Problems with Many Worlds Interpretation

[Ken G]

The lost causes in physics website gives technical arguments against MWI.

If you will make that claim, please cite them. I didn't see any.

Evidently, the criticism of MWI, which I have pointed out before is purely technical and has been published in journal of physics (e.g., Int. J. Mod. Phys. A 5 1745-1762 1990), not in philosophical magazines, as you seem to believe.

And you think MWI proponents have no answer to that article?

It is very ironic that you write about the role of axioms, because precisely one of the main criticism of the MWI literature is that its main advocates either lack to give a complete set of axioms, from which one could explain the physical world (reason for which the theory has been labeled «unscientific») or them give us a set of self-contradictory axioms (reason for the which «The theory is false because it is inconsistent»; quote X5 in this same thread).

The MWI camp generally holds that their axioms are the smallest set of anyone's. I think that's true, I just don't think that suffices as a reason to make it one's world view. Their axioms are indeed quite simple-- closed systems evolve according to the Schroedinger equation, and quantum mechanics describes what is really happening. That's it, those are the axioms of MWI. The irony is, a lot of people think those things are true, but simply don't realize that means they are adopting MWI.

Max Tegmark confounds physics with philosophy in his post-modern Radical Platonism: MUH.

Tegmark does not appear to view MUH as physics, he understands that it is philosophy. It is more the people like the Nobel laureate Weinberg who blur that distinction, when they invoke the anthropic principle in scientific arguments.

Steven Weinberg is also aware of the differences between physics and maths. Precisely in his textbook gravitation and cosmology, Weinberg explains why he follows what he calls a non-geometrical presentation of the subject, and remarks in the preface how the electromagnetic interaction cannot be understood in geometrical terms.

I don't see how your logic follows from that example. All he is saying is that geometric maths doesn't cut it-- he is a believer in complete unification. But he certainly feels that physics is converging on a true (mathematical) description of reality, he regards the anthropic principle as a scientific principle useful in making predictions, and he holds that a "landscape' of multiple universes is a valid scientific theory. All this while claiming that he sees no role for philosophy in physics. Like many, his own philosophy doesn't seem to count.

You have completely misinterpreted Feynman's point of view. He was not talking about the limitations of Euclidean geometry in regard to more general geometries. He was talking about the limits of mathematics and the differences with physics. He chose Euclidean geometry as an simple illustrative example adequate to his audience (people taking an introductory physics course).

What I said is that Feynman tends toward empiricism. That's quite true, yet identifying Feynman's philosophical preferences certainly does not support your position that philosophical preferences are irrelevant.

 

[BruceW]

juanrga, that's an interesting paper you mentioned. I found the preprint here: http://xxx.lanl.gov/PS_cache/gr-qc/pdf/9703/9703089v1.pdf
Just to make it clear at the start: In this paper, the guy is using the word 'axioms' to mean mathematical axioms (i.e. not to do with the philosophical meaning of the theory, but the actual physical core of it).

I think these 2 quotes summarise the paper pretty well:
Even in modern formulations MWI still seem seriously inadequate. Thus the aim of this paper is to argue that the literature neither contains nor suggests a plausible set of axioms for an MWI that describes known physics.
This means that the argument in the paper assumes that MWI must have different axioms to standard QM. So the guy who wrote this paper is talking about MWI as a separate theory to QM (not just a particular interpretation of QM).

The useful criticisms of MWI do not stem from an inability to accept the picture of multiple branching universes, nor do serious critics merely say that they do not see how to reduce macroscopic physics to an MWI. They assert either that particular physical facts are demonstrably not logically deducible from the axioms of MWI, or else they criticize the axioms proposed (usually on grounds of complexity or arbitrariness)
At the end of this quote, he seems to imply that it is possible to make MWI a different theory to QM and to make it agree with known physics, but then this makes the axioms complex/arbitrary. So this is a philosophical argument against MWI. (To paraphrase: 'yeah, it works, but I don't like the axioms.')

For most of the paper, he provides a few possible axiomatisations of MWI (as a separate theory to QM) and then shows that they each fail as a theory. So he's not providing a technical argument against MWI as an interpretation. He's providing technical argument against MWI as a different theory.

 

[juanrga]

If you will make that claim, please cite them. I didn't see any.
And you think MWI proponents have no answer to that article?

That was not the point.

The MWI camp generally holds that their axioms are the smallest set of anyone's. I think that's true, I just don't think that suffices as a reason to make it one's world view. Their axioms are indeed quite simple-- closed systems evolve according to the Schroedinger equation, and quantum mechanics describes what is really happening. That's it, those are the axioms of MWI. The irony is, a lot of people think those things are true, but simply don't realize that means they are adopting MWI.

The 'simple' Schrödinger postulate is already in QM. MWI advocates copied it but misinterpreted and misapplied (as correctly stated in the lost causes site).

What is more, there is not a single and consistent set of MWI axioms, with each MWI advocate proposing his owns. The irony is the pretension of the existence of one MWI formulation when there exist one per author.

Tegmark does not appear to view MUH as physics, he understands that it is philosophy.

He writes «physics» and has been precisely criticized by that.

It is more the people like the Nobel laureate Weinberg who blur that distinction, when they invoke the anthropic principle in scientific arguments.

Weinberg has been criticized by his use of such unscientific principle. But that was not the point.

I don't see how your logic follows from that example. All he is saying is that geometric maths doesn't cut it-- he is a believer in complete unification. But he certainly feels that physics is converging on a true (mathematical) description of reality, he regards the anthropic principle as a scientific principle useful in making predictions, and he holds that a "landscape' of multiple universes is a valid scientific theory. All this while claiming that he sees no role for philosophy in physics. Like many, his own philosophy doesn't seem to count.
What I said is that Feynman tends toward empiricism. That's quite true, yet identifying Feynman's philosophical preferences certainly does not support your position that philosophical preferences are irrelevant.

You misinterpret both Feynman and me again. He is not talking about philosophy but about the difference between physics and maths. If you read what he wrote, you will discover, with irony, that he starts his lecture with a critic of philosophers and of how the point of view of physics is superior when dealing with physical objects.

 

[juanrga]

juanrga, that's an interesting paper you mentioned. I found the preprint here: http://xxx.lanl.gov/PS_cache/gr-qc/pdf/9703/9703089v1.pdf
Just to make it clear at the start: In this paper, the guy is using the word 'axioms' to mean mathematical axioms (i.e. not to do with the philosophical meaning of the theory, but the actual physical core of it).

I think these 2 quotes summarise the paper pretty well:
Even in modern formulations MWI still seem seriously inadequate. Thus the aim of this paper is to argue that the literature neither contains nor suggests a plausible set of axioms for an MWI that describes known physics.
This means that the argument in the paper assumes that MWI must have different axioms to standard QM. So the guy who wrote this paper is talking about MWI as a separate theory to QM (not just a particular interpretation of QM).

The useful criticisms of MWI do not stem from an inability to accept the picture of multiple branching universes, nor do serious critics merely say that they do not see how to reduce macroscopic physics to an MWI. They assert either that particular physical facts are demonstrably not logically deducible from the axioms of MWI, or else they criticize the axioms proposed (usually on grounds of complexity or arbitrariness)
At the end of this quote, he seems to imply that it is possible to make MWI a different theory to QM and to make it agree with known physics, but then this makes the axioms complex/arbitrary. So this is a philosophical argument against MWI. (To paraphrase: 'yeah, it works, but I don't like the axioms.')

For most of the paper, he provides a few possible axiomatisations of MWI (as a separate theory to QM) and then shows that they each fail as a theory. So he's not providing a technical argument against MWI as an interpretation. He's providing technical argument against MWI as a different theory.

