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?
My understanding is that this is just the law of large numbers. Most branches match the mathematical probabilities very closely, and hence that’s what we observe. Yes, people on one of the rare branches where things behave differently wouldn’t observe that, but we simply happen to not be on one of those rare branches.
So you’re endorsing Many Worlds with an appeal to the anthropic principle. That’s fine, but you do have to assume MWI is the true interpretation of the mathematical formalism.
The Many-Worlds Interpretation is not really an interpretation. It just says that the known laws of Quantum Mechanics are correct, and that any measurement process itself has to obey the laws of Quantum Mechanics. In other words, nothing un-Quantum-Mechanical happens during measurement.
It’s an interpretation because we don’t have any empirical evidence for the other worlds. Science requires evidence, math alone isn’t enough. MWI is metaphysics, which is fine. We all wax philosophical sometimes as humans. Even the great Feynman couldn’t help himself.
There is a massive amount of evidence that Quantum Mechanics is the way the Universe works, and the MWI is simply vanilla Quantum Mechanics, with zero further assumptions.
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).
QM isn’t a complete description of the universe because of gravity, dark energy, dark matter, the arrow of time, and it doesn’t explain probability. So it’s a little premature to say that’s how the universe works.
Gravity, dark energy, dark matter or the arrow of time in no way conflict with QM.
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.
I don't see why that has to be the case other than mathematically it looks like QM "infects" everything as the theory stands now. But nature doesn't have to play along. Also, I forgot about spacetime. Is it quantum mechanical, relativistic or something else? And saying the universe began at al low entropy doesn't explain why it started out in that state.
You cannot construct a logical theory of physics in which some aspects of physics are quantum and others aren't. That's what I mean by Quantum Mechanics infecting the rest of physics.
This is why after the discovery of Quantum Mechanics, there was a drive to formulate quantum versions of all fundamental theories.
Nature does have to play along, because whatever the correct theory of physics, it has to be logically coherent.
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.
> It’s an interpretation because we don’t have any empirical evidence for the other worlds. Science requires evidence, math alone isn’t enough.
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.
That's quite correct though. Assuming distant parts of the universe still exist is metaphysics; it's relying on Occam's Razor to assert that there isn't a cosmic Alioth out there eating everything that passes beyond the red-shift horizon, but there's no way to know there isn't.
MVI doesn't solve wave function collapses, if it did it would be able to tell exactly when the universe will split into many worlds, but it can't. So it doesn't solve anything, the difficulty with the theory is still there.
The perceived wave function collapse is explained by decoherence. There is no extra “split” that happens. “World” is just a term referring to the parts of the universal wave function that are entangled with each other.
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.
So when does decoherence happen? Provide a formula for it. That is what people struggle with in quantum mechanics, MWI just deflects the question. Without a formula for when this phenomena happens any "interpretation" is just nonsense, except as a tool to get towards that formula.
Decoherence of a system happens when the entropy of entanglement is maximal, so if you want a formula then it's S(Tr_a(p_ab)) -> N/e. In practice a complex system is probably never fully decoherent, but the separability is small enough to not matter; if we're being truly rigorous we work with it as a limit, similar to how we use the "classical limit" in other parts of QM or other contexts.
(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")
Relativity is a real formula, you just say that decoherence seems to correlate with entropy and then gave a formula for entropy. We don't have a formula for decoherence. Any explanation for decoherence that doesn't help us find a formula for it is nonsense.
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.
This notion does not explain how the thermal bath appears. I.e. why the system interacts with a particular bath and not a superposition of such baths?
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.
Again, models of decoherence assume existence of an external bath resembling classical state. By interacting with it the system becomes classical itself if it is and the bath is sufficiently big. But it does not explain how that external bath appears.
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.
> models of decoherence assume existence of an external bath resembling classical state
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.
What is necessary is to find in the big wave function a subsystem consisting of, say, a particle with a spin and something approximating a classical measurement device.
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.
