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Is Everett's relative state interpretation logically sound?

+ 2 like - 0 dislike
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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.

asked Nov 1, 2015 in Theoretical Physics by Arnold Neumaier (12,570 points) [ revision history ]
edited Nov 3, 2015 by Arnold Neumaier

2 Answers

+ 3 like - 2 dislike

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.

answered Nov 1, 2015 by Arnold Neumaier (12,570 points) [ no revision ]
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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". 

@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.

@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.

@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. 

@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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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?

@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...

+ 1 like - 2 dislike

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.

answered Nov 3, 2015 by Giulio Prisco (150 points) [ no revision ]
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See here for some evidence that speaks against MWI ...

Thanks for the link @Dilaton, but I think none of that applies to the formulation of the MWI (or MMI) that I am defending here, because the universe doesn't split. What splits is the data processing work in our mind.

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.

@Dilaton, Lubos doesn't provide any "evidence" (which as we all should know is impossible, given that MWI is physically indistinguishable from any other "interpretation" by definition). All he does is beg the question, showing that if you assume the "+" symbol means "OR" rather than "AND" that tautologically such states are exclusive. To do so is to entirely miss the point... ie to ignore the core axiomatic move the MWI makes, which is to interpret the wave function as a real "thing" rather than as a mere bookkeeping device, in which case the "+" trivially means "AND" rather than "OR."

To be taken seriously, you should give some references to justify what you think is true. Just asserting something is not enough.

Everett's MWI is not only logically sound, but the only logically sound interpretation of quantum physics

Since I pointed out a logical flaw in his reasoning, you should either tell me why my observation is wrong, or give up your claim of logical soundness.

Everett says the universe evolves according to the deterministic laws of quantum physics, without collapse. Collapse is an artifact of our limited perception

Where does Everett say that collapse is an artifact of our limited perception? Or is this your own modification of his views?

Many-Minds Interpretation (MMI) but I believe it's what Everett had in mind.

It seems to me that you are splitting Everett's mind! Or where from Everett's writing do you take your cues to support your belief?

Every observer splits reality into manageable chunks of information and splits itself into multiple instances

How often does this happen? Once a minute? Slower? faster? What decides upon the rate of splitting? How can one find out? If one cannot find out, it is no science.

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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.

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.

There are levels of fundamental-ness.

Dissipative hydrodynamics is surely one of the basic (hence fundamental) facts of physics before and after conscious beings existed. This serves to prove that minds cannot play any significant role in physics, including its interpretation. (The interpretation, like all physics, is done by conscious beings, but the content must be independent of it.)

It is well-known how hydrodynamics including its dissipative aspects can be derived through coarse-graining (i.e., by ignoring very high frequency information) from traditional quantum mechanics - i.e., QM in its usual stochastic form based on an interpretation that takes the Born rule as given. Thus quantum mechanics is more fundamental than hydromechanics.

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. 

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