I think that all of this was answered before:

The preprint correctly states that none of the different MWI formulations found in the literature contains an internally consistent and complete set of axioms that reproduces the known physics. Either the axioms are contradictory or the predictions do not agree with what we observe in labs or both.

You already asked me about if MWI is an interpretation of QM or another theory, and you received at least two answers, one from mine.

 

[Ken G]

That was not the point.

In any event, I disagree with your "point". All I notice is you chose not to provide any of the support I requested that you provide.

You misinterpret both Feynman and me again. He is not talking about philosophy but about the difference between physics and maths. If you read what he wrote, you will discover, with irony, that he starts his lecture with a critic of philosophers and of how the point of view of physics is superior when dealing with physical objects.

Feynman was a terrific physicist, but his knowledge of, and appreciation for, anything else was not so legendary. In particular, he had nothing but disdain for both psychology and philosophy, but was never considered a master of either, indeed he was positively ignorant of both. I think we'll just have to give him a pass for his closedmindedness on both those counts. All I can say is, among those who don't know much about philosophy, there is a very clear tendency to adopt the attitude that philosophy is counted as anything that other people think.

 

[juanrga]

In any event, I disagree with your "point". All I notice is you chose not to provide any of the support I requested that you provide.
Feynman was a terrific physicist, but his knowledge of, and appreciation for, anything else was not so legendary. In particular, he had nothing but disdain for both psychology and philosophy, but was never considered a master of either, indeed he was positively ignorant of both. I think we'll just have to give him a pass for his closedmindedness on both those counts. All I can say is, among those who don't know much about philosophy, there is a very clear tendency to adopt the attitude that philosophy is counted as anything that other people think.

Well, since that (i) I cited the excellent technical remarks on physics by Feynman, the physicist, since (ii) I emphasized that we are not discussing about philosophy, and since (iii) he was correctly criticizing philosophers when they try to discuss the nature and properties of physical objects, your repetitive answer has very little to see with the points that I was making.

 

[Ken G]

Well, since that (i) I cited the excellent technical remarks on physics by Feynman, the physicist, since (ii) I emphasized that we are not discussing about philosophy, and since (iii) he was correctly criticizing philosophers when they try to discuss the nature and properties of physical objects, your repetitive answer has very little to see with the points that I was making.

Actually, it is your answer that is simply not in keeping with the facts. The comment from Feynman that I reacted to was not at all a technical point of physics. To quote you:

If you read what he wrote, you will discover, with irony, that he starts his lecture with a critic of philosophers and of how the point of view of physics is superior when dealing with physical objects.

Now, it is not at all surprising that physics is superior "when dealing with physical objects", that's what it is for. The real question is, why do you think Feynman is expert enough to critique philosophers? Philosophers don't even ask the same questions that physicists do, and indeed it is quite apparent from the history of both that physics was invented by philosophers to answer certain types of questions. This is why physics was originally called natural philosophy. It expanded into its own field, but it still has the same charge originally given to it by natural philosophy. Feynman is critiquing the gun on grounds that the bullet is more effective.

Even more ironic is the fact that Feynman certainly waxed philosophical on many occasions, even in regards to physics (his brilliant definition of science as distrust in experts was a classical example of his own philosophy). Despite his great brilliance, and my own personal admiration for him, he, like you, tended to fall into the error that "philosophy is what other people think."

 

[BruceW]

I think that all of this was answered before:

The preprint correctly states that none of the different MWI formulations found in the literature contains an internally consistent and complete set of axioms that reproduces the known physics. Either the axioms are contradictory or the predictions do not agree with what we observe in labs or both.

You already asked me about if MWI is an interpretation of QM or another theory, and you received at least two answers, one from mine.

Well, the preprint says that if we formulate an MWI with different mathematical axioms to standard QM, then we get inconsistent answers. So if we formulate an MWI with the same mathematical axioms as standard QM, then we don't necessarily get inconsistent answers.
So this is equivalent to saying that MWI as a separate theory to QM is inconsistent, but MWI as an interpretation of QM is not inconsistent.

And the author of that paper argues that the proponents of MWI were using it as a separate theory to QM. And I think he is probably right. So I'd probably agree that the proponents of MWI did not achieve what they were hoping for. (But we'd only really know by asking them).

But just because I don't agree with some of the possible MWI's (i.e. the MWI's that are effectively new theories), it doesn't mean I disagree with MWI's that are simply interpretations of standard QM.

 

[Ken G]

Well put. 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-- to either a new theory or a kind of world view that asserts some new reality. Those things require new predictions and new successes to be justified.

 

[Samshorn]

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...

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.

 

[juanrga]

The real question is, why do you think Feynman is expert enough to critique philosophers?

In the context of point (iii) made above... he was expert in physics, philosophers do not.

 

[juanrga]

Well, the preprint says that if we formulate an MWI with different mathematical axioms to standard QM, then we get inconsistent answers. So if we formulate an MWI with the same mathematical axioms as standard QM, then we don't necessarily get inconsistent answers.
So this is equivalent to saying that MWI as a separate theory to QM is inconsistent, but MWI as an interpretation of QM is not inconsistent.

And the author of that paper argues that the proponents of MWI were using it as a separate theory to QM. And I think he is probably right. So I'd probably agree that the proponents of MWI did not achieve what they were hoping for. (But we'd only really know by asking them).

But just because I don't agree with some of the possible MWI's (i.e. the MWI's that are effectively new theories), it doesn't mean I disagree with MWI's that are simply interpretations of standard QM.

The preprint analyzes the published MWI literature (does not invent MWI) and find the flaws and contradictions in the formulations.

Does not exists «an MWI with the same mathematical axioms as standard QM». Contrary to what you seem to believe, this never was the aim of the MWI folks.

 

[Ken G]

There's another possibility: One points out that what is claimed to be an interpretation of a given theory is really no such thing.

Sure, but that's much more difficult, and must be held to a higher standard of proof. For example, that's just what the "lost causes" article did not successfully do. All too often, a criticism of an interpretation gets intermingled with implicit philosophical priorities that go unnoticed, rather than a logical proof that some interpretation is incorrect. 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?

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).

I suspect Bell was referring, as usual, to certain philosophical priorities. The basic idea behind MWI is completely simple-- it merely asserts that all closed systems, including closed systems that include observers and physicists (and even including open systems where the external constraints are fixed and not self-consistently updated with the system), must evolve according to the Schroedinger equation. That's it, that's MWI as an interpretation of quantum mechanics (and not as a new theory like the way BruceW was talking about). I'm always surprised how many people think that closed systems do evolve that way, in the sense that it should provide a complete description of their evolution, yet they reject MWI. That's an internally inconsistent stance, because if evolution by the Schroedinger equation provides a complete description of closed systems, then closed systems evolve completely unitarily. MWI is the sole interpretation which allows that to be a complete description. That doesn't mean we should all adopt it, but it does mean that 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 Schroedinger equation without any additional bells and whistles like pilot waves or empirical perceptions of collapse.

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.

I think the problem is that MWI users try to go farther than simply saying that closed systems, even those including observers, are described completely by the Schroedinger equation. They further build a kind of world view that can make additional predictions, along the lines of what the multiverse is used for with the anthropic principle. That goes beyond an interpretation of quantum mechanics, it is something closer to the creation of a new theory that makes new predictions, and this is the place where all the stumbling occurs, because no such new theory really exists at present. There are no clear new predictions made by MWI that could justify imagining those "other worlds" really exist, and whether Weinberg's cosmological constant prediction counts as a new prediction of anthropic thinking is clearly a debatable issue (one that I would be dubious of, but that's another thread).

