Different interpretations? No, different theories

[JK423]

I was reading Everett's paper
http://rmp.aps.org/abstract/RMP/v29/i3/p454_1
on the "Relative State" Formulation of Quantum Mechanics, and i realized that this is not an interpretation experimentally equivalent to other "interpretations" like the Copenhagen.. These are different theories that give different predictions!
For example, Everett's (elegant and simple) formulation of quantum mechanics is based on the hypothesis that everything is quantum mechanical, hence the observer and apparatus are all quantum mechanical systems decribed by the deterministic Schrodinger's equation. The Copenhagen formulation of quantum theory denies that, which means that it's something testable to experiments. If someone is able to design an experiment which proves the quantum mechanical nature of an apparatus and an observer, then he disproves the Copenhagen theory, hence Everett's theory will be the correct one..

Someone may object that proving the quantum mechanical nature of the observer is mission impossible. Indeed. But is this relevant? The different predictions are there. The fact that one cannot design an experiment, for practical reasons and not of principle, to investigate these predictions is another thing. I never saw anyone calling string theory a "different interpretation" of nature (..not implying ofcourse that the degree of "impossibility" is the same in the two cases! :) ). To my understanding, we have to do with different theories and should stop calling them different "interpretations".

 

[Fredrik]

Observers and measuring devices are obviously not classical, since their component parts aren't. This has nothing to do with Copenhagen vs. many worlds.

An experiment that "proves the quantum nature of an apparatus and an observer" is impossible to carry out in practice. But a much more relevant fact is that even if we could carry it out, it wouldn't shed any light on which interpretation is correct. The reason is that what we would use to "prove the quantum nature" of some measuring device, is another measuring device, and its necessary that this second measuring device can for all practical purposes be treated as classical when we're doing this experiment. The reason is that we couldn't possibly interpret the final state of that second measuring device as a result of the experiment unless a human observer can easily distinguish that final state from the other possible final states.

What's relevant in practice may not be relevant to a theorist or a philosopher, but what's relevant in principle certainly should be. And it's not possible in principle for the indicator component of the measuring device that's supposed to tell us the result of the experiment to behave in a way that is distinguishable from classical during the experiment, because if it did, we wouldn't consider it a measuring device.

My thoughts on Everett's idea is that it's just a crippled version of QM that fails to make any predictions at all. The problem is that he removed the Born rule, which is what we use to assign probabilities to possible results of experiments. Some people claim that the Born rule can be recovered, but that's only true if you make some other assumptions instead of it, and I think those assumptions can always be derived from the Born rule. So it seems to me that those derivations don't really tell us anything.

 

[JK423]

What you are saying implies that an observer can be both classical and quantum mechanical at the same time, which is a contradiction. For example consider the Schrodinger's cat experiment where the cat is an observer.

1) The cat, inside the box, is doing it's own experiments collapsing wavefunctions non-unitarily. Cat=classical

2)However cat+box is a closed quantum mechanical system, for an external observer, that evolves unitarily. The latter implies that all the interactions inside the box are unitary. Cat=quantum mechanical

Since (1) and (2) should hold simultaneously, we are lead to a contradiction hence this cannot be true.

Am i right?

 

[Nugatory]

I was reading Everett's paper
http://rmp.aps.org/abstract/RMP/v29/i3/p454_1
on the "Relative State" Formulation of Quantum Mechanics, and i realized that this is not an interpretation experimentally equivalent to other "interpretations" like the Copenhagen.. These are different theories that give different predictions!

Different predictions aren't enough, we'd need different testable predictions. Sure, MWI seems to be predicting that the cat in the unopened box is alive or dead and Copenhagen seems to be predicting that the cat in the unopened box is alive and dead; but they both agree that no conceivable (in principle; it's not just a matter of practical difficulties) experiment can distinguish the two.

 

[JK423]

Different predictions aren't enough, we'd need different testable predictions. Sure, MWI seems to be predicting that the cat in the unopened box is alive or dead and Copenhagen seems to be predicting that the cat in the unopened box is alive and dead; but they both agree that no conceivable (in principle; it's not just a matter of practical difficulties) experiment can distinguish the two.

