Is Everett's relative state interpretation logically sound?

Question

Is Everett's relative state interpretation (Rev. Mod. Phys. 29 (1957), 454-462), usually called Many Worlds (MWI) logically sound?

Note that I am not asking about one of the many variations of the MWI formulated not in precise mathematical terms, of which it is therefore difficult to ascertain their logical status. However Everett himself tried to carefully pin down the formal meaning of his interpretation as part of his Ph.D. thesis in physics, so that the question can be meaningfully asked about his version of the MWI.

H. Stein, The Everett interpretation of quantum mechanics: Many worlds or none? Nous 18 (1984), 635-652.

A. Kent, Against many-worlds interpretations, Int. J. Mod. Phys. A5 (1990), 1745.

E.J. Squires, On an alleged 'proof' of the quantum probability law, Phys. Lett. A145 (1990), 67-68.

Comments

many "sciences" turn around the questions of the fundamental interpretations. For each, scientists, thinking having found the good formalism to ask and answer, write thesis and books, when it is not worship books, quickly popular. But, as far I know, all end in apparent circularity, which denotes the lacks of evaluation criteria or merely of any sciences basis. Physics cannot answer to anything  ( today ). History of sciences is full of similar states of knowledge before discoveries and revolutions.

Answer 1

To me, it seems that the answer is no.

Everett's argumentation seems to be flawed by a well-disguised circularity:

In his original paper Rev. Mod. Phys. 29 (1957), 454-462, Everett claims that his theory is one without the need for state reduction (what he calls 'process 1'). But when he discusses observation, he brings in at the very beginning an apparently innocent additional concept, that of a 'good observation'. The formal definition of the latter is the sentence around (10)-(11) of his paper. 

According to Everett, a 'good observation' is an interaction that transforms each state $\phi_S \otimes\psi_O$ such that $\phi_S$ is a fixed eigenstate of the measured variable with eigenvalue alpha into a state $\phi_S \otimes\psi_O(\alpha)$ where $\psi_O(\alpha)$ belongs to a set $X(\alpha)$ of states which belong to the awareness of $\alpha$. In particular, this entails that for different $\alpha$, the sets $X(\alpha)$ must be disjoint. Since Everett only allows the unitary dynamics (his 'process 2', see first line of his Section 3), any interaction 'in a specified period of time', must result in a unitary mapping $U$ on the state space of system plus observer.

Therefore, $U$ corresponds a 'good observation' (of the system in state $\Phi_S$) iff there is a self-mapping $\psi_O \to\psi_O(\alpha)$ of the observer state space $X$ such that 
$$ U(\phi_S \otimes\psi_O) = \phi_S \otimes\psi_O(\alpha) \forall \psi_O \in X. $$
 From his definition, we also see that the mapping $\psi_O \to\psi_O(\alpha)$ maps $X(\alpha)$ into itself, and the whole observer state space $X$ into $X(\alpha)$. Since the interaction is unitary, it is invertible; but the restriction of $U$ to $\phi_S \otimes X $can be invertible only if $X(\alpha)=X$. But this means that there is only a single eigenvalue $\alpha$. 

Therefore, under the assumptions made by Everett, there are no 'good observations', and since his analysis of the observational process depends on the latter, it is void of any meaning. Indeed, looking closer at the concept of a 'good observation', one can see that it is the projection postulate in disguise. (The above argument loses its power once one allows $U$ to be nonunitary.) 

Thus Everett's analysis simply derives the projection postulate by having assumed it, without any discussion, in disguise.

Comments

I'm not going to respond to your specific complaint with Everett's argument because you are entirely missing the point of his argument, which does not at all hinge on the particular move you take issue with. The point is very simple: is psi epistemic or ontic? If you answer "epistemic" then you don't believe in the MWI. If you answer "ontic" then the "many worlds" are unavoidable because superposition of an ontic thing is definitionally equivalent to "many worlds." In other words if you think an atom's wave function is a real "thing" and that this "thing" can be split apart into a lump that goes through a left slit and a lump that goes through a right slit, then in a clear and objective sense the atom traverses multiple paths simultaneously. We refer to such behavior as definitionally equivalent to the atom existing in multiple "worlds". 