 

[juanrga]

Sure, but that's much more difficult, and must be held to a higher standard of proof. For example, that's just what the "lost causes" article did not successfully do. All too often, a criticism of an interpretation gets intermingled with implicit philosophical priorities that go unnoticed, rather than a logical proof that some interpretation is incorrect. 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?I suspect Bell was referring, as usual, to certain philosophical priorities. The basic idea behind MWI is completely simple-- it merely asserts that all closed systems, including closed systems that include observers and physicists (and even including open systems where the external constraints are fixed and not self-consistently updated with the system), must evolve according to the Schroedinger equation. That's it, that's MWI as an interpretation of quantum mechanics (and not as a new theory like the way BruceW was talking about). I'm always surprised how many people think that closed systems do evolve that way, in the sense that it should provide a complete description of their evolution, yet they reject MWI. That's an internally inconsistent stance, because if evolution by the Schroedinger equation provides a complete description of closed systems, then closed systems evolve completely unitarily. MWI is the sole interpretation which allows that to be a complete description. That doesn't mean we should all adopt it, but it does mean that 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 Schroedinger equation without any additional bells and whistles like pilot waves or empirical perceptions of collapse.
I think the problem is that MWI users try to go farther than simply saying that closed systems, even those including observers, are described completely by the Schroedinger equation. They further build a kind of world view that can make additional predictions, along the lines of what the multiverse is used for with the anthropic principle. That goes beyond an interpretation of quantum mechanics, it is something closer to the creation of a new theory that makes new predictions, and this is the place where all the stumbling occurs, because no such new theory really exists at present. There are no clear new predictions made by MWI that could justify imagining those "other worlds" really exist, and whether Weinberg's cosmological constant prediction counts as a new prediction of anthropic thinking is clearly a debatable issue (one that I would be dubious of, but that's another thread).

MWI is a misinterpretation of quantum mechanics next misapplied to the cosmos as a whole. A simple but enough discussion of the misconceptions and mistakes involved in Everett and posterior works is given in the lost causes article.

Another revision of the mistakes and fallacies of the different versions of MWI are in the Int. J. Mod. Phys. A 5 1745-1762 1990 paper and its preprint update, with the same conclusion that the lost causes article. All known MWIs are internally inconsistent and do not agree with observations.

 

[Ken G]

All known MWIs are internally inconsistent and do not agree with observations.

Let's look at a simple question. Do you, or do you not, think that closed systems always evolve according to the Schoedinger equation?

 

[Samshorn]

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.

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 proposer to show that his 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.

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?

Anyone who espouses anyone 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 maintain 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.

…MWI merely asserts that all closed systems… must evolve according to the Schroedinger equation… MWI is the sole interpretation which allows that to be a complete description.

Unitary evolution according to the Schrodinger 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.

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 Schroedinger equation without any additional bells and whistles like pilot waves or empirical perceptions of collapse.

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 Schroedinger 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.)

 

[juanrga]

Let's look at a simple question. Do you, or do you not, think that closed systems always evolve according to the Schoedinger equation?

First, as Born, von Neuman, and others fathers of QM correctly emphasized, the Schrödinger equation is not the equation that describes the motion of any closed [*] system even in the pure state approximation.

Even the lost causes site cited here starts with some technical explanations of why, if you consider the universe as an isolated system, the assumption that its state is described by a pure state is not valid.

[*] I assume that you really mean isolated.

 

[juanrga]

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.

Anyone who espouses anyone 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.

That is an excellent remark. Not only the myth of the existence of one MWI is destroyed by the existence of many MWIs in the specialised literature, but that the versions of different authors (Everett, Tegmark, Deutsch, Hartle...) contradict between themselves.

 

[Ken G]

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.”

But you have not supported your claim here. Your claim is that Deutsch is saying Everett would make wrong calculations, but the evidence you cite is a quote that is not saying anything about calculations at all. This is the widespread problem-- an inability to tell the difference between a scientific difference and a difference in philosophical priorities. Give me a quote by Deutsch in which he is saying that Everett does wrong quantum mechanics, not a quote where Deutsch is quite clearly saying that he demands some ontological "connection" between the wave function and the universes. That looks to me like Deutsch is simply raising a philosophical objection, which I claim is exactly where all the debates about interpretations are held.

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!”.

Remind me-- what extra mathematical structure are you talking about? The main proponent of MWI, early in this thread, was Hurkyl, and I am aware of the writings of Max Tegmark, and neither of them ever refer to any "extra mathematical structures", indeed their support of MWI invariably rests on what they perceive as an absence of extra mathematical structures (like the deBB pilot waves, or the Copenhagen manual postulate about wavefunction collapse). In my view, they are right about that-- MWI is clearly the mathematically minimalist description, it is just not the empirically minimalist description (that's CI) or the most neoclassical (that's deBB).

There is no interpretation of MWI that motivates correct calculations.

That will come as a big surprise to Hurkyl, he seems to have no trouble making correct calculations. The grandiose claims made about the failings of MWI as a viable interpretation seem highly unresponsive to the facts of the matter. All I see are objections that are ontological and philosophical in nature, and a bunch of empty claims that they are more than that. I think the real problem is that MWI proponents are trying to arm their interpretation with more completeness than has been demonstrated by either deBB or CI, and that's where they have not succeeded-- because that would make MWI more than just a different interpretation, it would make it a different theory (as it invariably comes with suggestions for different predictions it would make, like if influences from "other worlds" could actually be measured).

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.

Says you, but that very clearly is a question that must be answered by the person using that motivation. An interpretation is just not anything more than whatever the physicist is imagining is happening when he/she thinks about the result they are calculating. Why don't we see people claiming that Newtonians "may be capable of performing correct calculations, but those calculations are not warranted" by imagining that forces are real, rather than that action is minimized or some such equivalent interpretation of what is really happening there? Why do people argue about this in quantum mechanics, but not classical mechanics, even though saying that action is minimized is just as ontologically vastly different from saying that there are real forces, as is saying that there are many worlds is different from there being pilot waves. For some reason, when we get to quantum mechanics, everyone seems to suddenly forget what an equivalent interpretation means any more.

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.

That just doesn't make sense to me. No one "adheres to" an interpretation when they do quantum mechanics (that's why some people claim they only "shut up and calculate"), they apply the postulates of quantum mechanics, which you can read in any textbook on quantum mechanics (some of which make no mention at all of any interpretation whatsoever). No one uses an interpretation to do quantum mechanics, they use an interpretation to give them something to picture in their minds when they do quantum mechanics. The interpretation motivates the equations they are using, it does not provide the equations they are using. Indeed, quantum mechanical interpretations are often even less important than interpretations of classical mechanics, because in classical mechanics the equations can start out being different (as in minimizing action vs. Newton's laws), even though they end up being the same before the motion is solved. That's more akin to deBB, which starts out with a different equation before it ends up solving Schroedinger, but MWI and CI don't even do that-- the equations are never different one iota. Often, interpretations in QM, like MWI and CI, appear after the fact of the calculation-- they tend to be a priori types of interpretations, which is the least significant type.

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.

Let's look at an example. You can easily solve for the motion of the Earth around the Sun by treating the Earth-Sun system as closed and applying the Schroedinger equation, we just approximate the Earth as having a pure-state wavefunction when we know if we had more precision we'd have to treat is as a mixed-state subsystem.

No one knows if large suitably closed systems have pure-state wavefunctions or if they have to be treated as mixed states, it has never been put to the test. The expectation from quantum mechanics is that the more closed the system is, the less of a mixed-state description it requires, leading ultimately to a pure state in the limit of complete closure. So the MWI proponent holds that if we had truly closed systems, they would evolve unitarily, but we always actually have mixed-state subsystems projected from larger systems that we are not treating. By "large" I don't necessarily mean spatially large, I just mean there is a way larger amount of information in that system than we would ever be able to use our intelligence and senses to analyze or track, so we instead track a remotely tiny subset of that full complexity. The MWI proponent sees that fact as the reason that we do not perceive the full "unity" of the effectively closed systems we participate in.

