Dialogue on Many Worlds

The antithesis Empiricism vs. Rationalism does not appear as a controversial point in Galileo's work. Galileo opposes the deductive methods of Aristotle only when he considers their premises arbitrary or untenable. His endeavors are not so much directed at "factual knowledge" as at "comprehension." But to comprehend is essentially to draw conclusions from an already accepted logical system.

                                                                                Einstein’s Forward to Galileo’s Dialogue

                                                                                Concerning the Two Chief World Systems

The following is a transcript of a dialogue on the so-called “Many Worlds Interpretation” (or MWI) of quantum mechanics.

Salviati:  For an observer tossing a quantum coin, the MWI maintains unitarity by saying that following the toss we have [observer1,observer2] reporting [heads,tails]. The problem with this is that it does not account for why we don’t get [observer1,observer2] reporting [tails,heads]. All we can say is that we don't care about the difference – but try telling that to observer1 if "heads" means he loses his.

Sagredo:  But Salviati, your observer labels 1 and 2 have no significance. An advocate of MWI would say that, if we have a sequence of 50 coin tosses, there are 2⁵⁰ distinct observers, one for each possible sequence of outcomes, and we identify those observers with their respective sequences of outcomes. So it's self-contradictory to talk about permuting the observers to different sequences of outcomes. The sequences of outcomes are the observers. On the other hand, the multiplicity of these outcomes is strictly unobservable, in the empiricist sense, so one can argue that the unitarity is only a fantasy (to any given observer). In this sense MWI represents a highly rationalist – rather than empiricist – approach to science.

Salviati:  I agree, Sagredo, and I would add that highly rationalist interpretations invariably fail because they are grounded in a specific set of postulates. History has shown that our postulates are always imperfect, so rationalist interpretations like the MWI are bound to fail.

Sagredo:  I disagree. We already know that, for example, Schrödinger’s equation is not relativistic, and yet the transition to quantum field theory doesn’t significantly change the case for or against MWI. In fact, one can hypothesize a "many worlds" interpretation of any theory – even classical physics. We can always imagine that the world of our experience is embedded in a larger structure consisting of infinitely many such worlds, which do not interact with each other (at least not into the future). Indeed, we can imagine this in infinitely many ways. One can argue that quantum mechanics is more suggestive of such an embedding than some other – past, and possibly future – theories, but it's always possible to construct an MWI of any theory. Obviously the details of any specific MWI would change if the details of the underlying experiential theory changed, but it would still be a MWI. I don't think MWI is falsifiable as an abstract concept.

Also, according to your statement, Salviati, the problem with MWI is that although not presently falsified it is overly exposed to falsification. Even if that were true (which it isn’t), it would be a virtue rather than a weakness. The strongest theory is the one most exposed to falsification that has not yet been falsified. For example, special relativity is more exposed to falsification than Lorentz's ether interpretation, as a conceptual framework for physics, which is why special relativity is regarded as a stronger (better) framework. The spacetime interpretation has less flexibility than an ether interpretation, and yet is has never (yet) failed. I would say the problem with MWI (well, one of the problems) is not that it's overly falsifiable, but to the contrary that it's not falsifiable at all. (This isn't the most serious problem with MWI, but it's still serious.)

Salviati:  I wasn't aware that special relativity was more easily falsified than Lorentz’s Ether Theory, because they both make all the same predictions. I felt special relativity was favored more on Occam's razor-- if you don't need an aether, why have one? But if special relativity was proved wrong, and there is an "aether frame", then Lorentz' version would be wrong too.

Sagredo:  It’s true that the Lorentzian ether interpretation and the spacetime interpretation are empirically equivalent for all presently known phenomena, but they stand differently in regard to falsifiability in the face of any future phenomena that might be discovered. In the etheristic interpretation, Lorentz invariance represents a large number of independent coincidental facts: electromagnetism happens to be Lorentz invariant, the strong nuclear force happens to be Lorentz invariant, mechanical inertia of every known elementary particle happens to be Lorentz invariant, and so on. There is no conceptual link between these (once the electromagnetic view of the world was ruled out), so for any new class of phenomena that might be discovered, the ether interpretation really gives no warrant to believe it would be Lorentz invariant. The ether can be given whatever properties it needs to conform to any new facts. Indeed this was Lorentz’s professed reason for continuing to prefer his interpretation. He said we shouldn’t relinquish the language of an absolute rest frame, because we might need it some day. In contrast, the spacetime interpretation takes all those coincidences and removes them from the individual phenomena, and accounts for them in terms of the Minkowskian structure of spacetime itself. In this interpretation, any new particle or interaction that might be discovered tomorrow is constrained to be (at least locally) Lorentz invariant. The only way the spacetime interpretation is viable is if (local) Lorentz invariance is universal and complete. If it fails for any phenomenon, then the single unified spacetime interpretation fails, and we must go back to treating the Lorentz invariance (or lack thereof) of each phenomena as an independent fact, as it is in the ether interpretation. It’s in this sense that the spacetime interpretation is much more exposed to falsifiability than is the etheristic interpretation. Think of all the new phenomena, interactions, and particles that have been discovered subsequent to 1905, not to mention the increase in the range of parameters explored by experiment. Any one of these new classes of phenomena or observations might have been found to violate (local) Lorentz invariance (think CERN neutrinos...) and rendered the spacetime interpretation unviable, but none of them did – not even the entanglement aspects of quantum mechanics. But the Lorentzian framework would not have been invalidated by whatever might have been found.

The question of whether we insist that our current theory is precisely correct, or whether we acknowledge that our current theory may be subject to future revision, is separate from the question of whether a many-worlds interpretation is useful or sensible. I think the espousal of MWI doesn’t necessarily commit someone to the position that the postulates of quantum mechanics are precisely correct, nor does it imply that they would have to abandon MWI if/when the postulates of quantum mechanics were revised. (As noted above, we already know that the postulates of quantum mechanics are actually not correct, since it is not relativistic, but I presume you would make the same arguments for quantum field theory.)

Salviati:  Since MWI is never falsifiable, it is only the motivation for it that is falsifiable (the aesthetic structure of the postulates).

Sagredo:  Well, if the experiential theory (in this case, quantum mechanics) changes, it is conceivable that the revised theory might give people less – or more – motivation to think in terms of MWI. For example, David Deutch thinks we could perceive the other worlds after all, and he would take this as proof of the reality of the many worlds. This would entail a revision of quantum mechanics, but would actually (according to Deutsch) increase our motivation for MWI. Of course, one could also imagine changes to quantum mechanics that would make MWI seem less plausible. So the fact that the postulates of quantum mechanics (or quantum field theory) might be revised at some point doesn’t really argue unequivocally either way, for or against MWI, because as a conceptual framework it has none of the rigidity of, say, the spacetime interpretation of special relativity. It is much more akin to an ether theory, that could accommodate any set of observations.

Salviati:  Deutsch’s position is not entirely clear to me. He apparently contends that the many worlds are not being continuously split, but if so, how is unitarity preserved?  Maybe "split" is the wrong word, and "sub-sectioned" would be more suitable, but most people would consider those to be synonymous.

Sagredo:  I believe Deutsch prefers the word "partitioned". He imagines a fixed (albeit possibly infinite) number of worlds, none being created or destroyed, and at any given time they are partitioned into equivalence classes of identical worlds, but these equivalence classes are re-shuffled, so two worlds that were equivalent before are not any more, and two worlds that used to be distinct can merge and become equivalent. So he imagines a constant re-partitioning of these worlds into these equivalence classes.

Salviati:  By the way, Sagredo, what is the "theory" that Deutsch refers to?  I was not aware that MWI was a theory distinct from quantum mechanics.  Is there a suggestion of some kind of new prediction being generated?

Sagredo:  Yes, Deutsch argues (or at least he has in the past) that in fact a sufficiently sensitive observer actually would perceive a superposition of states, because the worlds merge back together sometimes. He has suggested that this could be tested by some kind of artificial intelligence machine that is more sensitive to subtle memories than are humans. There is some irony in the fact that a prominent proponent of MWI essentially agrees with all the past critics of MWI who always argued that an observer should see a superposition of states. What then becomes of all the iron-clad arguments of the other MWI proponents who claim that only an idiot would think that MWI implies the possible perception of superpositions?

In essence, Deutsch has argued that observers (and universes) not only proliferate, they must also re-aggregate, and hence it is possible in principle for an observer to remember a superposition of histories. So there are versions of MWI that are compatible with observers perceiving superpositions, and there are versions of MWI that are compatible with observers not perceiving superpositions. In a playful spirit we might invoke a Many Many Worlds Interpretation (MMWI), according to which the universe is actually a superposition of Many Worlds's, in some of which the identities re-aggregate and in some of which they do not.

Salviati:  Let’s be serious, Sagredo.  Returning to your earlier point, it’s very hard to say just what it is exactly about quantum mechanics that supports an MWI approach, when no other theory ever did.

Sagredo:  I agree that it’s interesting to consider what motivates the MWI approach, and whether some experiential theories give more motivation than others, or if it is just an accident of fashion. Throughout history, people have contemplated the notion that the world of our experience is just one of many “possible worlds”, along with the ancient idea that every mathematical form has physical meaning. Ideas like this have been around forever. Leibniz discussed what sounded a lot like the principle of least action (which corresponded to the “Born rule” in quantum mechanics), asserting that we live in “the best of all possible worlds”, which is quite similar to how many modern advocates of MWI conceive of things, i.e., possible worlds rather than actual worlds.

