Are many-worlds and the multiverse really the same thing? Are many-worlds and the multiverse really the same thing?
Not too long ago, Susskind and Bousso uploaded the article "The Multiverse Interpretation of Quantum Mechanics" with the thesis that the many-worlds interpretation and the multiverse of eternal inflation are one and the same thing. The parallel worlds of one are exactly the same thing as the parallel worlds of the other. 
First, they claim decoherence can't happen over a complete description of the future light-cone of the measurement. Then, they apply that principle to eternal inflation. Without decoherence, superpositions of nucleating bubbles and metastable vacua can't decohere. According to the anthropic principle, most bubbles have no conscious observers, but an exponentially small minority do. Apply black hole complementarity to causal horizons.
Then, somehow, in a way I can't follow, they combine causal diamond worlds into a global multiverse.  Then they claim decoherence is reversible.
My head is spinning. What are your opinions on this paper?
 A: No, they're not the same thing and the paper is meaningless pretty much at all levels, see

http://motls.blogspot.com/2011/05/bousso-susskind-hypermultiverse.html

A: The standard global picture of eternal inflation doesn't predict domain walls, vacua and metric take on definite classical values! It predicts a quantum superposition, and what's wrong with that?

Definition I Consider an instance of decoherence (or "collapse of a wave function")
  in a Hilbert space $\mathcal{H}_S$, which occurs as a result of entanglement with another Hilbert space $\mathcal{H}_E$. The event will be said to happen if the entanglement between $\mathcal{H}_E$ and $\mathcal(H)_S$ is irreversible; and the system S can then be treated as if it was in one of the pure states that constitute the basis that diagonalizes the density matrix obtained by tracing over the Hilbert space $\mathcal(H)_E$.
Postulate I Things happen.
In other words, there exist some entanglements in Nature that will not be reversed with
  any finite probability.

And by finite probability, he means nonzero, and by nonzero, $\exp(-\exp(10^{123}))$ is considered nonzero because it's not exactly zero.
WOW! That's all I can say!
This is followed by another bizarre claim that to make any sense of probabilities, the number of trials needs to be infinite. Not the limit of infinite size, or very large sizes, but infinite itself. They insist upon infinitely many trials. Even defenders of the frequentist camp of probabilities don't make such an extreme claim.

And by observable, I mean that the world is big enough that the observable can be measured infinitely many times by irreversible entanglement.

