Dear Hans, Thank you for your explanation about probability amplitudes, that clarifies a lot. My only worry was about the *epistemological* implications of quantum mechanics in its standard formulation, that in my opinion point to a paradigm shift, which is felt not only in this domain, but in all fields where *emergent* phenomena are accounted for—a process that I thought was hinted to by Wheeler's famous words "It from Bit," that I remember reading for the first time precisely in your book on information. That's the ground for expressing my worry that reverting to classical probability theory might entail a drawback to this decisive epistemological turn.
But I might misunderstand the whole story, that is certainly not over yet :-) -dino On 22 January 2014 00:21, Hans von Baeyer <henrikrit...@gmail.com> wrote: > Dear Dino and friends, thanks for bringing up the issue of probability > amplitudes. Since they are technical tools of physics, and since I didn't > want to go too far afield, I did not mention them in my lecture. The > closest I came was the wavefunction, which, indeed, is a probability > amplitude. In order to make contact with real, measurable quantities, it > must be multiplied by its complex conjugate. This recipe is called the Born > rule, and it is an ad hoc addition to the quantum theory. It lacks any > motivation except that it works. > > In keeping with Einstein's advice (which he himself often flouted) to try > to keep unmeasurable concepts out of our description of nature, physicists > have realized long ago that it must be possible to recast quantum mechanics > entirely in terms of probabilities, not even mentioning probability > amplitudes or wavefunctions. The question is only: How complicated would > the resulting formalism be? (To make a weak analogy, it must be possible > to recast arithmetic in the language of Roman numerals, but the result > would surely look much messier than what we learn in grade school.) > Hitherto, nobody had come up with an elegant solution to this problem. > > To their happy surprise, QBists have made progress toward a "quantum >> theory without probability amplitudes." Of course they have to pay a >> price. Instead of "unmeasurable concepts" they introduce, for any >> experiment, a very special set of standard probabilities (NOT AMPLITUDES) >> which are measurable, but not actually measured. When they re-write the >> Born rule in terms of these, they find that it looks almost, but not quite, >> like a fundamental axiom of probability theory called Unitarity. Unitarity >> decrees that for any experiment the sum of the probabilities for all >> possible outcomes must be one. (For a coin, the probabilities of heads and >> tails are both 1/2. Unitarity states 1/2 + 1/2 = 1.) > > > This unexpected outcome of QBism suggests a deep connection between the > Born rule and Unitarity. Since Unitarity is a logical concept unrelated to > quantum phenomena, this gives QBists the hope that they will eventually > succeed in explaining the significacne of the Born rule, and banishing > probability amplitudes from quantum mechanics, leaving only (Bayesian) > probabilities. > > So, I'm afraid dear Dino, that the current attitude of QBists is that > probability amplitudes are LESS fundamental than probabilities, not MORE. > But the story is far from finished! > > Hans > >> > > > > > _______________________________________________ > fis mailing list > fis@listas.unizar.es > https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis > >
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