The notion of multiple possible worlds (and counterfactual definiteness, etc) arises in any theory based on differential equations. Newton and his contemporaries were acutely aware of this “deficiency” in any such theory, and some even argued that Newton’s “mathematical principles” were non-scientific and vacuous, complaining that a theory such as Newton’s tells us nothing that is not already implicit in the initial conditions, which must be put in by hand. It’s difficult for us to grasp this today, but when the idea of a differential equation representing a physical theory was new, it was not immediately accepted as a valuable or meaningful way of thinking about nature. The equations of Newtonian mechanics may be said to imply a giant phase space, within which our universe is represented by a single trajectory, so it is a superb descriptive tool, but the theory doesn’t tell us which trajectory in this enormous phase space is the trajectory of the universe, which is what many people regarded as the main task of a theory of natural philosophy. In Newton’s theory we have to specify a full set of initial conditions, sufficient to fully define everything of interest (per Laplace’s vision of determinism). This specification provides nearly all the information of the theory, and yet it is purely ad hoc and separate from the differential equations that supposedly define the theory. This could easily lead someone to eschew the task of specifying the trajectory, and simply take the equations themselves as the entire theory, which entails all possible trajectories within the phase space. This certainly yields a more symmetrical and less ad hoc interpretation... but it's also sterile and pointless.

Salviati:  It’s true that we encountered lack of complete information in theories before quantum mechanics (such as in thermodynamics), but I think it was the discovery of a fundamental limit on information, Heisenberg’s uncertainty principle, that is the real source of MWI.

Sagredo:  I agree that the inherent uncertainty in quantum mechanics is what leads to the extra motivation for MWI. The key difference between Newtonian mechanics and quantum mechanics (for motivating MWI) is that in Newtonian mechanics the equations of motion range only over the set of observable states, so there is no ambiguity when translating from the variables in the equations to the measures of our experience, whereas in quantum mechanics the equations of motion range over the set of superpositions of observable states. People tried hard to avoid this, and to come up with equations that range only over observable states, but eventually it came to be seen as an impossible task. Quantum phenomena apparently cannot be modeled effectively except by equations that range over superpositions of observable states. This means that an extra step is required when going from the variables of the equations of motion to an actual observed outcome. This is the “collapse of the wave function”, in accord with the Born rule, and the special challenge for interpreting quantum mechanics is how to conceive of this extra step, selecting just one trajectory through phase space, and calling it our trajectory.

But this is not really as different as it might seem from the extra step that is required in Newtonian clockwork mechanics, i.e., the stipulation of initial conditions, which essentially represents a collapse from the set of all possible trajectories down to the single trajectory that we experience. The difference is that Newtonian mechanics requires only one “collapse” step, because for any given exact specification of the state, the equations of motion give exact specifications of all subsequent (and prior!) observable states. Hence we never need to repeat the collapse step, and we can set aside the single collapse step and not worry about it too much. In contrast, because of the inherent uncertainty in quantum mechanics, after stipulating an initial state, the equations of motion lead to a superposition, and even if we stipulate an observation and update our state, the equations of motion again lead to a superposition, and so on. Thus we encounter the need for collapse repeatedly, making it more difficult to ignore. But it isn’t a qualitative difference, it’s just a quantitative difference, relative to the collapse required in Newtonian mechanics.

Ultimately I think a MWI is no more useful for quantum mechanics than it is for Newtonian mechanics. We can always imagine that the world of our experience is embedded in a larger structure of other worlds, but if this imagined embedding doesn’t tell us anything new about the world of our experience, then it’s pointless.

Salviati:  Perhaps so, but I don’t think being pointless (in that sense) is enough to cause any MWI advocate to lose faith. On the other hand, if unitarity were broken in observations, I think the rationalists in the MWI camp would jump ship immediately. But broken unitarity wouldn’t both adherents of the Copenhagen Interpretation, because they already think unitarity is broken in the act of perception.

Sagredo:  I think we agree that, at least from an empiricist standpoint, unitarity is already abundantly falsified, and yet this doesn't cause anyone to jump ship. It’s not easy to imagine what additional observations could possibly “break unitarity” for those who - in the face of all the empirical evidence to the contrary - have adopted unitarity as a first principle, and who are willing to posit an infinity of unobservable worlds in order to preserve it.

Maybe you have in mind the idea that the part of quantum mechanics presently believed by everyone to be unitary – namely, the Schrödinger evolution - might be found to fail, and need to be modified in such a way that the state evolution was no longer precisely unitary, and you think such a “change of postulates” threatens the motivation for MWI. Without knowing the details of the hypothetical modification, it’s hard to comment on how it would affect people’s enthusiasm for MWI. However, bear in mind that the quo ante postulates of quantum mechanics already included the non-unitary projection postulate, which was included to match observations, but this didn’t prevent MWI advocates from simply claiming we can do without it – even though from an empirical standpoint we obviously can’t.

Regardless of our observations, one can always bifurcate our theory into a unitary part and a non-unitary part (as we do in traditional quantum mechanics), and then someone who adopts unitarity as a first principle can rationalize away the non-unitary part (as the MWI advocate does for quantum mechanics), with the understanding that the “unitarity” applies only to some posited unobservable meta-world in which the world of our experience is embedded as just an infinitesimal and non-unitary part. But this is silly. Suppose the conservation of momentum was found to be violated in physics, but nevertheless we really like the principle of momentum conservation, so we ‘preserve it’ by saying that objects sometimes exchange momentum with unobservable objects from other parallel universes, so in the overall meta-universe, including these other parallel universes, we have conservation of momentum! Obviously no observation can “break conservation of momentum” for us if we are willing to invoke other worlds like this, but just as obviously this method of maintaining momentum conservation would be absurd. The same applies to the “unitarity” of MWI. (As an aside, in the early 1900s Poincare and Lorentz actually did discuss the prospect of needing to invoke interactions with an unobservable entity in order to maintain conservation of momentum according to the ether interpretation of electrodynamics.)

But I would say this is all somewhat of a red herring, since it is tangential to the main issues.

Salviati:  I don't think MWI-enthusiasts are attracted to MWI because of its many-worlds element, which you are quite right they could preserve in any theory.  They only like it because of the simplicity and generality of the unitarity postulate, and the many worlds just come along for the ride.

Sagredo:  I think you were nearer the truth in your previous comment, when we agreed the main motivation (at least technically) for MWI in quantum mechanics is the uncertainty principle and its consequences, not a yearning for unitarity per se. If some new phenomena came to light, violating existing quantum mechanics, and people decided the best way fix the theory was to modify the Schrödinger equation to make it non-unitary (rather than modifying the Born rule or the projection postulate, which I think is what would actually happen, but never mind), would this necessarily invalidate the uncertainty principle, eliminate the fundamental quantum of action (h=0), or make all observables commute? Unless we do all these things, we will still have a theory that entails some kind of “state reduction” or "collapse" in the mapping from the variables in the Schrödinger equation to the measures of our experience, and it is the desire to rationalize the palpable non-classical features of this "collapse" - rather than a yearning for unitarity as an abstract nicety - that motivates MWI (over and above the motivation that already exists for non-quantum theories).

Admittedly I have no idea what a revised quantum mechanics with a non-unitary Schrödinger equation would look like. Maybe it really would eliminate uncertainty and imply that all observables commute (perhaps on some deep level that isn’t readily perceivable), in which case we're just back to something like the Newtonian theory… but I have a hard time imagining such a theory accounting for all observations, and even in that case there would still be motive and opportunity to commit MWI – just as there is for Newtonian mechanics.

So, I still think over-exposure to falsification is not a problem of MWI. In fact, quite the opposite, on both counts. Exposure to falsification is good, but MWI doesn’t have any.

The main problem with MWI is that it would be sterile and pointless, even it succeeded in giving a satisfactory account of observations – which it doesn’t. To illustrate that, recall a previous comment of yours, when you said

One universe fragments more and more with time (by "fragment" I mean "spawns incoherent islands that have no further influence on each other"). So it's rather like a river forking over and over-- it still all traces back to the same upstream watershed.

That’s a fairly typical prosaic description of MWI, but there are problems. To give just one example, remember that Schrödinger’s equation is time-symmetrical, and yet you say that (according to MWI) the universe evolving according to this equation “fragments more and more with time”. In which direction does this fragmenting increase? Shouldn’t we actually have worlds fusing back together just as much as we have them fragmenting? But then a given stream would be fed by infinitely many different pasts, as well as fragmenting into infinitely many different futures. This has led some prominent MWI advocates to adopt the view that the number of self-coherent worlds is actually constant, and they just are partitioned into shifting equivalence classes. Our lack of awareness of the many futures of our current equivalence class of worlds may be explained away by noting that we aren’t aware of our futures (for some reason), but surely we are aware of our past. Indeed, some MWI advocates (e.g., Deutsch) contend that MWI implies it actually is possible for an observer to gain awareness of their multiple, mutually exclusive, histories.

One might argue that it’s unfair to expect MWI to resolve the “arrow of time” problem, because it is also an open problem for other interpretations, but I would answer that it is an especially acute problem for MWI, because without a clear and explicit resolution of the arrow problem, we can’t even really say that MWI gives any intelligible account of observations at all. It relies fundamentally on time-asymmetrical proliferation – at least in its standard formulations. Thus MWI isn’t really an interpretation of quantum mechanics, it is (at best) an idea for an interpretation of quantum mechanics.

Salviati:  I would say we are like an ant floating on a log that takes, seemingly at random, a certain fork each time, but the rest of the river is still there, and all branches share a consistent history up until they forked off.

Sagredo:  Careful with the ant and the log there Salviati.  You are smuggling in the very dualism that MWI seeks to exclude on principle. According to MWI, there is no log or ant, there is only water. You are nothing but one particular streamline in the flow. I realize this is inconsistent with your concept of empiricism, which is wedded to dualism, but that's precisely what MWI most vehemently denies. The main motivation for MWI isn't a yearning for unitarity, it is an abhorrence of dualism (which of course underlies the kind of empiricism that you've described).

Salviati:  One doesn't "disagree" with an interpretation, one cites reasons for "preferring" a different one, which largely amounts to identifying philosophical priorities. Or one criticizes elevating an interpretation to something more than an interpretation...

