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.
What happens when I measure an entangled particle at A after choosing an orientation, you measure it at B, and we're a light-year apart, moving at different speeds, and each measuring "first" in our frame of reference?
Why do these so-called "probabilities" resolve into probabilities when I measure something, but not when they're just being microscopic? When exactly do they resolve? How do you know?
Why is the wavefunction real enough to run a quantum computer but not real enough to contain intelligences?
These are all questions that mus...
Eliezer recently posted an essay on "the fallacy of privileging the hypothesis". What it's really about is the fallacy of privileging an arbitrary hypothesis. In the fictional example, a detective proposes that the investigation of an unsolved murder should begin by investigating whether a particular, randomly chosen citizen was in fact the murderer. Towards the end, this is likened to the presumption that one particular religion, rather than any of the other existing or even merely possible religions, is especially worth investigating.
However, in between the fictional and the supernatural illustrations of the fallacy, we have something more empirical: quantum mechanics. Eliezer writes, as he has previously, that the many-worlds interpretation is the one - the rationally favored interpretation, the picture of reality which rationally should be adopted given the empirical success of quantum theory. Eliezer has said this before, and I have argued against it before, back when this site was just part of a blog. This site is about rationality, not physics; and the quantum case is not essential to the exposition of this fallacy. But given the regularity with which many-worlds metaphysics shows up in discussion here, perhaps it is worth presenting a case for the opposition.
We can do this the easy way, or the hard way. The easy way is to argue that many-worlds is merely not favored, because we are nowhere near being able to locate our hypotheses in a way which permits a clean-cut judgment about their relative merits. The available hypotheses about the reality beneath quantum appearances are one and all unfinished muddles, and we should let their advocates get on with turning them into exact hypotheses without picking favorites first. (That is, if their advocates can be bothered turning them into exact hypotheses.)
The hard way is to argue that many-worlds is actually disfavored - that we can already say it is unlikely to be true. But let's take the easy path first, and see how things stand at the end.
The two examples of favoring an arbitrary hypothesis with which we have been provided - the murder investigation, the rivalry of religions - both present a situation in which the obvious hypotheses are homogeneous. They all have the form "Citizen X did it" or "Deity Y did it". It is easy to see that for particular values of X and Y, one is making an arbitrary selection from a large set of possibilities. This is not the case in quantum foundations. The well-known interpretations are extremely heterogeneous. There has not been much of an effort made to express them in a common framework - something necessary if we want to apply Occam's razor in the form of theoretical complexity - nor has there been much of an attempt to discern the full "space" of possible theories from which they have been drawn - something necessary if we really do wish to avoid privileging the hypotheses we happen to have. Part of the reason is, again, that many of the known options are somewhat underdeveloped as exact theories. They subsist partly on rhetoric and handwaving; they are mathematical vaporware. And it's hard to benchmark vaporware.
In his latest article, Eliezer presents the following argument:
"... there [is] no concrete evidence whatsoever that favors a collapse postulate or single-world quantum mechanics. But, said Scott, we might encounter future evidence in favor of single-world quantum mechanics, and many-worlds still has the open question of the Born probabilities... There must be a trillion better ways to answer the Born question without adding a collapse postulate..."
The basic wrong assumption being made is that quantum superposition by default equals multiplicity - that because the wavefunction in the double-slit experiment has two branches, one for each slit, there must be two of something there - and that a single-world interpretation has to add an extra postulate to this picture, such as a collapse process which removes one branch. But superposition-as-multiplicity really is just another hypothesis. When you use ordinary probabilities, you are not rationally obligated to believe that every outcome exists somewhere; and an electron wavefunction really may be describing a single object in a single state, rather than a multiplicity of them.
A quantum amplitude, being a complex number, is not an ordinary probability; it is, instead, a mysterious quantity from which usable probabilities are derived. Many-worlds says, "Let's view these amplitudes as realities, and try to derive the probabilities from them." But you can go the other way, and say, "Let's view these amplitudes as derived from the probabilities of a more fundamental theory." Mathematical results like Bell's theorem show that this will require a little imagination - you won't be able to derive quantum mechanics as an approximation to a 19th-century type of physics. But we have the imagination; we just need to use it in a disciplined way.
So that's the kernel of the argument that many worlds is not favored: the hypotheses under consideration are still too much of a mess to even be commensurable, and the informal argument for many worlds, quoted above, simply presupposes a multiplicity interpretation of quantum superposition. How about the argument that many worlds is actually disfavored? That would become a genuinely technical discussion, and when pressed, I would ultimately not insist upon it. We don't know enough about the theory-space yet. Single-world thinking looks more fruitful to me, when it comes to sub-quantum theory-building, but there are versions of many-worlds which I do occasionally like to think about. So the verdict for now has to be: not proven; and meanwhile, let a hundred schools of thought contend.