No, you read it right. However, instrumentally, the map-territory relation is just a model, like any other, though somewhat more general. It postulates existence of some immutable objective reality with fixed laws, something to be studied ("mapped"). While this may appear self-evident to a realist, one ought to agree that it is still an assumption, however useful it might be. And it is indeed very useful: it explains why carefully set up experiments are repeatable, and assures you that they will continue to be. Thus it is easy to forget that it is impossible to verify that "territory exists independently of our models of it", and go on arguing which of many experimentally indistinguishable territories is the real one. And once you do, behold the great "MWI vs Copehagen" LW debate. If you remember that territory is in the map, not in the territory, the debate is exposed as useless, until different models of the territory can be distinguished experimentally. Which will hopefully happen in the cantilever experiment.
The territory is not in the map, because that is nonsense.
That does not beg the question against instrumentalism and jn favour.of realism, because the territory does not have to exist at all.
Realists and anti realists are arguing about whether the territory exists, not where.
That's the standard reaction here, yes. However "that is nonsense" is not a rational argument. You can present evidence to the contrary or point out a contradiction in reasoning. If you have either, feel free.
I don't understand what you are saying here.
Maybe so, then I am neither.
I'll point out a contradiction: territory is defined as not-map.
"I am neither"
... in the sense that you are using the word territory in a way that no one else does.
This is one of those times it really is useful to pull out definitions... and for any reasonable definition of 'territory' and 'map', that's self-evidently true. Our models, even if correct, are underdetermined to the point that they cannot completely explain everything. Therefore, there's something else. That's what we call the 'territory'.
Whether the territory is vastly different from our models or simply more detailed, they do not coincide. And on the word 'independent' - well, the territory contains the map, so there's no short-circuit if the territory has map dependence.
Again, that's the realist approach. The minimum one can state is much less certain than that: all we know for certain is that carefully repeated experiments produce expected results. Period. Full stop. Why they produce expected results (e.g. because there is "something else" that you want to call the territory) is already a model. It's a better model than, say, Boltzmann brains, but it is still a model. The instrumental approach is to consider all models giving the same predictions isomorphic, and, in particular, all experimentally indistinguishable territories isomorphic.
It's on par with cogito, ergo sum. I don't know everything, therefore something else exists. I don't feel obliged to cater to people who are unwilling to go along with this.
If not from Everett, I would expect from David Deutch to say: "You and I have a completely different sets of parallel worlds, for the Relativity sake. Every slightly different observer comes with his own Multiverse collection of parallel worlds."
Those people should update to the GR, it's about time.
I think the short version is that you don't need math that covers the wavefunction collapse, because you don't need the wave function to collapse.
For a longer version, you'd need someone who knows more QM than I do.
The thing that's always bugged me about the MWI is that it doesn't seem physically sensible. If something isn't physically sensible, than you need to check on your model. This happens all the time in physics - there are so many basic problems where you discard solutions or throw out different terms because they don't make sense. This is the path to successful understanding, rather than stubbornly sticking to your model and insisting that it must be correct.
The impression I get is that, if the math leads you to make a conclusion which seems like physical nonsense, then you ought to trust your gut, rather than trusting the math. MWI sounds like nonsense, and completely physically implausible, and that's far more convincing to me than claims that "the math must make it so."
By "physically sensible," what do you mean? When I say that, I usually mean something that my brain is good at modeling,
In what sort of situation would you expect a correct theory to not be physically sensible?
It's hard to put my finger on this exactly. To me, physically sensible just means it sounds reasonable under the context of observations and everything else that we know. In this specific case, the idea of infinitely many universe branches constantly forking off doesn't seem physically sensible to me when all we observe is a single universe.
This just happens all the time. For example, to get the free-fall time for a falling object, you have to take a quadratic root of an expression, which in principle gives a "negative time" root/solution. This solution is obviously nonsense, so you just discard it and don't pay attention to it, but you don't conclude that the theory is wrong.
If you don't discard it, and do pay attention to it, you discover it is sensible.
"Negative time" is time before the time you labelled as zero. The negative solution is the time at which the object would have been at the end point, moving upwards, to get to the starting point at time zero.
Well, the negative-time solution can be eliminated by using math too - "the theory" was never the equation with two roots - it was the process you used to get the right answer. What I want to know is, can you grok a case where the actual correct theory isn't physically intuitive, but is correct?
First of all, I disagree that the negative time solution can be removed using math; the math will tell you that the solution is perfectly valid.
Secondly, yes, there are cases like in statistical mechanics or basic QM where the theory isn't that intuitive, dealing with huge numbers of particles (as in SM) or dealing with position probabilities (as in QM), but where the process makes sense (I can grok it).
But these theories have clear interpretations in terms of observables; SM has a systematic justification in terms of physical intuition (in terms of the preferred configurations being those with the most probability, or something of that nature), and QM develops right from the beginning how the wave-function picture can be seen as a generalization of the classical picture (positions directly become position operators, as with momenta and so on). There's no such obvious justification for the MWI, in my mind; the linkage between there being many branches of the solution, and there being many universes, is weakly justified at best.
But you could, say, write a computer program that gave you the right answer to classical mechanics problems, right? In order to write this program, the knowledge you have that tells you that when you want a length of time, you want a positive number would have be translated into "computer language," i.e. math.
That is, when I say "you can remove nonsense solutions by using math" I mean "all you have to do is make the theory already contain your knowledge of what's a nonsense solution."
Well, the negative-time solution can be eliminated by using math too - "the theory" was never the equation with two roots - it was the process you used to get the right answer. What I want to know is, can you grok a case where the actual correct theory isn't physically intuitive, but is correct?