Please take note of the qualifier infinitely many times, and irreversible entanglement, by which they mean exactly zero probability of reversal. Such absolutism!
This reminds me of some cosmologists who some time back, came up with the absolute postulate that the universe has to be a computer with infinite resources, with infinite memory, and able to compute infinitely many time steps. From such a dubious postulate, they concluded the universe must end in an Omega point big crunch with some future civilization taking over the entire universe, and constructing a gigantic computer which can run faster and faster with no limit as time approaches the big crunch singularity.
A: I see Lenny has done it again. I have to say I disagree with this paper. For the sake of argument, let's grant him the hat complementarity conjecture, which he has yet to justify or derive in any convincing way. By his own admission, complementarity scrambles states in the most efficient manner possible. Consequently, the pointer basis states for the many-worlds to split into do not align in any way with the basis states describing macroscopic multiverse bubbles. I rest my case.
I should also add the Bondi mass in the terminal supersymmetric bubble with zero cosmological constant, i.e. the "hat", is small enough it probably can't accommodate all the holographic multiverses.
As another poster before me had pointed out, insisting upon irreversible decoherence beyond the level of one in $e^{e^{10^{-123}}}$ is ridiculous. If by "unhappen", Lenny means no recoherence at that probability, let me point out a lot of more drastic things will happen before then, like Boltzmann brains and the decay of our vacuum into a supersymmetric vacuum.
A: The authors are spouting pure drivel about decoherence. The choice of which environment to trace over is not arbitrary. Decoherence can happen for closed systems. Even if the entire solar system right up to Pluto is included in the system, decoherence does not take minutes to happen. It happens in less than a microsecond. The immediate environment of the measurement already contains degrees of freedom which can decohere the system. Placing mirrors at Pluto is nowhere near enough to reverse decoherence.
What decoherence is needs to be spelled out clearly. Decoherence is the exponential suppression of off-diagonal terms in the reduced density matrix. Nothing more, and nothing less.
The authors are under the mistaken impression they can draw any boundary between the system and the environment that they like. You can't just take a causal diamond and call anything outside or the boundary itself the environment, and anything inside the system. The environment is determined dynamically from the interactions. A sharp boundary which is at most a Planck length thick is a bad choice for dividing the environment from the system. The vacuum in quantum field theory has quantum correlations, i.e. quantum entanglement, right up to the correlation length and this can be infinite if massless fields like electromagnetism or gravity exist. A dynamically determined system-environment boundary has to be smeared over the vacuum correlation length at the very least. With a Planck thick boundary, tracing over the environment will lead to a density matrix with most of the von Neumann entropy comming from Planck temperature Unruh radiation near the boundary itself. Defining many-worlds in this manner promotes Planck scale short-lived quantum fluctuations into many-worlds. I don't think that is what the authors have in mind.
In short, I give this article a thumbs down.
A: In Figure 6 of their article, they draw a causal diamond, and divide the future null boundary into $B^+$ and $B^-$. They implicitly assumed that the Hilbert space of $B$ is the tensor product of the Hilbert space of $B^+$ with the Hilbert space of $B^-$. If $B$ were a spacelike surface, that would be true, but it's not. It's null, and null separated operators don't commute. The operation of taking the partial trace over $B^-$ to get the density matrix over $B^+$ is not correct.
The authors also can't agree upon whether time evolution between the different $\beta$ slices are unitary or not. They claim it isn't, but cite another article "The Census Taker's Hat" written by Susskind claiming the contrary. One gets the impression Bousso and Susskind aren't in agreement on this issue.
In Section 2.5, the authors forgot their own insight that distinct maximal causal diamonds are complementarity to each other. Because of this, it makes no sense to combine the local states of different overlapping causal diamonds together to get a more global description of a "superobserver" state.
A: I will not say yeah or nay on this.  Besides I have only read part of the paper.  A lot of negativity is being thrown at this, which frankly I can understand.  I am rather guarded on this.  The one problem I have is that the MWI is an interpretation of quantum mechanics, and is not what I would call a theory.  There is no way of testing it.  There does not appear to be any way of falsifying quantum interpretations, so hanging a theory of quantum cosmology on that seems problematic.
There are four levels of so called multiverse.  If all of these are real, using the word real in a difference sense than reality is used in QM issues of Bell or GHZ states etc, these are the Linde pocket universes, brane-world or quantum fluctuation universes, MWI universes and the rather speculative ideas of an ultimate ensemble by Tegmark.  Lumped all in one pile we might suspect these all fit into a single scheme.  So maybe how branes and strings are wrapped and give rise to a vacuum in a universe is decoherence and this fits into MWI.  However, if MWI is the “bird’s eye” perspective on the universe, it seems difficult to say the splitting off of world due to an electron double slit experiment is the same as bubble nucleation of the vacuum or brane-brane interactions and so forth.
To be honest some of the post-selected state work in QM to my mind brings question to the whole MWI conjecture.  If post selected states determine an entanglement in the past, then this gives me some pause on the whole worlds splitting off idea of MWI with decoherence or measurement.  Further MWI, and frankly with all quantum interpretations, is just a way to trying to make some aspects of quantum mechanics fit into our classical or macroscopic perceptual bias of the world.  Quantum mechanics is just plain weird in some ways and it butts up against our intuitive ideas about the world.  So we have come up with various ways of trying to transduce this strangeness into our biases.