Sagredo:  There's another possibility: One points out that what is claimed to be an interpretation of a given theory is really no such thing. For example, if I claim that my dog Smithers is an interpretation of quantum mechanics, i.e., that Smithers gives predictions identical with those of quantum mechanics, etc., you are not limited to simply citing reasons for preferring a different interpretation. You are also free to question whether Smithers really does constitute an intelligible interpretation of quantum mechanics. I tell you that Smithers entails (so to speak) a certain quantum wave function, and that somehow if you look at the Smithers wave function - or some projection of it - in just the right way, and squint a little, and defocus your eyes, you can see all physical reality by some kind of implication (or interpolation or extrapolation), but, again, you are free to dispute my claims, and to point out why Smithers cannot reasonably be regarded as a meaningful interpretation of quantum mechanics. This is the situation with MWI. On its face, it does not give an intelligible account of the world of our experience. As John Bell said, when you examine it closely, you find that it is not coherent (so to speak).

So, although I think you've expressed some valid views about the tension between rationalism and empiricism, and about the hazards of thinking our current rationalizations are the ultimate ones, etc., I would say that to some extent they are wasted on a consideration of MWI, because the real problem with MWI is that it isn't really an interpretation of quantum mechanics; at best it is just an idea for an interpretation - and not a successful one. That's what forces its believers to continue modifying it, trying to somehow shape it into something that could genuinely be called an interpretation of quantum mechanics. And that's why its critics continue to point out that, at the very least, something more would be needed before one could even claim that MWI is an interpretation of quantum mechanics.

Salviati:  Sure [i.e., one obviously can argue that a purported interpretation is incorrect, meaning it is not a valid or viable interpretation of the theory it claims to represent], but that's much more difficult, and must be held to a higher standard of proof.

Sagredo:  I don’t see the issue as involving different standards of proof. The burden of proof for any proposed interpretation of a physical theory is on the proposers to show that their idea actually represents a coherent and viable interpretation of the theory. This means they must show explicitly how the observable measures of the theory correspond to the terms of the interpretation (model). No proponent of any of the mutually exclusive versions of MWI has ever succeeded in showing this – at least not to the satisfaction of anyone other than himself.

Salviati:  How can an interpretation be incorrect if a physicist is not led to doing incorrect calculations by employing that interpretation to motivate those calculations? What incorrect calculation does MWI motivate?

Sagredo:  Anyone who espouses any one of the mutually exclusive versions of MWI can explain to you why each of the other versions “motivates incorrect calculations”. For example, read Deutsch on why he believes Everett was wrong to think unitary evolution of the wave function, all by itself, represents a viable interpretation of quantum mechanics, i.e., it cannot serve as a legitimate basis for correct calculations. He says MWI needs something more, an additional mathematical structure to “provide the connection between the wave function and the concept of the many parallel universes.” Note, however, that when, earlier in this thread, I outlined for you the extra mathematical structure that this particular advocate of MWI thinks is necessary to turn MWI into a viable interpretation that motivates correct calculations, you responded with something like “Well, that is obviously not a viable interpretation of quantum mechanics!”. And you were correct … but the point is that Deutsch is also correct in his conclusion that MWI without that extra structure is not a viable interpretation. There is no interpretation of MWI that motivates correct calculations.

Of course, those who advocate some version of MWI may be capable of performing correct calculations, but those calculations are not warranted (“motivated”) by their version of MWI. If they adhered strictly to MWI, they would be unable to correctly calculate anything connected with the observables of our experience in accord with quantum mechanics.

The problem is that, above a certain complexity, there are no effectively closed systems smaller than the entire universe, and no MWI advocate can tell you the Hamiltonian of the universe, nor even what such a thing could possibly look like, even in principle, since a Hamiltonian is sui generis an external constraint of some kind. And even if they could provide the Hamiltonian of the universe (of a form that doesn’t violate their own premises), and even if they could provide plausible initial conditions, they would face the problem Deutsch mentioned, about not having the structure to actually define how “any individual universe in the vast stack of cosmic alternatives fits into the stack”, which immediately leads to problems like temporal symmetry: How can we claim that unitary evolution (under the unknown and unknowable Hamiltonian of the universe from some unknown and unknowable initial conditions) leads to “splitting” or “differentiating” or “re-shuffling” of self-consistent universes in one time direction but not in the other? Or if we accept that unitary evolution must be time-symmetrical, how can we reconcile with our experience and with quantum mechanics the re-converging of universes that this entails? (This is the point that led you to baulk previously.) And of course the Born rule is external to unitary evolution, etc. The point is that MWI is very far from being an intelligible interpretation of quantum mechanics, and it certainly doesn’t warrant any correct calculations at all.

Salviati:  I disagree Sagredo.  MWI merely asserts that all closed systems must evolve according to the Schrödinger equation. MWI is the sole interpretation which allows that to be a complete description.

Sagredo:  But unitary evolution according to the Schrödinger equation does not, by itself, constitute an interpretation of quantum mechanics. At the very least, some additional structure would be needed in order to establish a viable mapping from the wave function to the measures of our experience in accord with quantum mechanics – and it is far from clear that any such approach could ever work. If someone orders a statue of David, you cannot simply deliver a block of marble and say “It’s in there”. As John Bell said “the many universes interpretation is a kind of heuristic, simplified theory, which people have done on the backs of envelopes but haven’t really thought through. When you do try to think it though it is not coherent.” He was not talking about philosophical priorities, he was saying MWI does not represent a coherent interpretation on a technical level.

Salviati:  To say MWI is an invalid interpretation is identical with claiming that it is invalid to imagine that a complete description of closed systems evolution could be given by the Schrödinger equation without any additional bells and whistles like pilot waves or empirical perceptions of collapse.

Sagredo:  Right. It is invalid to imagine that a complete description of closed systems evolution – consistent with the quantum mechanical account – could be given by the Schrödinger equation without any additional bells and whistles. Even most advocates of MWI (who have thought about it carefully) agree with this. And of course it’s also invalid to imagine any closed systems containing a physicist and smaller than the entire universe. (I choose the measurement angle of my Stern-Gerlach device today based on my memory of a constellation my grandfather pointed out to me in the night sky when I was a little boy.)

Salviati:  But you have not supported your claim here....

Sagredo:  Let me try to explain more succinctly what I mean. At issue is the claim that every isolated system can be modeled as nothing but a quantum wave function represented by a state vector in some suitable Hilbert space, evolving in accord with Schrödinger’s equation for some suitable Hamiltonian and initial conditions, and that this model, with no additional axioms, yields all the empirical content of quantum mechanics. I say this claim is false, because (among other reasons) all the measurement correlations predicted by quantum mechanics correspond to one particular definition of the “measure” of a state, but there is nothing in the single axiom of Schrödinger evolution that warrants any physical meaning for this particular measure. So, at the very least, some further axiom or principle is needed in order to actually have a viable interpretation of quantum mechanics.

Now, you may agree or disagree with this objection, but hopefully you at least agree that it isn’t a question of philosophical preferences (except in the sense that reason itself is a philosophical preference). It is an objection to the validity of the claim that the single axiom of Schrödinger evolution of a wave function for isolated systems is sufficient to constitute an interpretation of quantum mechanics. You can explain why you disagree with the objection, or you can agree with the objection and offer some additional axiom(s) in the hopes of arriving at a genuine interpretation of quantum mechanics, but in the latter case you commit yourself to defending the additional axiom(s). (There are problems with all such supplementary axioms that I’ve ever seen.) But what you can’t do, I think, is claim that this is all just arguing about philosophical priorities.

Salviati:  I actually do think it is just a philosophical preference-- it is the preference that a physics theory should describe a true mathematical ontology, rather than the "empirical content" of that same theory.

Sagredo:  I think we've isolated the basic difference in our views. I differ with your above statement on two counts. First, essentially as a matter of definition, I think that in order for a conceptual model to qualify as an interpretation of a physical theory, it must establish an explicit and unambiguous mapping from the elements/features of the model to the empirical content of the theory. Your definition of "interpretation" is based just on the ontological elements, which I'll discuss below, but I really don't think that's a valid definition of a physical interpretation, because models could have the same ontology but different empirical behavior, and we surely wouldn't say they were interpretations of the same theory.

I think we agree that the hypothesis of Schrödinger evolution for isolated systems doesn't constitute an interpretation under my definition of "interpretation", in the sense of providing a mapping to the empirical content of a theory, although you believe this can be repaired by simply adding the Born rule. But that doesn't really establish the mapping, for the following reason.

Let V(t) denote the state vector of the overall universe, existing within the Hilbert space S, and let v(t) denote the state of the sub-world that we experience. The MWI tells us that at any given time t, our sub-world vector v is some kind of projection of V into a certain sub-space s, and it also tells us that the system described by v is perfectly isolated (going forward in time), so it's future evolution is, by hypothesis, also governed by the Schrödinger equation, as is the future evolution of V. The problem is that s cannot be constant if v is going to consistently represent the world of our experience over time, and if both V and v are evolving unitarily according to Schrödinger’s equation.

In other words, if the world of our experience is going to be represented in MWI by a projection from the universal Hilbert space S down to some sub-space s, then s must be continually evolving. So, in order to say explicitly how the world of our experience corresponds to the elements of the MW model (which is the bare minimum requirement for a model to qualify as an interpretation), we need not only the rule for the evolution of V and v, we also need the rule for the evolution of s (and perhaps S, depending on how you conceive of the Hamiltonian of the entire universe, which is really a "one hand clapping" concept already, but never mind...) And the rule for the evolution of s is essentially none other than the CI or something similar. So the axioms of a viable MWI, augmented to the point of actually being a genuine interpretation, are not a subset of the axioms of CI, they are a superset.

