How to recover the Born rule in MWI is an important current research topic. I have no idea what the answer is.
Then you must admit that many worlds simply isn't a full-fledged interpretation. Its might "feel good", but it gives you no way of making measurements. What is preferable- a non-unitary collapse, or a total inability to make predictions? Naive many-worlds will give you the wrong answers for experiments the majority of the time (the probability is high you find yourself in a maverick world with a non-born probability).
Right now we can just take the Born rule as an axiom based on experimentation. We don't necessarily need it to fall out of the interpretation itself, though it would be nice. Like I said, there is ongoing research on how to recover it directly from the interpretation.
I assume by "naive MWI" you mean something like "one world, one vote", or that every world has an equal amount of "reality". Yes, this is naive and gives incorrect results; it's roughly equivalent to assuming that every binary outcome is 50/50. That's irrelevant to the actual forms of MWI that physicists believe in. (I'm not a physicist, but I play one on the internet.) Like lightvector said, while the total "number" of worlds that can't derive the born probabilities is much larger than the number of worlds that can, the "amount of reality" of the two groups has the opposite ratio. (This assumes the Born probabilities, but fuck it, let's just roll with it.)
There's also probably a bit of anthropic principle at play here. A lot of the worlds in which you can't derive the born probabilities are pretty strange and may very well be inimicable to life, at least as we know it.
doogly wrote:But if you do not get the born rule 100% of the time, you do not have identical predictions as other interpretations. Which means you aren't an "other interpretation" anymore, you're a distinct theory.
You don't have a 100% chance of getting the Born rule in collapse-based interpretations, either. The chance of things occurring in such a way that you can't do that is miniscule, but so is the chance that you find yourself in a world where the Born rule isn't derivable.
Xanthir wrote:Hmm, you're still attaching too much ontological significance to this whole "worlds" things.
Indeed! What else is an "interpretation" supposed to be? I'm down with Hilbert space, but it says nothing about how (where, through what mechanism) its superpositions are to be embedded in actual physical reality, that's just not in Hilbert's lexicon.
So how does MWI inform your personal intuitive ontology of qm? Or are you saying that it has nothing to say about your intuitive ontology of qm, and by "interpretation" you mean something other than that?
I've tried to answer a few times, and we're not quite communicating properly. Hopefully this post by Charlie! helps, as it's a very clear statement of what I'm trying to say:
thoughtfully wrote:Where do the probabilities come from in MWI, then? If there are two outcomes from an event, does that mean the expectation is necessarily 50%? How can it possibly make the right predictions in that case?
Important question of quantum mechanics: if you're at one spot in possibility-space and the world is left to evolve, what will the world look like later? The answer is probabilistic, regardless of interpretation. And it's not "half one way, half the other." The universe can be represented by a complex function in possibility-space: the bigger the function at a certain point in possibility-space after the universe is left to evolve, the bigger the probability of the world looking like that later.
The "universes splitting" picture is common in some popularizations, but totally misleading. Especially for continuous variables! What you might call "splitting" is really just the universe becoming more spread out in possibility-space.
SU3SU2U1 wrote:Thats fine, but why don't we evolve over time into an area where the born rule stops working?
"We" do. "We" also evolve into areas where it keeps working. The "we" that do the latter are more likely/"real" than the "we" that do the former.
Malconstant wrote:One other quick note, is there any reason MWI can't be stated to accommodate for differing probabilities? For example, suppose I have a wavefunction^2 with a 2/3 bump at point A and a 1/3 bump at point B. I agree it's an awkward solution to say that "there are two worlds resulting from this and you're twice as likely to find yourself in A" due to the invisible hand of qm (don't. I regretted saying it even as I was typing it). But what would be wrong with interpreting it instead as "three worlds split off from this, and you have equal probability of finding yourself in either of them, it's just that two of the worlds are identical. Does that harsh the "it's literally Hilbert space" ontological interpretation's charm too much?
The MWI *is* stated to accommodate differing probabilities. Only naive pop-science versions of it don't, and that's more due to lack of detail than an explicit or purposeful lack. It's not "the invisible hand of qm" that does, but the fact that different worlds have different amounts of reality (or, equivalently, that different regions of hilbert-space have different distributions/densities of amplitude).
PM 2Ring wrote:That's pretty much the way that David Deutsch describes it. In his version of MWI, the number of universes doesn't increase: it started as an infinite ensemble and always remains infinite, but at the start all the universes were in the exact same location of the configuration space, and thereafter tended to move in tandem. Each "splitting" event merely involves universes that had traveled in parallel up to that point diverging from one another.
Right. Whether you refer to it as (infinite) distinct universes or as an infinitely-divisible amount of "reality" is just a naming issue.
thoughtfully wrote:I'm not really satisfied with the playing around in Hilbert space aspect. That doesn't really feel like an "interpretation" in the usual sense; it's almost tautological from the bare math.
That's precisely why I prefer it. You don't need any extra concepts - you just look at the math, and lo, that's reality! Yay! Like doogly says, there is still a philosophical difference between MWI and "the bare math", but it's small.
Technical Ben wrote:So the previous MWI was that there was 4 universes, and a 1/4 (25%) chance to be in each one. This is the model I had trouble with, because we would have an even probability to end up in the universes with the ridiculously improbable outcomes. The more complete description of MWI is there are 26% of the universes with HH (with a 51% bias coin) but our probability to end up in a different universe to that one is 74%? That works mathematically.
So the "ridiculously improbable" universes are still ridiculously improbable? I'm still uneasy about the resultant universes where unicorns exist (because the maths says they do ) but I'm a lot more confident about the maths.
Yes, they're exactly as ridiculously improbable as collapse-based interpretations would say.