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@user1247 The trouble is in making the "lump" idea precise. 1. because the splitting is an artifact of the position basis, and would look like an arbitrary mess in most others, and 2. because the wavefunction has not decohered as long as the experiment is running, and so there is no meaningful sense in which the chunks, even arbitrarily defined, are meaningfully separate until decoherence.

You can't make that *definitionally* equivalent to the atom being in "multiple worlds" because the phrase "worlds" is primarily meant to refer to possible classical descriptions as seen by some entangled superposition of observers, some particular decomposition of which "really exists", and it would be a nontrivial fact that these coincide given any particular procedure for producing such a decomposition. There is certainly no room for it in normal QM unless you make the branch splitting/world counting occur dynamically through decoherence (which I understand is the usual claim), and if you tack on an extra postulate to pick out some preferred basis by force then the extra postulate is doing all of the actual work, and there's really no sense in which you have an ontology of QM. You have a vague world-ontology that you could slap onto any theory at all, with no sharp description of the things which are supposedly ontologically primary. Regardless, the usual approach to MWI would not claim that there was one world in which the particle "really" went through one slit unless and until you actually measure that slit in the first place, producing the decoherence that separates the possibilities. You can't wave away arbitrary superpositions by claiming that the possibilities are arbitrarily populated by unspecified worlds.

Yes, *if* you answer ontic and keep unitarity, then you're led to MWI. But it's by no means evidently sensible that you *can* do that at all, which is clearly what Everrett intends to claim, so there's still a nontrivial rebuttal to make.

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@RM (EDIT: added @RM since I originally thought I was replying to Arnold, but leaving the rest as-is)

1. But of course superposition exists in other bases, so no, "splitting" is not an "artifact of the position basis," though it is of course a unique and important basis, since interactions are local in it. 

2. Whether the wave function has decohered is irrelevant to the main point, but sure, if you want your "worlds" to be definitionally "separate" then you have to wait for decoherence, but so what? This obviously isn't a problem for MWI since decoherence is a well-understood process. 

You can't wave away arbitrary superpositions by claiming that the possibilities are arbitrarily populated by unspecified worlds.

The MWI doesn't attempt to "wave away" anything. Maybe you could expand on what you think the MWI is doing here, because you still seem to be under a very confused impression of what the MWI is. The MWI doesn't claim that magically once decoherence happens that worlds "pop into existence." Decoherence is completely irrelevant to the core philosophic move, which is to take superposition seriously. It doesn't matter whether decoherence has happened or not, other than that after decoherence the "worlds" are entropically separated. Any hand-wringing about when or with what granularity the splitting occurs is only of definitional importance. It really doesn't matter to the ontology; so what if two "worlds" can re-cohere? Hashing that out is a mundane exercise that can't cast any doubt on the core philosophic move unless you don't understand it in the first place. 

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@ArnoldNeumaier OK I'll reply to your particular complaint here, since it is easy enough. Your confusion seems to be related to your previous confusion (see your question here) about how apparent collapse and subjective randomness is possible in the MWI. What you are confused about is the process which generates the self-mapping described in your post, which you complain is tautological. That process, which I explained in the linked thread, is just anthropic selection among the reference class of observers in the wave function. If we decompose the wave function of observers into a superposition indexed by \(\alpha\), then there will be an observer for which everything Everett says is true. This seems to be, generally, the core conceptual confusion that most complaints about the MWI are founded on. The point is that even though the observer indexed by \(\alpha\) is still in superposition with other observers, it cannot be aware of said superposition by linearity.

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@user1247: My logical complaint has nothing to do with ''the process which generates the self-mapping described in your post''. No matter how it is generated, my argument shows that its existence implies that Everett's "good observations" either don't exist, or don't have the formal properties needed to make Everett's subsequent arguments valid.