In order to promote an "interpretation" to a "theory", you just need different predictions that can be tested in principle. In this thread i just want to argue that they are different theories, not different intepretations, and i don't argue on which is the correct one (because i don't know) and how to devise an experiment to prove it.. So, it doesn't matter if these predictions are testable with today's technology or not, it matters only that they are testable in principle.

 

[stevendaryl]

Observers and measuring devices are obviously not classical, since their component parts aren't. This has nothing to do with Copenhagen vs. many worlds.

I don't agree. If you analyze people and measuring devices and the universe by the same Rules of Quantum Mechanics that you use to analyze electrons and atoms, then it seems to me that Many Worlds is where you end up. If an electron is in a superposition of spin-up and spin-down, and a human measures its spin, then the human will enter into a superposition of "human measuring spin-up" and "human measuring spin-down". Very quickly, the Earth is in a superposition of "Earth where that human measured spin up" and "Earth where that human measured spin down". The "Many Worlds" aspect is, it seems to me, inevitable unless you impose some non-unitary evolution step that destroys some branch of a superposition.

My thoughts on Everett's idea is that it's just a crippled version of QM that fails to make any predictions at all. The problem is that he removed the Born rule, which is what we use to assign probabilities to possible results of experiments.

But it's hard for me to understand what possible role there can be for a postulated Born rule if you treat macroscopic objects quantum mechanically. What does it mean to say "The experimenter has a 50/50 chance of measuring spin-up or spin-down?" if what actually happens is that he deterministically evolves into a superposition of "human measuring spin-up" and "human measuring spin-down"? It seems to me that there are only two possibilities:

1. There is something nonunitary that happens, that breaks the superposition and destroys all branches except one.
2. There is some way to understand the Born rule from the point of view of pure unitary evolution of the wavefunction.

I agree with you, that it seems that there is no noncircular way to derive Born probabilities from Many Worlds. On the other hand, if you imagine a wave function $\vert \Psi \rangle$ for the entire universe, you can mathematically decompose it into a superposition of macroscopically distinguishable states (plus maybe some junk states that can't be understood as a classical universe, at all). It seems plausible to me (although I haven't done it, and I don't know whether anyone has) that one could start with a pure theory of smooth wave function evolution and derive an "effective" theory for the evolution of "macroscopically distinguishable states of the universe" that would look a lot like Copenhagen with its Born rule and wave function collapse.

 

[JK423]

I don't agree. If you analyze people and measuring devices and the universe by the same Rules of Quantum Mechanics that you use to analyze electrons and atoms, then it seems to me that Many Worlds is where you end up. If an electron is in a superposition of spin-up and spin-down, and a human measures its spin, then the human will enter into a superposition of "human measuring spin-up" and "human measuring spin-down". Very quickly, the Earth is in a superposition of "Earth where that human measured spin up" and "Earth where that human measured spin down". The "Many Worlds" aspect is, it seems to me, inevitable5 unless you impose some non-unitary evolution step that destroys some branch of a superposition.

I agree with you.
I just don't like the name "Many Worlds" because i feel like extra assumptions are hidden in this name. Everett's original paper only states that everything evolves unitarily, and says nothing about "Many Worlds" and "Universes being continuously created", and personally i think that it's more safe to stay with the original paper.

 

[Nugatory]

In order to promote an "interpretation" to a "theory", you just need different predictions that can be tested in principle. In this thread i just want to argue that they are different theories, not different intepretations, and i don't argue on which is the correct one (because i don't know) and how to devise an experiment to prove it.. So, it doesn't matter if these predictions are testable with today's technology or not, it matters only that they are testable in principle.

But both Copenhagen and MWI agree that none of their different predictions are testable in principle. So I don't understand how to reconcile the first sentence of the above with the argument you're making.

