It is often claimed that the the Uncertainty Principle of quantum mechanics [10] makes the future unpredictable [11], but in the terms of the above analysis this is far from the whole story.
The predominant interpretation of quantum dynamics on LessWrong seems Many Worldism. I think it would make sense to address it shortly.
I have now added a hopefully suitable paragraph to the post.
Yeah, that's it. In case of quantum event, the probability (or indexical uncertainty) is in the territory; but in both quantum and non-quantum events, there is a probability in the map, just for different reasons.
In both cases we can use Many Worlds as a tool to visualize what those probabilities in the map mean. But in the case of non-quantum events we need to remember that there can be a better map with different probabilities.
In replying initially, I assumed that "indexical uncertainty" was a technical terms for a variable that plays the role of probability given that in fact "everything happens" in MW and therefore everything strictly has a probability of 1. However, now I have looked up "indexical uncertainty" and find that it means an observer's uncertainty as to which branch they are in (or more generally, uncertainty about one's position in relation to something even though one has certain knowledge of that something). That being so, I can't see how you can describe it as being in the territory.
Incidentally, I have now added an edit to the quantum section of the OP.
Yeah, that's it. In case of quantum event, the probability (or indexical uncertainty) is in the territory; but in both quantum and non-quantum events, there is a probability in the map, just for different reasons.
In both cases we can use Many Worlds as a tool to visualize what those probabilities in the map mean. But in the case of non-quantum events we need to remember that there can be a better map with different probabilities.
In other words, the states are a continuum with markedly varying density so that if you zoom out there is the appearance of branches?
Yes, but it's still continuous. There's always some influence, it can just get arbitrarily small. I'm unsure if this hypothetically allows MWI to be experimentally confirmed.
(The thesis of mangled-worlds seems to be that, in fact, in some cases that doesn't happen - that is, world A's influence on world B stays large.)
Schroedinger's cat
If it helps, think of half-silvered mirrors. Those are actually symmetric, letting through half the light either way; the trick is that the ambient lighting on the "reflective" side is orders of magnitude brighter, so the light shining through from the dark side is simply washed out.
To apply that to quantum mechanics, consider that the two branches - cat dead and not-dead - can still affect each other, but as if through a 99.9-whatever number of nines-silvered mirror. By the time a divergence gets to human scale, it'll be very, very close to an absolute separation.
Thanks, so to get back to the original question of how to describe the different effects of divergence and convergence in the context of MW, here's how it's seeming to me. (The terminology is probably in need of refinement).
Considering this in terms of the LW-preferred Many Worlds interpretation of quantum mechanics, exact "prediction" is possible in principle but the prediction is of the indexical uncertainty of an array of outcomes. (The indexical uncertainty governs the probability of a particular outcome if one is considered at random.) Whether a process is convergent or divergent on a macro scale makes no difference to the number of states that formally need to be included in the distribution of possible outcomes. However, in the convergent process the cases become so similar that there appears to be only one outcome at the macro scale; whereas in a divergent process the "density of probability" (in the above sense) becomes so vanishingly small for some states that at a macro scale the outcomes appear to split into separate branches. (They have become decoherent.) Any one such branch appears to an observer within that branch to be the only outcome, and so such an observer could not have known what to "expect" - only the probability distribution of what to expect. This can be described as a condition of subjective unpredictability, in the sense that there is no subjective expectation that can be formed before the divergent process which can be reliably expected to coincident with observation after the process.
There are no discrete "worlds" and "branches" in quantum physics as such. Once two regions in state space are sufficiently separated to no longer significantly influence each other they might be considered split, which makes the answer to your question "yes" by definition.
There are no discrete "worlds" and "branches" in quantum physics as such.
This seems to conflict with references to "many worlds" and "branch points" in other comments, or is the key word "discrete"? In other words, the states are a continuum with markedly varying density so that if you zoom out there is the appearance of branches? I could understand that expect for cases like Schroedinger's cat where there seems to be a pretty clear branch (at the point where the box is opened, i.e. from the point of view of a particular state if that is the right terminology).
Once two regions in state space are sufficiently separated to no longer significantly influence each other...
From the big bang there are an unimaginably large number of regions in state space each having an unimaginably small influence. It's not obvious, but I can perfectly well believe that the net effect is dominated by the smallness of influence, so I'll take your word for it.
If it is about quantum uncertaintly, assuming our knowledge of quantum physics is correct, the calculated probabilities will be correct. And there will be no hidden variables, etc.
If instead I just say "the probability of rain tomorrow is 50%", then I may be (1) wrong about the probability, and my model also does not include the fact that I or someone else (2) could somehow influence the weather. Therefore modelling subjective probabilities as Many Worlds would provide unwarranted feeling of reliability.
Having said this, we can use something similar to Many Worlds by describing a 80% probability by saying -- in 10 situations like this, I will be on average right in 8 of them and wrong in 2 of them.
There is just the small difference that it is about "situations like this", not this specific situation. For example the specific situation may be manipulated. Let's say I feel 80% certainty and someone wants to bet money against me. I may think outside of the box and realise: wait a moment, people usually don't offer me bets, so what is different about this specific situation that this person decided to make a bet? Maybe they have some insider information that I am missing. And by reflecting this I reduce my certainty. -- While in a quantum physics situation, if my model says that with 80% probability something will happen, and someone offers to make bets, I would say: yes, sure.
Thanks, I think I understand that, though I would put it slightly differently, as follows...