Even if we restrict ourselves to just considering the ontology, I would say that without the rule for the evolution of s, the MWI cannot rightly claim to even represent a meaningful ontology consistent with quantum mechanics. It's the same as claiming that ontologically Michelangelo's statue of David is contained in a giant block of stone. Sure, a certain subset s of the stone S is in the shape of David, but there is nothing about the stone itself that represents this - or any other - subset. If you ask for a statue of David, and I deliver to you a billion statues, one of which is of David, I can rightly claim to have delivered what was requested (along with much that was not requested). But if I just deliver to you a single giant block of stone, it is a different situation. This is basically why people like Dewitt felt the need to talk about actual splitting of universes into multiple distinct versions (statues), because they recognized the conceptual deficiency of arguing that all the worlds are merely implicit as all possible subsets of a giant block. This is not an ontology that includes David in any meaningful sense. But of course if we follow Dewitt with his actually proliferating statues, we encounter other problems. That's why I say I'm not aware of any viable MWI - aside from the trivial one that postulates CI and then advises us to embed all possible outcomes into a superstructure whose overall shape (unitary) we find more pleasing.

Simplicius:  If I may interject, note that, in general, the state of a subsystem can't be written as a vector in Hilbert space but only as a density operator.

Sagredo:  The hypothesis in question, Simplicius, is that every isolated system (which may be a sub-system of some larger system) undergoes unitary evolution in accord with Schrödinger’s equation - and nothing else. Whether it is represented by a single vector in some suitable space, or as a linear combination of vectors, it must be expressible in some form that can undergo unitary evolution under the Schrödinger equation, or else the hypothesis is false. If you say an isolated subsystem cannot be represented in this way, then you are denying the hypothesis. I'm denying the hypothesis too, although for a slightly different (but related) reason.

Simplicius:  I'm not very familiar with the MWI, but this doesn't sound right. Decoherence only occurs when there are interactions with the environment. Since MWI uses decoherence to explain collapse, it certainly doesn't assume the subsystem of "the world of our experience" to be isolated.

Sagredo:  According to the usual version of MWI (excluding those that introduce anti-measurements and re-converging worlds, making them empirically distinguishable from ordinary quantum mechanics), each new branch never interacts with any of the other branches, so it's a completely isolated system. Decoherence is part of ordinary quantum mechanics. It doesn't imply that the branching worlds of MWI interact with each other... in fact, just the opposite, it explains why they don't. When people talk about "interactions with the environment", they are explaining how the elements of a single sub-world become entangled with each other, so the universe gets partitioned into self-coherent islands of mutually entangled features. This does not refer to interactions between those islands.

Salviati:  There are certainly some subtle points here. If you look at a MWI-favoring physicist doing a quantum mechanics calculation, you are not going to be able to tell they hold to MWI, because MWI proponents don't shun the Born rule, they use it just like everyone else.

Sagredo:  But by dealing with apparently classical outcomes and using the Born rule to compute the probabilities of those outcomes they are not holding to MWI, because according to MWI they should really be making decoherence calculations on the wave function of an entire isolated system including both the experimental subject and the observer, with the suitable Hamiltonian for this whole isolated system (which, for the reasons explained before, can hardly be smaller than the entire universe), and at best this will lead only to approximately classical outcomes, so the application of the Born rule to the results of this hypothetical calculation, even if it could be carried out, would be inherently ambiguous... But of course no one has ever made such a calculation, and of course no one ever will, and they have never offered more than hand-wavy plausibility arguments that they ever could do such a calculation, even in principle.

The point is that just because someone who espouses (some version of) MWI avails himself of the calculational recipes of ordinary quantum mechanics, it doesn't follow that his calculations really are consistent with his philosophical beliefs. This consistency needs to be established. Much ink has been spent by people trying to establish this, and making adjustments to their conceptions of MWI in order to help establish this, but there are deep and subtle issues involving the concept of a wave function and Hamiltonian of the entire universe (for example), the arrow of time, etc., not to mention the fact that we know Schrödinger’s equation is wrong, because it isn't relativistic, so we're led to consider quantum field theory, which has its own issues. You may choose to carry on your philosophical considerations based on the assumption that some version of MWI actually is consistent with quantum mechanics, but this is far from having been established.

Salviati:  I have to correct one thing you said, Sagredo. The "worlds" of MWI are not evolving unitarily. If they did, we wouldn't need MWI at all!

Sagredo:  What I mean is that at some instant t there is a self-consistent subworld described by v that branches off into isolation from all the rest of the universe. Now, v immediately can be regarded as splitting into sub-sub-worlds v₁, v₂, v₃..., and each of those splits into sub-sub-sub-worlds such as v_2a, v_2b, v_2c,..., and each of those splits into worlds such as v_2b1, v_2b2, v_2b3,... But the point is that these are all constituents of the isolated system v, which does not interact with anything else. The isolated system v(t), by your hypothesis, can be modeled by unitary evolution according to the Schrödinger equation in some suitable Hilbert space with some suitable Hamiltonian and initial conditions. All the sub-sub-worlds that it spawns within itself are, according to MWI, implicit within the unitarily evolving wave function v(t).

Now, according to MWI, the state v(t₁) at some time t₁ is some projection from the universal wave function V(t₁) in the universal Hilbert space S down into some subspace s, and of course by making this projection we gloss things and would arrive at a mixed state for the subsystem, but thereafter that subsystem is isolated, so according to your hypothesis it undergoes unitary evolution thereafter, within some suitable Hilbert space s with suitable... etc.

But of course the world we experience at a sequence of times t₁, t₂, t₃, t₄... is not v(t₁), v(t₂), v(t₃), v(t₄)..., it is something like v(t₁), v₂(t₂), v_2b(t₃), v_2b1(t₄),... and so on. Obviously this sequence of worlds is not evolving in a unitary way (viewed by itself), but the point is that the projections from the universal wave function V(t) (which is evolving in a unitary way) down to each of these instantaneous worlds cannot be going to the same subspace s, they must be projections to a sequence of sub-spaces s, s₂, s_2b, s_2b1,... so in order to place the terms of the MWI model into explicit correspondence with the measures of our experience in accord with quantum mechanics, we need more than just the Schrödinger rule for evolving isolated systems, we also need the rule for evolving the projection subspaces... and this is much more than just the Born rule for assigning probabilities, we need the rule to define the (approximate) subspaces to which the Born rule is applied. Explicitly defining this sequence of subspaces is what the projection postulate in ordinary quantum mechanics does, on a piece-meal basis.

Salviati:  I contend that MWI is not mechanically different from CI, even if some practitioners hoped to find a way to make it so.

Sagredo:  I don't agree. MWI actually is mechanically different from CI, for the reasons explained above (e.g., CI has classical entities, whereas MWI has only approximately classical entities, even according to the hand-wavy defenses of it). Now, I personally don't think CI is free of conceptual difficulties either. But I would say that CI comes closer to being a legitimate interpretation of quantum mechanics than does MWI, probably because CI is really not too far removed from just shutting up and calculating.

Simplicius:  If you’ll permit me to interject again, I’d like to point out that the cause of decoherence is interactions with the environment.

Sagredo:  Well, interactions with the environment lead to entanglement and coherence (not decoherence) of the elements of an individual sub-world. Each projection of some entity becomes inextricably entangled with it's own environment (including a version of the scientists that observed it), so we get these islands of coherence, and these islands tend to quickly decohere from each other, meaning they do not interact with each other, but of course they are all still just components of a single unitarily evolving universal wave function.

Simplicius:  For a system in isolation there is no splitting. If v splits it is not isolated.

Sagredo:  But the universe is an isolated system, so according to you there is no splitting, and MWI is impossible. Is this the point you are trying to make, Simplicius?

Simplicius:  If you omit the "and MWI is impossible" yes, this is one of the points I'm trying to make. Maybe this seems nonsensical to you...

Sagredo:  Yes, I'm afraid it does. According to the "many worlds interpretation", the overall universal wave function is continually evolving into more and more proliferating self-consistent "worlds". You've stated that, since the universe is an isolated system, no such "splitting" of the overall universe into self-consistent sub-worlds can possibly occur. The obvious implication is that MWI is impossible, but you deny this implication... so I don't understand you at all.

Salviati:  Getting back to our line of discussion, Sagredo, you seem to be saying that anyone who claims to have an interpretation must make a demonstrable link from their interpretation to the equations they are using...

Sagredo:  Yes, in order for a conceptual model to qualify as an interpretation of a theory, we must establish a clear correspondence between the elements and features of the model and the empirical content of the theory, which is generally expressed in mathematical terms. I wouldn’t have thought this was controversial.

Salviati:  I actually don't think any interpretation in the history of physics can satisfy that demand... If I interpret forces as real but action as a mathematical trick, according to your stated criteria, I could never use a Lagrangian approach to calculate a constraint force...

Sagredo:  My criterion didn't say anything about "real" or "mathematical tricks". The issue isn't about ontology. We're free to use whatever mathematical tricks we wish... but they must correspond in some definite way to the features of our conceptual model in order for that model to qualify as an interpretation of the theory. For example, there is no difficulty translating between a force/vector formulation of mechanics to a Lagrangian formulation. This is a perfectly well defined correspondence. No problem at all. But there is a problem with an advocate of MWI using the von Neumann recipe for quantum mechanics, because he lacks a well-defined correspondence between the features of the conceptual model and the mathematical methods. Now, there is a mathematical formalism based on the axioms of MWI, and it consists of the Schrödinger equation applied to a universal wave function with some universal Hamiltonian and initial conditions. So hopefully we agree that an advocate of MWI is entitled to make that kind of calculation. But they never do. Instead, they use the von Neumann recipe, and they justify this use by claiming that the mathematics associated with their model reduces to the von Neumann recipe (at least for all practical purposes). But does it?

