on probability
"We take issue with Kent's arguments against many-world interpretations of quantum mechanics. We argue that his reasons for preferring single-world interpretations are logically flawed and that his proposed singleworld alternative to probability theory suffers from conceptual problems. We use a few thought-experiments which show that the problems he raises for probabilities in multiverses also apply in a single universe."
Guildenstern and Rosencrantz in Quantumland
It seems to me that the debate about many worlds has finally reached the point of asking 'what exactly do we mean with probability?' and I doubt this will be settled any time soon.
To be, or not to be, that really seems to be the question...
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The overwhelming problem for MWI, which most MWI advocates have not faced, is that the only reasonable way to obtain the Born rule from a multiverse scenario, is to have the Born probabilities correspond to the frequencies with which the different outcomes actually occur in the multiverse; and this requires that the various "worlds" are duplicated or almost-duplicated in proportion to the Born probabilities. But almost no-one proposes *that* sort of MWI; the only example I can think of is Robin Hanson's 'mangled worlds', which has a special preferred basis chosen in order to produce precisely the necessary near-duplication.
I have not tried to read right through the paper that you link, but it appears to be one long attempt to dodge this problem - that in MWI without duplication of worlds, the observed statistics of events in most worlds don't obey the Born rule. The authors don't offer any counterargument that I can see; they just refuse to accept that this is a valid objection.
I agree with you, but there is one loophole for mwi: nobody can observe the frequency of worlds in the multiverse directly (we only observe a history of events in one world [btw only God knows why this is])
so there is no direct argument that the Born probabilities have to correspond directly to frequencies of the many worlds.
Hi wolfgang,
There is this problem in a single universe too. In the sense that you can't observe every single quantum event, you just observe a tiny section of them. You only observe a subsequence within the full sequence.
I don't necessarily believe in multiworld. My goal isn't to argue in favor of it.
Oops, the previous comment was mine!
The fact that you can't obseve but a very tiny fraction of event is why you cannot claim you know the frequency in a single world.
The question of typicality still apply.
It is a question every statistician have to deal with.
Sorry for three replies in a row... I am new to this.
Paul,
maybe we arrived at a new level of Bohr's complimentarity:
If one wants to depict what is happening (during a measurement) then the mwi provides for a good picture, without the problems associated with a collapse.
On the other hand, if one wants to calculate probabilities then Born's rule from the Copenhagen interpretation has to be used.
The two are not really compatible but on the other hand one cannot really prove a contradiction.
Just another case of Bohr complimentarity ...
>> the question of typicality
but the problem with mwi is that in many cases the worlds are *not* typical.
Consider a weak radioactive source and the Born probability taht it emits a particle os 50% (lets say over 1 minute).
This source is surrounded by N detectors.
There is only one way (and one world) how no particle is detected.
But there are N different ways (and worlds) how a decay can be detected.
Although the Born probability is 50% the counting of worlds gives you 1:N (unless you assume 'mangled worlds' as mentioned by Mitchell).
If N is very large and you repeat the experiment many times the multiverse will be dominated by worlds which always see particles.
But they are certainly not typical ...
see also this and that.
sorry for my typos above, the sentence should have been:
Consider a weak radioactive source and the Born probability that it emits a particle is 50% (lets say over 1 minute).
ps: now we are even on the number of comments 8-)
Paul Raymond-Robichaud, I have many unusual theories that may interest you!
For example, the "theory of the imminently exploding sun". According to this theory, every day in the life of a star, it has a 99% chance of exploding. I admit that it seems unlikely that our own sun survived 5 billion years without blowing up - but that just shows that our solar system is not typical.
Another theory is that most of the ancient Egyptian pharaohs were named after characters from Walt Disney, like Mickey Mouse and Donald Duck. I admit that so far, we only know about pharaohs with strange names like "Akhenaten" - but that just means that we have not been digging in typical sites.
If we had more time, inevitably we would discover the evidence of the dynasty of Bugs Bunny. Unfortunately, the theory will never be vindicated, because (as I mentioned) the sun will probably explode tomorrow. Too bad!
I fear that refuting MWI by counting worlds involves assuming non-unitary evolution in the first place.
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