Excellent post Eliezer. I have just a small quibble: it should be made clear that decoherance and the many worlds interpretations are logically distinct. Many physicists, especially condensed matter physicist working on quantum computation/information, use models of microscopic decoherance on a daily basis while remaining agnostic about collapse. These models of decoherance (used for so-called "partial measurement") are directly experimentally testable.

Maybe a better term for what you are talking about is macroscopic decoherance. As of right now, no one has ever created serious macroscopic superpositions. Macroscopic decoherance, and hence the many worlds interpretation, rely on extrapolating microscopic observed phenomena.

If there's one lesson we can take from the history of physics, it's that everytime new experimental "regimes" are probed (e.g. large velocities, small sizes, large mass densities, large energies), phenomena are observed which lead to new theories (special relativity, quantum mechanics, general relativity, and the standard model, respectively). This is part of the reason I find it likely that the peculiar implications of uncollapsed hermitian evolution are simply the artifacts of using quantum mechanics outside its regime of applicability.

Here at UC Santa Barbara, Dirk Bouwmeester is trying to probe this macroscopic regime by superposing a cantilever that is ~50 microns across--big enough to see with an optical microscope!

I own at least two distinct items of clothing printed with this theorem, so it must be important.

Isn't this an argumentum ad vestem fallacy?

Eliezer: No doubt I am missing a lot. I have the idea of the wavefunction as a real thing, and I am not advocating a collapse interpretation. I am also uncomfortable with any kind of preferred basis. My idea is that the configuration space of the universe is the classical configuration space, but that its evolution is determined by the wavefunction over the quantum mechanical configuration space (in whatever basis you choose). So a point-particle has a real momentum and a real position, which are not simultaneously measureable. For electromagnetism, the electric and magnetic fields have actual values, which are also not simultaneously measurable. The fields evolve continuously but non-deterministically in accordance with the evolution of the wavefunction. There are still blobs of amplitude in configuration space, but only one point in one of those blobs is the real configuration.

Anonymous: I'll look at your reference to refresh my memory of Bohm. The last I heard, there were problems with relativistic versions of that theory.

Oh and if in this many world interpretation photons would have to appear opposite to what is detected in our world, then when the experiment is over and the experimenters leave in opposite directions, does that mean the experimenters on the other side continuously crash into each other.

Both collapse and MWI have a it happens for an instant quality. As soon as the experiment is over they go back into the box like the Rosicrucians do with God's angels.

Wait it gets better. If there is a probability of your mothers getting pregnant here should there not be the opposite effect such that your double couldn't have been born?

Since both you and he are around that means the other world only begins with the original photons flying apart.

MWI has both local extent, good, and a divergent local behavior at every point in space, pathological. It requires a disjunction between neighborhood elements since the results have to be complementary. The fabric of complementary MWI layers have an increasing tendency to explode the minute something happens in their partner. Which would suggest in fact that collapse is the true picture, but we already know it's a collapse of a description not the event. This is a bit like how water waves travel but no water molecule actually goes beyond the next crest. The collapse is a figment and MWI is unstable. My God what have we done to reason?

"If P(Y|X) ≈ 1, then P(X∧Y) ≈ P(X). Which is to say, believing extra details doesn't cost you extra probability when they are logical implications of general beliefs you already have."

Shivers went down my spine when I read that; this is the first time that I actually looked at a formula and really saw what it meant. Ah, maths. Thank you, Yu-el.

I disagree on five points. The first is my conclusion too; the second leads to the third and the third explains the fourth. The fifth one is the most interesting.

1) In contrast with the title, you did not show that the MWI is falsifiable nor testable; I know the title mentions decoherence (which is falsifiable and testable), but decoherence is very different from the MWI and for the rest of the article you talked about the MWI, though calling it decoherence. You just showed that MWI is "better" according to your "goodness" index, but that index is not so good. Also, the MWI is not at all a consequence of the superposition principle: it is rather an ad-hoc hypothesis made to "explain" why we don't experience a macroscopic superposition, despite we would expect it because macroscopic objects are made of microscopic ones. But, as I will mention in the last point, the superposition of macroscopic objects in not an inevitable consequence of the superposition principle applied to microscopic objects.

2) You say that postulating a new object is better than postulating a new law: so why teach Galileo's relativity by postulating its transformations, while they could be derived as a special case of Lorents transformations for slow speeds? The answer is because they are just models, which gotta be easy enough for us to understand them: in order to well understand relativity you first have to understand non-relativistic mechanics, and you can only do it observing and measuring slow objects and then making the simplest theory which describes that (i.e., postulating the shortest mathematical rules experimentally compatible with the "slow" experiences: Galileo's); THEN you can proceed in something more difficult and more accurate, postulating new rules to get a refined theory. You calculate the probability of a theory and use this as an index of the "truthness" of it, but that's confusing the reality with the model of it. You can't measure how a theory is "true", maybe there is no "Ultimate True Theory": you can just measure how a theory is effective and clean in describing the reality and being understood. So, in order to index how good a theory is, you should instead calculate the probability that a person understands that theory and uses it to correctly make anticipations about reality: that means P(Galileo) >> P(first Lorentz, then show Galileo as a special case); and also P(first Galileo, after Lorentz) != P(first Lorentz, after Galileo), because you can't expect people to be perfect rationalists: they can be just as rational as possible. The model is just an approximation of the reality, so you can't force the reality of people to be the "perfect rational person" model, you gotta take in account that nobody's perfect.

