Why Many-Worlds Is Not The Rationally Favored Interpretation

The theories actually used in particle physics can generally be obtained by starting with some classical field theory and then "quantizing" it. You go from something described by straightforward differential equations (the classical theory) to a quantum theory on the configuration space of the classical theory, with uncertainty principle, probability amplitudes, and so forth. There is a formal procedure in which you take the classical differential equations and reinterpret them as "operator equations", that describe relationships between the elements of the Schrodinger equation of the resulting quantum field theory.

Many-worlds, being a theory which says that the universal wavefunction is the fundamental reality, starts with a quantum perspective and then tries to find the observable quasi-classical reality somewhere within it. However, given the fact that the quantum theories we actually use have not just a historical but a logical relationship to corresponding classical theories, you can start at the other end and try to understand quantum theory in basically classical terms, only with something extra added. This is what Hadley is doing. His hypothesis is that the rigmarole of quantization is nothing but the modification to probability theory required when you have a classical field theory coupled to general relativity, because microscopic time-loops ("closed timelike curves") introduce certain constraints on the possible behavior of quantities which are otherwise causally disjoint ("spacelike separated"). To reduce it all to a slogan: Hadley's theory is that quantum mechanics = classical mechanics + loops in time.

There are lots of people out there who want to answer big questions in a simple way. Usually you can see where they go wrong. In Hadley's case I can't, nor has anyone else rebutted the proposal. Superficially it makes sense, but he really needs to exactly re-derive the Schrodinger equation somehow, and maybe he can't do that without a much better understanding (than anyone currently possesses) of "non-orientable 4-manifolds". For (to put it yet another way) he's saying that the Schrodinger equation is the appropriate approximate framework to describe the propagation of particles and fields on such manifolds.

Hadley's theory is one member of a whole class of theories according to which complex numbers show up in quantum theory because you're conditioning on the future as well as on the past. I am not aware of any logical proof that complex-valued probabilities are the appropriate formalism for such a situation. But there is an intriguing formal similarity between quantum field theory in N space dimensions and statistical mechanics in N+1 dimensions. It is as if, when you think about initial and final states of an evolving wavefunction, you should think about events in the intermediate space-time volume as having local classically-probabilistic dependencies both forwards and backwards in time - and these add up to chained dependencies in the space-like direction, as you move infinitesimally forward along one light-cone and then infinitesimally backward along another - and the initial and final wavefunctions are boundary conditions on this chunk of space-time, with two components (real and imaginary) everywhere corresponding to forward-in-time and backward-in-time dependencies.

This sort of idea has haunted physics for decades - it's in "Wheeler-Feynman absorber theory", in Aharonov's time-symmetric quantum mechanics (where you have two state vectors, one evolving forwards and one evolving backwards)... and to date it has neither been vindicated nor debunked, as a possible fundamental explanation of quantum theory.

Turning now to your final questions: perhaps it is a little clearer now that you do not need magic to not have many-worlds at the macro level, you need only have an interpretation of micro-level superposition which does not involve two-things-in-the-one-place. Thus, according to these zigzag-in-time theories, micro-level superposition is a manifestation of a weave of causal/probabilistic dependencies oriented in two time directions, into the past and into the future. Like ordinary probability, it's mere epistemic uncertainty, but in an unusual formalism, and in actuality the quantum object is only ever in one state or the other.

Now let's consider Bohm's theory. How does a quantum computer work according to Bohm? As normally understood, Bohm's theory says you have universal wavefunction and classical world, whose evolution is guided by said wavefunction. So a Bohmian quantum computer gets to work because the wavefunction is part of the theory. However, the conceptually interesting reformulation of Bohm's theory is one where the wavefunction is just treated as a law of motion, rather than as a thing itself. The Bohmian law of motion for the classical world is that it follows the gradient of the complex phase in configuration space. But if you calculate that through, for a particular universal wavefunction, what you get is the classically local potential exhibited by the classical theory from which your quantum theory was mathematically derived, and an extra nonlocal potential. The point is that Bohmians do not strictly need to posit wavefunctions at all - they can just talk about the form of that nonlocal potential. So, though no-one has done it, there is going to be a neo-Bohmian explanation for how a quantum computer works in which qubits don't actually go into superposition and the nonlocal dynamics somehow (paging Dr Aaronson...) gives you that extra power.

