RogerS

20

I have now added a hopefully suitable paragraph to the post.

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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.

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Great. Incidentally, that seems a much more intelligible use of "territory" and "map" than in the Sequence claim that a Boeing 747 belongs to the map and its constituent quarks to the territory.

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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.

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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.

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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!

00

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).

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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.

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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)?

OK, thanks, I see no problems with that.