 

[stevendaryl]

But both Copenhagen and MWI agree that none of their different predictions are testable in principle. So I don't understand how to reconcile the first sentence of the above with the argument you're making.

I thought I remembered reading about a clever experiment that supposedly could detect the existence of macroscopic superpositions. Quantum computing almost counts, but it's not quite macroscopic.

 

[Nugatory]

I thought I remembered reading about a clever experiment that supposedly could detect the existence of macroscopic superpositions. Quantum computing almost counts, but it's not quite macroscopic.

The effects of macroscopic superpositions can be observed, but AFAIK can be analyzed in either Copenhagen or MWI terms... So no help there.

 

[Fredrik]

What you are saying implies that an observer can be both classical and quantum mechanical at the same time, which is a contradiction.

They are always quantum mechanical, but interactions with the environment will make their behavior indistinguishable from classical, and because of that, we usually don't use the words "quantum mechanical" when we talk about them.

1) The cat, inside the box, is doing it's own experiments collapsing wavefunctions non-unitarily. Cat=classical

Quantum mechanical, but in a state that's practically indistinguishable from a classical superposition.

2)However cat+box is a closed quantum mechanical system, for an external observer, that evolves unitarily. The latter implies that all the interactions inside the box are unitary. Cat=quantum mechanical

If the box can be sufficiently isolated from its environment, this is true. However, the stuff inside the box includes a particle detector and a mechanicsm that kills the cat if the detector signals that a particle has been detected. After a while, the atom will be in a superposition of "decayed" and "not decayed". You might expect that this will put the detector in a superposition of "signal" and "no signal". Let's denote those states by |s> and |n>. What will actually happen is that the detector will interact with its environment (in particular the mechanicsm that's supposed to kill the cat), and this interaction will change the state of the detector into a state that's for all practical purposes indistinguishable from a mixed state a|s><s| + b|n><n|, which is not equivalent to a superposition of |n> and |s>. So not even the cat would be correct to describe the detector as being in a superposition. And this prediction is made entirely using the unitary time evolution of quantum mechanics.

Since (1) and (2) should hold simultaneously, we are lead to a contradiction hence this cannot be true.

I think your argument doesn't quite work in its current form, because of the decoherence problem described above. But I think that the apparent contradiction will reemerge if you describe what's going on here in terms of state operators (mixed states) instead of in terms of wavefunctions. However, I would say that the contradiction isn't actually derived from quantum mechanics. It's derived from QM plus two additional assumptions:

1. In addition to being things that we can use to assign probabilities to possible results of experiments, states also describe what's actually happening in the real world, even at times between state preparation and measurement.
2. There's only one world.

Drop one of these assumptions (both of which are non-mathematical and unscientific), and there's no contradiction. The assumption that 1 is true and 2 is false can be taken as the starting point of a MWI. The assumption that 1 is false and 2 is true can be taken as the starting point of a Copenhagen/statistical/ensemble interpretation. Note that both can be false.

 

[stevendaryl]

However, I would say that the contradiction isn't actually derived from quantum mechanics. It's derived from QM plus two additional assumptions:

1. In addition to being things that we can use to assign probabilities to possible results of experiments, states also describe what's actually happening in the real world, even at times between state preparation and measurement.
2. There's only one world.

Drop one of these assumptions (both of which are non-mathematical and unscientific), and there's no contradiction. The assumption that 1 is true and 2 is false can be taken as the starting point of a MWI. The assumption that 1 is false and 2 is true can be taken as the starting point of a Copenhagen/statistical/ensemble interpretation. Note that both can be false.

I'm a little skeptical about the distinction that you're making. If you treat macroscopic things quantum mechanically, then there are no definite "results of experiments".

 

[stevendaryl]

The effects of macroscopic superpositions can be observed, but AFAIK can be analyzed in either Copenhagen or MWI terms... So no help there.

The assumption that a macroscopic measurement collapses the wave function into an eigenstate makes a difference in interference effects. Presumably, there's a way to observe these interference effects and decide whether wave function collapse happens, or not.