We have two mathematical formalisms, and a claim that one entails the other. This is easy to confirm in the case of force/vectors versus Lagrangian, but not nearly so easy to confirm for the mathematics of MWI and CI. We lack any demonstration that the axioms of MWI (whichever version you prefer) actually do lead to the von Neumann recipe, even just "for all practical purposes". This is why so many volumes have been filled by people striving to establish that correspondence, or at least to make it more plausible. I get the impression that you would advise them to stop wasting their time, because you think it has already been sufficiently established. But I suspect that even most advocates of MWI would not agree with that, and certainly the critics would not agree.

Salviati:  I feel the actual standard we should hold interpretations to needs to be much looser-- they need to give us a sense that we understand the meaning of the operations we are carrying out.

Sagredo:  Actually I agree with your standard, i.e., an interpretation needs to "give us a sense that we understand the meanings of the operations we are carrying out". That's essentially a paraphrase of my criterion. I think we differ only in having different ideas about what it takes to "give us a sense that we understand" something. For me, I don't have that sense unless I can see how the terms of my equations correspond to the features of the conceptual model in some definite way. You, on the other hand, get the sense that you understand the meanings of the operations in terms of the model, even in the absence of a clear correspondence between those terms and the model. To me, that’s a contradiction.

Salviati:  But it certainly isn't fair to drop any of those things on the doorstep of MWI, because they all fall on the doorstep of any interpretation of non-relativistic quantum mechanics.

Sagredo:  Yes, I only mention it to emphasize that the task of reconciling the MWI model with our actual computational physics is even more challenging than just the non-relativistic version might suggest, so we are very far from being able to really justify MWI as a viable model. Also, the transition to relativistic theory has important implications for the arrow-of-time problem that besets MWI, and it can’t really even be addressed in a non-relativistic context.

Salviati:  Actually, I don't think there is a requirement for the subsystem v to not interact with anything else, the sole requirement is that it not interact with anything else in a way that leaves a signature or trace.

Sagredo:  So if v does not interact with anything in a way that leaves a signature or trace, is that a strong enough condition to say that v(t) evolves in accord with Schrödinger’s equation? If not, wouldn’t the deviation itself constitute a signature?

Salviati:  The fundamental connection between the worlds is the maintenance of unitarity of the whole, and that might require all kinds of "interactions" between the systems, much like entanglements in the EPR paradox.

Sagredo:  True, and if we can’t regard branches as isolated systems, this tends to support the idea that the only really isolated system (containing any significant complexity), to which the hypothesis of pure Schrödinger evolution is strictly applicable, is the entire universe. This makes the task of demonstrating the correspondence with von Neumann recipes even more problematic – not to say hopeless.

Salviati:  I don't see where MWI is missing that, it uses the projection postulate just like it uses the Born rule, just like someone who doesn't think gravity is really a force can still write F=mg without making themselves some kind of liar!

Sagredo:  Well, if someone like William Kingdon Clifford, who vaguely imagined that gravity might be interpreted as curvature of space, had written F=mg and claimed that this equation was consistent with his conceptual model of gravity, he would indeed have been lying, because he could not establish that correspondence. It was Einstein’s great achievement to show – explicitly – precisely how the 4-dimensional tensor equations of his metrical theory of spacetime curvature actually do reduce to the simple Newtonian scalar equations in the lowest order approximation. Only by doing so was he able to claim that the spacetime curvature interpretation is consistent (approximately) with those simple equations.

That’s exactly what I’m saying is needed for MWI to justify the use of the simple von Neumann recipe for quantum mechanical calculations. You need to start with the wave function and Hamiltonian and initial conditions of the entire universe (none of which are knowable), and then show how the Schrödinger evolution of this wave function, taking decoherence into account, leads (at least approximately) to the time-asymmetrical behavior and empirical content represented by the von Neumann recipe.

Salviati:  All the MWI proponents are doing is parsing between what they know is an effective theory, and what they think is "actually happening".

Sagredo:  But surely we’re entitled to distinguish between actual “parsing” and mere wishful thinking. If I tell you I can parse the equations of quantum mechanics from contemplation of my dog Smithers, you would dismiss my claim out of hand – and rightly so. So you can’t maintain the position that you will accept any claim that any model represents a legitimate interpretation of any theory. You do have standards, i.e., you require some rational basis for thinking the model really is a representation of the theory.

It all comes down to what you said previously, about what it takes “to give us a sense that we understand the meaning of the operations we are carrying out”. You are convinced that if someone actually could make sense of the Hilbert space and Hamiltonian of the entire universe, and if they could somehow divine the initial conditions of a universal wave function such that, subject to the Hamiltonian under the Schrödinger equation (or, better, it’s relativistic counterpart) it leads to suitable time-asymmetric evolution, and that the result, taking decoherence into account, would yield something whose components or projections into some suitable sub-spaces, selected, combined, and arranged in some suitable order, would reduce in some approximation to the results of applying the usual recipe of quantum mechanics with the projection postulate and Born rule. To you this is sufficiently self-evident that you’re willing to take it as given. It isn’t so self-evident to me.

Salviati:  If those mathematics are different, then what is the difference?

Sagredo:  The projection postulate. According to ordinary non-relativistic quantum mechanics, a system in isolation (subject to a specified potential, etc) evolves according to the Schrödinger equation with a suitable Hamiltonian, and then a measurement of the system by an observer (say) yields an eigenvalue of the measurement operator, and the measured system jumps [projection postulate] to the corresponding eigenstate of that operator, and the probabilities of the various possible eigenvalues are given by the Born rule. Now, according to MWI, approximately this same behavior would appear to an observer if we combine the original system and the observer into a single isolated system (with suitable initial conditions, subject to specified constraints, and with the appropriate Hamiltonian) and this combined system evolves according to the Schrödinger equation, plus some form of the Born rule. But please note the word approximately, or, as Bell put it, “for all practical purposes” (FAPP). Decoherence is never complete or perfect in the unitary evolution of a wave function, whereas the von Neumann projection postulate doesn’t entail any fuzziness; it says the state after the measurement is nothing but one of the eigenstates of the measurement operator, and hence the Born rule has sharp applicability to just those precise eigenstates. This is not true in MWI, so the mathematics of MWI are not literally the same as the mathematics of ordinary quantum mechanics. The advocate of MWI just says it is close enough for all practical purposes. In other words, he is arguing that his mathematical model, consisting of applying Schrödinger’s equation to the combined system of observer & observed with suitable Hamiltonian and initial conditions, taking decoherence into account, etc., leads to predictions for the expectations of an observer that are sufficiently similar to the predictions yielded by the von Neumann recipe and the projection postulate so that we wouldn’t expect to be able to tell the difference – at least not in normal circumstances. On this basis, the believer in MWI claims the right to use the mathematical recipe of von Neumann rather than the recipe actually prescribed by MWI (which is convenient, because the latter is utterly impossible to apply in any realistic circumstance).

But there are obvious problems with the claim that the mathematics arising from the MWI model really are (even approximately) consistent with observation and ordinary quantum mechanics. It is only supported by rather vague and incomplete plausibility arguments, and references to putative isolated systems involving observers, even though any such system can hardly be smaller than the entire universe, which then leads to its own set of ambiguities. It’s far from clear that the MWI calculational prescription (the one that is actually manifest in the interpretation) could ever be carried out, even in principle. The plausibility arguments depend on viewing things within the context of some definite conditions, and then considering one little incremental (and time-asymmetrical) step being carried out according to the Schrödinger equation, and arguing that over this incremental step the divergence from ordinary quantum mechanics evident to some conception of an observer is too small to be noticed. This is already debatable, but even if one accepts this, it doesn't come close to substantiating the viability of the MWI model as a whole, because that ultimately involves the wave function of the entire universe, and needs to address all the ambiguities arising from that.

As I understand it, you deny that MWI entails any mathematical formulation distinct from ordinary quantum mechanics, but I don’t think that position is tenable (and I don’t think even the advocates of MWI would agree with you). The mathematics of MWI are clearly stated to be nothing but unitary evolution of the universal wave function, augmented if you like with something approximating the Born rule (it can’t be exactly the Born rule, for the reason explained before), but it definitely does not include the projection postulate, as already explained. Hence the mathematics of MWI are fundamentally different... but it is argued that, if we correctly account for decoherence, something closely approximating (but not identical to) the projection postulate emerges (for some suitable model of a conscious observer) from the unitary evolution of the universal wave function. But the mathematics are definitely not the same.

It really is very similar to the case of general relativity, where the metrical spacetime curvature interpretation of gravity consists of the proposition that isolated systems simply undergo geodesic motion through the spacetime manifold. People could ask “How can simple unforced geodesic motion possibly be consistent with anything resembling the observed phenomena of forced trajectories described by Newton’s laws!?”, and the task was to show that, in fact, Newton’s laws and all the observed behavior that they describe really do emerge [approximately enough for empirical viability] from the four-dimensional tensor equations describing the curved spacetime representation of events. The empirically accessible differences are so small as to be almost imperceptible in normal circumstances, so GR is deemed consistent with all the empirical success of Newton’s theory. The same task faces MWI. It needs to show that the ordinary equations of quantum mechanics really do emerge [approximately enough for empirical viability] from the Schrödinger equation description of the unitary evolution of the universal wave function. But this has never been shown, so MWI doesn’t really (at present) qualify as an interpretation of quantum mechanics. At best, it is an idea for an interpretation of quantum mechanics.

Salviati:  I think most physicists regard MWI as useless philosophical nonsense. I don't go that far.  I say it is a valid interpretation of a theory, and it only becomes useless philosophical nonsense when it is mistaken for a world view of how some behavior actually happens.

Sagredo:  Well, Salviati, I think there are two very distinct forms of MWI that often get confused. One is the "top down" MWI, and the other is the "bottom up" MWI. TopDownMWI is manifestly unitary (because that is one of its postulates), but it is very far from being manifestly consistent with the empirical content of quantum mechanics. BottomUpMWI is manifestly consistent with the empirical content of quantum mechanics (because that is one of its postulates), but it is very far from being manifestly unitary. Enthusiasts for MWI tend to think that MWI possesses both manifest unitarity and manifest consistency with the empirical content of quantum mechanics, but that isn't true. They can legitimately claim one or the other, but not both – but of course without being able to claim both, MWI is trivial and pointless.