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@ArnoldNeumaier, you don't seem to understand my comment. In your argument you say:

But this means that there is only a single eigenvalue α. Therefore...

Yes, there is only a single eigenvalue, because the observer cannot be aware of any other versions of himself that are entangled with other eigenvalues, by linearity. The process by which this one eigenvalue is selected from the spectrum of X is what I have described as the core conceptual move of the MWI: anthropic selection. That process itself isn't unitary (and it is indeed a kind of projection postulate), but the physical interaction is unitary, U is unitary, and objectively the wave function continues to evolve unitarily without collapse. This still seems to be a point of confusion for you -- the subjective (ie relative-state) vs objective (ie global wave function) dichotomy. 

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@user1247: But there is nothing anthropic about observation; any detector that creates a reasonably permanent record of an event causes a collapse. Otherwise wed have to think that the artifacts that tell us about the history of the earth would have been created at the moment they were first observed by a human. But this is ridiculous.

With your anthropic take on Everett's setting you cannot explain the history of the Earth before there were humans.

But the Earth was obviously already dissipative long before - else complex organic molecules could not have formed in substantial amounts, and radioactive decay were confined to the time since (and places where) humans exist. This disproves any anthropic explanation of the collapse.

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@ArnoldNeumaier, you just don't get it. No detectors ever cause objective collapse in unitary QM. There simply IS NO COLLAPSE, as you appear to understand it. There is only subjective "collapse," a basic point -- the core conceptual move of the MWI -- which you simply don't understand. 

Otherwise wed have to think that the artifacts that tell us about the history of the earth would have been created at the moment they were first observed by a human. But this is ridiculous.

With your anthropic take on Everett's setting you cannot explain the history of the Earth before there were humans.

Again, this displays simply a basic misunderstanding of even the basics of the MWI. It does not imply any of this.

To help explain. In the MWI, we would understand that an electron in superposition is in it's own "world" for each element in the superposition, before or after decoherence. Due to linearily, the electron is not "aware" of (ie does not interact with) any other electrons it is in superposition with: it is in its own "world." Now, before decoherence this world can interefer with other worlds, and so if we are pedants we can adopt the terminology interfery-world vs decohered-world to distinguish the pre and post-docherence worlds. Pre-decoherece worlds are strange in that they can disappear or reappear due to interference effects. But they are still "worlds" to the extent that they exist in our ontology. Now, an electron does not have self-awareness, but if it did, we must come to terms with the fact that it would not be aware of the other versions of itself that it is in superposition with (by linearity) -- it other words, from its perspective, collapse is subjectively manifest. But in no sense is the wave function in any objective sense collapsed. 

So when you speak of the state of the earth long before humans "dsiproving the anthropic explanation of collapse," you are just plainly confused. Before consciousness atoms formed, molecules formed, evolution by natural selection happened... it just all happened in superposition. Collapse never happened, not before humans or after humans, but that doesn't take away from the fact that for any subjective observer within the larger wavefunction they are not aware of their own superposition, and therefore FROM THEIR PERSPECTIVE the wave function has collapsed. This is why Everett called his formulation the relative state formulation -- the wave function never collapses, but if we consider what things would "look like" from the perspective of a subset of the wavefunction, it's reality will be defined relative to the subsets of the rest of the wave function whose properties are consistent (ie constrained by entanglement), and as a result things look very different from the objective description of the universal wave function that has never collapsed.   

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@user1247: But dissipation (irreversibility) is the most conspicuous fact of our universe, and it was there before any anthropic reasoning could apply. With a unitary evolution one has no irreversibility. MWI - at least in your variant - introduces it through subjectivity, which makes it anthropic.

Non-animated matter is not subjecive, but still behaves irreversibly. Therefore the collapse (short for any form of irreversibility) is a fact, so it must be explained in objective terms. MWI doesn't explain it objectively, hence is not a viable interpretation.