I remember some kind of thought experiment involving testing bombs. The premise was that some fraction of bombs are "duds" and the only way to tell was to try to trigger them to explode using a high energy laser. But quantum mechanics allows for some weird way of testing which are duds without exploding the nonduds. The duds have a different interference pattern when you split the laser beam, send one half through the bomb, and then recombine with the other half. Considering the bomb exploding to be a special case of "measuring the presence of a photon", it makes a difference whether this measurement collapses the wavefunction or not.

I don't remember the details.

 

[JK423]

@Fredrik
Decoherence just complicate things. For example, i could argue that decoherence has a time scale, and the external observer make measurements before decoherence destroy the superposition. However, i understand that it's difficult to devise a thought experiment to -even in principle- prove what i want to prove. (I'll think about it a little bit more)
What i cannot understand is how you can accept that everything is quantum mechanical but still refute Everett's proposal.. he says just that!

 

[Fredrik]

If you analyze people and measuring devices and the universe by the same Rules of Quantum Mechanics that you use to analyze electrons and atoms, then it seems to me that Many Worlds is where you end up.

Either that, or that QM doesn't describe the real world at all, and is just something we use to assign probabilities to possible results of experiments.

If an electron is in a superposition of spin-up and spin-down, and a human measures its spin, then the human will enter into a superposition of "human measuring spin-up" and "human measuring spin-down". Very quickly, the Earth is in a superposition of "Earth where that human measured spin up" and "Earth where that human measured spin down". The "Many Worlds" aspect is, it seems to me, inevitable unless you impose some non-unitary evolution step that destroys some branch of a superposition.

This is an aspect of the "measurement problem". However, if we don't make both of the non-mathematical and unscientific assumptions that "states describe what's actually happening", and "there's only one world", I don't see a need for a second kind of time evolution. I think that this sort of "collapse" is a solution to a problem that was created not by the theory, but by two unnecessary assumptions that aren't actually part of the theory.

I think it's accurate to say that quantum mechanics doesn't have a measurement problem. The problem is with the additional assumptions that we tend to make, sometimes without even realizing that they are additional assumptions.

 

[Fredrik]

I think you will have to describe what's going on in terms of state operators instead of wavefunctions to make this argument. Hm, didn't I do something like that myself once? I'll see if I can find it.

I didn't find anything like that in the time that I was willing to spend on it. You may however be interested in the quote below. It's similar to the argument you're making here. But I'm arguing that the problem isn't with the theory, but with the additional assumptions. (I think that I've posted another version of this argument somewhere, and that I was talking about state operators instead of wavefunctions in that one).

The main assumption of the CI is that state vectors can be identified with physical systems, i.e. that each state vector describes all the properties of the system it represents. Let's label that assumption (1). I said that if we add this on top of QM, we get a contradiction, but that's not quite right. What we get is many worlds. So QM+(1) contradicts the assumption that there's only one world. Let's label that assumption (2). Obviously, (2) should also be considered part of the definition of the CI.

So I'm not going to argue that QM+(1) is logically inconsistent, I'm going to argue that CI=QM+(1)+(2) is. The argument can't be made rigorous, since the assumptions (1) and (2) aren't mathematical statements. An informal argument is the best anyone can do.

The Schrödinger's cat thought experiment has taught us that the linearity of the SE implies that if microscopic systems can be in superpositions, then so can macroscopic systems. The details of this part of the argument are included both in Ballentine's 1970 article and in his more recent textbook. (Section 9.2).

(A calculation that includes decoherence effects would change the argument somewhat, but not enough to solve the problem).

Suppose that we prepare a large and complicated system, e.g. a system that includes you, in a state like |this>+|that>, where |this> and |that> describe two different experiences you can have in there. Now the problem is that (1) says that |this>+|that> is a complete description of the physical system. Clearly this means that neither |this> nor |that> can be a complete description of the physical system, and this means that what you actually experience as a part of that system is no more than half the story. If the complete description includes both of your possible experiences, then so does reality. Otherwise it wouldn't be a complete description.