BottonUpMWI simply stipulates all the empirical content of ordinary quantum mechanics as given by the projection postulate, etc., and then imagines that if we stitched together a sufficient multitude of possible sequences of outcomes (probably for the entire universe, since it is unclear whether any sub-systems could be truly isolated, at least for sub-systems of a certain complexity) consistent with this basis, we would arrive at an aggregate that, taken as a whole, is a unitary solution of Schrödinger’s equation for the entire universe for some suitable Hamiltonian and boundary/initial conditions. Now, this is a gigantic leap, and we have nothing like a rigorous - or even very plausible - justification for it, nor can we ever get one, because we don't (and can't) know the Hamiltonian and initial conditions of the universe.

TopDown MWI simply stipulates that the universe evolves unitarily in accord with Schrödinger’s equation, and then imagines that decoherence will somehow naturally lead to a partitioning of the wave function into essentially distinct components (worlds) within which the experience of a "person" sub-system will so closely approximate the empirical predictions of ordinary quantum mechanics that we cannot (presently, and perhaps not ever) distinguish them. Note that the mathematics of TopDown MWI are very different from the mathematics of ordinary quantum mechanics. In particularly, there is no projection postulate, there is only the Schrödinger equation, from which it is argued that something approximating the projection postulate with sufficient accuracy for all practical purposes (Bell's FAPP) would appear to some suitable model of an observer. Much effort has been put into trying to substantiate this notion, but I would argue that ultimately it can never really be fully substantiated, basically for the same reason that BottomUpMWI can never be substantiated - without being able to actually write down the Hamiltonian and suitable initial conditions for the universe, or even something as simple as a human being (!) along with a suitable model of consciousness, we can never really demonstrate the connection between unitary evolution and the empirical content of quantum mechanics.

That's why I say MWI is not an interpretation for quantum mechanics, it's an idea for an interpretation of quantum mechanics - and I doubt it can ever be more than that.

Salviati:  I disagree, Sagredo. To me the MWI enthusiast would always claim that top-down and bottom-up arrive at the same destination because they are both their interpretation of what is really happening.

Sagredo:  The two approaches are completely distinct, and there's no warrant for the belief that they arrive at the same destination. You apparently accept uncritically the claim that the bottom-up and the top-down approaches are equivalent, and hence that MWI is a viable interpretation of quantum mechanics, and that the empirical content of quantum mechanics is compatible with a unitary interpretation. I'm saying you accept far too much. There is no proof that top-down and bottom-up lead to the same result, and even most serious proponents of MWI realize this, which is why some of them have devoted many years to trying (without success) to establish that correspondence.

Salviati:  I will stipulate that the projection postulate is indispensable for actual calculations, even with the MWI.  Without it, the MWI would be useless. The projection postulate is required any time anyone is using quantum mechanics to do anything practical, and of course any MWI enthusiast will recognize this.

Sagredo:  But the projection postulate is only available to someone who either postulates it or else can deduce it from his postulates. The Bottom-Up approach does indeed invoke the projection postulate, but it's not manifestly unitary. The TopDown approach postulates unitary evolution, but isn't manifestly consistent with the projection postulate. Surely you don't really believe that the MWI enthusiast has the right to invoke the projection postulate even if that postulate is inconsistent with his other postulates? You stated that unitarity is the key postulate of MWI. I'm saying that the use of the projection postulate for doing practical quantum mechanics is not manifestly consistent with unitarity. It might conceivably be consistent, but it certainly has not been established.

Salviati:  I understand your point, I’m just not sure if I agree with it. Also, you’ve said several times that MWI is just an idea for an interpretation, but I'm not sure any of the interpretations are more than ideas for interpretations. We need some observation to discriminate them, but it must be an observation that quantum mechanics does not predict, because all the interpretations are consistent with the predictions of quantum mechanics.

Sagredo:  It would be more accurate to say that all the putative interpretations aspire to be consistent with the predictions of quantum mechanics, but the question is whether a given putative interpretation actually is consistent with the predictions of quantum mechanics. There are some minimalist interpretations that can hardly be inconsistent in any very significant way, but MWI (by which you mean TopDownMWI) could conceivably be very inconsistent with the predictions of quantum mechanics... we have no way of even assessing this, because no one can make any actual predictions from the postulates of TopDown MWI. Whenever they make predictions they invoke BottomUpMWI, but then when they claim unitarity it is on the basis of TopDownMWI... with no proof that these are consistent. It's a shell game.

I suspect this all comes back to an earlier discussion, where we concluded that our irreducible difference is that (in my admittedly tendentious paraphrase) you believe any idea qualifies as a viable interpretation of quantum mechanics, no matter how half-baked it is, even if it makes no rational sense, and even if there is no clear and definite correspondence between the terms of the putative interpretation and the empirical content of the theory. I honestly think that hardly anyone would agree with your loose criteria for what qualifies as a viable interpretation of a physical theory – not even proponents of MWI. Every scientist and almost every philosopher of science I've ever known would say that a set of ideas qualifies as an interpretation of a physical theory only if the ideas correspond in some clear and definite way to the empirical content of the theory. MWI does not do this.

Salviati:  I don't see that as apparent at all from anything I said. Instead, what I said is that the MWI enthusiast sees them as equivalent, and you have not proven that they aren't. I don't see them as equivalent at all, but it is a matter of opinion-- the distinction is not proven.

Sagredo:  I would say the burden of proof is on any putative interpretation of a physical theory to prove that its concepts can indeed be consistently applied to yield the predictions of the theory. Since this has never been (and probably can never be) done for MWI, it remains just a vague wishful idea for an interpretation. It's true that many putative interpretations of quantum mechanics (not just MWI) are really just ideas for interpretations, e.g., the transactional interpretation. The foundational issues of quantum mechanics are notoriously swampy. But in other physical theories throughout history the interpretations have been more cogent... which is precisely why we tend to feel dissatisfied (by comparison) with the interpretations of quantum mechanics.

Salviati:  Well, I think there are plenty of MWI enthusiasts who understand quantum mechanics well enough to know what it predicts.

Sagredo:  Sure, but the point is they don't understand MWI well enough to know what it predicts. They like to think it predicts the same thing, but believing and espousing something because we "like to think it" isn't very scientific.

Salviati:  I don't think they are equivalent, but I cannot prove they are not equivalent, so I must allow that they could be equivalent.

Sagredo:  I allow that MWI - or rather something like MWI but augmented with important new features to enable us to actually use it instead of just vaguely thinking about using it – could conceivably be consistent with the empirical content of quantum mechanics. But given the present state of affairs, I wouldn't say MWI qualifies as a viable interpretation of quantum mechanics. I think you would say it is, so that's where we differ.

Salviati:  A critic might even call it wishful thinking, as I have done above, but that still doesn't make it wrong, it makes it wishful.

Sagredo:  I agree it's not wrong to be wishful – although being wishful about very implausible things isn't terribly sensible – but I contend that it is wrong to be wishful and claim that you are being more than wishful, i.e., for a person to claim that MWI is known to be a viable interpretation of quantum mechanics when in fact it is just a vague idea that he hopes or fantasizes is a viable interpretation.

Salviati:  You have not shown that it is inconsistent with the MWI postulates. If it could be shown to be inconsistent, then MWI enthusiasts could not do quantum mechanics. But they do.

Sagredo:  Here we disagree. When an MWI enthusiast "does quantum mechanics" he is not making any use at all of MWI. True, he fantasizes that his calculations bear some relation to the idea of MWI, but my point is that he is deluded, because he doesn't have the slightest capability of actually performing a calculation or making a prediction legitimately from the postulates of MWI (unitary evolution, etc).

Salviati:  That still doesn't make MWI wrong, because it only aspires to the weak standard of not being manifestly inconsistent with observations. I think that's a low bar, but there is no proof that MWI doesn't get over that bar. It is an interpretation that is held for other, highly rationalistic, reasons, and is held by those who like it as long as there is no direct inconsistency.

Sagredo:  I think this discussion gets a bit confused, because TopDownMWI actually is a different theory from von Neumann quantum mechanics, i.e., the postulates and the mathematics actually are different, so at best the claim is that TopDownMWI matches the predictions of von Neumann quantum mechanics (which are incorporated into BottomUpMWI by postulate) to sufficient accuracy that we can't rule out TopDownMWI based on the empirical success of von Neumann quantum mechanics, just as general relativity is a distinct theory from Newton's theory, but it's predictions are close enough to explain why Newton's theory seems to work as well as it does. The difference here is that we can actually extract predictions from general relativity, and show that it does indeed reduce to Newtonian predictions in most cases, whereas we are utterly incapable of extracting any predictions from TopDownMWI.

That's where I think we differ - you believe MWI is well-defined and it may be right or wrong (i.e., may or may not be consistent with the empirical content of quantum mechanics), and you're willing to give it the benefit of the doubt until proven inconsistent, whereas I contend that it isn't even well-defined, so it can't even be wrong (let alone right).

Salviati:  Well, you have certainly not proven that MWI makes "no rational sense."