I normally say that probability is not a fact about an event, but a fact about a model of an event, or about our knowledge of an event, because there needs to be an implied population, which depends on a model. When speaking of "situations like this" you are modelling the situation as belonging to a particular class of situations whereas in reality (unlike in models) every situation is unique. For example, I may decide the probability of rain tomorrow is 50% because that is the historic probability for rain where I live in late July. But if I know the current value of the North Atlantic temperature anomaly, I might say that reduces it to 40% - the same event, but additional knowledge about the event and hence a different choice of model with a smaller population (of rainfall data at that place & season with that anomaly) and hence a greater range of uncertainty. Further information could lead to further adjustments until I have a population of 0 previous events "like this" to extrapolate from!
Now I think what you are saying is that subject to the hypothesis that our knowledge of quantum physics is correct, and in the thought experiment where we are calculating from all the available knowledge about the initial conditions, that is the unique case where there is nothing more to know and no other possible correct model - so in that case the probability is a fact about the event as well. The many worlds provide the population, and the probability is that of the event being present in one of those worlds taken at random.
Incidentally, I'm not sure where my picture of probability fits in the subjective/objective classification. Probabilities of models are objective facts about those models, probabilities of events that involve "bets" about missing facts are subjective, while what I describe is dependent on the subject's knowledge of circumstantial data but free of bets, so I'll call it semi-subjective until somebody tells me otherwise!
Rather, the significant point is that you can predict the future with arbitrary precision, but the prediction will say things like "you are superpositioned into these three states". That result is deterministic, but it doesn't help you predict your future subjective experience when you're facing down the branch point.
(You know that there will be three yous, each thinking "Huh, I was number 1/2/3" -- but until you check, you won't know which you you are.)
So, to get this clear (being well outside my comfort zone here), once a split into two branches has occurred, they no longer influence each other? The integration over all possibilities is something that happens in only one of the many worlds? (My recent understanding is based on "Everything that can happen does happen" by Cox & Forshaw).
If someone is able to understand 10% as 10%, then this works. But most people don't. This is why CFAR uses the calibration game.
People buy lottery tickets with chances to win smaller than one in a million, and put a lot of emotions in them. Imagine that instead you have a quantum event that happens with probability one in a million. Would the same people feel correctly about it?
In situations like these, I find Many Worlds useful for correcting my intuitions (even if in the specific situation the analogy is incorrect, because the source of randomness is not quantum, etc.). For example, if I had the lottery ticket, I could imagine million tiny slices of my future, and would notice that in the overwhelming majority of them nothing special happened; so I shouldn't waste my time obsessing about the invisible.
Similarly, if a probability of succeeding in something is 10%, a person can just wave their hands and say "whatever, I feel lucky"... or imagine 10 possible futures, with labels: success, failure, failure, failure, failure, failure, failure, failure, failure, failure. (There is no lucky in the Many Worlds; there are just multiple outcomes.)
Specifically, for a quantum suicide, imagine a planet-size graveyard, cities and continents filled with graves, and then zoom in to one continent, one country, one city, one street, and amoung the graves find a sole survivor with a gigantic heap of gold saying proudly: "We, the inhabitants of this planet, are so incredibly smart and rich! I am sure all people from other planets envy our huge per capita wealth!" Suddenly it does not feel like a good idea when someone proposes you that your planet should do the same thing.
even if in the specific situation the analogy is incorrect, because the source of randomness is not quantum, etc.
This seems a rather significant qualification. Why can't we say that the MW interpretation is something that can be applied to any process which we are not in a position to predict? Why is it only properly a description of quantum uncertainty? I suspect many people will answer in terms of the subjective/objective split, but that's tricky terrain.
At the risk of starting yet another quantum interpretation debate, the argument that 'Copenhagen is simpler than MWI' is not a well-presented one. For instance, a quantum computer with 500 qubits will, at some point in processing, be in the superposition of 2^500 states at once. According to Copenhagen, one of these is randomly chosen at measurement. But to know the probability, you still have to keep track of 2^500 states. It's not simple at all. If you could get by with many fewer states (like, say, a polynomial function of the number of qubits), it would be possible to efficiently simulate a quantum computer on a classical one. While the impossibility of this hasn't been proven, the consensus opinion seems to be that it is unlikely.
MWI simply acknowledges this inherent complexity in quantum mechanics, and tries to deal with it directly instead of avoiding it. If it makes you more comfortable, you can consider the whole universe as a big quantum computer, and you're living in it. That's MWI.
And another attractive aspect of MWI is that it is entirely deterministic. While each individual universe may appear random, the mulitverse as a whole evolves deterministically.
you can consider the whole universe as a big quantum computer, and you're living in it
I recall hearing it argued somewhere that it's not so much "a computer" as "the universal computer" in the sense that it is impossible to principle for there to be another computer performing the calculations from the same initial conditions (and for example getting to a particular state sooner). I like that if it's true. The calculations can be performed, but only by existing.
the multiverse as a whole evolves deterministically
So to get back to my question of what predictability means in a QM universe under MW, the significant point seems to be that prediction is possible starting from the initial conditions of the Big Bang, but not from a later point in a particular universe (without complete information about the all other universes that have evolved from the Big Bang)?
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I probably meant that the fact that indexical uncertainty is unavoidable, is part of the territory.
You can't make a prediction about what exactly will happen to you, because different things will happen to different versions of you (thus, if you make any prediction of a specific outcome now, some future you will observe it was wrong). This inability to predict a specific outcome feels like probability; it feels like a situation where you don't have perfect knowledge.
So it would be proper to say that "unpredictability of a specific outcome is part of the territory" -- the difference is that one model of quantum physics believes there is intrinsic randomess involved, other model believes that in fact multiple specific outcomes happen (in different branches).
OK, thanks, I see no problems with that.