Therefore QM+(1) implies that there are many worlds. This means that QM+(1)+(2) is inconsistent.

 

[JK423]

What I'm refuting is the idea to drop the Born rule. Once we do that, what we have left is broken and incomplete. Since it can't make predictions about results of experiments, it's not a theory.

It's also not an interpretation, because an interpretation is supposed to be a guess at what the mathematical components of a theory really means. If you want to interpret QM, you don't start by removing an essential part of the theory.

I see.. i need to think about this as well.

 

[stevendaryl]

@Fredrik
Decoherence just complicate things. For example, i could argue that decoherence has a time scale, and the external observer make measurements before decoherence destroy the superposition. However, i understand that it's difficult to devise a thought experiment to -even in principle- prove what i want to prove. (I'll think about it a little bit more)
What i cannot understand is how you can accept that everything is quantum mechanical but still refute Everett's proposal.. he says just that!

I don't think that decoherence changes anything, fundamentally, except that it means that we very rapidly go from "a single object is in a superposition" to "the entire universe is in a superposition".

 

[stevendaryl]

What I'm refuting is the idea to drop the Born rule. Once we do that, what we have left is broken and incomplete. Since it can't make predictions about results of experiments, it's not a theory.

I agree that the Born rule is needed to make predictions. But it seems very weird to me that it can be added as an additional assumption without assuming that some things are NOT described by quantum mechanics.

 

[Fredrik]

Sigh...I don't know how I managed to do this, but I was going to quote a sentence from my post #16 in a new post here, but I apparently clicked the edit button and ended up replacing the content of #16 with what I wanted to say here.

Oh well, I hope that what I had previously said in #16 wasn't very important. :)

 

[JK423]

xaxaxa

 

[stevendaryl]

For some reason, MWI gives people vertigo thinking about what probability really means, but actually, classical notions of probability are just as weird, philosophically, when you think about it. What does it mean, empirically, to say that a coin flip has a 50% chance of resulting in "heads"? Well, it means that if we repeat the flip many many times, we can expect that about half will be "heads" and half will be "tails". But what does "we can expect that..." mean?

Ultimately, the only way we can extract something testable from a probabilistic theory is to make the assumption that the history that's unfolding is somehow "typical".

In a Many-Worlds type model, you can make the same sort of assumption.

 

[Nugatory]

I remember some kind of thought experiment involving testing bombs...

Elitzur-Vaidman? http://en.wikipedia.org/wiki/Elitzur–Vaidman_bomb_tester

I'm not seeing any different prediction if analyzed in MWI terms instead of Copenhagen or statistical terms... But best to start a new thread about it if this fork is worth following, I'd think.

 

[bohm2]

Speaking about MWI and probabilities what do others think about Andreas Albrecht and Daniel Phillip's recent work/arguments on this issue?

But a new paper by physics professor Andreas Albrecht and graduate student Dan Phillips at the University of California, Davis, makes the case that these quantum fluctuations actually are responsible for the probability of all actions, with far-reaching implications for theories of the universe.

Does Probability Come from Quantum Physics?
http://www.sciencedaily.com/releases/2013/02/130205151450.htm

According to the latest research, this view is not correct. Andreas Albrecht and Daniel Phillips of the University of California at Davis argue that the probabilities we use in our everyday lives and in science do not "quantify our ignorance" but instead reflect the inherently random nature of the physical world as described by quantum mechanics. They maintain that quantum fluctuations can be amplified sufficiently by known physical processes to the point where they can entirely account for the outcome of these everyday macroscopic events. In fact, they claim that all practically useful probabilities can be accounted for in this way. In other words, all classical probabilities can be reduced to quantum ones.

The quantum coin toss
http://physicsworld.com/cws/article/news/2013/feb/13/the-quantum-coin-toss

We argue using simple models that all successful practical uses of probabilities originate in quantum fluctuations in the microscopic physical world around us, often propagated to macroscopic scales. Thus we claim there is no physically verified fully classical theory of probability. We comment on the general implications of this view, and specifically question the application of classical probability theory to cosmology in cases where key questions are known to have no quantum answer.