For a sufficiently simplified model of a measuring device you can do that. I mean there's no getting away from having to use the Born rule, and I'm not as sanguine as Aaronson about the idea that that's adequately justified, but it's not like there's a better alternative.
So far nobody was able to get such model unless I missed something. And the whole point of the decoherence exercise is to avoid Born rule as it implies a truly classical subsystem and we are back to where we started.
> So far nobody was able to get such model unless I missed something.
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.
I don’t think it’s black & white, either coherent or decoherent, for subsystems. It’s rather a scale. In that sense there may not be discrete “worlds”, but rather a continuum of them, matching the degree to which particles are entangled or not entangled, and in superposition or not in superposition.
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.
The other cat is being observed by the other you. When you open the box and look, you entangle your state with the cat's, and the wavefunction describing both of you becomes one that could be decomposed as a superposition of two "worlds", one with a live cat and a you who's observed a live cat, the other with a dead cat and a you who's observed a dead cat.
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..
But the other me isn't observed. There's no empirical evidence for that other world. It's an interpretation of the mathematical formalism that there would be other mes making different observations. But there's nothing observational saying I have to choose the MWI interpretation as the correct one.
There's no empirical evidence that the world continues to exist when you close your eyes, it's just the most natural interpretation of our best available mathematical formalism.
Other than the fact your other senses are working, the ground continues to hold you up, gravity is still at play, you're still breathing, etc. That's a ridiculous standard for empirical. 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.
> Other than the fact your other senses are working, the ground continues to hold you up, gravity is still at play, you're still breathing, 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.
You are "in" the wave function still associated with the live cat, but not with the dead cat wave function. Obviously neither you or a cat is a single wave function, but that's basically the explanation.
I understand that's the interpretation, but I don't observe the dead cat, so I don't feel compelled to accept MWI. I'm not saying it's wrong (who knows), only that it's not scientific (lacking empirical evidence for the dead cat) and one of the other interpretations could be correct (again who knows if any of them are representative of the true state of affairs).
The two cats are what the Schroedinger equation implies. The fact that you don't observe the dead cat is perfectly consistent with the Schroedinger equation. To deny the dead cat means that the Schroedinger equation doesn't describe physical reality, and that it has to be modified or added to in some way. There are ways to do so, but it makes the underlying model more complicated and more awkward. Occam's razor would suggest that the Schroedinger equation is the simplest and most parsimonious explanation for what we observe, despite it also predicting the unobservable (for us) other branches of the wave function.
I understand, but Schrodinger himself came up with the cat thought experiment to demonstrate that he felt something was obviously wrong. A version of the Copenhagen interpretation would just say the wave equation is a useful tool for predicting experimental outcomes. We can't say what's really happening when we're not observing. So you don't need to add anything, you just give up on saying what's real. Which seems defeatist or anti-realist, but then one can always hold out hope for better experiments to one day show us what is really going on.
As for parsimonious interpretations, what does superdeterminism add?
All the other interpretations require additional assumptions on top of the mathematical formalism, hence MW seems the most plausible to me. The GP wrote “[in a] universe-as-a-wave-function”, which basically is the MWI.
I’m not a fan of Many Worlds. Communication or even detection of the split universes is impossible, which means it is impossible to measure. And science requires measurement to confirm our theories. Which means the MWI is equivalent to a simpler interpretation that doesn’t require split universes.
If something moves far enough away from us that it exits our observable universe, should we assume it still exists, or that physics has a special collapse rule that makes it stop existing at that point? Just like the split universes, it's impossible to directly measure the existence of objects outside of our observable universe.
> MWI is equivalent to a simpler interpretation that doesn’t require split universes.
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.
> In universe-as-a-wave-function there are no probabilities.
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.
probabilities are, by definition, not precisely measured. "Real world" probabilities are derived from imprecise measurements, and model probabilities are dictated by (simplified) model constraints.
Once you can locate yourself in a system, the system is adequate as a physical theory of your phenomenological state.