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 maintain 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?

CI does not escape this problem either, it just makes different philosophical choices about how to deal with it. CI says that effectively closed systems evolve by the Schroedinger equation until you open them up, and the mixed states that appear when one considers open subsystems should be interpreted as definite outcomes that there is a lack of information about until the definite result is recorded. There is no evidence of any time-symmetry breaking there in anything that is happening independently of how we do physics, it is merely by fiat that the arrow of time is applied. It has our fingerprints all over it, just as does the second law of thermodynamics. So CI is pretty much standing up and saying "physics is done by physicists, and is all about what we can say about nature and nothing more." It is all the things so many on this thread reject, in the same breath that they reject MWI, even though MWI provides a way to avoid having a very clear role of the mind of the physicist in the ontology of the interpretation.

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.)

I did balk at that point, but my way of balking was not to say MWI is invalid, I merely used the example to point out how radically rationalistic MWI is-- it represents the complete denial of the role of the mind of the physicist in physics (rationalists view mathematics as existing outside the mind of the mathematician). I don't think it's invalid to do that, I think it's invalid to do that and claim that a fairly narrow set of philosophical priorities is not being invoked in the process. The rationalistic MWI proponent thinks that the arrow of time is an illusion, as is the whole concept of a definite unique outcome of an experiment. MWI is a symmetry principle-- the symmetry that any outcome that can occur cannot be distinguished in the full reality from any other outcome that can occur, so the distinctions we perceive are illusory. It is the culmination of the Parmenides philosophy that A cannot become B unless A and B are the same thing.

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.

Not so, MWI proponents have no trouble applying the Born rule. It is as though you think they are schizophrenic, as if their interpretation forces them to reject the Born rule postulate, so whenever they do a QM calculation they enter an unconscious state when they apply the Born rule, and wake up seconds later with no memory of having used it!

That's not what they do, they simply apply the Born rule when they determine the weights of the mixed state they get when they consider a subsystem (like a measured object). MWI has no problem at all with the Born rule, they simply view it as the weights of a mixed state, rather then as probabilities of what "really happens." They only get into trouble when they are unwilling to think of the Born rule as an additional postulate to the wavefunction evolution, they, being lovers of unification, would rather see it as stemming from something more fundamental. But that's asking MWI to be more ontologically complete than CI is, to be something demonstrably better-- that's where it has not succeeded, not in its own internal viability. It has failed to be something better than CI, and it is die-hard rationalism, rather than embracing the empiricism of CI.

Unitary evolution according to the Schrodinger 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.

Sure, MWI requires the Born rule postulate too. It is not something demonstrably better than CI.

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.

I think he is very clearly talking about philosophical priorities-- he is talking about MWI as providing the ontological completeness that CI lacks. He is saying that MWI does not in fact achieve that completeness-- it is not better than CI. But if he would criticize MWI for not being coherent, then he would have to explain how the CI collapse postulate is "coherent." It works, it is empirically borne out, but it is completely ad hoc. The CI user is not bothered by this, but only because empiricists always think theories are ontologically incomplete.

So the only problem the MWI rationalists face is they cannot accept ontological incompleteness, they want to have an answer for why the Born rule holds. They are trying to be more ontologically complete than CI, and that's where they fail. I believe that is also what Bell is saying-- the MWI camp has set an unreachable goal for themselves, and that unreachable goal is the thing that cannot be coherently addressed. But if they simply relax that goal, and allow MWI to simply assert the Born rule as a postulate, then they still have many worlds as long as they still have closed systems evolving solely by the Schroedinger equation, and if the meaning of that evolving wavefunction is given by the Born rule as the means of calculating the weights of the mixed state when the effectively closed system becomes effectively open. The defining characteristic of MWI, despite its various flavors and failed efforts to be something more than this, is the interpretation of a mixed state as a projection from something unitary, rather than as an expression of a definite outcome that we the physicists simply don't have full information about.

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 Schroedinger equation without any additional bells and whistles.

This is the key point that we agree on. This is the only basis that MWI can be criticized as an interpretation of QM, because it makes a different claim about what QM is saying, but then one must be able to offer proof that closed systems are not completely described that way, and that is lacking here (that's the "higher standard" I alluded to above).

Also, given the absence of evidence to the contrary, a lot of people do think that a complete account of closed systems that don't contain observers or macroscopic measuring devices can be given by the Schroedinger equation, so they effectively assert that the Schroedinger equation "doesn't work" for the larger "self-measuring" systems. The problem with that view is that an understanding of decoherence has clarified that the Schroedinger equation never actually breaks down when you go to larger systems-- it still provides us with the correct mixed state that happens when you decohere a subsystem by coupling it to a macrosystem. So QM is quite clear on the mixed state you get, that is interpretation independent. The interpretation, then, doesn't even appear until you go to interpret what the mixed state means physically. But that's pure philosophy-- all the physics is over with once you have the mixed-state outcome. You're done with doing calculations and making predictions even before the interpretation, be it MWI or CI, even appears. So none of the interpretations can be "wrong" when the science is already over before you get to them. Instead, they merely reflect different philosophical priorities.

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.)

The absence of completely closed systems is a bugbear for all of physics, not just MWI interpretations of quantum mechanics. It is the reason we have empiricists in the first place-- people who are skeptical that physical theories can ever describe the true reality, because theories always make idealizations to work at all. But rationalists have been over that terrain many times-- they know they are making idealizations, but like Plato, they see the ideal as the true reality. They don't think messy reality is the truth and idealizations are some simplified version that fits in our heads, they think idealized principles are the truth and messy reality is a reflection of how poorly our five senses are able to penetrate to the underlying truth of what reality actually is. That's why they say things like "God is a mathematician". We don't have to agree with rationalism, but we do have to recognize this is the fundamental debate we are entering.

 

[dreamland37]

I believe I may have solved the Many Worlds Problem and it is published in my Book: Science of One: the hidden connection.

The answer as I have published lies in the inherent connection between mind and matter which can otherwise be stated as the collapse of the wave function.

What I mean is that by using Probability Theory we are able to distinguish between those thoughts we call our own, and every day objects. It is the collapse of the wave function which transforms our thoughts (Many Worlds) of Possibilities into the tangent world.

According to Schrödinger, the wave function evolves into a linear superposition of different states, but actual measurements of observation always find it in a single state, meaning that the measurement did something to the process under examination.

Superposition means the placement of one thing on top of another. Schrödinger’s equation of quantum superposition says that any linear combination (sum) of solutions to a particular equation will also be a solution for it. Thus, there can be many right answers to a solution or equation, and the combination of these answers will yield the same
result.

If the world can be in any configuration, any possible arrangement of particles or fields, and if the world can also be in another configuration, then the world can also be in a state that is a superposition of the two. The characteristic of an electron being in more places at once at the same time seems to explain how it can also exist in multiple superpositions. Things only become fixed or come into existence when we perceive (collapse of the wave function) them, as Martin Rees says,

"In the beginning there were only probabilities.
The universe could only come into existence if someone observed it.
It does not matter that the observers turned up several billion years later.
The universe exists because we are aware of it. "

So what I am proposing is that the Many Worlds Interpretation is correct only in the sense that it exists only in the World of our Imagination, the world of possibilities, which make up the world of reality- which is the world of probability.