Origin of probabilities and their application to the multiverse
http://arxiv.org/pdf/1212.0953v1.pdf

 

[stevendaryl]

Speaking about MWI and probabilities what do others think about Andreas Albrecht and Daniel Phillip's recent work/arguments on this issue?

Does Probability Come from Quantum Physics?
http://www.sciencedaily.com/releases/2013/02/130205151450.htm

The quantum coin toss
http://physicsworld.com/cws/article/news/2013/feb/13/the-quantum-coin-toss

Origin of probabilities and their application to the multiverse
http://arxiv.org/pdf/1212.0953v1.pdf

I don't think it's correct to think that probability only can come from quantum fluctuations. Any time you have lack of knowledge, you can use probability as a way of reasoning in spite of your imperfect understanding of the situation. There doesn't need to be any real underlying nondeterminacy for there to be nondeterminacy for all practical purposes.

I don't see that the "pocket universe" idea in any way calls for a radically different notion of probability. The Bayesian notion of probability works perfectly fine.

 

[Demystifier]

For example, Everett's (elegant and simple) formulation of quantum mechanics is based on the hypothesis that everything is quantum mechanical, hence the observer and apparatus are all quantum mechanical systems decribed by the deterministic Schrodinger's equation. The Copenhagen formulation of quantum theory denies that, which means that it's something testable to experiments.

Someone may object that proving the quantum mechanical nature of the observer is mission impossible. Indeed. But is this relevant? The different predictions are there. The fact that one cannot design an experiment, for practical reasons and not of principle, to investigate these predictions is another thing. I never saw anyone calling string theory a "different interpretation" of nature

I think these are excellent points.

However, in the case of string theory, we know how to test it at least in principle. For example, in principle it is possible to build an accelerator big as our galaxy, which could be used to accelerate elementary particles to Planck energies. With such energy, it would not be difficult to test string theory.

Do you have any equally concrete idea how to test MWI vs CI in principle? In other words, can you propose a THOUGHT experiment which could distinguish between them?

 

[kith]

My thoughts on Everett's idea is that it's just a crippled version of QM that fails to make any predictions at all. The problem is that he removed the Born rule, which is what we use to assign probabilities to possible results of experiments. Some people claim that the Born rule can be recovered, but that's only true if you make some other assumptions instead of it, and I think those assumptions can always be derived from the Born rule. So it seems to me that those derivations don't really tell us anything.

Just to get you right: your point of view is that Everett's idea with the additional assumption of the Born rule is a reasonable interpretation?

 

[JK423]

I think these are excellent points.

However, in the case of string theory, we know how to test it at least in principle. For example, in principle it is possible to build an accelerator big as our galaxy, which could be used to accelerate elementary particles to Planck energies. With such energy, it would not be difficult to test string theory.

Do you have any equally concrete idea how to test MWI vs CI in principle? In other words, can you propose a THOUGHT experiment which could distinguish between them?

Before trying to answer your question, i need to know if the following hypothesis that i make is correct:
Does the CI assume that the observer is classical (or better, non-quantum mechanical)? I think yes, because if not then we are lead to Everett's view (which simply says that everything is quantum mechanical). If the observer is assumed to be non-quantum mechanical, then doesn't this mean that quantum mechanics fail at some point? Isn't the failure of quantum mechanics, in the description of the observer, in principle testable?

I agree with Fredrik, that Everett's view has difficulties with the Born rule but let's ignore this for a moment.

 

[Quantumental]

I agree with Fredrik, that Everett's view has difficulties with the Born rule but let's ignore this for a moment.

Let's not forget preferred basis and ontology issues.
Demystifier has written a blogpost about it here actually: www.physicsforums.com/blog.php?b=4289

 

[Fredrik]

Just to get you right: your point of view is that Everett's idea with the additional assumption of the Born rule is a reasonable interpretation?

