Another little essay on MWI. tl;dr : Eliezer is wrong on the Internet! Won't somebody please think of the mind children?...

I have spent many years studying and thinking about interpretations of quantum theory. Eliezer's peculiar form of dogmatism about many worlds is a new twist. I have certainly encountered dogmatic many-worlds supporters before. What's exceptional is Eliezer's determination to make belief in many worlds a benchmark test of rationality in general. He's not just dogmatic about it as a question of physics, but now he even calls it a rationalist "slam-dunk", a thing which should be obvious to any sufficiently informed clear thinker, and which can be used to rank a person's rationality.

My position, I suppose, is that it is Eliezer who is insufficiently informed. He has always been a wavefunction realist - a believer in the existence of the wavefunction - and simply went from a belief in collapse of the wavefunction, to a belief in no collapse. If that was the only choice, he'd have a point. But it is far from being the only choice.

One thing I wonder about (when I adopt the perspective of trying to draw lessons regarding general rationality from this affair) is whether he ought to regard himself as culpable for this error, or whether ignorance is a valid excuse. Yesterday I was promoting "quantum causal histories" as an example of an alternative class of interpretation. Those are rather obscure papers. He's certainly not at fault for not having heard of them. Yet he surely should have heard of John Cramer's transactional interpretation, and there's no trace of it in his writings on this topic.

I suspect that another factor in his thinking is a belief in the minimalism of many-worlds. All you need is the wavefunction. You even get to remove something from the theory - the collapse postulate. But the complexities reenter - and the handwaving begins - when you try to find the worlds in the wavefunction. Naive onlookers to this discussion may think of a world as a point in configuration space. But this is not the usual notion of "world" in the technical literature on many worlds. Worlds are themselves represented by lesser wavefunctions: components of the total wavefunction, or tensor factors thereof. It is a chronic question in many-worlds theory as to which such components are the worlds, or whether one even needs to specify a particular algebraic breakdown of the universal wavefunction as the decomposition corresponding to reality. I don't even know what Eliezer's position on this debate is. Is a world a point in configuration space? Is it a blob of amplitude stretching across a small contiguous region of configuration space? What about a wavefunction component which stretches across most of configuration space, and has multiple peaks - is it legitimate or not to treat that as a world? Eliezer is impressed by Robin Hanson's mangled worlds proposal; should we take Robin's definition of worlds as the one to use, if we wish to understand his thought?

I don't object to many-worlds advocates having their theoretical disputes; certainly better that they have them, than that their concepts should remain fuzzy and undeveloped! But I find it very hard to justify this harsh advocacy of many-worlds as obviously superior when the theoretical details of the interpretation remain so confused. The confusion, the unfinished work, seems comparable to that still existing with respect to the zigzag interpretations like Cramer's. And since a zigzag interpretation only requires a single, basically classical space-time, and does away with the wavefunction entirely except as the sort of probability distribution appropriate to a situation in which causality runs backwards and forwards in time, it has its own claim to elegance and minimalism.

My own position is the anodyne one that Further Research Is Required, and that theoretical pluralism should be tolerated. I respect the rigor of Bohmian mechanics; I don't believe it is the truth, but working on it might lead to the truth, and the same goes for a number of other interpretations. I tilt towards single-world interpretations because I anticipate that in most completed many-worlds theories (many-worlds theories in which the confusions have truly been resolved, by an exact theoretical framework), you will be able to find self-contained histories, akin to Bohmian trajectories but perhaps metaphorically "thicker" in cross-section. And my ultimate message for many-worlds enthusiasts is that the apparent simplicity of many worlds is an illusion because of the theoretical work necessary to finish the job. You will end up either adding lots of extra structure, or compromising on objectivity and theoretical exactness (e.g. by being blase about what is and is not a "world").