[skissane]

If it is true, doesn’t it follow that there are (very rare) universes where unlikely events happen so often that anyone in such a universe would effectively observe a different probability distribution of events?

The thing is, if the theory is true, how do we know we are not in such a universe? We can say it is extremely unlikely because they are very rare - but we say it is “unlikely” and “rare” because we assume the global (multiverse-wide) probability distribution is similar to the local (this universe) one - but isn’t that assumption effectively equivalent to the assumption that we are not in such a universe? An argument which begins by assuming its conclusion is not much of an argument.

However, if we can’t rely on that assumption, it seems in principle impossible for us to know what the global probability distribution is - how is that not a lethal blow to the entire theory?

[_yb2s]

If you insist on using old fashioned logic to reason when in a probabilistic universe where that kind of reasoning is only an approximation, you can say that the universes you are talking about don't exist. They are such a small fraction of possible universes, that you can safely 'know' you aren't in any of them without checking.

[realgeniushere]

This comment misses the point and just plays with the meaning of “know”. Not that epistemology isn’t interesting, but parent was referring to absolute certainty (contingent on your senses being accurate, of course).

[skissane]

Not sure which parent you mean, but if you mean my comment, I wasn't talking about absolute certainty at all. Rather, I was attempting a reductio ad absurdum against theories which talk about the probability of different universes within a multiverse. Nothing I said is an argument against probabilistic reasoning/knowledge limited to the confines of this universe only.

[_yb2s]

I don't understand your criticism, and I think you might have been mis-understanding my intent. The Everettian (Many Worlds) interpretation of Quantum Mechanics is itself at odds with the concept of absolute certainty. I am thinking about this in terms of E. T. Jaynes perspective that probability theory is an extension of traditional logic, and is required for reasoning about the MWI.

I'll also note that I did miss the point of the OPs comment, but I think not in the way you suggested.

[_yb2s]

skissane, after re-reading your comment, I realize I did mis-understand your point, but in a different way than the other commenter suggested.

I don't think MWI is assuming the global (multiverse-wide) probability distribution is similar to the local (this universe) one, but rather than local probabilities directly arise from the global probability distribution, they are the same. If you do an experiment (e.g. wavefunction collapse) the outcomes we observe in a given experiment are each a single sample from the global distribution. Some outcomes can be highly unlikely and give a skewed view of the global distribution, but a larger number of experiments will always converge to the global distribution.

[skissane]

> but a larger number of experiments will always converge to the global distribution

But don't there exist universes in which that fails to happen? Consider a binary quantum experiment for which the global distribution is 0.5 (we might call it a "quantum coin flip"). If I repeat the experiment often enough, will it always converge to the global distribution? Well, suppose I have an ordinary (non-quantum) fair coin, and flip it one million times – what is the odds of it coming up heads every time? If I've got my maths right, 2^(-10^6) – so beyond astronomically unlikely, its probability is for all practical purposes indistinguishable from zero.

And yet, if MWI is right, then if I flip a "fair quantum coin" one million times, there are universes (just as "real" as ours) in which it comes up heads every single time. 2^(-10^6) is unbelievably small, but it isn't zero. Indeed, no matter how many observations occur, the probability of getting them all wrong just by chance remains non-zero – and, according to the MWI, everything with a non-zero probability in the global distribution actually exists. If MWI is true, there is no limit to how misled some actually existent observers will be.

Hence, by MWI, there are universes, just as real as ours, containing observers who (purely by chance) are consistently misled by their experiments, and therefore conclude that the global distribution is very different from what it actually is. But, if such observers exist, how do we know we are not them? We can say that, by the global distribution, they must be exceedingly rare, so it is exceedingly unlikely we are among them – but that argument relies on the assumption that our locally observed distribution is a reliable guide to the global distribution, which is the very thing it is setting out to prove – and hence must fail as a circular argument. With that argument dismissed, we are left with this conclusion: if MWI is true, we cannot know what the global distribution actually is. That contradicts one of the foundational claims of MWI; therefore, reductio ad absurdum, MWI is false.

This is different from classical sceptical arguments "what if our senses mislead us?", because it argues (if MWI is true) that such misled observers will exist, and the only question is how do we know we are not among them. Classical sceptical arguments are a lot weaker because they are not arguing from the (assumed) actual existence of such deceived observers, only from the (even remote) abstract possibility of their existence. But, if MWI gives sceptical arguments a huge boost - isn't that in itself a good argument against MWI? It renders MWI a self-undermining theory, and theories which undermine themselves ultimately refute themselves.

One might save MWI from this argument by assuming there is some "minimum probability", such that only universes whose probability rises to that minimum actually exist – if all the "misleading" universes are beneath that probability cutoff, no misleading universes exist, so we who exist could not possibly belong to any of them. However, this solution seems rather reminiscent of Ptolemy's epicycles.