I'm not entirely sure, but I'm leaning towards yes.

 

[Quantumental]

I'm not entirely sure, but I'm leaning towards yes.

What about the preferred basis issue ?
Have you read demystifiers blgopost that I linked to?

 

[kith]

I'm not entirely sure, but I'm leaning towards yes.

This is also my impression. There are reasonable objections against the MWI, but I don't get why people reject Everett's basic idea because of the supposable impossibility to derive the Born rule.

What about the preferred basis issue?

In order to apply the Born rule, you have to say which part of the whole Hilbert space corresponds to your physical system of interest. So the necessary separation is introduce by hand. Once you have done this, decoherence solves the preferred basis issue.

 

[Fredrik]

What about the preferred basis issue ?
Have you read demystifiers blgopost that I linked to?

I have read it before. I haven't read the article that he links to, because its main claim is something that I never doubted:

In modern literature, one often finds the claim that the basis problem is solved by decoherence. What J-M Schwindt points out is that decoherence is not enough. Namely, decoherence solves the basis problem only if it is already known how to split the system into subsystems (typically, the measured system and the environment). But if the state in the Hilbert space is all what exists, then such a split is not unique.

However, I suspect that the following (standard) idea is misguided:

To define separate worlds of MWI, one needs a preferred basis, which is an old well-known problem of MWI.

To explain why, I'm going to have to speculate a bit. I can't prove any of this rigorously at this point, and I'm not working on it.

I think it makes more sense to postulate (as part of a definition of an MWI) something like "every 1-dimensional subspace is a world". If we do, we don't need a preferred basis to tell us which 1-dimensional subspaces are worlds, because they all are. For each decomposition of the universe into subsystems (like "the cat"+"everything else"), the Born rule selects a "preferred" basis. Instead of the statement "the 1-dimensional subspaces identified by the basis are worlds and all the other ones aren't", I propose that "the 1-dimensional subspaces identified by the basis are especially interesting worlds".

In what sense are they "interesting"? I think it might be possible to prove something like "the worlds singled out by the preferred basis are the ones where the subsystems store the maximum amount of information about each other". If this can be done, then things get pretty interesting. The inner product gives us a way to assign a numerical value to how "close" two worlds are. Worlds that are very close to the "interesting" ones will be practically indistinguishable from them. And in worlds that are far from the "interesting" ones, the subsystems are going to be bad at storing information about each other. That could mean that they don't contain any conscious observers, since consciousness involves information storage.

Please don't misinterpret this as a suggestion that consciousness plays some active role in the MWI, or that consciousness transcends the physical, or some other nonsense like that. I'm just saying that I consider worlds where consciousness is present more interesting than worlds without consciousness.

 

[stevendaryl]

I think it makes more sense to postulate (as part of a definition of an MWI) something like "every 1-dimensional subspace is a world". If we do, we don't need a preferred basis to tell us which 1-dimensional subspaces are worlds, because they all are. For each decomposition of the universe into subsystems (like "the cat"+"everything else"), the Born rule selects a "preferred" basis. Instead of the statement "the 1-dimensional subspaces identified by the basis are worlds and all the other ones aren't", I propose that "the 1-dimensional subspaces identified by the basis are especially interesting worlds".

I'm sorry, what do you mean by "1-dimensional" here? In what sense is a cat one-dimensional?

 

[Fredrik]

I'm sorry, what do you mean by "1-dimensional" here? In what sense is a cat one-dimensional?

I'm talking about subspaces of the Hilbert space of the "universe", and by "universe" I mean the physical system that the interpretation we're trying to define claims that QM describes. Penrose calls it "the omnium". Pure states are, as always, represented by 1-dimensional subspaces. (Edit: It's of course more common to represent pure states as state vectors, but for all state vectors f and all complex numbers c, cf represents the same state as f. Because of this, the 1-dimensional subspace $\mathbb Cf=\{cf|c\in\mathbb C\}$ is a better representation of the pure state than the state vector f).