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@ArnoldNeumaier, The entropic decoherence process is objective, doesn't require any kind of collapse whatsoever, has nothing to do with anthropics, and is not in conflict with unitarity. This is not at all controversial. The entropic growth of entanglement as a system interacts with its surroundings is a purely unitary process. 

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@user1247: In this case, the MWI would be superfluous, since it adds only irrelevant notions of worlds that are purely subjective, hence have no scientific content.

But unitary quantum mechanics models not a single history but only an ensemble of histories. Where is then the explanation for the fact that different humans perceive and agree upon essentially the same world history with the same irreversible dynamics?

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@ArnoldNeumaier , as others have pointed out, you don't seem to understand what an "interpretation" of QM is. It is not a scientific distinction, by definition. It is a philosophic one.

But unitary quantum mechanics models not a single history but only an ensemble of histories. Where is then the explanation for the fact that different humans perceive and agree upon essentially the same world history with the same irreversible dynamics?

Entanglement

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@user1247:  Thanks for agreeing with me that your MWI is no longer science. Once you remove from an interpretation of quantum mechanics its physical content it becomes irrelevant for physics.

But Everett's relative state interpretation was supposed to be science, not philosophy. He got for it a science Ph.D.

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@ArnoldNeumaier, the issue of your scientism aside, the answer to your question "Everett's relative state interpretation logically sound?" has been answered in the affirmative. I don't see the relevance of whether or not Everett received a PhD in physics for his thesis. It is rightly viewed as a major contribution in quantum foundations, regardless of exactly where we draw the scientific demarcation line. Is Feynman's path integral approach to QM science? If we had a chip on our shoulder like you seem to have, we could say his work here was just mathematical formalism or philosophy rather than science. But we usually don't say that because we don't have a chip on our shoulder about it. It was, like Everett's work, an attempt to better understand QM...

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@user1247:  Your view on MWI doesn't add understanding.

The understanding (gain in physical insight) is according to your answers in the analysis of decoherence and entanglement.

Your MWI view only adds irrelevant subjective bla bla on many worlds that has no impact on the unique observed world or its understanding . Therefore I am no longer interested in discussing this with you.

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@ArnoldNeumaier , Decoherence and entanglement alone do not explain state reduction, so you are seemingly confused about the logical utility of the MWI viewpoint. If you are interested in MWI or quantum foundations at all, then you have to be prepared to make contact with philosophy. The MWI view explains state reduction in a logically coherent and parsimonious way, whereas naive Copenhagen does not (as Everett goes at length to explain in his thesis). There are some viewpoints such as the objective collapse models that are scientific in that they are potentially falsifiable (though like string theory, not necessarily in practice), but most attempts to explain state reduction in a logically coherent way, such as Bohmian mechanics or MWI or Qbism add some philosophic baggage. Most physicists seem to agree that it is desirable that their physical models be logically self-consistent and parsimonious... a philosophic claim.

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if the quantum superposition is ontic, then it is easy to create a literally ontic many-world scenario; basically make a war or not depending of a quantum measurement, divide the nation or not depending on another, and eliminate government regulations or not depending on another. Revisit 10 years later and you have vastly different versions of the world, entangled to 3 qubits.

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one of the things that put me off about MWI, is that Von Neumann entropy does not seem to regard a pure state as 'many possibilities' since it says that a pure state has always zero entropy, so a 'single' possible microstate. I don't know how to reconcile the fact that a quantum superposition of two 'worlds', being pure, must have no entropy?

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@CharlesJQuarra, that's because in MWI the various branches of the wave function can theoretically recohere. Von neumann entropy is useful for relative states, but for pure states it correctly encapsulates the fact that the dynamics are fully reversible in principle. There are plenty of other entropic definitions out there to suit whatever intuition you have about the increasing complexity of the universal wave function...

Answer 2

I think Everett's MWI is not only logically sound, but the only logically sound interpretation of quantum physics that I have seen.