"Imagination is more important than knowledge.
For knowledge is limited to all we now know
and understand, while imagination embraces the entire world,
and all there ever will be to know and understand. "
—Einstein

WWW.SCIENCEOFONE.COM[/URL]

 

[juanrga]

But you have not supported your claim here. Your claim is that Deutsch is saying Everett would make wrong calculations, but the evidence you cite is a quote that is not saying anything about calculations at all. This is the widespread problem-- an inability to tell the difference between a scientific difference and a difference in philosophical priorities. Give me a quote by Deutsch in which he is saying that Everett does wrong quantum mechanics, not a quote where Deutsch is quite clearly saying that he demands some ontological "connection" between the wave function and the universes. That looks to me like Deutsch is simply raising a philosophical objection, which I claim is exactly where all the debates about interpretations are held.
Remind me-- what extra mathematical structure are you talking about? The main proponent of MWI, early in this thread, was Hurkyl, and I am aware of the writings of Max Tegmark, and neither of them ever refer to any "extra mathematical structures", indeed their support of MWI invariably rests on what they perceive as an absence of extra mathematical structures (like the deBB pilot waves, or the Copenhagen manual postulate about wavefunction collapse). In my view, they are right about that-- MWI is clearly the mathematically minimalist description, it is just not the empirically minimalist description (that's CI) or the most neoclassical (that's deBB).
That will come as a big surprise to Hurkyl, he seems to have no trouble making correct calculations. The grandiose claims made about the failings of MWI as a viable interpretation seem highly unresponsive to the facts of the matter. All I see are objections that are ontological and philosophical in nature, and a bunch of empty claims that they are more than that. I think the real problem is that MWI proponents are trying to arm their interpretation with more completeness than has been demonstrated by either deBB or CI, and that's where they have not succeeded-- because that would make MWI more than just a different interpretation, it would make it a different theory (as it invariably comes with suggestions for different predictions it would make, like if influences from "other worlds" could actually be measured).
Says you, but that very clearly is a question that must be answered by the person using that motivation. An interpretation is just not anything more than whatever the physicist is imagining is happening when he/she thinks about the result they are calculating. Why don't we see people claiming that Newtonians "may be capable of performing correct calculations, but those calculations are not warranted" by imagining that forces are real, rather than that action is minimized or some such equivalent interpretation of what is really happening there? Why do people argue about this in quantum mechanics, but not classical mechanics, even though saying that action is minimized is just as ontologically vastly different from saying that there are real forces, as is saying that there are many worlds is different from there being pilot waves. For some reason, when we get to quantum mechanics, everyone seems to suddenly forget what an equivalent interpretation means any more.
That just doesn't make sense to me. No one "adheres to" an interpretation when they do quantum mechanics (that's why some people claim they only "shut up and calculate"), they apply the postulates of quantum mechanics, which you can read in any textbook on quantum mechanics (some of which make no mention at all of any interpretation whatsoever). No one uses an interpretation to do quantum mechanics, they use an interpretation to give them something to picture in their minds when they do quantum mechanics. The interpretation motivates the equations they are using, it does not provide the equations they are using. Indeed, quantum mechanical interpretations are often even less important than interpretations of classical mechanics, because in classical mechanics the equations can start out being different (as in minimizing action vs. Newton's laws), even though they end up being the same before the motion is solved. That's more akin to deBB, which starts out with a different equation before it ends up solving Schroedinger, but MWI and CI don't even do that-- the equations are never different one iota. Often, interpretations in QM, like MWI and CI, appear after the fact of the calculation-- they tend to be a priori types of interpretations, which is the least significant type.
Let's look at an example. You can easily solve for the motion of the Earth around the Sun by treating the Earth-Sun system as closed and applying the Schroedinger equation, we just approximate the Earth as having a pure-state wavefunction when we know if we had more precision we'd have to treat is as a mixed-state subsystem.

No one knows if large suitably closed systems have pure-state wavefunctions or if they have to be treated as mixed states, it has never been put to the test. The expectation from quantum mechanics is that the more closed the system is, the less of a mixed-state description it requires, leading ultimately to a pure state in the limit of complete closure. So the MWI proponent holds that if we had truly closed systems, they would evolve unitarily, but we always actually have mixed-state subsystems projected from larger systems that we are not treating. By "large" I don't necessarily mean spatially large, I just mean there is a way larger amount of information in that system than we would ever be able to use our intelligence and senses to analyze or track, so we instead track a remotely tiny subset of that full complexity. The MWI proponent sees that fact as the reason that we do not perceive the full "unity" of the effectively closed systems we participate in.
CI does not escape this problem either, it just makes different philosophical choices about how to deal with it. CI says that effectively closed systems evolve by the Schroedinger equation until you open them up, and the mixed states that appear when one considers open subsystems should be interpreted as definite outcomes that there is a lack of information about until the definite result is recorded. There is no evidence of any time-symmetry breaking there in anything that is happening independently of how we do physics, it is merely by fiat that the arrow of time is applied. It has our fingerprints all over it, just as does the second law of thermodynamics. So CI is pretty much standing up and saying "physics is done by physicists, and is all about what we can say about nature and nothing more." It is all the things so many on this thread reject, in the same breath that they reject MWI, even though MWI provides a way to avoid having a very clear role of the mind of the physicist in the ontology of the interpretation.
I did balk at that point, but my way of balking was not to say MWI is invalid, I merely used the example to point out how radically rationalistic MWI is-- it represents the complete denial of the role of the mind of the physicist in physics (rationalists view mathematics as existing outside the mind of the mathematician). I don't think it's invalid to do that, I think it's invalid to do that and claim that a fairly narrow set of philosophical priorities is not being invoked in the process. The rationalistic MWI proponent thinks that the arrow of time is an illusion, as is the whole concept of a definite unique outcome of an experiment. MWI is a symmetry principle-- the symmetry that any outcome that can occur cannot be distinguished in the full reality from any other outcome that can occur, so the distinctions we perceive are illusory. It is the culmination of the Parmenides philosophy that A cannot become B unless A and B are the same thing.
Not so, MWI proponents have no trouble applying the Born rule. It is as though you think they are schizophrenic, as if their interpretation forces them to reject the Born rule postulate, so whenever they do a QM calculation they enter an unconscious state when they apply the Born rule, and wake up seconds later with no memory of having used it!

That's not what they do, they simply apply the Born rule when they determine the weights of the mixed state they get when they consider a subsystem (like a measured object). MWI has no problem at all with the Born rule, they simply view it as the weights of a mixed state, rather then as probabilities of what "really happens." They only get into trouble when they are unwilling to think of the Born rule as an additional postulate to the wavefunction evolution, they, being lovers of unification, would rather see it as stemming from something more fundamental. But that's asking MWI to be more ontologically complete than CI is, to be something demonstrably better-- that's where it has not succeeded, not in its own internal viability. It has failed to be something better than CI, and it is die-hard rationalism, rather than embracing the empiricism of CI.
Sure, MWI requires the Born rule postulate too. It is not something demonstrably better than CI.
I think he is very clearly talking about philosophical priorities-- he is talking about MWI as providing the ontological completeness that CI lacks. He is saying that MWI does not in fact achieve that completeness-- it is not better than CI. But if he would criticize MWI for not being coherent, then he would have to explain how the CI collapse postulate is "coherent." It works, it is empirically borne out, but it is completely ad hoc. The CI user is not bothered by this, but only because empiricists always think theories are ontologically incomplete.

So the only problem the MWI rationalists face is they cannot accept ontological incompleteness, they want to have an answer for why the Born rule holds. They are trying to be more ontologically complete than CI, and that's where they fail. I believe that is also what Bell is saying-- the MWI camp has set an unreachable goal for themselves, and that unreachable goal is the thing that cannot be coherently addressed. But if they simply relax that goal, and allow MWI to simply assert the Born rule as a postulate, then they still have many worlds as long as they still have closed systems evolving solely by the Schroedinger equation, and if the meaning of that evolving wavefunction is given by the Born rule as the means of calculating the weights of the mixed state when the effectively closed system becomes effectively open. The defining characteristic of MWI, despite its various flavors and failed efforts to be something more than this, is the interpretation of a mixed state as a projection from something unitary, rather than as an expression of a definite outcome that we the physicists simply don't have full information about.
This is the key point that we agree on. This is the only basis that MWI can be criticized as an interpretation of QM, because it makes a different claim about what QM is saying, but then one must be able to offer proof that closed systems are not completely described that way, and that is lacking here (that's the "higher standard" I alluded to above).

