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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@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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@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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@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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@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...

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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?

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.