Everett says the universe evolves according to the deterministic laws of quantum physics, without collapse.

Collapse is an artifact of our limited perception, which has evolved to specialize in quick and dirty processing of things directly and urgently relevant to our survival and reproduction. The brain is a portable, low-power processing device that must focus on a small subset of inputs and discard the rest.

Every observer splits reality into manageable chunks of information and splits itself into multiple instances that focuses on one chunk (branch) each. Information is only exchanged between observer instances that share a branch.

This formulation of the MWI is often indicated as Many-Minds Interpretation (MMI) but I believe it's what Everett had in mind.

Many physicists and philosophers have tried to determine where the collapse happens and concluded that it happens in the conscious mind. But thinking that consciousness creates reality seems too anthropocentric to me. Also, how to sync different observers? In the MWI/MMI there is no collapse. The splitting that other interpretations call collapse does happen in the mind, but that doesn't imply that consciousness creates reality.

Comments

Note: I am not saying that the MWI / MMI is the correct interpretation of quantum physics. I am saying that, on the basis of the current mathematical formulation of quantum physics, its proposed interpretations, and my own awareness, knowledge, and understanding thereof, at this moment the MWI / MMI make more sense to me than other interpretations. That may change, as always in science. In particular, we can't rule out changes in quantum physics itself that might radically change its interpretation.

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My arguments imply that quantum mechanics in its current probabilistic form cannot be fundamental, since the probabilities do not make operational sense when applied to the whole universe. This implies that there must be an even more fundamental deterministic layer. A workable version of this layer is of course currently unknown, but finding one is not inconceivable.

Why you appeal to the whole universe? No physical theory is applicable to the whole universe. Applied where it belongs, QM with probabilities makes perfect sense since even QM implies many-many measurements. Without many-many measurements one cannot reconstitute the wave function ;-) Thus one separate measurement is meaningless per se.

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The focus is made on many worlds at the same time at the same location. We know that the latter is a difficult concept, meaningless in many contexts. What about having the same at a time and location, probably different but unspecified while staying in the same universe ??? - Yes, interesting but it is just common QM without pretensions to any "world" interpretation ! Unless one having nothing interesting to do , claims that the 2 approaches are very similar and  searches what became the mwi causality ( states inheritance from parents to childs universes ) in the common theory... I don't know what may happen if the wine is good ...

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@igael - that's "another many-worlds," the inflationary many-worlds. Some physicists including Susskind and Tegmark think these two many-worlds are strongly related.

https://arxiv.org/abs/1105.3796

https://en.wikipedia.org/wiki/Our_Mathematical_Universe

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@Giulio Prisco : the Rousso Susskind publication is very elaborated... Thank you

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"dissipation was as essential as it is now" is an assumption, not an established fact.

In this sense, all history is only an assumption, not an established fact.

In order to model that the earth cools down, one needs to assume the validity of hydrodynamics, which is dissipative. Also to model the emergence of the first complex organic molecules. That these are facts is at least the consensus of the mainstream in physics.

Do you really want to claim that hydrodynamics started to become valid only with the first conscious observer? You drastically overestimate the role of consciousness in physics.

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@ArnoldNeumaier re "Do you really want to claim that hydrodynamics started to become valid only with the first conscious observer? You drastically overestimate the role of consciousness in physics."

I guess I failed to make my point clear. I am not "overestimating the role of consciousness in physics." - On the contrary, I am saying that consciousness doesn't play a role in fundamental physics, and those aspects of reality that are often invoked to give a fundamental role to consciousness are really artifacts of consciousness itself.

The idea that some properties of reality, starting with space and time, are really properties of our own built-in way to perceive reality, has a long pedigree in philosophy starting with Kant.

I should find the time to study your slides and book, because I still don't understand your core point. On the one hand you are saying that dissipative hydrodynamics and, in general, macroscopic irreversibility are fundamental, and on the other hand you insist that quantum physics (which is more fundamental) is deterministic.