To round this out, I want to say that my personally preferred interpretation is none of the above. I'd prefer something like this so I can have my neo-monads. In a quasi-classical, space-time-based one-world interpretation, like Hadley's theory or neo-Bohmian theory, Hilbert space is not fundamental. But if we're just thinking about what looks promising as a mathematical theory of physics, then I think those options have to be mentioned. And maybe consideration of them will inspire hybrid or intermediate new theories.

I hope this all makes clear that there is a mountain of undigested complexity in the theoretical situation. Experiment has not validated many-worlds, it has validated quantum mechanics, and many worlds is just one interpretation thereof. If the aim is to "think like reality" - the epistemic reality is that we're still thinking it through and do not know which, if any, is correct.

From a purely theoretic or philosophical point of view, I'd agree.

However, physical theories are mostly used to make predictions.

Even if you a firm believer in MWI, in 99% of the practical cases, whenever you use QM, you will use state reductions to make predictions.

Now you have an interesting situation: You have two formalisms: one is butt-ugly but usable, the other one is nice and general, but not very helpful. Additionally, the two formalisms are mostly equivalent mathematically, at least as long as it comes to making verifiable predictions.

Additionally there are these pesky probabilities, that the nice formalism may account for automatically, but it's still unclear. These probabilities are essential to every practical use of the theory. So from a practical point of view, they are not just a nuance, they are essential.

If you assess this situation with a purely positivist mind-set: you could ask: "What additional benefits does the elegant formalism give me besides being elegant?"

Now, I don't want to say that MWI does not have a clear and definite theoretical edge, but it would be quite hypocritical to throw out the usable formalism as long as it is even unclear how to make the new one at least as predictive as the old one.

I take it you don't think much of Bohmian mechanics, then. ;)

Many-worlds are there at the level of quantum mechanics, and there is the single world at the level of classical mechanics, both views correct in their respective frameworks for describing reality. The world-counting is how human intuitions read math, not obviously something inherent in reality (unless there is a better understanding of what "inherent in reality" should mean). What picture is right for a deeper level can be completely different once again.

Another, more important question, is how morally relevant are these conceptions of reality, but I don't know in what way to trust my intuition about morality of concepts it's using for interpreting math. So far, MWI looks to me morally indistinguishable from epistemic uncertainty, and so many-worlds of QM are no more real than single-world of classical mechanics. Many-worldness of QM might well be more due to the properties of math rather than "character of reality", whatever that should mean.

The fact that quantum mechanics is deeper in physics places it further away from human experience and from human morality, and so makes it less obviously adequately evaluated intuitively. The measure of reality lies in human preference, not in the turtles of physics. Exploration of physics starts from human plans, and the fact that humans are made of the stuff doesn't give it more status than a distant star -- it's just a substrate.

You actually have to select the "draft" option from the dropdown menu. "save and continue" basically just means "publish what I have here to wherever I selected to publish it, but keep me in the editor so I can keep working on it"

I'm looking forward to reading more! What I'd really like to see is an expert rebuttal to Eliezer's arguments for multiple worlds (which I find compelling).

Things still publish even when you save to drafts, or at least they have for me. You need to click "Hide" after you save it; then others can't see it and you can edit at your leisure, then unhide.

If this is true, why doesn't this count as straight-forward induction? It certainly looks like induction and if it is, why is this a philosophical rather than scientific case? Also, if we think CI and MWI make the same predictions what does it mean to say "tended to be more correct"? Doesn't that require experimental evidence falsifying one of the interpretations at a later date?

It is not scientific induction, since you can't measure elegance quantitatively. However scientists have subjective intuition based on the successes and failures of past other physical theories. This is what I meant by "philosophical edge".

Come on, you don't seriously believe that in physics simplicity always wins over correctness?

If you look at physicists, they work in both directions:

• Make better approximations
• Develop more complete theories

And physicists clearly distinguish between the above two.

Would you seriously believe that e.g. Kepler's model of planetary orbits survived rather than that of Ptolemy just because his was simpler or because it was closer to truth?

My reply was mostly triggered by this sentence;

Yet I find no reference anywhere in the article to 'faster than light' or, in fact, any of the critical elements to Eliezer's claim.

However, I'd be really curious which specific claim don't you agree with.

The absence of evidence against a hypothesis that other hypotheses predict you would encounter is evidence in favor of that hypothesis.