Also, given the absence of evidence to the contrary, a lot of people do think that a complete account of closed systems that don't contain observers or macroscopic measuring devices can be given by the Schroedinger equation, so they effectively assert that the Schroedinger equation "doesn't work" for the larger "self-measuring" systems. The problem with that view is that an understanding of decoherence has clarified that the Schroedinger equation never actually breaks down when you go to larger systems-- it still provides us with the correct mixed state that happens when you decohere a subsystem by coupling it to a macrosystem. So QM is quite clear on the mixed state you get, that is interpretation independent. The interpretation, then, doesn't even appear until you go to interpret what the mixed state means physically. But that's pure philosophy-- all the physics is over with once you have the mixed-state outcome. You're done with doing calculations and making predictions even before the interpretation, be it MWI or CI, even appears. So none of the interpretations can be "wrong" when the science is already over before you get to them. Instead, they merely reflect different philosophical priorities.

The absence of completely closed systems is a bugbear for all of physics, not just MWI interpretations of quantum mechanics. It is the reason we have empiricists in the first place-- people who are skeptical that physical theories can ever describe the true reality, because theories always make idealizations to work at all. But rationalists have been over that terrain many times-- they know they are making idealizations, but like Plato, they see the ideal as the true reality. They don't think messy reality is the truth and idealizations are some simplified version that fits in our heads, they think idealized principles are the truth and messy reality is a reflection of how poorly our five senses are able to penetrate to the underlying truth of what reality actually is. That's why they say things like "God is a mathematician". We don't have to agree with rationalism, but we do have to recognize this is the fundamental debate we are entering.

Since this is going repetitive, this is my last contribution to this thread. I will be succinct.

Everett's work has been showed wrong. As a consequence modern MWI advocates differ from Everett's early work and propose other formulations that try to correct the deficiencies.

The own literature on MWI is self-contradictory, with some advocates claiming that MWI is just another interpretation of QM (this is not true), whereas others claiming that it is really another theory than QM and giving different predictions (none verified).

There is not such one thing as "The MWI", but different inconsistent (their axioms and mathematical formalism are flawed) and/or falsified (they do not describe observations) formulations.

Standard texbooks on QM deal with the Copenhagen formulation.

The postulates used in the different formulations of MWI are not the postulates of QM, because MWI is not an interpretation of QM. Moreover, the postulates of the MWI formulation given by Hartle et al, are not the same that those given by Everett, neither those the same that the postulates given by Deutsch, for instance.

One cannot treat the Earth-Sun system as a closed quantum system following the Schrödinger equation. Even if one was to assume that its state is given by some wavefunction at t_0 this wavefunction ceases to describe the state about 10^-23 seconds latter. This is well-known.

Quantum mechanics does not say that any isolated (you insist on confounding with 'closed') is described by the Schrödinger equation. And any decent textbook in QM that I know avoid to use the words closed and isolated in their postulates. What you are describing is not QM but your own misunderstanding of QM.

Fathers of QM as Born and von Neuman were very clear about the subject. For instance, Born insisted that the isolated supersystem (measuring device plus system under study) is not described by the Schrödinger equation. And Von Neuman introduced the collapse postulate because he showed that it is not derivable from the other postulates. Concretely, the collapse postulate cannot be derived from Schrödinger evolution postulate for any supersystem (including the universe as a whole).

There is many more flaws behind the MWIs approach, such as the misunderstanding about basic aspects of the scientific method and its introduction of extranatural «superobservers» (living outside universe), the fact cannot explain the Born rule, (the derivations claimed by MWI advocates are either wrong or are not derivations at all because use some initial extra assumption equivalent to the rule), and so on.

MWIs will continue to play a role in science-fiction and in all the metaphysics about multiverses, and in no doubt new versions will be invented and published in literature by people who do not understand QM or who cannot do the maths. But MWI is already discredited as a serious theory, it is a lost cause as the cited website correctly points.

 

[Ken G]

I can see you have a quite a few personal opinions on the topic. Unfortunately they are not consistent with opinions I have heard expressed by others I consider to be experts in quantum mechanics, so without further elucidation of your opinions, I just don't see much reason to be convinced by them, though I will certainly store them under "additional opinions I have heard expressed".

The only issue that seems to be on a firm basis that you raise is that "what is MWI" is a complicated issue, but then so is "what is CI" or "what is deBB". All those labels are just general ways of characterizing whole classes of interpretations. I've seen people who associate CI with the idea that wavefunctions are real and they really mystically collapse, even though Bohr was always quite clear that he did not see the wavefunction as something real. I've seen people discuss nondeterministic versions of deBB even though the entire point of that interpretation seems to be to maintain strict determinism. So all these interpretations spawn variants, there's nothing special about MWI in that department, and it certainly does not serve as a logical point of criticism about MWI.

To clarify the language, to me the defining characteristics of those classes of interpretations is what matters, not all the variants on the theme. I would say that the defining characteristic of CI is a dogged empiricism, which asserts that wave functions are tools used by physicists to make predictions, so can evolve either unitarily, or be puncutated by sudden collapses, entirely at the whim of the physicist using them to achieve some goal. So CI is defined as the "no mathematical ontology" standpoint.

I would say the defining characteristic of deBB is that, like CI, the wavefunction is not viewed as physically real, but instead of saying there are no mathematical realities at all, it asserts a rationalistic allegiance to a deeper mathematical reality (the pilot wave) that underlies the wavefunction. This allows for a neoclassical interpretation where particles are still particles and still follow completely deterministic trajectories, but when we address the things we cannot know about the particle (stemming from the pilot wave), we are forced to use a quasi-indeterminate treatment (the wave function) that is not the physical reality.

And I would say the defining characteristic of MWI is its highly rationalistic ontology of the wavefunction, and its unitary evolution via the Schroedinger equation, as the fundamentally real mathematical entity that quantum mechanics is about. Variants on that theme are of no particular interest to anyone but those who take these interpretations highly seriously (like Deutsch), but they are doing ontology not physics. Anyone who holds the basic core value that the wavefunction and its unitary evolution is the core reality of QM is adopting MWI, because the re-establishment of unitarity under that arrangement requires many worlds that we do not perceive in our empirical physics.

What's more, since all of those interpretations look, in actual practice of doing science, like solving the Schroedinger equation and applying the Born rule, there are actually no scientific differences between them in regards to doing quantum mechanics. Claims made about different predictions, that could support thinking of these as different theories, are always unfounded in practice-- no such different predictions are being tested anywhere in physics, though some might imagine they are trying (they aren't succeeding). If and when there really is experimental data that QM does not handle admirably, only then will the interpretations have scientific meaning, because each might inspire different ways to react to the anomalous data and spawn truly new theories (likely different from anything we have now). And only then will discussions of interpretations be anything but a discussion about philosophical priorities.

 

[kith]

juanrga, do you think the de-Broglie-Bohm interpretation and the ensemble interpretation are flawed, too? To me it seems whenever you say quantum mechanics, you actually mean the Copenhagen interpretation, because many of your statements equally affect other interpretations.

Lets take the ensemble interpretation for example, because it is very close to Copenhagen. The axioms are the same, except that there is no collapse, because |ψ> is not the state of a single system, but of an ensemble of systems (see for example Ballentine, Rev. Mod. Phys. 42, 358–381 (1970)). On what physical grounds do you reject such an interpretation?

