This does not explain how a classical observer gets probabilities that are precisely measured. In universe-as-a-wave-function there are no probabilities. So how exactly do they arise and what they mean?
The problem is that the name "Many Worlds Interpretation" sounds grandiose. "Many worlds" is simply an imaginative way of describing the existence of different states of the wavefunction - a concept that is extremely well established and universally accepted. MWI just says that we should assume that Quantum Mechanics holds in all situations, including when we make measurements (i.e., there's nothing special about the measurement process).
There isn't yet any successful quantum theory of gravity, but it's universally believed in the physics community that there will eventually be a quantum description of gravity. Dark energy and dark matter are merely components of the universe whose precise character is not yet known, but again, everyone believes that whatever they are, they will be described quantum mechanically. The arrow of time is merely a consequence of entropy being low in the early Universe.
The reason why physicists universally believe that the Universe is quantum mechanical is that it's impossible for QM to describe only a part of physics. If one aspect of physics is quantum mechanical, it "infects" every other aspect of physics and forces it to be quantum mechanical. You can't have elections obey quantum mechanical laws, but the gravity they produce be classical. It's really all or nothing.
This is why after the discovery of Quantum Mechanics, there was a drive to formulate quantum versions of all fundamental theories.
Either everything is quantum, or nothing is. Given that we are pretty darn sure that most of physics is quantum, we're pretty sure the answer is that everything is quantum, not that nothing is quantum.
There are different ways of formulating quantum theories of gravity (in fact, you can derive the Einstein equations fairly straightforwardly by trying to formulate a quantum theory of a massless spin-2 boson). We don't know which of those theories is correct yet, but it's not as if there's no way to quantize gravity.
By that logic assuming that distant parts of the universe still exist is metaphysics (since it would take many years for any information from there to reach us), yet few people feel the need to call it such.
As to “exactly when the universe will split into many worlds”, it happens zillions of times per second pretty much everywhere. It’s even not clear whether the branching is a discrete and countable occurrence, it could really be a continuous fanning out.
(Analogy: imagine saying "Relativity doesn't explain how we live in a Newtonian world. If relativity is valid, it should be able to say at exactly what speed motion becomes nonrelativistic. Provide a formula for it")
Here is a better theory than MWI: We live in a simulation, the computer is optimized so when there are too complex interactions in an area it simplifies the state into some probable untangled version. This theory predicts that decoherence thus happens at certain computational complexity levels, that is something we could try to find and test experimentally making this theory more scientific than MWI. MWI doesn't lead anywhere, it isn't science, it is just nonsense. I'm not saying my theory here is a good one, but it is better than MWI which isn't a high bar.
Relativity is a real formula and the classical limit is a real phenomenon, but there's no formula for when a relativistic situation "becomes classical".
> you just say that decoherence seems to correlate with entropy and then gave a formula for entropy
If the observed system and the observer/external universe are fully entangled (i.e. their entropy of entanglement is maximal) then decoherence has occurred and all observations of the observed system by that observer will be indistinguishable from if the system were not in superposition. That is a mathematical fact that falls right out of the equations. So I don't know what else you're asking for.
Decoherence is a phenomenon that's been studied mathematically and experimentally, not simply an interpretation or hand-waving.
At best the decoherence can try to explain how appearance of a sufficiently big classical object may trigger appearance of other objects, but it does not explain how the initial object appears.
The point of the bath is it's a generic model of a large system with lots of states and interactions.
> I.e. why the system interacts with a particular bath and not a superposition of such baths?
The bath can be in a superposition state at the start, that's fine. (Indeed the whole model would be pretty useless otherwise).
In universe-as-a-wave-function there is no external bath. The system as whole is always coherent and is described by a single wave function.
Then the idea of the decoherence is that perhaps during evolution of this big wave function it is possible to find a subsystem that looks like it is approximately decoherent during some time interval. Then one claim that our visible universe is just such subsystem.
The trouble is that so far nobody came up with a model where such temporary approximately classical subsystem appears.
Perhaps we have not tried hard enough or this is a really difficult problem, but at this point I am rather skeptical that decoherence is the right approach at all.
They don't assume it's classical. They assume it's a system with lots of states and interactions, because if you want to have a model of "the external universe" then you have to have some kind of concept of what that looks like.
> In universe-as-a-wave-function there is no external bath. The system as whole is always coherent and is described by a single wave function.
Sure; the point is that if you split the universe into "these two entangled particles" and "the rest of the universe", because you want to understand how we observe that entanglement "decaying" as the particles interact with the rest of the universe, then you can model that as "these two entangled particles" interacting with "a thermal bath".
> The trouble is that so far nobody came up with a model where such temporary approximately classical subsystem appears.
This is nonsense? Wavefunctions generally have a lot of structure and decomposing them into smaller subsystems and functions happens all the time.
Such 2-part subsystem should explain then how the classically-looking part gets the value it measures and the nature of probabilities.
Despite attempts nobody was able to find such subsystem.
If you model it as e.g. a quantum system with a state space that describes what you're measuring, coupled to a thermal bath, then it works. What kind of model are you looking for? Real measuring instruments are probably too big to ever model the full quantum state space of all the particles they're made up of, for example.
> And the whole point of the decoherence exercise is to avoid Born rule as it implies a truly classical subsystem
What do you mean by "truly classical"? The Born rule implies that our experience is the same as if we found ourselves within one of an ensemble of possible classical-like states with a certain probability, but, well, experimentally that's what we do; any interpretation of quantum mechanics needs to be able to recover that reality.
This is the problem with MWI gospel, people come and say that it solves all the math but it leaves gaping holes like this. And you didn't even solve the randomness, since as you say it is "statistical", although that is just a theory we currently have no formula for this.
Calling it a wave function collapse is much more honest since it accurately describes the situation, that we have no clue at what it is, why or when it happens. All we know how to do is calculate what possibly happens when we know that a wave function collapse will happen in a certain way.
As far as I can see people's objection to this tends to be that they don't feel like they're in a superposition. To which my response is: what would you expect it to feel like? Bearing in mind that the wavefunction is describing all the states of your neurons etc..
Sure; I was being poetic. We could talk about when you sleep, or distant regions of the universe that you simply can't measure within a human lifetime.
> MWI isn't the only interpretation, and there isn't a current experiment which can determine which if any of the interpretations are correct. This is the same problem String Theory has had. You can't just base reality on the math.
When other "interpretations" require extra assumptions, you can, and should. Otherwise you can never rule out theories that add extra epicycles that have no observable consequences.
As for parsimonious interpretations, what does superdeterminism add?
That simpler interpretation is also equivalent to a simpler implementation that doesn’t require apparently-arbitrary resolutions of quantum probabilities (MWI). It’s essentially a question of where you hide the “weird”.
It seems likely to me that they’re both wrong, and the in-principle-untestability of all this points to our mental machinery just failing to map intuitive concepts onto this space, but I’m totally agnostic to this. I do find MWI more conceptually appealing.
Under aforementioned requirement, of course. If some sort of MWI is true, there may be just no way to confirm it, and that’s it.
There are probability amplitudes in the universal wave function, and those are complex square roots of probabilities.
It is true that deriving the Born Rule purely from the unitary dynamics of the wave function is an unsolved problem. This is discussed a fair bit in the comments to Aaronson's article.