Sagredo:  When I say it makes no rational sense I just mean it isn't well defined, and it makes no actual predictions at all. As always, I have to qualify that remark by saying it refers to TopDownMWI, based on the unitary postulate. I would say your main critique of MWI is actually aimed at the other variant, which I call BottomUpMWI. This takes all of empirical quantum mechanics as a postulate, including the projection postulate, and then for purely rationalistic reasons it proposes to embed this empirical world of our experience conceptually within an uncountable infinity of other such worlds, in each of which ordinary quantum mechanics is also postulated to be valid, and then asserts that this multiplicity of quantum mechanics worlds is the real state of affairs. As I read your comments, you don't view this kind of unbridled rationalistic fantasizing very favorably - and neither do I. But it's worth remembering that this applies only to BottomUpMWI, which is not manifestly unitary. Without unitarity - i.e., without being able to say everything just evolves according to the Schrödinger equation - even the most ardent MWI enthusiast would agree that it is trivial and pointless, so they need to assert unitarity, but you don't get that from BottomUpMWI. To get unitarity, the MWI enthusiast adopts a completely different theory, based on the unitary postulate, with no projection postulate. This is a mathematically distinct theory, even when restricted to just what an individual observer would experience. But no one is competent to extract any actual calculations from this theory, because we have no way of knowing the applicable Hamiltonians and other constraints. So it's really a fatuous claim.

Salviati:  There is still a projection postulate in TopDownMWI, because even the concept of a pure state evolving unitarily must come with a concept of what it means to project onto a subspace (and that result is a mixed state). There is no interpretation necessary at this point, it's all pure quantum mechanics, even shut up and calculate quantum mechanics. The interpretations only come in when you ask, what does a mixed state mean?

Sagredo:  With that I completely disagree. The whole point of MWI is to dispense with the projection postulate, and to argue that the approximate appearance of quantum mechanics with a projection postulate emerges purely from unitary evolution, taking decoherence and other things into account - but not a projection postulate. The mathematics of decoherence is totally different from the mathematics of projection, and the correspondence is acknowledged even by proponents of MWI to be only approximate (i.e., close enough for all practical purposes). The off-diagonal terms of the density matrix are never exactly zero with decoherence. MWI based on the postulate of unitary evolution most definitely does not include a projection postulate - which is why it's consistency with the empirical content of quantum mechanics is not established (and, I argue, can never be established).

Salviati:  It is never the interpretation that yields the predictions, it is always the theory itself that does that.

Sagredo:  A genuine interpretation (as opposed to vague hand-waving fantasizing) expresses and entails the theory that it represents, and it does so in a clear, self-consistent, and definite way. There needs to be a clear and definite correspondence between the calculations of the theory and the features of the interpretation. I wouldn't have thought this was controversial. Surely we would not accept just any arbitrary idea as a legitimate interpretation of a given physical theory.

Salviati:  Of all the interpretations, the "no interpretation" is on the most solid logical foundation, but it is essentially never actually used because it is simply unsatisfying (not because it is necessary to apply an interpretation to yield the predictions of a theory, but because interpretations convey a sense of meaning to predictions that can easily be made without them.)

Sagredo:  I'd say there are different levels of interpretation, and there's no such thing as a "no interpretation", because even the bare theory must assert a correspondence between some terms of the calculations and some aspect of our experience. If it doesn't do this, it isn't a theory at all. This is already a necessary (and sufficient) interpretation. MWI doesn't satisfy this bare minimal requirement, so there isn't much point in going on to consider the higher level aspects of interpretation, which really involve model-building within some conceptual framework that we find appealing for some rationalistic reason, like the die-hard Cartesians who labored to interpret Newton's gravity in a Cartesian context as the shadow effect of a flux of ultra-mundane particles moving at high speed in all directions.

Salviati:  I'd say that even seemingly basic interpretations always get swampy when you poke and prod them enough.

Sagredo:  The higher level interpretations, i.e., models, always get swampy, basically because the context of the model is ultimately no more justifiable or explicable than the thing being modeled. The "shadow gravity" example I just mentioned relied on inertia, but ultimately the primitive property of inertia is no more explainable than a primitive force of gravity, so invoking either one the "explain" the other (both have been tried) is sort of pointless.

Salviati:  This hinges on the criteria used to establish the "viability" of an interpretation. You seem to saying that viability requires that as soon as we lay out the details of an interpretation, the predictions of a theory should follow.

Sagredo:  Yes, that's right.

Salviati:  But that doesn't actually happen. If I interpret acceleration as being due to physical forces, it still does not follow that F=ma. I can tell students that there are these things called forces out there which cause acceleration, but I haven't told them anything they can use.  I still never get F=ma until I assert F=ma, and when I do that, I don't really need the interpretation at all (except to give myself a sense of meaning to what I'm saying, which is quite different from the ability to predict observations).

Sagredo:  An interpretation doesn't exclude the details, it encompasses them. An interpretation is a superset of a theory. In other words, it is simply a description of the theory in terms of some context that seems to make sense or be appealing (like the mechanical billiard balls to the Cartesians). The algebraic equation "F=ma" is meaningless until its terms and usage are defined, at least well enough that someone can check to see whether, in fact, F=ma. This correspondence between the terms of an equation and elements of our experience is what needs to be conveyed, and it is conveyed by an "interpretation". So one way of establishing that correspondence is to "tell students that there are these things called forces out there (which we can quantify in a specified way and call the number F) which cause acceleration (which can quantify in a specified way and call the number a) of a mass (which we can quantify in a specified way and call the number m). Once we've done all this, we have what can be called a fairly minimal interpretation of Newton's second law. The interpretation entails the theory.

Salviati:  When you look over the shoulder of someone doing a quantum mechanics problem, and watch the equations they manipulate on their paper, you never get any idea which interpretation is happening in their heads.

Sagredo:  We're talking about two different levels of interpretation. You're talking about model building. I'm talking about the basic bare interpretational statements sufficient to establish the required correspondence between the terms of the calculation and the identifiable elements of our experience. We can dispense with model building (which tends to be pointless anyway), but we can't dispense with the clear and definite correspondence between our calculations and our experience.

Salviati:  I still say there's always projection, it is just part of quantum mechanics.

Sagredo:  Yes, it's part of quantum mechanics, but it isn't part of MWI. That's the point.

Salviati:  That's all true in MWI as well, the only difference is that MWI sees the projection postulate as nothing fundamental, nothing requiring a separate "postulate" to treat, because it is pure quantum mechanics.

Sagredo:  It is a postulate of quantum mechanics, but it isn't a postulate of (top-down unitary) MWI, so MWI advocates claim that something approximating the appearance of projection arises for an "observer" in MWI, but this claim is unfounded.

Salviati:  The main point is, you still cannot tell if someone has CI or MWI in their heads when they carry out any quantum mechanics calculation.

Sagredo:  As I've said before, to me the concept of "having MWI in your head while you carry about quantum mechanics calculations" is meaningless at best. The calculations of quantum mechanics have nothing whatsoever to do with the idea of MWI.

Salviati:  At issue is whether a projection shall be regarded as looking at only a piece of the whole, or if it will be taken to throw away everything orthogonal and scale up the amplitude of the projection to renormalize it to unit amplitude once it is registered as an outcome by an observer.

Sagredo:  That's just the introductory preface to what's at issue. If that alone was the issue, then the whole discussion would be trivial and pointless. The real issue is whether a genuinely coherent theory can be constructed from that first option you mentioned, i.e., from regarding a projection "as looking at only a piece of the whole". In quantum mechanics, when we project down to a definite eigenvector (by the projection postulate) and renormalize to unit amplitude, this then establishes the initial conditions and to some extent the boundary conditions within a suitably defined Hilbert space for the future evolution... but if we do not project, and instead simply note that the original state vector of the universe can be decomposed in various ways, and we consider abstract projections of that vector onto various bases, one of which we might place into correspondence with some quantum mechanical world, the issue is how we are to identify such a correspondence and what reason we have for imagining that any such correspondence would persist. And when you talk about throwing away everything orthogonal, remember decoherence doesn't really make the different worlds orthogonal, except approximately. Now, you can argue that the mutual projections are small, but smallness of projections has no meaning once you decide to never renormalize your world-vectors. If you think it though carefully, MWI just collapses (so to speak) into an ill-defined mess with no definite content at all.

Salviati:  There's nothing special about decoherence or quantum mechanics that the off-diagonal elements are treated as exactly zero. Nothing anywhere in physics is "exactly" anything, only the idealizations are ever exact.

Sagredo:  The issue isn't exactness or idealizations, the issue is whether unitary evolution taking decoherence into account leads to mathematically identical predictions (experiences) for an observer as does quantum mechanics with the projection postulate. And the answer is no, it doesn't. The projection postulate results in the system being left in an eigenvector, but unitary evolution with decoherence does not. No one that I know of, aside from you Sagredo, disputes this. What people dispute is whether unitary+decoherence yields predictions that are close enough to be empirically viable. But the mathematics and predictions are definitely distinct.

Salviati:  I say again, Sagredo, MWI does have a projection postulate, if it didn't no one could call it quantum mechanics.

Sagredo:  No, Salviati, MWI definitely does not have a projection postulate. I agree that no one can (legitimately) call it quantum mechanics. Bear in mind that this refers to TopDownMWI, which is unitary. It is certainly true that BottomUpMWI has a projection postulate, and is observationally equivalent to quantum mechanics - but there's no good reason to think it is unitary.

Salviati:  That's a straw man, there is no question that a lot of physics theorists use the MWI interpretation of quantum mechanics.

Sagredo:  I would say just the opposite: There is no question that no physics theorists use the MWI interpretation. Some espouse it, but none use it, because it is utterly ill-defined and perfectly unusable.

Salviati:  All that is required for an interpretation to be valid is that a rational and reasonable expert of some theory uses that interpretation to help them picture what the theory is doing, or how the theory helps them understand the reality it predicts.

Sagredo:  I think that's an extremely lax standard for what qualifies as an interpretation, but even with that standard I would say MWI does not qualify, because it doesn't help anyone do or understand anything.

Salviati:  It really comes down to what "interpreting" is, I agree.

