We argue that an infinite space actually renders the Born rule redundant, by physically realizing all outcomes of a quantum measurement in different regions, with relative frequencies given by the square of the wave function amplitudes. [...] Finally, the analysis suggests a “cosmological interpretation” of quantum theory in which the wave function describes the actual spatial collection of identical quantum systems, and quantum uncertainty is attributable to the observer’s inability to self-locate in this collection.
Fascinating. Does the math work out? If so how do you go about deciding whether to accept this kind of interpretation in terms of simplicity and or predictions?
I've been yapping on about how the 'quantum' in quantum immortality is redundant in a spatially infinite universe for awhile now, and also gave a suggestion as to how something like this explained the Born rule. Fortunately I was rather inebriated at the time and thus don't remember the details. At any rate, these memes have been around for awhile, though people seem reluctant to take them seriously. These days it seems decision theoretic metaphysics is getting more interesting than physical cosmology, though. Exciting times in ultra-abstract-conceptual-playground land.
The interesting ideas come up when you try to determine what counts as a mind-computation (there are probably lots of them going on in your head, and without a coherent ontology of agency or universal induction approximations we have no way to order the infinite possible interpretations) and what counts as almost-identical (if you're instantiating a Bayesian inference approximation algorithm in this universe, is it almost identical to the equivalent algorithm in a universe with totally different physical constants but also with the DAG nature?). Throw in some stuff about the importance of relative causal significance and it starts becoming clear that it is unlikely that anything adds up to anything close to normality.
Your second paragraph seems to point at the mystery of subjective anticipation, aka probability. I had some ideas about that, but no conclusive answer. It does seem to be a very confusing problem.
the importance of relative causal significance
Please explain this phrase?
Once upon a time, there was a prisoner in solitary confinement, a former public enemy number one of France, aside the wards alone in the prison and allowed only to read science books. When he came across an astronomy textbook by Lagrange, he suddenly had the same idea as you express. http://ideafoundlings.blogspot.com/2009/10/nemo-eternal-returning.html
Once I see the possibility that some idea may be expressed in crisp mathematics, I'm no longer interested in vague philosophical treatments of that idea.
Why do you think, the arxiv article is more precise than classical astronomy? Actually, it is about "vague" philosophical interpretations of QM, in this case leading it back to classical, newtonean concepts. Whereas the classical physics was free of such issues.
Why do you think, the arxiv article is more precise than classical astronomy?
If you think I think that, then communication has failed. Let's try again. Could you explain your first comment in more detail?
We haven't discussed it here yet, have we? Article from August 2010. ArXiv link. The upshot:
We study the quantum measurement problem in the context of an infinite, statistically uniform space, as could be generated by eternal inlfation. It has recently been argued that when identical copies of a quantum measurement system exist, the standard projection operators and Born rule method for calculating probabilities must be supplemented by estimates of relative frequencies of observers. We argue that an infinite space actually renders the Born rule redundant, by physically realizing all outcomes of a quantum measurement in different regions, with relative frequencies given by the square of the wave function amplitudes. [...] Finally, the analysis suggests a “cosmological interpretation” of quantum theory in which the wave function describes the actual spatial collection of identical quantum systems, and quantum uncertainty is attributable to the observer’s inability to self-locate in this collection.
The notion that I am this huge equivalence class of almost-identical human beings (just similar enough to be running the same mind-computation at this moment), scattered over a spatially infinite universe, sounds very UDT-ish. Unfortunately I don't know enough physics to judge the paper properly. Please halp.