And regarding your arguments from authority (Born, Neumann): there has been much progress in QM since the 1930s. For the current debate, the progress in understanding decoherence is probably the most important. See for example Schlosshauer, Rev. Mod. Phys. 76, 1267–1305 (2005), who discusses the implications on different interpretations.

 

[dreamland37]

You say that the wavefunction is not viewed as physically real, but instead an allegiance to a deeper mathematical reality (the pilot wave) that underlies the wavefunction. And that this allows that particles are still particles which follow completely deterministic trajectories, but when we address the things we cannot know about the particle (stemming from the pilot wave), we are forced to use a quasi-indeterminate treatment (the wave function) that is not the physical reality.

In my opinion, as far as simple English is concerned, I think the double slit experiment confirmed that an electron has an interference pattern when it passes through both the slits. Meaning that it behaves as a wave when left unobserved. However, when you try to measure which slit it goes through, the interference pattern vanishes and merely the particle behavior arises.

In other words, the wave function is not only a mathematical tool, but a real description of reality. Einstein gave up many of his unified field theories which were mathematically correct and even beautiful as described, he gave them up because he failed to find any true connection to reality behind the equations. That is the one problem that many people have with mwi.

That is why I posed a new interpretation of MWI, one that unifies all the theories and ascribes a physical reality to the equations. It is the only explanation that fits the math, but if the theory is correct than it implies that on a fundamental level, all quantum possibilities are inherent realities possessing a hint of the true essence of things but reside only within the Mind. Since matter is nothing more than the manifestation of the Mind as the collective data via our senses, it means that the collapse of the wave function is nothing more than the most probable state of these quantum possibilities. It is the act of measuring (something that can make a judgement) which collapses the wave function.

Therefore the difference between the Mind and Matter, possibility and probability is nothing other than the collapse of the wave function. This is the best interpretation I have found for the Many worlds

 

[Ken G]

In my opinion, as far as simple English is concerned, I think the double slit experiment confirmed that an electron has an interference pattern when it passes through both the slits. Meaning that it behaves as a wave when left unobserved. However, when you try to measure which slit it goes through, the interference pattern vanishes and merely the particle behavior arises.

Yes, we agree that is the experimental fact. But the Bohmian perspective has an account for that which is entirely deterministic. The trajectories the particles follow is altered by the presence of the experiment that determines the which-way information-- it has an effect on the pilot wave, and the pilot wave shepherds all the possible particle trajectories into doing what the Schroedinger equation says it should do, subject also to the informational constraints. It is "one stop shopping" for Bohm, you just say "the pilot wave did it". Unfortunately the pilot wave has no requirement to be there, so many view it as superfluous, but for those who like determinism, they are welcome to hold that it is actually there and their belief cannot be falsified by experiments of the kind you describe (or any other known).

In other words, the wave function is not only a mathematical tool, but a real description of reality.

The two ways to hold that, MWI and consciousness-based collapsed, both seem rather mystical to a lot of physicists. I know you hold to the latter of those, and just like the Bohmians, if you are inclined to believe that there is no known experiment that can falsify your belief.

That is why I posed a new interpretation of MWI, one that unifies all the theories and ascribes a physical reality to the equations. It is the only explanation that fits the math, but if the theory is correct than it implies that on a fundamental level, all quantum possibilities are inherent realities possessing a hint of the true essence of things but reside only within the Mind.

That isn't really a theory because it doesn't make any new predictions. However, it is a perfectly valid interpretation, albeit somewhat mystical and inclined to lean on Cartesian mind/body dualism. Is that a strength or a weakness? I have no idea, it depends on one's philosophical priorities, and the next big theory that none of us know yet.

Since matter is nothing more than the manifestation of the Mind as the collective data via our senses, it means that the collapse of the wave function is nothing more than the most probable state of these quantum possibilities. It is the act of measuring (something that can make a judgement) which collapses the wave function.

Yes, I see no flaw in that position, I place it squarely amid all the other interpretations! One would associate it with either dualism or idealism, depending on whether or not you believe there really is a physical reality that the mind is in contact with.

Therefore the difference between the Mind and Matter, possibility and probability is nothing other than the collapse of the wave function. This is the best interpretation I have found for the Many worlds

Personally I would prefer that to many worlds, if I had to hold that the wavefunction is something real, but I tend to favor the empiricism of saying that the wavefunction isn't real and the next big theory probably won't even use it.

 

[Samshorn]

But you have not supported your claim here...

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 Schrodinger’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 particlar definition of the “measure” of a state, but there is nothing in the single axiom of Schrodinger 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 Schrodinger 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). (The 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.

 

[Ken G]

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 Schrodinger’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.

My take on this is that MWI should never claim to yield all the empirical content of quantum mechanics with just the unitarity postulate, it should claim to hold all the ontological content of quantum mechanics that way. MWI is an interpretation of what is really happening, we already know it does not gibe with our empirical experience. It claims that our empirical experience is not the complete story (as it is nonunitary), so we need the Born rule to describe our empirical experience. However, the Born rule is then seen as a description of the incompleteness of our experience-- the "full reality" has no Born rule, it is just the wavefunction evolution. One might then say that the Born rule controls some kind of measure of the "worlds" that split off into different experiential coherent islands that are mutually incoherent. So yes, it will always take an additional postulate to get the measure of that splitting (or fragmenting and re-merging, these aspects of MWI are not clear because they don't deal with what is "really happening" to the whole system but rather with the vagaries of coherent experiences of subsystems).

I say this claim is false, because (among other reasons) all the measurement correlations predicted by quantum mechanics correspond to one particlar definition of the “measure” of a state, but there is nothing in the single axiom of Schrodinger 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.

Yes, but we should not expect MWI to circumvent the Born postulate, it's still quantum mechanics. It is just a way to interpret quantum mechanics where the Born rule appears at the level of how physicists experience the reality, the piece they get to experience. It's too much to ask that they would have any better insight into that than the CI does (except for those who ask MWI to be better than CI)-- it's just the ad hoc way that the wavefunction passes into predictions about our experience. Of course, CI maintains that the latter is all that physics is ever about, so saying anything more is entering into a kind of rationalistic fantasy.

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).

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. To a rationalist, empirical content is of secondary importance, which you can tell when you see them use phrases like "the experiments test the theory, to determine which theory is true" rather than just "experiments determine truth." The key difference is that the theory survives if the observations don't falsify it, rather than establish it. To them it is the theory that is the truth, or at least the approximation to the truth if the theory is only "converging on" the truth. So if the theory says we have a wavefunction that evolves unitarily, then that's the truth as long as observations can be interpreted as not falsifying it, and the nonunitary experiences described by the Born rule are nothing more than trying to understand why people see mirages in the desert. Yes it's important to the progress of science to be able to explain why people see mirages in the desert, but it's not so critical to the ontology of what a desert "really is." When you look at MWI that way, you see that they can have a self-consistent ontology without the Born postulate, and no observations falsify the many worlds description, but they just can't use it for science until they tack on the Born rule. That doesn't make it less than CI, it makes it equivalent to CI, from the scientific perspective-- the end of the equivalence comes only in the ontology.

It is an objection to the validity of the claim that the single axiom of Schrodinger evolution of a wave function for isolated systems is sufficient to constitute an interpretation of quantum mechanics.

I don't think it is sufficient to constitute an interpretation of quantum mechanics, it is sufficient to constitute an interpretation of the ontology of quantum mechanics used by MWI. To actually get an interpretation of quantum mechanics, you have to be able to interpret the Born rule somehow. So you have to be able to say that the Born rule gives the measures of the many worlds, and that is always going to be ad hoc-- because it is the part of the ontology that deals with physicists' perceptions, and no one has any kind of model for that.

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). (The 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.