3) Because nobody's perfect, you must take in account the needed RAM too. You said in the previous post that "Occam's Razor was raised as an objection to the suggestion that nebulae were actually distant galaxies—it seemed to vastly multiply the number of entities in the universe", in order to justify that the RAM account is irrelevant. But that argument is not valid: we rejected the hypothesis that nebulae are not distant galaxies not because the Occam's Razor is irrelevant, but because we measured their distance and found that they are inside our galaxy; without this information, the simpler hypothesis would be that they are distant galaxies. The Occam's Razor IS relevant not only about the laws, but about the objects too. Yes, given a limited amount of information, it could shift toward a "simpler yet wrong model", but it doesn't annihilate the probability of the "right" model: with new information you would find out that you were previously wrong. But how often does the Occam's Razor induce you to neglect a good model, as opposed to how often it let us neglect bad models? Also, Occam's Razor may mislead you not only when applied to objects, but when applied to laws too, so your argument discriminating Occam's Razor applicability doesn't stand.

4) The collapse of the wave function is a way to represent a fact: if a microscopic system S is in an eigenstate of some observable A and you measure on S an observable B which is non commuting with A, your apparatus doesn't end up in a superposition of states but gives you a unique result, and the system S ends up in the eigenstate of B corresponding to the result the apparatus gave you. That's the fact. As the classical behavior of macroscopic objects and the stochastic irreversible collapse seems in contradiction with the linearity, predictability and reversibility of the Schrödinger equation ruling the microscopic systems, it appears as if there's an uncomfortable demarcation line between microscopic and macroscopic physics. So, attempts have been made in order to either find this demarcation line, or show a mechanism for the emergence of the classical behavior from the quantum mechanics, or solve or formalize this problem however. The Copenhagen interpretation (CI) just says: "there are classical behaving macroscopic objects, and quantum behaving microscopic ones, the interaction of a microscopic object with a macroscopic apparatus causes the stochastic and irreversible collapse of the wave function, whose probabilities are given by the Born rule, now shut up and do the math"; it is a rather unsatisfactory answer, primarily because it doesn't explain what gives rise to this demarcation line and where should it be drawn; but indeed it is useful to represent effectively what are the results of the typical educational experiments, where the difference between "big" and "small" is in no way ambiguous, and allows you to familiarize fast with the bra-ket math. The Many Worlds Interpretation (MWI) just says: "there is indeed the superposition of states in the macroscopic scale too, but this is not seen because the other parts of the wave function stay in parallel invisible universes". Now imagine Einstein did not develop the General Relativity, but we anyway developed the tools to measure the precession of Mercury and we have to face the inconsistency with our predictions through Newton's Laws: the analogous of the CI would be "the orbit of Mercury is not the one anticipated by Newton's Laws but this other one, now if you want to calculate the transits of Mercury as seen from the Earth for the next million years you gotta do THIS math and shut up"; the analogous of the MWI would be something like "we expect the orbit of Mercury to precede at this rate X but we observe this rate Y; well, there is another parallel universe in which the preceding rate of Mercury is Z such that the average between Y and Z is the expected X due to our beautiful indefeasible Newton's Law". Both are unsatisfactory and curiosity stoppers, but the first one avoids to introduce new objects. The MWI, instead, while explaining exactly the same experimental results, introduces not only other universes: it also introduces the concept itself that there are other universes which proliferate at each electron's cough attack. And it does just for the sake of human pursuit of beauty and loyalty to a (yes, beautiful, but that's not the point) theory.

5) you talk of MWI and of decoherence as they are the same thing, but they are quite different. Decoherence is about the loss of coherence that a microscopic system (an electron, for instance) experiences when interacting with a macroscopic chaotic environment. As this sounds rather relevant to the demarcation line and interaction between microscopic and macroscopic, it has been suggested that maybe these are related phenomenons, that is: maybe the classical behavior of macroscopic objects and the collapse of the wave function of a microscopic object interacting with a macroscopic apparatus are emergent phenomenons, which arise from the microscopic quantum one through some interaction mechanism. Of course this is not an answer to the problem: it is just a road to be walked in order to find a mechanism, but we gotta find it. As you say, "emergence" without an underlying mechanism is like "magic". Anyway, decoherence has nothing to do with MWI, though both try (or pretend) to "explain" the (apparent?) collapse of the wave function. In the last decades decoherence has been probed and the results look promising. Though I'm not an expert in the field, I took a course about it last year and made a seminar as exam for the course, describing the results of an article I read (http://arxiv.org/abs/1107.2138v1). They presented a toy model of a Curie-Weiss apparatus (a magnet in a thermal bath), prepared in an initial isotropic metastable state, measuring the z-axis spin component of a 1/2 spin particle through induced symmetry breaking. Though I wasn't totally persuaded by the Hamiltonian they wrote and I'm sure there are better toy models, the general ideas behind it were quite convincing. In particular, they computationally showed HOW the stochastic indeterministic collapse can emerge from just: a) Schrödinger's equation; b) statistical effects due to the "large size" of the apparatus (a magnet composed by a large number N of elementary magnets, coupled to a thermal bath); c) an appropriate initial state of the apparatus. They did not postulate neither new laws nor new objects: they just made a model of a measurement apparatus within the framework of quantum mechanics (without the postulation of the collapse) and showed how the collapse naturally arose from it. I think that's a pretty impressive result worth of further research, more than the MWI. This explains the collapse without postulating it, nor postulating unseen worlds.

Eliezer's mistake here was that he didn't, before the QM sequence, write a general post to the effect that you don't have an additional Bayesian burden of proof if your theory was proposed chronologically later. Given such a reference, it would have been a lot simpler to refer to that concept without it seeming like special pleading here.