Sagredo:  Yes, there are operational interpretations, and then there are conceptual models, and I think what you are talking about is conceptual models. There isn't really a sharp line, but we tend to distinguish between what we regard as raw sense perceptions and conceptual models. (Actually, even raw sense perceptions represent conceptual models, but we usually agree on a distinction.) So, for example, we may have an elaborate sequence of "uninterpreted" operational steps to quantify something called "distance" between two entities, and we may choose to encode this within a conceptual model of a 3-dimensional space with a Euclidean metric, and we find that this model (interpretation) works very well. This is an example of a genuine interpretation. It isn't necessarily the only interpretation that could be used to encode and coordinate the quantification and organization of the sense perceptions that we associate with "distance", but it is one that "works". MWI is nothing like this, because it doesn't "work", i.e., it doesn't accurately place our sense perceptions into any correspondence with our calculations.

Salviati:  Doesn't it bother you, Sagredo, that your position that MWI isn't quantum mechanics seems very far away from the views of all the quantum mechanics experts who hold to the MWI?

Sagredo:  The most prominent advocates of MWI actually have views that are fairly consistent with my position, at least to the extent that they agree unitary evolution by itself (even augmented with a Born rule) is not sufficient to yield an intelligible interpretation, and is not self-evidently even consistent with quantum mechanics. For example, David Deutch explicitly says that some further ingredient is necessary, and that the necessary further ingredient leads to a theory in which a sufficiently sensitive observer actually can perceive superpositions - just as many critics of MWI had said from the start. Now, you would probably not call this quantum mechanics any more, you would call it a different theory... but that's my point. Here is one of the most prominent advocates of MWI, and I think you would agree that what he espouses really isn't quantum mechanics. Likewise each advocate of "MWI" seems to mean something different by MWI - and each of them regards all the other flavors of MWI as obvious nonsense (like the three Christs of Ypsilanti).

Salviati:  Deutsch is trying to meet certain criticisms of the MWI to make it more acceptable. That is not a requirement of the MWI being a valid interpretation of quantum mechanics, it relates to whether or not it can be regarded as a preferred interpretation.

Sagredo:  I think you're mistaken about that. Here's a little excerpt from a discussion between Deutch and Paul Davies (reproduced in the book "The Ghost in the Atom"):

Deutch: "When Everett first put forward his interpretation, he believed that it was a pure interpretation in the technical sense of the word. In other words, that the physical predictions of quantum theory under his system were precisely identical with those under any other system. Now, I believe that this is not so, and I have recently done some work trying to elaborate the exact experimental difference between the Everett and the conventional 'interpretations'. I now have to say 'interpretations' in quotes because I believe that there are actually different formal structures for quantum theory."

Davies: "So we're talking, not about two different ways of looking at the same theory, but two completely different theories?"

Deutch: "Yes..."

So I think you have not really understood Deutch's position - and I would argue that the same applies to other prominent advocates of MWI. It's fairly clear that the explicitly unitary version of MWI (which is all anyone cares about) is a distinct theory from quantum mechanics.

Salviati:  By the way, when I refer to the "use" it, all I mean is they use it to motivate the well-known process of doing quantum mechanical calculations.

Sagredo:  Yes, I just don't think anyone "uses" MWI to do that. It doesn't motivate any quantum mechanics calculations. TopDownMWI is devoid of any definite content at all, and BottomUpMWI is nothing but ordinary quantum mechanics performed by someone with a "MWI" button on their lapel.

Salviati:  But that's all anyone uses any of the interpretations for, to help them decide what it means while they are doing all the same things.

Sagredo:  I'd say that "deciding what the calculations mean" in an operational sense is the role of the low-level interpretation of the terms of the equations, i.e., the bare minimum of establishing the correspondence between the terms and some features of our experience. In contrast, I think the kind of interpretations you have in mind are what I would call models, whereby our messy low-level operational raw processes and perceptions are placed in a rationalistic context of some kind, that makes them easier for our brains to grasp - almost like mnemonic aids - based on how our brains are wired. We seek visceral and spatio-temporal "pictures" in terms with which we are familiar - just the 18th century Cartesians trying to model Newton's mysterious force of gravity in mechanistic terms of bouncing billiard balls, or the 19th century physicists trying to model electromagnetism in terms of some palpable mechanistic ether. We always try to represent unknown things in terms of familiar concepts - even though those familiar concepts are usually no more self-evident than the new unfamiliar ones. We can tell we're getting into trouble when our efforts to do this lead us to postulate fantastically elaborate contraptions - and usually we eventually decide to abandon our old familiar conceptual framework once it no longer serves a useful heuristic purpose.

Salviati:  I do think that when a truly different theory comes along, it may be inspired by one of those interpretations of quantum theory.

Sagredo:  I agree that's possible - even though I'm inclined to think that models are usually backward-looking, i.e., they are attempts to represent new unfamiliar phenomena in terms of old familiar concepts. Often we succeed in fitting the new phenomena into old concepts, with some adjustments perhaps, and so we feel satisfied that we understand it. Occasionally we can't find a satisfactory representation for new phenomena in terms of old concepts, and we go through a long period of feeling dissatisfied, like we don't understand it. This happened with the concept of inertia, and with Newton's force of gravity, and with the phenomena of electromagnetism, and so on. In each case there was a long period of reactionary attempts to interpret the phenomena in terms of prior concepts. In this same tradition, I'd say MWI is a very backward-looking attempt (so far unsuccessful) to rationalize quantum phenomena in classical terms.

Salviati:  I can very easily give an MWI interpretation that is as valid and consistent with quantum mechanics as CI-- we simply interpret all closed systems as having a Hamiltonian and a wave function... that evolves via the Schrödinger equation. Then we just do everything that CI does when we refer to decohered subspaces of that closed system...

Sagredo:  Your first sentence describes the unitary (top down) version of MWI, but your second sentence describes bottom up version of MWI. It isn't legitimate to claim unitarity from the first version and consistency with quantum mechanics from the second version. I know you think the two versions are equivalent, and I've tried to explain in various ways why they are not equivalent, and I've cited at least one prominent advocate of MWI who contends they are not equivalent... but none of this seems to make any impression on you. Maybe we can make some progress by examining this statement:

We simply interpret all closed systems as having a Hamiltonian and a wave function, even if we can't stipulate either, that's why it's an interpretation and not a theory, but note CI doesn't stipulate them either so we have changed nothing but our way of thinking...

I would say both clauses of that sentence are wrong. First, I think it's wrong to say an idea can qualify as an interpretation of a theory involving Hamiltonians and initial conditions even if that idea is incapable of ever identifying the applicable Hamiltonian or initial conditions. This gets us back to our fundamental difference over whether or not an interpretation is required to actually make some kind of rational sense. Second, I think it's wrong to say that CI likewise fails to make such an identification... the whole point of Bohr's insistence on the need for the measuring instruments to be treated as classical objects is because he recognized that without this we just have "one hand clapping", and can never hope to identify the Hamiltonian and initial conditions and potential functions for any specific physical situation. CI is a (relatively, though not entirely) well-defined interpretation of quantum mechanics as a theory that describes how a quantum system interacts with a classical system. This is what gives CI whatever degree of well-definedness it possesses. But MWI lacks this.

Salviati:  An interpretation is not a theory, it is merely a way to achieve some personally satisfying degree of cognitive resonance while a theory is being used.

Sagredo:  We strongly disagree about this. As I said before, every scientists and almost every philosopher of science I know would not accept such a lax definition of "interpretation" for a physical theory - and furthermore, even under this (to me) ridiculously lax definition, MWI still doesn't qualify as an interpretation, unless you go on to define "cognitive resonance" to mean "whatever anyone thinks is cognitive resonance". And even furthermore, if we were to accept all these "whatever floats your boat" definitions, it would surely be permissible to criticize "interpretations" in this context.

Salviati:  Above all, we must recognize that interpretations are not unique, and we should never expect there to be a "correct" interpretation of any physical theory.

Sagredo:  Of course interpretations are not unique, but I would differ with the "above all", because I think above all is the requirement for the concept of an interpretation to be meaningful and well-defined. Obviously if we were to apply the boat-floating definition of "interpretation", then it would never even occur to anyone that they might be unique. The interesting point is that even with meaningful and well-defined interpretations it turns out there is non-uniqueness. But we wouldn't be able to see this interesting point if we held to the boat-floating definition of "interpretation".

Salviati:  That's not what I mean by "mean". The example I gave above is how x(t) emerges from classical trajectory calculations....So interpretations are simply not what you ask them to be.

Sagredo:  I don't see the disagreement. What you described there is exactly what I described, in terms of the contrast between operational definitions of x and t versus the abstract concepts of time and three-dimensional space. If there is any difference in our views about this, I guess it's that I think there is a fairly meaningful and well-defined correspondence between the operational definitions of x & t and the conceptual model of 3D space and time, and that this degree of correspondence between operational variables and concepts is lacking in MWI.

Salviati:  That same criticism is leveled by every person who rejects a given interpretation.

Sagredo:  I don't see it as a criticism of one interpretation versus another, I see it as an aspect of interpretations in general, i.e., they are a way of placing something within some conceptual context, and they tend not to be regarded as satisfactory unless the conceptual context is one with which people are already comfortable.

Salviati:  MWI enthusiasts say CI is backward-looking because it cannot accept that reality might transcend our ability to perceive it.

Sagredo:  I don't think that's true. The rap against CI hasn't traditionally been that it is reactionary, but rather that it is wooly and adventurous and even quasi-mystical. It is an exceptional interpretation precisely because it denies the quo ante categories. Those are the features that repel people, and that motivate things like MWI, which sees itself as dispensing with Bohr's mystical dualism and tries to eliminate "those damned jumps" and restore the classical basis of a deterministic continuous differential equation. There's nothing unclassical about imagining infinitely many "sub-worlds". It's extravagant, but not unclassical. So I would still say that MWI is a (so far unsuccessful) reactionary idea for an interpretation of quantum mechanics in classical terms, and I think most advocates of MWI would actually agree with this, which they regard as its motivation - eliminating Bohr's mystical dualism.

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