What is your objection to MWI simply saying that the true ontology of the universe is the unitary evolution of the wave function, and the Born rule is just a rule about how the wavefunction controls the creation of "coherent islands" of analytical intelligent agents? Certainly MWI cannot say why the Born rule does that, nor can CI, nor can Einstein say why mass curves spacetime. It just isn't different physics, it's still quantum mechanics-- and that's why debates about interpretations have to involve nothing more than philosophical priorities (until someone claims MWI is demonstrably better than CI, in which case they need to be able to explain the Born rule better than CI does-- I agree that I have never seen that pulled off, but that only supports my contention that the differences are all philosophical).

 

[dreamland37]

Dear Ken G,

I agree with you on most points, you seem most wise and I enjoy reading your thoughts. I also agree that my theory isn't a new one in that I haven't been able to form any new predictions with it yet. In essence it is only an extension of probability theory to incorporate QM and Relativity based on a deeper understanding of the collapse of the Wave function. It does however give explanation to all unexplained phenomena in the sense that every thought is a reality as in the case of MWI, and the consequences that follow from that assumption is that if a person could form an exact idea of an object than there would be no way to distinguish between the two.

On the other hand, quite contrary to Cartesian mind/body dualism which Spinoza was not able to unify, my theory or extension of probability theory unifies the mind/body dualism via the collapse of the wave function which incorporates George Berkeley's "esse est percipi" (to exist is to be perceived) which is more or less the philosophical reality behind the collapse of the wave function. I have not yet however been able to explain absolute motion with this theory in the case of Isaac Newton's rotating spheres argument.

The development of Bells theorem does not incline the notion of hidden variable theories such as the Pilot wave theory. Bell's theorem suggests in the opinion of most physicists and contrary to Einstein's assertion that local hidden variables are impossible. It allows action at a distance which is one of the assumptions that the EPR paper was aimed at pointing out in an attempt to show that QM is incomplete.

Therefore the Pilot wave theory can't be seen as a complete interpretation because it is deterministic which doesn't allow action at a distance contrary to Bell's theory and Classical Quantum mechanics.

On subtler levels of existence many scientists agree that elementary particles seem to know about the changes in their surrounding environment and will act as if they are consciously aware of these changes, but of course, the varying degree of consciousness
pertaining to each particle will be relative. However, some particles seem to lose their properties of consciousness when they become entwined with other particles to the point where a state of incoherence sets in. The particle’s consciousness is subdued as a result of the other particles interfering with it; however, if the particles are in accord with each other, then a harmony of consciousness will once again emerge
among them.

Max Planck said,

"There is no matter as such. All matter
originates and exists only by virtue of a force which brings the particle
of an atom to vibration and holds this most minute solar system of the
atom together. We must assume behind this force the existence of a
conscious and intelligent mind. This mind is the matrix of all matter. "

So I feel that without an observer to single out the reality of possibilities we live in, it is meaningless to even talk about many worlds. For an observer and reality are complementary to each other, just as the dream and the dreamer.

 

[Ken G]

On the other hand, quite contrary to Cartesian mind/body dualism which Spinoza was not able to unify, my theory or extension of probability theory unifies the mind/body dualism via the collapse of the wave function which incorporates George Berkeley's "esse est percipi" (to exist is to be perceived) which is more or less the philosophical reality behind the collapse of the wave function.

Yes, I suspected yours was essentially the "idealist" interpretation of quantum mechanics. I don't dispute that interpretation is fully available if one is inclined to idealism, Berkeley would probably have liked quantum mechanics a lot. One thing I will personally agree with you is that quantum mechanics may be the first time that we are seeing, in our physics, the reflections of our own minds. I'm not sure that the role of the mind is neatly or clearly laid out in quantum mechanics, but I do get the sense we are seeing through that glass darkly. That's why I think the next big advance in physics might come from neuroscience or artificial intelligence-- we may be at the point where we need to understand our own minds to progress further in physics. Or maybe we're not at that place yet, and string theory is the next place to go. Only time will tell!

The development of Bells theorem does not incline the notion of hidden variable theories such as the Pilot wave theory. Bell's theorem suggests in the opinion of most physicists and contrary to Einstein's assertion that local hidden variables are impossible.

Yes, but pilot waves are not local hidden variables. The purpose of the pilot wave is to get the same behavior that the Schroedinger equation gets, so any experiment (like those of Bell type) that quantum mechanics gets right is just fine with Bohmian mechanics.

Therefore the Pilot wave theory can't be seen as a complete interpretation because it is deterministic which doesn't allow action at a distance contrary to Bell's theory and Classical Quantum mechanics.

Determinism is not incompatible with action at a distance. Champions of Bohmian mechanics might revel in the holistic character of Bell's theorem-- they'd say "see, we told you there was a nonlocal pilot wave there."

Max Planck said,

"There is no matter as such. All matter
originates and exists only by virtue of a force which brings the particle
of an atom to vibration and holds this most minute solar system of the
atom together. We must assume behind this force the existence of a
conscious and intelligent mind. This mind is the matrix of all matter. "

That's the great thing about quantum mechanics-- it admits to a host of wildly differing interpretations about what it all means. However, we must recognize that there is no appeal to authority when choosing an interpretation-- for there are "authorities" on every side of the issue. All we can do is say "gee isn't it grand that such a seemingly dry and impartial endeavor as physics can be so vibrantly alive with vastly differing interpretations."

So I feel that without an observer to single out the reality of possibilities we live in, it is meaningless to even talk about many worlds.

I certainly agree that it is meaningless to talk about anything in physics without an observer, for the simple reason that physics is an empirical science, and also there wouldn't be anyone to do the talking.

For an observer and reality are complementary to each other, just as the dream and the dreamer.

The metaphor is poetic, and certainly apt to some interpretations, but I point out that others would see in that metaphor the basic flaw: physics is supposed to be the description we get when we are awake, not when we are asleep. But I personally agree with the complementarity of observer and reality, as I believe would Bohr.

 

[BruceW]

Ken G - Can I ask about the word holistic? I see it being used a lot but I'm not totally sure what it means..

Holism means something like 'the whole is more than just the parts together' right?

So a 'holistic theory' is a theory that can be applied to many different questions? And as an example, Einstein's general theory of relativity is holistic because it tells us that the laws of physics are the same for any observer. So this one theory tells us something about all other theories that obey relativity. Is all this roughly correct?

 

[dreamland37]

Dear Ken G,

You make very valid points and thank you for providing a more wholesome view Bohemian mechanics. You draw out your arguments in a clear and concise way, but I fail to see how pilot waves are not local hidden variables.

Even according to the wiki, the Pilot wave description is listed as

"Principles
The Pilot Wave theory is a hidden variable theory...
The position and momentum of every particle are considered hidden variables; they are defined at all times, but not known by the observer; the initial conditions of the particles are not known accurately, so that from the point of view of the observer, there are uncertainties in the particles' states which conform to Heisenberg's Uncertainty Principle." http://en.wikipedia.org/wiki/Pilot_wave

In other words, if it is not a hidden variable theory it will break Heisenberg's Uncertainty Principle.

 

[Samshorn]

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.

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 Schrodinger 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 Schrodinger 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 Schrodinger'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 embedd all possible outcomes into a superstructure whose overall shape (unitary) we find more pleasing.

 

[kith]

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 Schrodinger equation, as is the future evolution of V.

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.

Also 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.

 

[Samshorn]

...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.

The hypothesis in question is that every isolated system (which may be a sub-system of some larger system) undergoes unitary evolution in accord with Schrodinger'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 Schrodinger 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.

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.

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.

 

[kith]

The hypothesis in question is that every isolated system (which may be a sub-system of some larger system) undergoes unitary evolution in accord with Schrodinger's equation - and nothing else.

Ok. But this is the case in the CI as well as in the MWI. Collapse occurs only in measurements and in order to perform a measurement, you have to interact with your system. Thus it is not isolated anymore.